WorldWideScience

Sample records for two-dimensional incompressible flow

  1. Three-dimensional nonlinear ideal MHD equilibria with field-aligned incompressible and compressible flows

    International Nuclear Information System (INIS)

    Moawad, S. M.; Ibrahim, D. A.

    2016-01-01

    The equilibrium properties of three-dimensional ideal magnetohydrodynamics (MHD) are investigated. Incompressible and compressible flows are considered. The governing equations are taken in a steady state such that the magnetic field is parallel to the plasma flow. Equations of stationary equilibrium for both of incompressible and compressible MHD flows are derived and described in a mathematical mode. For incompressible MHD flows, Alfvénic and non-Alfvénic flows with constant and variable magnetofluid density are investigated. For Alfvénic incompressible flows, the general three-dimensional solutions are determined with the aid of two potential functions of the velocity field. For non-Alfvénic incompressible flows, the stationary equilibrium equations are reduced to two differential constraints on the potential functions, flow velocity, magnetofluid density, and the static pressure. Some examples which may be of some relevance to axisymmetric confinement systems are presented. For compressible MHD flows, equations of the stationary equilibrium are derived with the aid of a single potential function of the velocity field. The existence of three-dimensional solutions for these MHD flows is investigated. Several classes of three-dimensional exact solutions for several cases of nonlinear equilibrium equations are presented.

  2. Differential geometric structures of stream functions: incompressible two-dimensional flow and curvatures

    International Nuclear Information System (INIS)

    Yamasaki, K; Iwayama, T; Yajima, T

    2011-01-01

    The Okubo-Weiss field, frequently used for partitioning incompressible two-dimensional (2D) fluids into coherent and incoherent regions, corresponds to the Gaussian curvature of the stream function. Therefore, we consider the differential geometric structures of stream functions and calculate the Gaussian curvatures of some basic flows. We find the following. (I) The vorticity corresponds to the mean curvature of the stream function. Thus, the stream-function surface for an irrotational flow and that for a parallel shear flow correspond to the minimal surface and a developable surface, respectively. (II) The relationship between the coherency and the magnitude of the vorticity is interpreted by the curvatures. (III) Using the Gaussian curvature, stability of single and double point vortex streets is analyzed. The results of this analysis are compared with the well-known linear stability analysis. (IV) Conformal mapping in fluid mechanics is the physical expression of the geometric fact that the sign of the Gaussian curvature does not change in conformal mapping. These findings suggest that the curvatures of stream functions are useful for understanding the geometric structure of an incompressible 2D flow.

  3. An incompressible two-dimensional multiphase particle-in-cell model for dense particle flows

    Energy Technology Data Exchange (ETDEWEB)

    Snider, D.M. [SAIC, Albuquerque, NM (United States); O`Rourke, P.J. [Los Alamos National Lab., NM (United States); Andrews, M.J. [Texas A and M Univ., College Station, TX (United States). Dept. of Mechanical Engineering

    1997-06-01

    A two-dimensional, incompressible, multiphase particle-in-cell (MP-PIC) method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to a Eulerian grid and then mapping back computed stress tensors to particle positions. This approach utilizes the best of Eulerian/Eulerian continuum models and Eulerian/Lagrangian discrete models. The solution scheme allows for distributions of types, sizes, and density of particles, with no numerical diffusion from the Lagrangian particle calculations. The computational method is implicit with respect to pressure, velocity, and volume fraction in the continuum solution thus avoiding courant limits on computational time advancement. MP-PIC simulations are compared with one-dimensional problems that have analytical solutions and with two-dimensional problems for which there are experimental data.

  4. Investigation of the use of Prandtl/Navier--Stokes equation procedures for two-dimensional incompressible flows

    International Nuclear Information System (INIS)

    Anderson, C.R.; Reider, M.B.

    1994-01-01

    The technique of combining solutions of the Prandtl equations with solutions of the Navier--Stokes equations to compute incompressible flow around two-dimensional bodies is investigated herein. Computational evidence is presented which shows that if the ''obvious'' coupling is used to combine the solutions, then the resulting solution is not accurate. An alternate coupling procedure is described which greatly improves the accuracy of the solutions obtained with the combined equation approach. An alternate coupling that can be used to create a more accurate vortex sheet/vortex blob method is then shown

  5. A two pressure-velocity approach for immersed boundary methods in three dimensional incompressible flows

    International Nuclear Information System (INIS)

    Sabir, O; Ahmad, Norhafizan; Nukman, Y; Tuan Ya, T M Y S

    2013-01-01

    This paper describes an innovative method for computing fluid solid interaction using Immersed boundary methods with two stage pressure-velocity corrections. The algorithm calculates the interactions between incompressible viscous flows and a solid shape in three-dimensional domain. The fractional step method is used to solve the Navier-Stokes equations in finite difference schemes. Most of IBMs are concern about exchange of the momentum between the Eulerian variables (fluid) and the Lagrangian nodes (solid). To address that concern, a new algorithm to correct the pressure and the velocity using Simplified Marker and Cell method is added. This scheme is applied on staggered grid to simulate the flow past a circular cylinder and study the effect of the new stage on calculations cost. To evaluate the accuracy of the computations the results are compared with the previous software results. The paper confirms the capacity of new algorithm for accurate and robust simulation of Fluid Solid Interaction with respect to pressure field

  6. Magnetohydrodynamics effect on three-dimensional viscous incompressible flow between two horizontal parallel porous plates and heat transfer with periodic injection/suction

    Directory of Open Access Journals (Sweden)

    R. C. Chaudhary

    2004-11-01

    Full Text Available We investigate the hydromagnetic effect on viscous incompressible flow between two horizontal parallel porous flat plates with transverse sinusoidal injection of the fluid at the stationary plate and its corresponding removal by periodic suction through the plate in uniform motion. The flow becomes three dimensional due to this injection/suction velocity. Approximate solutions are obtained for the flow field, the pressure, the skin-friction, the temperature field, and the rate of heat transfer. The dependence of solution on M (Hartmann number and λ (injection/suction is investigated by the graphs and tables.

  7. Finite element method with quadratic quadrilateral unit for solving two dimensional incompressible N-S equation

    International Nuclear Information System (INIS)

    Tao Ganqiang; Yu Qing; Xiao Xiao

    2011-01-01

    Viscous and incompressible fluid flow is important for numerous engineering mechanics problems. Because of high non linear and incompressibility for Navier-Stokes equation, it is very difficult to solve Navier-Stokes equation by numerical method. According to its characters of Navier-Stokes equation, quartic derivation controlling equation of the two dimensional incompressible Navier-Stokes equation is set up firstly. The method solves the problem for dealing with vorticity boundary and automatically meets incompressibility condition. Then Finite Element equation for Navier-Stokes equation is proposed by using quadratic quadrilateral unit with 8 nodes in which the unit function is quadratic and non linear.-Based on it, the Finite Element program of quadratic quadrilateral unit with 8 nodes is developed. Lastly, numerical experiment proves the accuracy and dependability of the method and also shows the method has good application prospect in computational fluid mechanics. (authors)

  8. Development of a discrete gas-kinetic scheme for simulation of two-dimensional viscous incompressible and compressible flows.

    Science.gov (United States)

    Yang, L M; Shu, C; Wang, Y

    2016-03-01

    In this work, a discrete gas-kinetic scheme (DGKS) is presented for simulation of two-dimensional viscous incompressible and compressible flows. This scheme is developed from the circular function-based GKS, which was recently proposed by Shu and his co-workers [L. M. Yang, C. Shu, and J. Wu, J. Comput. Phys. 274, 611 (2014)]. For the circular function-based GKS, the integrals for conservation forms of moments in the infinity domain for the Maxwellian function-based GKS are simplified to those integrals along the circle. As a result, the explicit formulations of conservative variables and fluxes are derived. However, these explicit formulations of circular function-based GKS for viscous flows are still complicated, which may not be easy for the application by new users. By using certain discrete points to represent the circle in the phase velocity space, the complicated formulations can be replaced by a simple solution process. The basic requirement is that the conservation forms of moments for the circular function-based GKS can be accurately satisfied by weighted summation of distribution functions at discrete points. In this work, it is shown that integral quadrature by four discrete points on the circle, which forms the D2Q4 discrete velocity model, can exactly match the integrals. Numerical results showed that the present scheme can provide accurate numerical results for incompressible and compressible viscous flows with roughly the same computational cost as that needed by the Roe scheme.

  9. On a method of construction of exact solutions for equations of two-dimensional hydrodynamics of incompressible liquids

    International Nuclear Information System (INIS)

    Yurov, A.V.; Yurova, A.A.

    2006-01-01

    The simple algebraic method for construction of exact solutions of two-dimensional hydrodynamic equations of incompressible flow is proposed. This method can be applied both to nonviscous flow (Euler equations) and to viscous flow (Navier-Stokes equations). In the case of nonviscous flow, the problem is reduced to sequential solving of three linear partial differential equations. In the case of viscous flow, the Navier-Stokes equations are reduced to three linear partial differential equations and one differential equation of the first order [ru

  10. Approximate characteristics for one-dimensional two-phase flows

    International Nuclear Information System (INIS)

    Sarayloo, A.; Peddleson, J.

    1985-01-01

    An approximate method for determining the characteristics associated with one-dimensional particulate two-phase flow models is presented. The method is based on iteration and is valid for small particulate volume fractions. The method is applied to several special cases involving incompressible particles suspended in a gas. The influences of certain changes in the physical model are investigated

  11. Two-dimensional convection of an incompressible viscous fluid with the heat exchange on the free border

    Directory of Open Access Journals (Sweden)

    Svetlana S. Vlasova

    2016-09-01

    Full Text Available The exact stationary solution of the boundary-value problem that describes the convective motion of an incompressible viscous fluid in the two-dimensional layer with the square heating of a free surface in Stokes's approach is found. The linearization of the Oberbeck–Boussinesq equations allows one to describe the flow of fluid in extreme points of pressure and temperature. The condition under which the counter-current flows (two counter flows in the fluid can be observed, is introduced. If the stagnant point in the fluid exists, six non-closed whirlwinds can be observed.

  12. Qualitative behaviour of incompressible two-phase flows with phase ...

    Indian Academy of Sciences (India)

    Jan Prüss

    2017-11-07

    Nov 7, 2017 ... Qualitative behaviour of incompressible two-phase flows with phase ... Germany. 2Graduate School of Human and Environmental Studies, Kyoto University, ... Note that j is a dummy variable as it can be eliminated from the ...

  13. Unique encoding for streamline topologies of incompressible and inviscid flows in multiply connected domains

    Energy Technology Data Exchange (ETDEWEB)

    Sakajo, T [Department of Mathematics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502 (Japan); Sawamura, Y; Yokoyama, T, E-mail: sakajo@math.kyoto-u.ac.jp [JST CREST, Kawaguchi, Saitama 332-0012 (Japan)

    2014-06-01

    This study considers the flow of incompressible and inviscid fluid in two-dimensional multiply connected domains. For such flows, encoding algorithms to assign a unique sequence of words to any structurally stable streamline topology based on the theory presented by Yokoyama and Sakajo (2013 Proc. R. Soc. A 469 20120558) are proposed. As an application, we utilize the algorithms to characterize the evolution of an incompressible and viscid flow around a flat plate inclined to the uniform flow in terms of the change of the word representations for their instantaneous streamline topologies. (papers)

  14. TURBO: a computer program for two-dimensional incompressible fluid flow analysis using a two-equations turbulence model

    International Nuclear Information System (INIS)

    Botelho, D.A.; Moreira, M.L.

    1991-06-01

    The Reynolds turbulent transport equations for an incompressible fluid are integrated on a bi-dimensional staggered grid, for velocity and pressure, using the SIMPLER method. With the resulting algebraic relations it was developed the TURBO program, which final objectives are the thermal stratification and natural convection analysis of nuclear reactor pools. This program was tested in problems applications with analytic or experimental solutions previously known. (author)

  15. Streamline topologies near simple degenerate critical points in two-dimensional flow away from boundaries

    DEFF Research Database (Denmark)

    Brøns, Morten; Hartnack, Johan Nicolai

    1998-01-01

    Streamline patterns and their bifurcations in two-dimensional incompressible flow are investigated from a topological point of view. The velocity field is expanded at a point in the fluid, and the expansion coefficients are considered as bifurcation parameters. A series of non-linear coordinate c...

  16. Streamline topologies near simple degenerate critical points in two-dimensional flow away from boundaries

    DEFF Research Database (Denmark)

    Brøns, Morten; Hartnack, Johan Nicolai

    1999-01-01

    Streamline patterns and their bifurcations in two-dimensional incompressible flow are investigated from a topological point of view. The velocity field is expanded at a point in the fluid, and the expansion coefficients are considered as bifurcation parameters. A series of nonlinear coordinate ch...

  17. Simulation of three-dimensional, time-dependent, incompressible flows by a finite element method

    International Nuclear Information System (INIS)

    Chan, S.T.; Gresho, P.M.; Lee, R.L.; Upson, C.D.

    1981-01-01

    A finite element model has been developed for simulating the dynamics of problems encountered in atmospheric pollution and safety assessment studies. The model is based on solving the set of three-dimensional, time-dependent, conservation equations governing incompressible flows. Spatial discretization is performed via a modified Galerkin finite element method, and time integration is carried out via the forward Euler method (pressure is computed implicitly, however). Several cost-effective techniques (including subcycling, mass lumping, and reduced Gauss-Legendre quadrature) which have been implemented are discussed. Numerical results are presented to demonstrate the applicability of the model

  18. Three-dimensional multi-relaxation-time lattice Boltzmann front-tracking method for two-phase flow

    International Nuclear Information System (INIS)

    Xie Hai-Qiong; Zeng Zhong; Zhang Liang-Qi

    2016-01-01

    We developed a three-dimensional multi-relaxation-time lattice Boltzmann method for incompressible and immiscible two-phase flow by coupling with a front-tracking technique. The flow field was simulated by using an Eulerian grid, an adaptive unstructured triangular Lagrangian grid was applied to track explicitly the motion of the two-fluid interface, and an indicator function was introduced to update accurately the fluid properties. The surface tension was computed directly on a triangular Lagrangian grid, and then the surface tension was distributed to the background Eulerian grid. Three benchmarks of two-phase flow, including the Laplace law for a stationary drop, the oscillation of a three-dimensional ellipsoidal drop, and the drop deformation in a shear flow, were simulated to validate the present model. (paper)

  19. Bracket formulations and energy- and helicity-preserving numerical methods for incompressible two-phase flows

    Science.gov (United States)

    Suzuki, Yukihito

    2018-03-01

    A diffuse interface model for three-dimensional viscous incompressible two-phase flows is formulated within a bracket formalism using a skew-symmetric Poisson bracket together with a symmetric negative semi-definite dissipative bracket. The budgets of kinetic energy, helicity, and enstrophy derived from the bracket formulations are properly inherited by the finite difference equations obtained by invoking the discrete variational derivative method combined with the mimetic finite difference method. The Cahn-Hilliard and Allen-Cahn equations are employed as diffuse interface models, in which the equalities of densities and viscosities of two different phases are assumed. Numerical experiments on the motion of periodic arrays of tubes and those of droplets have been conducted to examine the properties and usefulness of the proposed method.

  20. Computational fluid dynamics incompressible turbulent flows

    CERN Document Server

    Kajishima, Takeo

    2017-01-01

    This textbook presents numerical solution techniques for incompressible turbulent flows that occur in a variety of scientific and engineering settings including aerodynamics of ground-based vehicles and low-speed aircraft, fluid flows in energy systems, atmospheric flows, and biological flows. This book encompasses fluid mechanics, partial differential equations, numerical methods, and turbulence models, and emphasizes the foundation on how the governing partial differential equations for incompressible fluid flow can be solved numerically in an accurate and efficient manner. Extensive discussions on incompressible flow solvers and turbulence modeling are also offered. This text is an ideal instructional resource and reference for students, research scientists, and professional engineers interested in analyzing fluid flows using numerical simulations for fundamental research and industrial applications. • Introduces CFD techniques for incompressible flow and turbulence with a comprehensive approach; • Enr...

  1. Predicting transition in two- and three-dimensional separated flows

    International Nuclear Information System (INIS)

    Cutrone, L.; De Palma, P.; Pascazio, G.; Napolitano, M.

    2008-01-01

    This paper is concerned with the numerical prediction of two- and three-dimensional transitional separated flows of turbomachinery interest. The recently proposed single-point transition model based on the use of a laminar kinetic energy transport equation is considered, insofar as it does not require to evaluate any integral parameter, such as boundary-layer thickness, and is thus directly applicable to three-dimensional flows. A well established model, combining a transition-onset correlation with an intermittency transport equation, is also used for comparison. Both models are implemented within a Reynolds-averaged Navier-Stokes solver employing a low-Reynolds-number k-ω turbulence model. The performance of the transition models have been evaluated and tested versus well-documented incompressible flows past a flat plate with semi-circular leading edge, namely: tests T3L2, T3L3, T3L5, and T3LA1 of ERCOFTAC, with different Reynolds numbers and free-stream conditions, the last one being characterized by a non-zero pressure gradient. In all computations, the first model has proven as adequate as or superior to the second one and has been then applied with success to two more complex test cases, for which detailed experimental data are available in the literature, namely: the two- and three-dimensional flows through the T106 linear turbine cascade

  2. Evolution of the vorticity-area density during the formation of coherent structures in two-dimensional flows

    NARCIS (Netherlands)

    Capel, H.W.; Pasmanter, R.A.

    2000-01-01

    It is shown: (1) that in two-dimensional, incompressible, viscous flows the vorticity-area distribution evolves according to an advection-diffusion equation with a negative, time dependent diffusion coefficient and (2) how to use the vorticity-stream function relations, i.e., the so-called

  3. Time evolution of the eddy viscosity in two-dimensional navier-stokes flow

    Science.gov (United States)

    Chaves; Gama

    2000-02-01

    The time evolution of the eddy viscosity associated with an unforced two-dimensional incompressible Navier-Stokes flow is analyzed by direct numerical simulation. The initial condition is such that the eddy viscosity is isotropic and negative. It is shown by concrete examples that the Navier-Stokes dynamics stabilizes negative eddy viscosity effects. In other words, this dynamics moves monotonically the initial negative eddy viscosity to positive values before relaxation due to viscous term occurs.

  4. A meshless local radial basis function method for two-dimensional incompressible Navier-Stokes equations

    KAUST Repository

    Wang, Zhiheng

    2014-12-10

    A meshless local radial basis function method is developed for two-dimensional incompressible Navier-Stokes equations. The distributed nodes used to store the variables are obtained by the philosophy of an unstructured mesh, which results in two main advantages of the method. One is that the unstructured nodes generation in the computational domain is quite simple, without much concern about the mesh quality; the other is that the localization of the obtained collocations for the discretization of equations is performed conveniently with the supporting nodes. The algebraic system is solved by a semi-implicit pseudo-time method, in which the convective and source terms are explicitly marched by the Runge-Kutta method, and the diffusive terms are implicitly solved. The proposed method is validated by several benchmark problems, including natural convection in a square cavity, the lid-driven cavity flow, and the natural convection in a square cavity containing a circular cylinder, and very good agreement with the existing results are obtained.

  5. Local mesh refinement for incompressible fluid flow with free surfaces

    Energy Technology Data Exchange (ETDEWEB)

    Terasaka, H.; Kajiwara, H.; Ogura, K. [Tokyo Electric Power Company (Japan)] [and others

    1995-09-01

    A new local mesh refinement (LMR) technique has been developed and applied to incompressible fluid flows with free surface boundaries. The LMR method embeds patches of fine grid in arbitrary regions of interest. Hence, more accurate solutions can be obtained with a lower number of computational cells. This method is very suitable for the simulation of free surface movements because free surface flow problems generally require a finer computational grid to obtain adequate results. By using this technique, one can place finer grids only near the surfaces, and therefore greatly reduce the total number of cells and computational costs. This paper introduces LMR3D, a three-dimensional incompressible flow analysis code. Numerical examples calculated with the code demonstrate well the advantages of the LMR method.

  6. Three dimensional simulation of compressible and incompressible flows through the finite element method

    International Nuclear Information System (INIS)

    Costa, Gustavo Koury

    2004-11-01

    Although incompressible fluid flows can be regarded as a particular case of a general problem, numerical methods and the mathematical formulation aimed to solve compressible and incompressible flows have their own peculiarities, in such a way, that it is generally not possible to attain both regimes with a single approach. In this work, we start from a typically compressible formulation, slightly modified to make use of pressure variables and, through augmenting the stabilising parameters, we end up with a simplified model which is able to deal with a wide range of flow regimes, from supersonic to low speed gas flows. The resulting methodology is flexible enough to allow for the simulation of liquid flows as well. Examples using conservative and pressure variables are shown and the results are compared to those published in the literature, in order to validate the method. (author)

  7. Topology of Flow Separation on Three-Dimensional Bodies

    Science.gov (United States)

    Chapman, Gary T.; Yates, Leslie A.

    1991-01-01

    In recent years there has been extensive research on three-dimensional flow separation. There are two different approaches: the phenomenological approach and a mathematical approach using topology. These two approaches are reviewed briefly and the shortcomings of some of the past works are discussed. A comprehensive approach applicable to incompressible and compressible steady-state flows as well as incompressible unsteady flow is then presented. The approach is similar to earlier topological approaches to separation but is more complete and in some cases adds more emphasis to certain points than in the past. To assist in the classification of various types of flow, nomenclature is introduced to describe the skin-friction portraits on the surface. This method of classification is then demonstrated on several categories of flow to illustrate particular points as well as the diversity of flow separation. The categories include attached, two-dimensional separation and three different types of simple, three-dimensional primary separation, secondary separation, and compound separation. Hypothetical experiments are utilized to illustrate the topological terminology and its role in characterizing these flows. These hypothetical experiments use colored oil injected onto the surface at singular points in the skin-friction portrait. Actual flow-visualization information, if available, is used to corroborate the hypothetical examples.

  8. Unsteady two-dimensional potential-flow model for thin variable geometry airfoils

    DEFF Research Database (Denmark)

    Gaunaa, Mac

    2010-01-01

    In the present work, analytical expressions for distributed and integral unsteady two-dimensional forces on a variable geometry airfoil undergoing arbitrary motion are derived under the assumption of incompressible, irrotational, inviscid flow. The airfoil is represented by its camber line...... in their equivalent state-space form, allowing for use of the present theory in problems employing the eigenvalue approach, such as stability analysis. The analytical expressions for the integral forces can be reduced to Munk's steady and Theodorsen's unsteady results for thin airfoils, and numerical evaluation shows...

  9. Lattice Boltzmann simulations of three-dimensional incompressible flows in a four-sided lid driven cavity

    Energy Technology Data Exchange (ETDEWEB)

    Li, Cheng Gong [National Engineering Laboratory for MTO, Dalian National Laboratory for Clean Energy, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, 457 Zhongshan Road, Dalian 116023 (China); Maa, Jerome P-Y, E-mail: chenggongli@dicp.ac.cn [Virginia Institute of Marine Science, College of William and Mary, Gloucester Point, VA 23062 (United States)

    2017-04-15

    Numerical study on three-dimensional (3D), incompressible, four-sided lid (FSL) driven cavity flows has been conducted to show the effects of the transverse aspect ratio, K , on the flow field by using a multiple relaxation time lattice Boltzmann equation. The top wall is driven from left to right, the left wall is moved downward, whereas the right wall is driven upward, and the bottom wall is moved from right to left, all the four moving walls have the same speed and the others boundaries are fixed. Numerical computations are performed for several Reynolds numbers for laminar flows, up to 1000, with various transverse aspect ratios. The flow can reach a steady state and the flow pattern is symmetric with respect to the two cavity diagonals (i.e., the center of the cavity). At Reynolds number = 300, the flow structures of the 3D FSL cavity flow at steady state with various transverse aspect ratio, i.e., 3, 2, 1, 0.75, 0.5 and 0.25 only show the unstable symmetrical flow pattern. The stable asymmetrical flow pattern could be reproduced only by increasing the Reynolds number that is above a critical value which is dependent on the aspect ratio. It is found that an aspect ratio of more than 5 is needed to reproduce flow patterns, both symmetric and asymmetric flows, simulated by using 2D numerical models. (paper)

  10. Computation of Viscous Incompressible Flows

    CERN Document Server

    Kwak, Dochan

    2011-01-01

    This monograph is intended as a concise and self-contained guide to practitioners and graduate students for applying approaches in computational fluid dynamics (CFD) to real-world problems that require a quantification of viscous incompressible flows. In various projects related to NASA missions, the authors have gained CFD expertise over many years by developing and utilizing tools especially related to viscous incompressible flows. They are looking at CFD from an engineering perspective, which is especially useful when working on real-world applications. From that point of view, CFD requires two major elements, namely methods/algorithm and engineering/physical modeling. As for the methods, CFD research has been performed with great successes. In terms of modeling/simulation, mission applications require a deeper understanding of CFD and flow physics, which has only been debated in technical conferences and to a limited scope. This monograph fills the gap by offering in-depth examples for students and engine...

  11. Preconditioned characteristic boundary conditions based on artificial compressibility method for solution of incompressible flows

    Science.gov (United States)

    Hejranfar, Kazem; Parseh, Kaveh

    2017-09-01

    The preconditioned characteristic boundary conditions based on the artificial compressibility (AC) method are implemented at artificial boundaries for the solution of two- and three-dimensional incompressible viscous flows in the generalized curvilinear coordinates. The compatibility equations and the corresponding characteristic variables (or the Riemann invariants) are mathematically derived and then applied as suitable boundary conditions in a high-order accurate incompressible flow solver. The spatial discretization of the resulting system of equations is carried out by the fourth-order compact finite-difference (FD) scheme. In the preconditioning applied here, the value of AC parameter in the flow field and also at the far-field boundary is automatically calculated based on the local flow conditions to enhance the robustness and performance of the solution algorithm. The code is fully parallelized using the Concurrency Runtime standard and Parallel Patterns Library (PPL) and its performance on a multi-core CPU is analyzed. The incompressible viscous flows around a 2-D circular cylinder, a 2-D NACA0012 airfoil and also a 3-D wavy cylinder are simulated and the accuracy and performance of the preconditioned characteristic boundary conditions applied at the far-field boundaries are evaluated in comparison to the simplified boundary conditions and the non-preconditioned characteristic boundary conditions. It is indicated that the preconditioned characteristic boundary conditions considerably improve the convergence rate of the solution of incompressible flows compared to the other boundary conditions and the computational costs are significantly decreased.

  12. CONVEC: a computer program for transient incompressible fluid flow based on quadratic finite elements. Part 1: theoretical aspects

    International Nuclear Information System (INIS)

    Laval, H.

    1981-01-01

    This report describes the theoretical and numerical aspects of the finite element computer code CONVEC designed for the transient analysis of two-dimensional plane or three-dimensional axisymmetric incompressible flows including the effects of heat transfer. The governing equations for the above class of problems are the time-dependent incompressible Navier-Stokes equations and the thermal energy equation. The general class of flow problems analysed by CONVEC is discussed and the equations for the initial-boundary value problem are represented. A brief description of the finite element method and the weighted residual formulation is presented. The numerical solution of the incompressible equations is achieved by using a fractional step method. The mass lumping process associated with an explicit time integration scheme is described. The time integration is analysed and the stability conditions are derived. Numerical applications are presented. Standard problems of natural and forced convection are solved and the solutions obtained are compared with other numerical solutions published in the literature

  13. Self-organization phenomena and decaying self-similar state in two-dimensional incompressible viscous fluids

    International Nuclear Information System (INIS)

    Kondoh, Yoshiomi; Serizawa, Shunsuke; Nakano, Akihiro; Takahashi, Toshiki; Van Dam, James W.

    2004-01-01

    The final self-similar state of decaying two-dimensional (2D) turbulence in 2D incompressible viscous flow is analytically and numerically investigated for the case with periodic boundaries. It is proved by theoretical analysis and simulations that the sinh-Poisson state cω=-sinh(βψ) is not realized in the dynamical system of interest. It is shown by an eigenfunction spectrum analysis that a sufficient explanation for the self-organization to the decaying self-similar state is the faster energy decay of higher eigenmodes and the energy accumulation to the lowest eigenmode for given boundary conditions due to simultaneous normal and inverse cascading by nonlinear mode couplings. The theoretical prediction is demonstrated to be correct by simulations leading to the lowest eigenmode of {(1,0)+(0,1)} of the dissipative operator for the periodic boundaries. It is also clarified that an important process during nonlinear self-organization is an interchange between the dominant operators, which leads to the final decaying self-similar state

  14. Coupled, parabolic-marching method for the prediction of three-dimensional viscous incompressible turbomachinery flows. Doctoral thesis

    Energy Technology Data Exchange (ETDEWEB)

    Kirtley, K.R.

    1988-10-01

    A new coupled parabolic-marching method was developed to solve the three-dimensional incompressible Navier-Stokes equation for turbulent turbomachinery flows. Earlier space-marching methods were analyzed to determine their global stability during multiple passes of the computational domain. The methods were found to be unconditionally unstable even when an extra equation for the pressure, namely the Poisson equation for the pressure, was used between passes of the domain. Relaxation of one constraint during the solution process was found to be necessary for the successful calculation of a complex flow.Thus, the method of pseudocompressibility was introduced into the partially parabolized Navier-Stokes equation to relax the mass flow constraint during a forward-marching integration as well as globally stable during successive passes of the domain. With consistent discretization, the new method was found to be convergent.

  15. GIS-based two-dimensional numerical simulation of rainfall-induced debris flow

    Directory of Open Access Journals (Sweden)

    C. Wang

    2008-02-01

    Full Text Available This paper aims to present a useful numerical method to simulate the propagation and deposition of debris flow across the three dimensional complex terrain. A depth-averaged two-dimensional numerical model is developed, in which the debris and water mixture is assumed to be continuous, incompressible, unsteady flow. The model is based on the continuity equations and Navier-Stokes equations. Raster grid networks of digital elevation model in GIS provide a uniform grid system to describe complex topography. As the raster grid can be used as the finite difference mesh, the continuity and momentum equations are solved numerically using the finite difference method. The numerical model is applied to simulate the rainfall-induced debris flow occurred in 20 July 2003, in Minamata City of southern Kyushu, Japan. The simulation reproduces the propagation and deposition and the results are in good agreement with the field investigation. The synthesis of numerical method and GIS makes possible the solution of debris flow over a realistic terrain, and can be used to estimate the flow range, and to define potentially hazardous areas for homes and road section.

  16. Incompressible viscous flow computations for the pump components and the artificial heart

    Science.gov (United States)

    Kiris, Cetin

    1992-01-01

    A finite difference, three dimensional incompressible Navier-Stokes formulation to calculate the flow through turbopump components is utilized. The solution method is based on the pseudo compressibility approach and uses an implicit upwind differencing scheme together with the Gauss-Seidel line relaxation method. Both steady and unsteady flow calculations can be performed using the current algorithm. Here, equations are solved in steadily rotating reference frames by using the steady state formulation in order to simulate the flow through a turbopump inducer. Eddy viscosity is computed by using an algebraic mixing-length turbulence model. Numerical results are compared with experimental measurements and a good agreement is found between the two.

  17. Incompressible Turbulent Flow Simulation Using the κ-ɛ Model and Upwind Schemes

    Directory of Open Access Journals (Sweden)

    V. G. Ferreira

    2007-01-01

    Full Text Available In the computation of turbulent flows via turbulence modeling, the treatment of the convective terms is a key issue. In the present work, we present a numerical technique for simulating two-dimensional incompressible turbulent flows. In particular, the performance of the high Reynolds κ-ɛ model and a new high-order upwind scheme (adaptative QUICKEST by Kaibara et al. (2005 is assessed for 2D confined and free-surface incompressible turbulent flows. The model equations are solved with the fractional-step projection method in primitive variables. Solutions are obtained by using an adaptation of the front tracking GENSMAC (Tomé and McKee (1994 methodology for calculating fluid flows at high Reynolds numbers. The calculations are performed by using the 2D version of the Freeflow simulation system (Castello et al. (2000. A specific way of implementing wall functions is also tested and assessed. The numerical procedure is tested by solving three fluid flow problems, namely, turbulent flow over a backward-facing step, turbulent boundary layer over a flat plate under zero-pressure gradients, and a turbulent free jet impinging onto a flat surface. The numerical method is then applied to solve the flow of a horizontal jet penetrating a quiescent fluid from an entry port beneath the free surface.

  18. A waveless two-dimensional flow in a channel against an inclined wall with surface tension effect

    International Nuclear Information System (INIS)

    Merzougui, Abdelkrim; Mekias, Hocine; Guechi, Fairouz

    2007-01-01

    Surface tension effect on a two-dimensional channel flow against an inclined wall is considered. The flow is assumed to be steady, irrotational, inviscid and incompressible. The effect of surface tension is taken into account and the effect of gravity is neglected. Numerical solutions are obtained via series truncation procedure. The problem is solved numerically for various values of the Weber number α and for various values of the inclination angle β between the horizontal bottom and the inclined wall

  19. A waveless two-dimensional flow in a channel against an inclined wall with surface tension effect

    Energy Technology Data Exchange (ETDEWEB)

    Merzougui, Abdelkrim [Departement de Mathematiques, Faculte des sciences, Universite Mohamed Boudiaf, M' sila, 28000 (Algeria); Mekias, Hocine [Departement de Mathematiques, Faculte des sciences, Universite Farhat Abbas Setif 19000 (Algeria); Guechi, Fairouz [Departement de Mathematiques, Faculte des sciences, Universite Farhat Abbas Setif 19000 (Algeria)

    2007-11-23

    Surface tension effect on a two-dimensional channel flow against an inclined wall is considered. The flow is assumed to be steady, irrotational, inviscid and incompressible. The effect of surface tension is taken into account and the effect of gravity is neglected. Numerical solutions are obtained via series truncation procedure. The problem is solved numerically for various values of the Weber number {alpha} and for various values of the inclination angle {beta} between the horizontal bottom and the inclined wall.

  20. Numerical simulations of incompressible laminar flows using viscous-inviscid interaction procedures

    Science.gov (United States)

    Shatalov, Alexander V.

    The present method is based on Helmholtz velocity decomposition where velocity is written as a sum of irrotational (gradient of a potential) and rotational (correction due to vorticity) components. Substitution of the velocity decomposition into the continuity equation yields an equation for the potential, while substitution into the momentum equations yields equations for the velocity corrections. A continuation approach is used to relate the pressure to the gradient of the potential through a modified Bernoulli's law, which allows the elimination of the pressure variable from the momentum equations. The present work considers steady and unsteady two-dimensional incompressible flows over an infinite cylinder and NACA 0012 airfoil shape. The numerical results are compared against standard methods (stream function-vorticity and SMAC methods) and data available in literature. The results demonstrate that the proposed formulation leads to a good approximation with some possible benefits compared to the available formulations. The method is not restricted to two-dimensional flows and can be used for viscous-inviscid domain decomposition calculations.

  1. Comparative study of incompressible and isothermal compressible flow solvers for cavitating flow dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Park, Sun Ho [Korea Maritime and Ocean University, Busan (Korea, Republic of); Rhee, Shin Hyung [Seoul National University, Seoul (Korea, Republic of)

    2015-08-15

    Incompressible flow solvers are generally used for numerical analysis of cavitating flows, but with limitations in handling compressibility effects on vapor phase. To study compressibility effects on vapor phase and cavity interface, pressure-based incompressible and isothermal compressible flow solvers based on a cell-centered finite volume method were developed using the OpenFOAM libraries. To validate the solvers, cavitating flow around a hemispherical head-form body was simulated and validated against the experimental data. The cavity shedding behavior, length of a re-entrant jet, drag history, and the Strouhal number were compared between the two solvers. The results confirmed that computations of the cavitating flow including compressibility effects improved the reproduction of cavitation dynamics.

  2. A Two-Phase Flow Solver for Incompressible Viscous Fluids, Using a Pure Streamfunction Formulation and the Volume of Fluid Technique

    DEFF Research Database (Denmark)

    Comminal, Raphaël; Spangenberg, Jon; Hattel, Jesper Henri

    Accurate multi-phase flow solvers at low Reynolds number are of particular interest for the simulation of interface instabilities in the co-processing of multilayered material. We present a two-phase flow solver for incompressible viscous fluids which uses the streamfunction as the primary variable...... of the flow. Contrary to fractional step methods, the streamfunction formulation eliminates the pressure unknowns, and automatically fulfills the incompressibility constraint by construction. As a result, the method circumvents the loss of temporal accuracy at low Reynolds numbers. The interface is tracked...

  3. A Two-Phase Flow Solver for Incompressible Viscous Fluids, Using a Pure Streamfunction Formulation and the Volume of Fluid Technique

    DEFF Research Database (Denmark)

    Comminal, Raphaël; Spangenberg, Jon; Hattel, Jesper Henri

    2014-01-01

    Accurate multi-phase flow solvers at low Reynolds number are of particular interest for the simulation of interface instabilities in the co-processing of multilayered material. We present a two-phase flow solver for incompressible viscous fluids which uses the streamfunction as the primary variable...... of the flow. Contrary to fractional step methods, the streamfunction formulation eliminates the pressure unknowns, and automatically fulfills the incompressibility constraint by construction. As a result, the method circumvents the loss of temporal accuracy at low Reynolds numbers. The interface is tracked...

  4. Numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow

    KAUST Repository

    Zhu, Guangpu

    2018-04-17

    In this paper, we consider the numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow. The nonlinearly coupled model consists of two Cahn-Hilliard type equations and incompressible Navier-Stokes equations. Using the Invariant Energy Quadratization (IEQ) approach, the governing system is transformed into an equivalent form, which allows the nonlinear potentials to be treated efficiently and semi-explicitly. we construct a first and a second-order time marching schemes, which are extremely efficient and easy-to-implement, for the transformed governing system. At each time step, the schemes involve solving a sequence of linear elliptic equations, and computations of phase variables, velocity and pressure are totally decoupled. We further establish a rigorous proof of unconditional energy stability for the semi-implicit schemes. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient and unconditionally energy stable. Using our schemes, we investigate the effect of surfactants on droplet deformation and collision under a shear flow. The increase of surfactant concentration can enhance droplet deformation and inhibit droplet coalescence.

  5. Numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow

    KAUST Repository

    Zhu, Guangpu; Kou, Jisheng; Sun, Shuyu; Yao, Jun; Li, Aifen

    2018-01-01

    In this paper, we consider the numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow. The nonlinearly coupled model consists of two Cahn-Hilliard type equations and incompressible Navier-Stokes equations. Using the Invariant Energy Quadratization (IEQ) approach, the governing system is transformed into an equivalent form, which allows the nonlinear potentials to be treated efficiently and semi-explicitly. we construct a first and a second-order time marching schemes, which are extremely efficient and easy-to-implement, for the transformed governing system. At each time step, the schemes involve solving a sequence of linear elliptic equations, and computations of phase variables, velocity and pressure are totally decoupled. We further establish a rigorous proof of unconditional energy stability for the semi-implicit schemes. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient and unconditionally energy stable. Using our schemes, we investigate the effect of surfactants on droplet deformation and collision under a shear flow. The increase of surfactant concentration can enhance droplet deformation and inhibit droplet coalescence.

  6. Two-dimensional numerical simulation of flow around three-stranded rope

    Science.gov (United States)

    Wang, Xinxin; Wan, Rong; Huang, Liuyi; Zhao, Fenfang; Sun, Peng

    2016-08-01

    Three-stranded rope is widely used in fishing gear and mooring system. Results of numerical simulation are presented for flow around a three-stranded rope in uniform flow. The simulation was carried out to study the hydrodynamic characteristics of pressure and velocity fields of steady incompressible laminar and turbulent wakes behind a three-stranded rope. A three-cylinder configuration and single circular cylinder configuration are used to model the three-stranded rope in the two-dimensional simulation. The governing equations, Navier-Stokes equations, are solved by using two-dimensional finite volume method. The turbulence flow is simulated using Standard κ-ɛ model and Shear-Stress Transport κ-ω (SST) model. The drag of the three-cylinder model and single cylinder model is calculated for different Reynolds numbers by using control volume analysis method. The pressure coefficient is also calculated for the turbulent model and laminar model based on the control surface method. From the comparison of the drag coefficient and the pressure of the single cylinder and three-cylinder models, it is found that the drag coefficients of the three-cylinder model are generally 1.3-1.5 times those of the single circular cylinder for different Reynolds numbers. Comparing the numerical results with water tank test data, the results of the three-cylinder model are closer to the experiment results than the single cylinder model results.

  7. The flow of an incompressible electroconductive fluid past a thin airfoil. The parabolic profile

    Directory of Open Access Journals (Sweden)

    Adrian CARABINEANU

    2014-04-01

    Full Text Available We study the two-dimensional steady flow of an ideal incompressible perfectly conducting fluid past an insulating thin parabolic airfoil. We consider the linearized Euler and Maxwell equations and Ohm's law. We use the integral representations for the velocity, magnetic induction and pressure and the boundary conditions to obtain an integral equation for the jump of the pressure across the airfoil. We give some graphic representations for the lift coefficient, velocity and magnetic induction.

  8. Axisymmetric ideal magnetohydrodynamic equilibria with incompressible flows

    International Nuclear Information System (INIS)

    Tasso, H.; Throumoulopoulos, G.N.

    1997-12-01

    It is shown that the ideal MHD equilibrium states of an axisymmetric plasma with incompressible flows are governed by an elliptic partial differential equation for the poloidal magnetic flux function ψ containing five surface quantities along with a relation for the pressure. Exact equilibria are constructed including those with non vanishing poloidal and toroidal flows and differentially varying radial electric fields. Unlike the case in cylindrical incompressible equilibria with isothermal magnetic surfaces which should have necessarily circular cross sections [G. N. Throumoulopoulos and H. Tasso, Phys. Plasmas 4, 1492 (1997)], no restriction appears on the shapes of the magnetic surfaces in the corresponding axisymmetric equilibria. The latter equilibria satisfy a set of six ordinary differential equations which for flows parallel to the magnetic field B can be solved semianalytically. In addition, it is proved the non existence of incompressible axisymmetric equilibria with (a) purely poloidal flows and (b) non-parallel flows with isothermal magnetic surfaces and vertical stroke B vertical stroke = vertical stroke B vertical stroke (ψ) (omnigenous equilibria). (orig.)

  9. Five-dimensional truncation of the plane incompressible navier-stokes equations

    Energy Technology Data Exchange (ETDEWEB)

    Boldrighini, C [Camerino Univ. (Italy). Istituto di Matematica; Franceschini, V [Modena Univ. (Italy). Istituto Matematico

    1979-01-01

    A five-modes truncation of the Navier-Stokes equations for a two dimensional incompressible fluid on a torus is considered. A computer analysis shows that for a certain range of the Reynolds number the system exhibits a stochastic behaviour, approached through an involved sequence of bifurcations.

  10. Three-Dimensional Incompressible Navier-Stokes Flow Computations about Complete Configurations Using a Multiblock Unstructured Grid Approach

    Science.gov (United States)

    Sheng, Chunhua; Hyams, Daniel G.; Sreenivas, Kidambi; Gaither, J. Adam; Marcum, David L.; Whitfield, David L.

    2000-01-01

    A multiblock unstructured grid approach is presented for solving three-dimensional incompressible inviscid and viscous turbulent flows about complete configurations. The artificial compressibility form of the governing equations is solved by a node-based, finite volume implicit scheme which uses a backward Euler time discretization. Point Gauss-Seidel relaxations are used to solve the linear system of equations at each time step. This work employs a multiblock strategy to the solution procedure, which greatly improves the efficiency of the algorithm by significantly reducing the memory requirements by a factor of 5 over the single-grid algorithm while maintaining a similar convergence behavior. The numerical accuracy of solutions is assessed by comparing with the experimental data for a submarine with stem appendages and a high-lift configuration.

  11. Numerical studies of unsteady coherent structures and transport in two-dimensional flows

    Energy Technology Data Exchange (ETDEWEB)

    Hesthaven, J.S.

    1995-08-01

    The dynamics of unsteady two-dimensional coherent structures in various physical systems is studied through direct numerical solution of the dynamical equations using spectral methods. The relation between the Eulerian and the Lagrangian auto-correlation functions in two-dimensional homogeneous, isotropic turbulence is studied. A simple analytic expression for the Eulerian and Lagrangian auto-correlation function for the fluctuating velocity field is derived solely on the basis of the one-dimensional power spectrum. The long-time evolution of monopolar and dipolar vortices in anisotropic systems relevant for geophysics and plasma physics is studied by direct numerical solution. Transport properties and spatial reorganization of vortical structures are found to depend strongly on the initial conditions. Special attention is given to the dynamics of strong monopoles and the development of unsteady tripolar structures. The development of coherent structures in fluid flows, incompressible as well as compressible, is studied by novel numerical schemes. The emphasis is on the development of spectral methods sufficiently advanced as to allow for detailed and accurate studies of the self-organizing processes. (au) 1 ill., 94 refs.

  12. Vorticity vector-potential method based on time-dependent curvilinear coordinates for two-dimensional rotating flows in closed configurations

    Science.gov (United States)

    Fu, Yuan; Zhang, Da-peng; Xie, Xi-lin

    2018-04-01

    In this study, a vorticity vector-potential method for two-dimensional viscous incompressible rotating driven flows is developed in the time-dependent curvilinear coordinates. The method is applicable in both inertial and non-inertial frames of reference with the advantage of a fixed and regular calculation domain. The numerical method is applied to triangle and curved triangle configurations in constant and varying rotational angular velocity cases respectively. The evolutions of flow field are studied. The geostrophic effect, unsteady effect and curvature effect on the evolutions are discussed.

  13. NACHOS: a finite element computer program for incompressible flow problems. Part I. Theoretical background

    International Nuclear Information System (INIS)

    Gartling, D.K.

    1978-04-01

    The theoretical background for the finite element computer program, NACHOS, is presented in detail. The NACHOS code is designed for the two-dimensional analysis of viscous incompressible fluid flows, including the effects of heat transfer. A general description of the fluid/thermal boundary value problems treated by the program is described. The finite element method and the associated numerical methods used in the NACHOS code are also presented. Instructions for use of the program are documented in SAND77-1334

  14. Soap film flows: Statistics of two-dimensional turbulence

    International Nuclear Information System (INIS)

    Vorobieff, P.; Rivera, M.; Ecke, R.E.

    1999-01-01

    Soap film flows provide a very convenient laboratory model for studies of two-dimensional (2-D) hydrodynamics including turbulence. For a gravity-driven soap film channel with a grid of equally spaced cylinders inserted in the flow, we have measured the simultaneous velocity and thickness fields in the irregular flow downstream from the cylinders. The velocity field is determined by a modified digital particle image velocimetry method and the thickness from the light scattered by the particles in the film. From these measurements, we compute the decay of mean energy, enstrophy, and thickness fluctuations with downstream distance, and the structure functions of velocity, vorticity, thickness fluctuation, and vorticity flux. From these quantities we determine the microscale Reynolds number of the flow R λ ∼100 and the integral and dissipation scales of 2D turbulence. We also obtain quantitative measures of the degree to which our flow can be considered incompressible and isotropic as a function of downstream distance. We find coarsening of characteristic spatial scales, qualitative correspondence of the decay of energy and enstrophy with the Batchelor model, scaling of energy in k space consistent with the k -3 spectrum of the Kraichnan endash Batchelor enstrophy-scaling picture, and power-law scalings of the structure functions of velocity, vorticity, vorticity flux, and thickness. These results are compared with models of 2-D turbulence and with numerical simulations. copyright 1999 American Institute of Physics

  15. Simulation of Free Airfoil Vibrations in Incompressible Viscous Flow — Comparison of FEM and FVM

    Directory of Open Access Journals (Sweden)

    Petr Sváček

    2012-01-01

    Full Text Available This paper deals with a numerical solution of the interaction of two-dimensional (2-D incompressible viscous flow and a vibrating profile NACA 0012 with large amplitudes. The laminar flow is described by the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian form. The profile with two degrees of freedom (2-DOF can rotate around its elastic axis and oscillate in the vertical direction. Its motion is described by a nonlinear system of two ordinary differential equations. Deformations of the computational domain due to the profile motion are treated by the arbitrary Lagrangian-Eulerianmethod. The finite volume method and the finite element method are applied, and the numerical results are compared.

  16. Kolmogorov flow in two dimensional strongly coupled dusty plasma

    Energy Technology Data Exchange (ETDEWEB)

    Gupta, Akanksha; Ganesh, R., E-mail: ganesh@ipr.res.in; Joy, Ashwin [Institute for Plasma Research, Bhat Gandhinagar, Gujarat 382 428 (India)

    2014-07-15

    Undriven, incompressible Kolmogorov flow in two dimensional doubly periodic strongly coupled dusty plasma is modelled using generalised hydrodynamics, both in linear and nonlinear regime. A complete stability diagram is obtained for low Reynolds numbers R and for a range of viscoelastic relaxation time τ{sub m} [0 < τ{sub m} < 10]. For the system size considered, using a linear stability analysis, similar to Navier Stokes fluid (τ{sub m} = 0), it is found that for Reynolds number beyond a critical R, say R{sub c}, the Kolmogorov flow becomes unstable. Importantly, it is found that R{sub c} is strongly reduced for increasing values of τ{sub m}. A critical τ{sub m}{sup c} is found above which Kolmogorov flow is unconditionally unstable and becomes independent of Reynolds number. For R < R{sub c}, the neutral stability regime found in Navier Stokes fluid (τ{sub m} = 0) is now found to be a damped regime in viscoelastic fluids, thus changing the fundamental nature of transition of Kolmogorov flow as function of Reynolds number R. A new parallelized nonlinear pseudo spectral code has been developed and is benchmarked against eigen values for Kolmogorov flow obtained from linear analysis. Nonlinear states obtained from the pseudo spectral code exhibit cyclicity and pattern formation in vorticity and viscoelastic oscillations in energy.

  17. Convergence of Discontinuous Galerkin Methods for Incompressible Two-Phase Flow in Heterogeneous Media

    KAUST Repository

    Kou, Jisheng; Sun, Shuyu

    2013-01-01

    A class of discontinuous Galerkin methods with interior penalties is presented for incompressible two-phase flow in heterogeneous porous media with capillary pressures. The semidiscrete approximate schemes for fully coupled system of two-phase flow are formulated. In highly heterogeneous permeable media, the saturation is discontinuous due to different capillary pressures, and therefore, the proposed methods incorporate the capillary pressures in the pressure equation instead of saturation equation. By introducing a coupling approach for stability and error estimates instead of the conventional separate analysis for pressure and saturation, the stability of the schemes in space and time and a priori hp error estimates are presented in the L2(H 1) for pressure and in the L∞(L2) and L2(H1) for saturation. Two time discretization schemes are introduced for effectively computing the discrete solutions. © 2013 Societ y for Industrial and Applied Mathematics.

  18. Immersed boundary-simplified lattice Boltzmann method for incompressible viscous flows

    Science.gov (United States)

    Chen, Z.; Shu, C.; Tan, D.

    2018-05-01

    An immersed boundary-simplified lattice Boltzmann method is developed in this paper for simulations of two-dimensional incompressible viscous flows with immersed objects. Assisted by the fractional step technique, the problem is resolved in a predictor-corrector scheme. The predictor step solves the flow field without considering immersed objects, and the corrector step imposes the effect of immersed boundaries on the velocity field. Different from the previous immersed boundary-lattice Boltzmann method which adopts the standard lattice Boltzmann method (LBM) as the flow solver in the predictor step, a recently developed simplified lattice Boltzmann method (SLBM) is applied in the present method to evaluate intermediate flow variables. Compared to the standard LBM, SLBM requires lower virtual memories, facilitates the implementation of physical boundary conditions, and shows better numerical stability. The boundary condition-enforced immersed boundary method, which accurately ensures no-slip boundary conditions, is implemented as the boundary solver in the corrector step. Four typical numerical examples are presented to demonstrate the stability, the flexibility, and the accuracy of the present method.

  19. On Analysis of Stationary Viscous Incompressible Flow Through a Radial Blade Machine

    Science.gov (United States)

    Neustupa, Tomáš

    2010-09-01

    The paper is concerned with the analysis of the two dimensional model of incompressible, viscous, stationary flow through a radial blade machine. This type of turbine is sometimes called Kaplan's turbine. In the technical area the use is either to force some regular characteristic to the flow of the medium going through the turbine (flow of melted iron, air conditioning) or to gain some energy from the flowing medium (water). The inflow and outflow part of boundary are in general a concentric circles. The larger one represents an inflow part of boundary the smaller one the outflow part of boundary. Between them are regularly spaced the blades of the machine. We study the existence of the weak solution in the case of nonlinear boundary condition of the "do-nothing" type. The model is interesting for study the behavior of the flow when the boundary is formed by mutually disjoint and separated parts.

  20. Fluidic Vectoring of a Planar Incompressible Jet Flow

    Science.gov (United States)

    Mendez, Miguel Alfonso; Scelzo, Maria Teresa; Enache, Adriana; Buchlin, Jean-Marie

    2018-06-01

    This paper presents an experimental, a numerical and a theoretical analysis of the performances of a fluidic vectoring device for controlling the direction of a turbulent, bi-dimensional and low Mach number (incompressible) jet flow. The investigated design is the co-flow secondary injection with Coanda surface, which allows for vectoring angles up to 25° with no need of moving mechanical parts. A simple empirical model of the vectoring process is presented and validated via experimental and numerical data. The experiments consist of flow visualization and image processing for the automatic detection of the jet centerline; the numerical simulations are carried out solving the Unsteady Reynolds Average Navier- Stokes (URANS) closed with the k - ω SST turbulence model, using the PisoFoam solver from OpenFOAM. The experimental validation on three different geometrical configurations has shown that the model is capable of providing a fast and reliable evaluation of the device performance as a function of the operating conditions.

  1. Wavelets for the stimulation of turbulent incompressible flows

    International Nuclear Information System (INIS)

    Deriaz, E.

    2006-02-01

    This PhD thesis presents original wavelet methods aimed at simulating incompressible fluids. In order to construct 2D and 3D wavelets designed for incompressible flows, we resume P-G Lemarie-Rieussets and K. Urbans works on divergence free wavelets. We show the existence of associated fast algorithms. In the following, we use divergence-free wavelet construction to define the Helmholtz decomposition of 2D and 3D vector fields. All these algorithms provide a new method for the numerical resolution of the incompressible Navier-Stokes equations. (author)

  2. One-dimensional transient unequal velocity two-phase flow by the method of characteristics

    International Nuclear Information System (INIS)

    Rasouli, F.

    1981-01-01

    An understanding of two-phase flow is important when one is analyzing the accidental loss of coolant or when analyzing industrial processes. If a pipe in the steam generator of a nuclear reactor breaks, the flow will remain critical (or choked) for almost the entire blowdown. For this reason the knowledge of the two-phase maximum (critical) flow rate is important. A six-equation model--consisting of two continuity equations, two energy equations, a mixture momentum equation, and a constitutive relative velocity equation--is solved numerically by the method of characteristics for one-dimensional, transient, two-phase flow systems. The analysis is also extended to the special case of transient critical flow. The six-equation model is used to study the flow of a nonequilibrium sodium-argon system in a horizontal tube in which the nonequilibrium sodium-argon system in a horizontal tube in which the critical flow condition is at the entrance. A four-equation model is used to study the pressure-pulse propagation rate in an isothermal air-water system, and the results that are found are compared with the experimental data. Proper initial and boundary conditions are obtained for the blowdown problem. The energy and mass exchange relations are evaluated by comparing the model predictions with results of void-fraction and heat-transfer experiments. A simplified two-equation model is obtained for the special case of two incompressible phases. This model is used in the preliminary analysis of batch sedimentation. It is also used to predict the shock formation in the gas-solid fluidized bed

  3. Calculation of incompressible fluid flow through cambered blades

    Science.gov (United States)

    Hsu, C. C.

    1970-01-01

    Conformal mapping technique yields linear, approximate solutions for calculating flow of an incompressible fluid through staggered array of cambered blades for the cases of flow with partial cavitation and supercavitation. Lift and drag coefficients, cavitation number, cavity shape, and exit flow conditions can be determined.

  4. Diffusion-limited mixing by incompressible flows

    Science.gov (United States)

    Miles, Christopher J.; Doering, Charles R.

    2018-05-01

    Incompressible flows can be effective mixers by appropriately advecting a passive tracer to produce small filamentation length scales. In addition, diffusion is generally perceived as beneficial to mixing due to its ability to homogenize a passive tracer. However we provide numerical evidence that, in cases where advection and diffusion are both actively present, diffusion may produce negative effects by limiting the mixing effectiveness of incompressible optimal flows. This limitation appears to be due to the presence of a limiting length scale given by a generalised Batchelor length (Batchelor 1959 J. Fluid Mech. 5 113–33). This length scale limitation may in turn affect long-term mixing rates. More specifically, we consider local-in-time flow optimisation under energy and enstrophy flow constraints with the objective of maximising the mixing rate. We observe that, for enstrophy-bounded optimal flows, the strength of diffusion may not impact the long-term mixing rate. For energy-constrained optimal flows, however, an increase in the strength of diffusion can decrease the mixing rate. We provide analytical lower bounds on mixing rates and length scales achievable under related constraints (point-wise bounded speed and rate-of-strain) by extending the work of Lin et al (2011 J. Fluid Mech. 675 465–76) and Poon (1996 Commun. PDE 21 521–39).

  5. Accurate solution algorithms for incompressible multiphase flows

    International Nuclear Information System (INIS)

    Rider, W.J.; Kothe, D.B.; Mosso, S.J.; Cerutti, J.H.; Hochstein, J.I.

    1994-01-01

    A number of advances in modeling multiphase incompressible flow are described. These advances include high-order Godunov projection methods, piecewise linear interface reconstruction and tracking and the continuum surface force model. Examples are given

  6. Turbulence in nearly incompressible fluids: density spectrum, flows, correlations and implication to the interstellar medium

    Directory of Open Access Journals (Sweden)

    S. Dastgeer

    2005-01-01

    Full Text Available Interstellar scintillation and angular radio wave broadening measurements show that interstellar and solar wind (electron density fluctuations exhibit a Kolmogorov-like k-5/3 power spectrum extending over many decades in wavenumber space. The ubiquity of the Kolmogorov-like interstellar medium (ISM density spectrum led to an explanation based on coupling incompressible magnetohydrodynamic (MHD fluctuations to density fluctuations through a 'pseudosound' relation within the context of 'nearly incompressible' (NI hydrodynamics (HD and MHD models. The NI theory provides a fundamentally different explanation for the observed ISM density spectrum in that the density fluctuations can be a consequence of passive scalar convection due to background incompressible fluctuations. The theory further predicts generation of long-scale structures and various correlations between the density, temperature and the (magneto acoustic as well as convective pressure fluctuations in the compressible ISM fluids in different thermal regimes that are determined purely by the thermal fluctuation level. In this paper, we present the results of our two dimensional nonlinear fluid simulations, exploring various nonlinear aspects that lead to inertial range ISM turbulence within the context of a NI hydrodymanics model. In qualitative agreement with the NI predictions and the in-situ observations, we find that i the density fluctuations exhibit a Kolmogorov-like spectrum via a passive convection in the field of the background incompressible fluctuations, ii the compressible ISM fluctuations form long scale flows and structures, and iii the density and the temperature fluctuations are anti-correlated.

  7. Two-dimensional turbulent flows on a bounded domain

    NARCIS (Netherlands)

    Kramer, W.

    2006-01-01

    Large-scale flows in the oceans and the atmosphere reveal strong similarities with purely two-dimensional flows. One of the most typical features is the cascade of energy from smaller flow scales towards larger scales. This is opposed to three-dimensional turbulence where larger flow structures

  8. A blended pressure/density based method for the computation of incompressible and compressible flows

    International Nuclear Information System (INIS)

    Rossow, C.-C.

    2003-01-01

    An alternative method to low speed preconditioning for the computation of nearly incompressible flows with compressible methods is developed. For this approach the leading terms of the flux difference splitting (FDS) approximate Riemann solver are analyzed in the incompressible limit. In combination with the requirement of the velocity field to be divergence-free, an elliptic equation to solve for a pressure correction to enforce the divergence-free velocity field on the discrete level is derived. The pressure correction equation established is shown to be equivalent to classical methods for incompressible flows. In order to allow the computation of flows at all speeds, a blending technique for the transition from the incompressible, pressure based formulation to the compressible, density based formulation is established. It is found necessary to use preconditioning with this blending technique to account for a remaining 'compressible' contribution in the incompressible limit, and a suitable matrix directly applicable to conservative residuals is derived. Thus, a coherent framework is established to cover the discretization of both incompressible and compressible flows. Compared with standard preconditioning techniques, the blended pressure/density based approach showed improved robustness for high lift flows close to separation

  9. A numerical method for the solution of three-dimensional incompressible viscous flow using the boundary-fitted curvilinear coordinate transformation and domain decomposition technique

    International Nuclear Information System (INIS)

    Umegaki, Kikuo; Miki, Kazuyoshi

    1990-01-01

    A numerical method is developed to solve three-dimensional incompressible viscous flow in complicated geometry using curvilinear coordinate transformation and domain decomposition technique. In this approach, a complicated flow domain is decomposed into several subdomains, each of which has an overlapping region with neighboring subdomains. Curvilinear coordinates are numerically generated in each subdomain using the boundary-fitted coordinate transformation technique. The modified SMAC scheme is developed to solve Navier-Stokes equations in which the convective terms are discretized by the QUICK method. A fully vectorized computer program is developed on the basis of the proposed method. The program is applied to flow analysis in a semicircular curved, 90deg elbow and T-shape branched pipes. Computational time with the vector processor of the HITAC S-810/20 supercomputer system, is reduced to 1/10∼1/20 of that with a scalar processor. (author)

  10. Numerical model for two-dimensional hydrodynamics and energy transport. [VECTRA code

    Energy Technology Data Exchange (ETDEWEB)

    Trent, D.S.

    1973-06-01

    The theoretical basis and computational procedure of the VECTRA computer program are presented. VECTRA (Vorticity-Energy Code for TRansport Analysis) is designed for applying numerical simulation to a broad range of intake/discharge flows in conjunction with power plant hydrological evaluation. The code computational procedure is based on finite-difference approximation of the vorticity-stream function partial differential equations which govern steady flow momentum transport of two-dimensional, incompressible, viscous fluids in conjunction with the transport of heat and other constituents.

  11. Surface representations of two- and three-dimensional fluid flow topology

    Science.gov (United States)

    Helman, James L.; Hesselink, Lambertus

    1990-01-01

    We discuss our work using critical point analysis to generate representations of the vector field topology of numerical flow data sets. Critical points are located and characterized in a two-dimensional domain, which may be either a two-dimensional flow field or the tangential velocity field near a three-dimensional body. Tangent curves are then integrated out along the principal directions of certain classes of critical points. The points and curves are linked to form a skeleton representing the two-dimensional vector field topology. When generated from the tangential velocity field near a body in a three-dimensional flow, the skeleton includes the critical points and curves which provide a basis for analyzing the three-dimensional structure of the flow separation. The points along the separation curves in the skeleton are used to start tangent curve integrations to generate surfaces representing the topology of the associated flow separations.

  12. Multigrid Computation of Stratified Flow over Two-Dimensional Obstacles

    Science.gov (United States)

    Paisley, M. F.

    1997-09-01

    A robust multigrid method for the incompressible Navier-Stokes equations is presented and applied to the computation of viscous flow over obstacles in a bounded domain under conditions of neutral stability and stable density stratification. Two obstacle shapes have been used, namely a vertical barrier, for which the grid is Cartesian, and a smooth cosine-shaped obstacle, for which a boundary-conforming transformation is incorporated. Results are given for laminar flows at low Reynolds numbers and turbulent flows at a high Reynolds number, when a simple mixing length turbulence model is included. The multigrid algorithm is used to compute steady flows for each obstacle at low and high Reynolds numbers in conditions of weak static stability, defined byK=ND/πU≤ 1, whereU,N, andDare the upstream velocity, bouyancy frequency, and domain height respectively. Results are also presented for the vertical barrier at low and high Reynolds number in conditions of strong static stability,K> 1, when lee wave motions ensure that the flow is unsteady, and the multigrid algorithm is used to compute the flow at each timestep.

  13. Rheology of dense granular flows in two dimensions: Comparison of fully two-dimensional flows to unidirectional shear flow

    Science.gov (United States)

    Bhateja, Ashish; Khakhar, Devang V.

    2018-06-01

    We consider the rheology of steady two-dimensional granular flows, in different geometries, using discrete element method-based simulations of soft spheres. The flow classification parameter (ψ ), which defines the local flow type (ranging from pure rotation to simple shear to pure extension), varies spatially, to a significant extent, in the flows. We find that the material behaves as a generalized Newtonian fluid. The μ -I scaling proposed by Jop et al. [Nature (London) 441, 727 (2006), 10.1038/nature04801] is found to be valid in both two-dimensional and unidirectional flows, as observed in previous studies; however, the data for each flow geometry fall on a different curve. The results for the two-dimensional silo flow indicate that the viscosity does not depend directly on the flow type parameter, ψ . We find that the scaling based on "granular fluidity" [Zhang and Kamrin, Phys. Rev. Lett. 118, 058001 (2017), 10.1103/PhysRevLett.118.058001] gives good collapse of the data to a single curve for all the geometries. The data for the variation of the solid faction with inertial number show a reasonable collapse for the different geometries.

  14. Unsteady free surface flow in porous media: One-dimensional model equations including vertical effects and seepage face

    Science.gov (United States)

    Di Nucci, Carmine

    2018-05-01

    This note examines the two-dimensional unsteady isothermal free surface flow of an incompressible fluid in a non-deformable, homogeneous, isotropic, and saturated porous medium (with zero recharge and neglecting capillary effects). Coupling a Boussinesq-type model for nonlinear water waves with Darcy's law, the two-dimensional flow problem is solved using one-dimensional model equations including vertical effects and seepage face. In order to take into account the seepage face development, the system equations (given by the continuity and momentum equations) are completed by an integral relation (deduced from the Cauchy theorem). After testing the model against data sets available in the literature, some numerical simulations, concerning the unsteady flow through a rectangular dam (with an impermeable horizontal bottom), are presented and discussed.

  15. A Diffuse Interface Model for Incompressible Two-Phase Flow with Large Density Ratios

    KAUST Repository

    Xie, Yu; Wodo, Olga; Ganapathysubramanian, Baskar

    2016-01-01

    In this chapter, we explore numerical simulations of incompressible and immiscible two-phase flows. The description of the fluid–fluid interface is introduced via a diffuse interface approach. The two-phase fluid system is represented by a coupled Cahn–Hilliard Navier–Stokes set of equations. We discuss challenges and approaches to solving this coupled set of equations using a stabilized finite element formulation, especially in the case of a large density ratio between the two fluids. Specific features that enabled efficient solution of the equations include: (i) a conservative form of the convective term in the Cahn–Hilliard equation which ensures mass conservation of both fluid components; (ii) a continuous formula to compute the interfacial surface tension which results in lower requirement on the spatial resolution of the interface; and (iii) a four-step fractional scheme to decouple pressure from velocity in the Navier–Stokes equation. These are integrated with standard streamline-upwind Petrov–Galerkin stabilization to avoid spurious oscillations. We perform numerical tests to determine the minimal resolution of spatial discretization. Finally, we illustrate the accuracy of the framework using the analytical results of Prosperetti for a damped oscillating interface between two fluids with a density contrast.

  16. A Diffuse Interface Model for Incompressible Two-Phase Flow with Large Density Ratios

    KAUST Repository

    Xie, Yu

    2016-10-04

    In this chapter, we explore numerical simulations of incompressible and immiscible two-phase flows. The description of the fluid–fluid interface is introduced via a diffuse interface approach. The two-phase fluid system is represented by a coupled Cahn–Hilliard Navier–Stokes set of equations. We discuss challenges and approaches to solving this coupled set of equations using a stabilized finite element formulation, especially in the case of a large density ratio between the two fluids. Specific features that enabled efficient solution of the equations include: (i) a conservative form of the convective term in the Cahn–Hilliard equation which ensures mass conservation of both fluid components; (ii) a continuous formula to compute the interfacial surface tension which results in lower requirement on the spatial resolution of the interface; and (iii) a four-step fractional scheme to decouple pressure from velocity in the Navier–Stokes equation. These are integrated with standard streamline-upwind Petrov–Galerkin stabilization to avoid spurious oscillations. We perform numerical tests to determine the minimal resolution of spatial discretization. Finally, we illustrate the accuracy of the framework using the analytical results of Prosperetti for a damped oscillating interface between two fluids with a density contrast.

  17. Relaxation and self-organization in two-dimensional plasma and neutral fluid flow systems

    International Nuclear Information System (INIS)

    Das, Amita

    2008-01-01

    Extensive numerical studies in the framework of a simplified two-dimensional model for neutral and plasma fluid for a variety of initial configurations and for both decaying and driven cases are carried out to illustrate relaxation toward a self-organized state. The dynamical model equation constitutes a simple choice for this purpose, e.g., the vorticity equation of the Navier-Stokes dynamics for the incompressible neutral fluids and the Hasegawa-Mima equation for plasma fluid flow system. Scatter plots are employed to observe a development of functional relationship, if any, amidst the generalized vorticity and its Laplacian. It is seen that they do not satisfy a linear relationship as the well known variational approach of enstrophy minimization subject to constancy of the energy integral for the two-dimensional (2D) system suggests. The observed nonlinear functional relationship is understood by separating the contribution to the scatter plot from spatial regions with intense vorticity patches and those of the background flow region where the background vorticity is weak or absent altogether. It is shown that such a separation has close connection with the known exact analytical solutions of the system. The analytical solutions are typically obtained by assuming a finite source of vorticity for the inner core of the localized structure, which is then matched with the solution in the outer region where vorticity is chosen to be zero. The work also demonstrates that the seemingly ad hoc choice of the linear vorticity source function for the inner region is in fact consistent with the self-organization paradigm of the 2D systems

  18. Numerical investigation of incompressible fluid flow and heat transfer across a bluff body in a channel flow

    Directory of Open Access Journals (Sweden)

    Taymaz Imdat

    2015-01-01

    Full Text Available The Lattice Boltzmann Method is applied to computationally investigate the laminar flow and heat transfer of an incompressible fluid with constant material properties in a two-dimensional channel with a built-in bluff body. In this study, a triangular prism is taken as the bluff body. Not only the momentum transport, but also the energy transport is modeled by the Lattice Boltzmann Method. A uniform lattice structure with a single time relaxation rule is used. For obtaining a higher flexibility on the computational grid, interpolation methods are applied, where the information is transferred from the lattice structure to the computational grid by Lagrange interpolation. The flow is investigated for different Reynolds numbers, while keeping the Prandtl number at the constant value of 0.7. The results show how the presence of a triangular prism effects the flow and heat transfer patterns for the steady-state and unsteady-periodic flow regimes. As an assessment of the accuracy of the developed Lattice Boltzmann code, the results are compared with those obtained by a commercial Computational Fluid Dynamics code. It is observed that the present Lattice Boltzmann code delivers results that are of similar accuracy to the well-established Computational Fluid Dynamics code, with much smaller computational time for the prediction of the unsteady phenomena.

  19. On two-dimensionalization of three-dimensional turbulence in shell models

    DEFF Research Database (Denmark)

    Chakraborty, Sagar; Jensen, Mogens Høgh; Sarkar, A.

    2010-01-01

    Applying a modified version of the Gledzer-Ohkitani-Yamada (GOY) shell model, the signatures of so-called two-dimensionalization effect of three-dimensional incompressible, homogeneous, isotropic fully developed unforced turbulence have been studied and reproduced. Within the framework of shell m......-similar PDFs for longitudinal velocity differences are also presented for the rotating 3D turbulence case....

  20. Analysis of a combined mixed finite element and discontinuous Galerkin method for incompressible two-phase flow in porous media

    KAUST Repository

    Kou, Jisheng; Sun, Shuyu

    2013-01-01

    We analyze a combined method consisting of the mixed finite element method for pressure equation and the discontinuous Galerkin method for saturation equation for the coupled system of incompressible two-phase flow in porous media. The existence and uniqueness of numerical solutions are established under proper conditions by using a constructive approach. Optimal error estimates in L2(H1) for saturation and in L∞(H(div)) for velocity are derived. Copyright © 2013 John Wiley & Sons, Ltd.

  1. Analysis of a combined mixed finite element and discontinuous Galerkin method for incompressible two-phase flow in porous media

    KAUST Repository

    Kou, Jisheng

    2013-06-20

    We analyze a combined method consisting of the mixed finite element method for pressure equation and the discontinuous Galerkin method for saturation equation for the coupled system of incompressible two-phase flow in porous media. The existence and uniqueness of numerical solutions are established under proper conditions by using a constructive approach. Optimal error estimates in L2(H1) for saturation and in L∞(H(div)) for velocity are derived. Copyright © 2013 John Wiley & Sons, Ltd.

  2. Design of two-dimensional channels with prescribed velocity distributions along the channel walls

    Science.gov (United States)

    Stanitz, John D

    1953-01-01

    A general method of design is developed for two-dimensional unbranched channels with prescribed velocities as a function of arc length along the channel walls. The method is developed for both compressible and incompressible, irrotational, nonviscous flow and applies to the design of elbows, diffusers, nozzles, and so forth. In part I solutions are obtained by relaxation methods; in part II solutions are obtained by a Green's function. Five numerical examples are given in part I including three elbow designs with the same prescribed velocity as a function of arc length along the channel walls but with incompressible, linearized compressible, and compressible flow. One numerical example is presented in part II for an accelerating elbow with linearized compressible flow, and the time required for the solution by a Green's function in part II was considerably less than the time required for the same solution by relaxation methods in part I.

  3. NASA-VOF2D, 2-D Transient Free Surface Incompressible Fluid Dynamic

    International Nuclear Information System (INIS)

    Torrey, M.D.

    1988-01-01

    1 - Description of program or function: NASA-VOF2D is a two- dimensional, transient, free surface incompressible fluid dynamics program. It allows multiple free surfaces with surface tension and wall adhesion forces and has a partial cell treatment which allows curved boundaries and interior obstacles. 2 - Method of solution: NASA-VOF2D simulates incompressible flows with free surfaces using the volume-of-fluid (VOF) algorithm. This technique is based on the use of donor-acceptor differencing to track the free surface across an Eulerian grid. The complete Navier-Stokes equations in primitive variables for an incompressible fluid are solved by finite differences with surface tension and wall adhesion included. Optionally the pressure equation can be solved by a conjugate residual method rather than the successive over-relaxation (SOR) method

  4. Transient two-dimensional flow in porous media

    International Nuclear Information System (INIS)

    Sharpe, L. Jr.

    1979-01-01

    The transient flow of an isothermal ideal gas from the cavity formed by an underground nuclear explosion is investigated. A two-dimensional finite element method is used in analyzing the gas flow. Numerical results of the pressure distribution are obtained for both the stemming column and the surrounding porous media

  5. A meshless scheme for incompressible fluid flow using a velocity-pressure correction method

    KAUST Repository

    Bourantas, Georgios

    2013-12-01

    A meshless point collocation method is proposed for the numerical solution of the steady state, incompressible Navier-Stokes (NS) equations in their primitive u-v-p formulation. The flow equations are solved in their strong form using either a collocated or a semi-staggered "grid" configuration. The developed numerical scheme approximates the unknown field functions using the Moving Least Squares approximation. A velocity, along with a pressure correction scheme is applied in the context of the meshless point collocation method. The proposed meshless point collocation (MPC) scheme has the following characteristics: (i) it is a truly meshless method, (ii) there is no need for pressure boundary conditions since no pressure constitutive equation is solved, (iii) it incorporates simplicity and accuracy, (iv) results can be obtained using collocated or semi-staggered "grids", (v) there is no need for the usage of a curvilinear system of coordinates and (vi) it can solve steady and unsteady flows. The lid-driven cavity flow problem, for Reynolds numbers up to 5000, has been considered, by using both staggered and collocated grid configurations. Following, the Backward-Facing Step (BFS) flow problem was considered for Reynolds numbers up to 800 using a staggered grid. As a final example, the case of a laminar flow in a two-dimensional tube with an obstacle was examined. © 2013 Elsevier Ltd.

  6. Three-dimensional investigation of the two-phase flow structure in a bubbly pipe flow

    International Nuclear Information System (INIS)

    Schmidl, W.; Hassan, Y.A.; Ortiz-Villafuerte, J.

    1996-01-01

    Particle image velocimetry (PIV) is a nonintrusive measurement technique that can be used to study the structure of various fluid flows. PIV is used to measure the time-varying, full-field velocity data of a particle-seeded flow field within either a two-dimensional plane or three-dimensional volume. PIV is a very efficient measurement technique since it can obtain both qualitative and quantitative spatial information about the flow field being studied. The quantitative spatial velocity information can be further processed into information of flow parameters such as vorticity and turbulence over extended areas. The objective of this study was to apply recent advances and improvements in the PIV flow measurement technique to the full-field, nonintrusive analysis of a three-dimensional, two-phase fluid flow system in such a manner that both components of the two-phase system could be experimentally quantified

  7. Finite element methods for incompressible flow problems

    CERN Document Server

    John, Volker

    2016-01-01

    This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations, and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.

  8. Gas-liquid Two Phase Flow Modelling of Incompressible Fluid and Experimental Validation Studies in Vertical Centrifugal Casting

    International Nuclear Information System (INIS)

    Zhou, J X; Shen, X; Yin, Y J; Guo, Z; Wang, H

    2015-01-01

    In this paper, Gas-liquid two phase flow mathematic models of incompressible fluid were proposed to explore the feature of fluid under certain centrifugal force in vertical centrifugal casting (VCC). Modified projection-level-set method was introduced to solve the mathematic models. To validate the simulation results, two methods were used in this study. In the first method, the simulation result of basic VCC flow process was compared with its analytic solution. The relationship between the numerical solution and deterministic analytic solution was presented to verify the correctness of numerical algorithms. In the second method, systematic water simulation experiments were developed. In this initial experiment, special experimental vertical centrifugal device and casting shapes were designed to describe typical mold-filling processes in VCC. High speed camera system and data collection devices were used to capture flow shape during the mold-filling process. Moreover, fluid characteristic at different rotation speed (from 40rpm, 60rpmand 80rpm) was discussed to provide comparative resource for simulation results. As compared with the simulation results, the proposed mathematical models could be proven and the experimental design could help us advance the accuracy of simulation and further studies for VCC. (paper)

  9. Some axisymmetric equilibria for certain ideal and resistive magnetohydrodynamics with incompressible flows

    Directory of Open Access Journals (Sweden)

    S.M. Moawad

    Full Text Available In this paper, the equilibrium properties of some ideal and resistive magnetohydrodynamics (MHD are investigated. The governing equations are taken in the steady state for parallel and non-parallel flow to magnetic filed. The governing equations are reduced to Bernoulli-Grad-Shafranov system. The problem of finding exact equilibria to the governing equations in the presence of incompressible mass flows is studied. Several nonlinear equilibria of the governing equations are obtained with aid of constructed constraints. The obtained results cover several previously configurations and include new considerations about the nonlinearity of magnetic flux stream variables. The possibility of applying the obtained results to magnetic confinement devices are discussed. Keywords: Magnetohydrodynamics, Axisymmetric plasma, Resistivity, Incompressible flows, Exact equilibria, Magnetic confinement devices

  10. Isogeometric analysis of sound propagation through laminar flow in 2-dimensional ducts

    DEFF Research Database (Denmark)

    Nørtoft, Peter; Gravesen, Jens; Willatzen, Morten

    2015-01-01

    We consider the propagation of sound through a slowly moving fluid in a 2-dimensional duct. A detailed description of a flow-acoustic model of the problem using B-spline based isogeometric analysis is given. The model couples the non-linear, steady-state, incompressible Navier-Stokes equation in ...

  11. High-velocity two-phase flow two-dimensional modeling

    International Nuclear Information System (INIS)

    Mathes, R.; Alemany, A.; Thilbault, J.P.

    1995-01-01

    The two-phase flow in the nozzle of a LMMHD (liquid metal magnetohydrodynamic) converter has been studied numerically and experimentally. A two-dimensional model for two-phase flow has been developed including the viscous terms (dragging and turbulence) and the interfacial mass, momentum and energy transfer between the phases. The numerical results were obtained by a finite volume method based on the SIMPLE algorithm. They have been verified by an experimental facility using air-water as a simulation pair and a phase Doppler particle analyzer for velocity and droplet size measurement. The numerical simulation of a lithium-cesium high-temperature pair showed that a nearly homogeneous and isothermal expansion of the two phases is possible with small pressure losses and high kinetic efficiencies. In the throat region a careful profiling is necessary to reduce the inertial effects on the liquid velocity field

  12. Universal Distribution of Centers and Saddles in Two-Dimensional Turbulence

    International Nuclear Information System (INIS)

    Rivera, Michael; Wu, Xiao-Lun; Yeung, Chuck

    2001-01-01

    The statistical properties of the local topology of two-dimensional turbulence are investigated using an electromagnetically forced soap film. The local topology of the incompressible 2D flow is characterized by the Jacobian determinant Λ(x,y)=1/4 (ω 2 -σ 2 ) , where ω(x,y) is the local vorticity and σ(x,y) is the local strain rate. For turbulent flows driven by different external force configurations, P(Λ) is found to be a universal function when rescaled using the turbulent intensity. A simple model that agrees with the measured functional form of P(Λ) is constructed using the assumption that the stream function, ψ(x,y) , is a Gaussian random field

  13. Calculation of three-dimensional fluid flow with multiple free surfaces

    International Nuclear Information System (INIS)

    Vander Vorst, M.J.; Chan, R.K.C.

    1978-01-01

    This paper presents a method for computing incompressible fluid flows with multiple free surfaces which are not restricted in their orientation. The method is presented in the context of the three-dimensional flow in a Mark I reactor pressure suppression system immediately following a postulated loss of coolant accident. The assumption of potential flow is made. The numerical method is a mixed Eulerian-Lagrangian formulation with the interior treated as Eulerian and the free surfaces as Lagrangian. The accuracy of solution hinges on the careful treatment of two important aspects. First, the Laplace equation for the potential is solved at interior points of the Eulerian finite difference mesh using a three-dimensional ''irregular star'' so that boundary conditions can be imposed at the exact position of the free surface. Second, the Lagrangian free surfaces are composed of triangular elements, upon each vertex of which is applied the fully nonlinear Bernoulli equation. One result of these calculations is the transient load on the suppression vessel during the vent clearing and bubble formation events of a loss of coolant accident

  14. Application of a method for comparing one-dimensional and two-dimensional models of a ground-water flow system

    International Nuclear Information System (INIS)

    Naymik, T.G.

    1978-01-01

    To evaluate the inability of a one-dimensional ground-water model to interact continuously with surrounding hydraulic head gradients, simulations using one-dimensional and two-dimensional ground-water flow models were compared. This approach used two types of models: flow-conserving one-and-two dimensional models, and one-dimensional and two-dimensional models designed to yield two-dimensional solutions. The hydraulic conductivities of controlling features were varied and model comparison was based on the travel times of marker particles. The solutions within each of the two model types compare reasonably well, but a three-dimensional solution is required to quantify the comparison

  15. POD-Galerkin Model for Incompressible Single-Phase Flow in Porous Media

    KAUST Repository

    Wang, Yi; Yu, Bo; Sun, Shuyu

    2017-01-01

    Fast prediction modeling via proper orthogonal decomposition method combined with Galerkin projection is applied to incompressible single-phase fluid flow in porous media. Cases for different configurations of porous media, boundary conditions

  16. Two-dimensional heat flow apparatus

    Science.gov (United States)

    McDougall, Patrick; Ayars, Eric

    2014-06-01

    We have created an apparatus to quantitatively measure two-dimensional heat flow in a metal plate using a grid of temperature sensors read by a microcontroller. Real-time temperature data are collected from the microcontroller by a computer for comparison with a computational model of the heat equation. The microcontroller-based sensor array allows previously unavailable levels of precision at very low cost, and the combination of measurement and modeling makes for an excellent apparatus for the advanced undergraduate laboratory course.

  17. Examination of the PCICE method in the nearly incompressible, as well as strictly incompressible, limits

    International Nuclear Information System (INIS)

    Berry, Ray A.; Martineau, Richard C.

    2007-01-01

    The conservative-form, pressure-based PCICE numerical method (Martineau and Berry, 2004) (Berry, 2006), recently developed for computing transient fluid flows of all speeds from very low to very high (with strong shocks), is simplified and generalized. Though the method automatically treats a continuous transition of compressibility, three distinct, limiting compressibility regimes are formally defined for purposes of discussion and comparison with traditional methods - the strictly incompressible limit, the nearly incompressible limit, and the fully compressible limit. The PCICE method's behavior is examined in each limiting regime. In the strictly incompressible limit the PCICE algorithm reduces to the traditional MAC-type method with velocity divergence driving the pressure Poisson equation. In the nearly incompressible limit the PCICE algorithm is found to reduce to a generalization of traditional incompressible methods, i.e. to one in which not only the velocity divergence effect, but also the density gradient effect is included as a driving function in the pressure Poisson equation. This nearly incompressible regime has received little attention, and it appears that in the past, strictly incompressible methods may have been conveniently applied to flows in this regime at the expense of ignoring a potentially important coupling mechanism. This could be significant in many important flows; for example, in natural convection flows resulting from high heat flux. In the fully compressible limit or regime, the algorithm is found to reduce to an expression equivalent to density-based methods for high-speed flow. (author)

  18. NASA-VOF3D: A three-dimensional computer program for incompressible flows with free surfaces

    Science.gov (United States)

    Torrey, M. D.; Mjolsness, R. C.; Stein, L. R.

    1987-07-01

    Presented is the NASA-VOF3D three-dimensional, transient, free-surface hydrodynamics program. This three-dimensional extension of NASA-VOF2D will, in principle, permit treatment in full three-dimensional generality of the wide variety of applications that could be treated by NASA-VOF2D only within the two-dimensional idealization. In particular, it, like NASA-VOF2D, is specifically designed to calculate confined flows in a low g environment. The code is presently restricted to cylindrical geometry. The code is based on the fractional volume-of-fluid method and allows multiple free surfaces with surface tension and wall adhesion. It also has a partial cell treatment that allows curved boundaries and internal obstacles. This report provides a brief discussion of the numerical method, a code listing, and some sample problems.

  19. Three dimensional simulation of compressible and incompressible flows through the finite element method; Simulacao tridimensional de escoamentos compressiveis e incompressiveis atraves do metodo dos elementos finitos

    Energy Technology Data Exchange (ETDEWEB)

    Costa, Gustavo Koury

    2004-11-15

    Although incompressible fluid flows can be regarded as a particular case of a general problem, numerical methods and the mathematical formulation aimed to solve compressible and incompressible flows have their own peculiarities, in such a way, that it is generally not possible to attain both regimes with a single approach. In this work, we start from a typically compressible formulation, slightly modified to make use of pressure variables and, through augmenting the stabilising parameters, we end up with a simplified model which is able to deal with a wide range of flow regimes, from supersonic to low speed gas flows. The resulting methodology is flexible enough to allow for the simulation of liquid flows as well. Examples using conservative and pressure variables are shown and the results are compared to those published in the literature, in order to validate the method. (author)

  20. Self-similarity in incompressible Navier-Stokes equations.

    Science.gov (United States)

    Ercan, Ali; Kavvas, M Levent

    2015-12-01

    The self-similarity conditions of the 3-dimensional (3D) incompressible Navier-Stokes equations are obtained by utilizing one-parameter Lie group of point scaling transformations. It is found that the scaling exponents of length dimensions in i = 1, 2, 3 coordinates in 3-dimensions are not arbitrary but equal for the self-similarity of 3D incompressible Navier-Stokes equations. It is also shown that the self-similarity in this particular flow process can be achieved in different time and space scales when the viscosity of the fluid is also scaled in addition to other flow variables. In other words, the self-similarity of Navier-Stokes equations is achievable under different fluid environments in the same or different gravity conditions. Self-similarity criteria due to initial and boundary conditions are also presented. Utilizing the proposed self-similarity conditions of the 3D hydrodynamic flow process, the value of a flow variable at a specified time and space can be scaled to a corresponding value in a self-similar domain at the corresponding time and space.

  1. Generalized similarity method in unsteady two-dimensional MHD ...

    African Journals Online (AJOL)

    user

    International Journal of Engineering, Science and Technology. Vol. 1, No. 1, 2009 ... temperature two-dimensional MHD laminar boundary layer of incompressible fluid. ...... Φ η is Blasius solution for stationary boundary layer on the plate,. ( ). 0.

  2. Twopool strategy and the combined compressible/incompressible flow problem

    International Nuclear Information System (INIS)

    Sienicki, J.J.; Abramson, P.B.

    1979-01-01

    Most recent numerical modeling of two-phase flow involves an implicit determination of a pressure field upon which computational efficiency is strongly dependent. While cell by cell schemes (which treat the pressures in adjacent cells as known source terms) offer fast running times, permit the use of large time steps limited by a Courant condition restriction based on material velocities, and favor enhanced implicit coupling between the thermodynamic and hydrodynamic variables within individual cells, strong implicit coupling (as obtained with elimination schemes) between pressures in adjacent cells in pure single-phase liquid regions is necessary for the calculation of combined two-phase (compressible)/single-phase (incompressible) flows. The TWOPOOL strategy, which consists of a separation in the determination of a pressure field between the single-phase liquid cells where elimination is used and the two-phase cells where a cell by cell scheme is used, constitutes the fastest running strategy which permits the use of large time steps limited only by a Courant condition restriction based on material velocities

  3. High order methods for incompressible fluid flow: Application to moving boundary problems

    Energy Technology Data Exchange (ETDEWEB)

    Bjoentegaard, Tormod

    2008-04-15

    Fluid flows with moving boundaries are encountered in a large number of real life situations, with two such types being fluid-structure interaction and free-surface flows. Fluid-structure phenomena are for instance apparent in many hydrodynamic applications; wave effects on offshore structures, sloshing and fluid induced vibrations, and aeroelasticity; flutter and dynamic response. Free-surface flows can be considered as a special case of a fluid-fluid interaction where one of the fluids are practically inviscid, such as air. This type of flows arise in many disciplines such as marine hydrodynamics, chemical engineering, material processing, and geophysics. The driving forces for free-surface flows may be of large scale such as gravity or inertial forces, or forces due to surface tension which operate on a much smaller scale. Free-surface flows with surface tension as a driving mechanism include the flow of bubbles and droplets, and the evolution of capillary waves. In this work we consider incompressible fluid flow, which are governed by the incompressible Navier-Stokes equations. There are several challenges when simulating moving boundary problems numerically, and these include - Spatial discretization - Temporal discretization - Imposition of boundary conditions - Solution strategy for the linear equations. These are some of the issues which will be addressed in this introduction. We will first formulate the problem in the arbitrary Lagrangian-Eulerian framework, and introduce the weak formulation of the problem. Next, we discuss the spatial and temporal discretization before we move to the imposition of surface tension boundary conditions. In the final section we discuss the solution of the resulting linear system of equations. (Author). refs., figs., tabs

  4. Upwind discontinuous Galerkin methods with mass conservation of both phases for incompressible two-phase flow in porous media

    KAUST Repository

    Kou, Jisheng

    2014-03-22

    Discontinuous Galerkin methods with interior penalties and upwind schemes are applied to the original formulation modeling incompressible two-phase flow in porous media with the capillary pressure. The pressure equation is obtained by summing the discretized conservation equations of two phases. This treatment is very different from the conventional approaches, and its great merit is that the mass conservations hold for both phases instead of only one phase in the conventional schemes. By constructing a new continuous map and using the fixed-point theorem, we prove the global existence of discrete solutions under the proper conditions, and furthermore, we obtain a priori hp error estimates of the pressures in L 2 (H 1) and the saturations in L ∞(L 2) and L 2 (H 1). © 2014 Wiley Periodicals, Inc.

  5. Upwind discontinuous Galerkin methods with mass conservation of both phases for incompressible two-phase flow in porous media

    KAUST Repository

    Kou, Jisheng; Sun, Shuyu

    2014-01-01

    Discontinuous Galerkin methods with interior penalties and upwind schemes are applied to the original formulation modeling incompressible two-phase flow in porous media with the capillary pressure. The pressure equation is obtained by summing the discretized conservation equations of two phases. This treatment is very different from the conventional approaches, and its great merit is that the mass conservations hold for both phases instead of only one phase in the conventional schemes. By constructing a new continuous map and using the fixed-point theorem, we prove the global existence of discrete solutions under the proper conditions, and furthermore, we obtain a priori hp error estimates of the pressures in L 2 (H 1) and the saturations in L ∞(L 2) and L 2 (H 1). © 2014 Wiley Periodicals, Inc.

  6. Helically symmetric equilibria with pressure anisotropy and incompressible plasma flow

    Science.gov (United States)

    Evangelias, A.; Kuiroukidis, A.; Throumoulopoulos, G. N.

    2018-02-01

    We derive a generalized Grad-Shafranov equation governing helically symmetric equilibria with pressure anisotropy and incompressible flow of arbitrary direction. Through the most general linearizing ansatz for the various free surface functions involved therein, we construct equilibrium solutions and study their properties. It turns out that pressure anisotropy can act either paramegnetically or diamagnetically, the parallel flow has a paramagnetic effect, while the non-parallel component of the flow associated with the electric field has a diamagnetic one. Also, pressure anisotropy and flow affect noticeably the helical current density.

  7. INS3D - NUMERICAL SOLUTION OF THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS IN THREE-DIMENSIONAL GENERALIZED CURVILINEAR COORDINATES (DEC RISC ULTRIX VERSION)

    Science.gov (United States)

    Biyabani, S. R.

    1994-01-01

    INS3D computes steady-state solutions to the incompressible Navier-Stokes equations. The INS3D approach utilizes pseudo-compressibility combined with an approximate factorization scheme. This computational fluid dynamics (CFD) code has been verified on problems such as flow through a channel, flow over a backwardfacing step and flow over a circular cylinder. Three dimensional cases include flow over an ogive cylinder, flow through a rectangular duct, wind tunnel inlet flow, cylinder-wall juncture flow and flow through multiple posts mounted between two plates. INS3D uses a pseudo-compressibility approach in which a time derivative of pressure is added to the continuity equation, which together with the momentum equations form a set of four equations with pressure and velocity as the dependent variables. The equations' coordinates are transformed for general three dimensional applications. The equations are advanced in time by the implicit, non-iterative, approximately-factored, finite-difference scheme of Beam and Warming. The numerical stability of the scheme depends on the use of higher-order smoothing terms to damp out higher-frequency oscillations caused by second-order central differencing. The artificial compressibility introduces pressure (sound) waves of finite speed (whereas the speed of sound would be infinite in an incompressible fluid). As the solution converges, these pressure waves die out, causing the derivation of pressure with respect to time to approach zero. Thus, continuity is satisfied for the incompressible fluid in the steady state. Computational efficiency is achieved using a diagonal algorithm. A block tri-diagonal option is also available. When a steady-state solution is reached, the modified continuity equation will satisfy the divergence-free velocity field condition. INS3D is capable of handling several different types of boundaries encountered in numerical simulations, including solid-surface, inflow and outflow, and far

  8. Coherent structures and flow topology of transitional separated-reattached flow over two and three dimensional geometrical shapes

    Science.gov (United States)

    Diabil, Hayder Azeez; Li, Xin Kai; Abdalla, Ibrahim Elrayah

    2017-09-01

    Large-scale organized motions (commonly referred to coherent structures) and flow topology of a transitional separated-reattached flow have been visualised and investigated using flow visualisation techniques. Two geometrical shapes including two-dimensional flat plate with rectangular leading edge and three-dimensional square cylinder are chosen to shed a light on the flow topology and present coherent structures of the flow over these shapes. For both geometries and in the early stage of the transition, two-dimensional Kelvin-Helmholtz rolls are formed downstream of the leading edge. They are observed to be twisting around the square cylinder while they stay flat in the case of the two-dimensional flat plate. For both geometrical shapes, the two-dimensional Kelvin-Helmholtz rolls move downstream of the leading edge and they are subjected to distortion to form three-dimensional hairpin structures. The flow topology in the flat plate is different from that in the square cylinder. For the flat plate, there is a merging process by a pairing of the Kelvin-Helmholtz rolls to form a large structure that breaks down directly into many hairpin structures. For the squire cylinder case, the Kelvin-Helmholtz roll evolves topologically to form a hairpin structure. In the squire cylinder case, the reattachment length is much shorter and a forming of the three-dimensional structures is closer to the leading edge than that in the flat plate case.

  9. A renormalization group scaling analysis for compressible two-phase flow

    International Nuclear Information System (INIS)

    Chen, Y.; Deng, Y.; Glimm, J.; Li, G.; Zhang, Q.; Sharp, D.H.

    1993-01-01

    Computational solutions to the Rayleigh--Taylor fluid mixing problem, as modeled by the two-fluid two-dimensional Euler equations, are presented. Data from these solutions are analyzed from the point of view of Reynolds averaged equations, using scaling laws derived from a renormalization group analysis. The computations, carried out with the front tracking method on an Intel iPSC/860, are highly resolved and statistical convergence of ensemble averages is achieved. The computations are consistent with the experimentally observed growth rates for nearly incompressible flows. The dynamics of the interior portion of the mixing zone is simplified by the use of scaling variables. The size of the mixing zone suggests fixed-point behavior. The profile of statistical quantities within the mixing zone exhibit self-similarity under fixed-point scaling to a limited degree. The effect of compressibility is also examined. It is found that, for even moderate compressibility, the growth rates fail to satisfy universal scaling, and moreover, increase significantly with increasing compressibility. The growth rates predicted from a renormalization group fixed-point model are in a reasonable agreement with the results of the exact numerical simulations, even for flows outside of the incompressible limit

  10. Newtonian heating effects in three-dimensional flow of viscoelastic fluid

    International Nuclear Information System (INIS)

    Qayyum, A.; Hayat, T.; Alhuthali, M. S.; Malaikah, H. M.

    2014-01-01

    A mathematical model is constructed to investigate the three-dimensional flow of a non-Newtonian fluid. An incompressible viscoelastic fluid is used in mathematical formulation. The conjugate convective process (in which heat the transfer rate from the bounding surface with a finite capacity is proportional to the local surface temperature) in three-dimensional flow of a differential type of non-Newtonian fluid is analyzed for the first time. Series solutions for the nonlinear differential system are computed. Plots are presented for the description of emerging parameters entering into the problem. It is observed that the conjugate heating phenomenon causes an appreciable increase in the temperature at the stretching wall. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

  11. Mean flow characteristics of two-dimensional wings in ground effect

    Directory of Open Access Journals (Sweden)

    Jae Hwan Jung

    2012-06-01

    Full Text Available The present study numerically investigates the aerodynamic characteristics of two-dimensional wings in the vicinity of the ground by solving two-dimensional steady incompressible Navier-Stokes equations with the turbulence closure model of the realizable k-ε model. Numerical simulations are performed at a wide range of the normalized ground clearance by the chord length (0.1≤h/C ≤ 1.25 for the angles of attack (0° ≤ α ≤ 10° in the pre-stall regime at a Reynolds number (Re of 2×106 based on free stream velocity U∞ and the chord length. As the physical model of this study, a cambered airfoil of NACA 4406 has been selected by a performance test for various airfoils. The maximum lift-to-drag ratio is achieved at α = 4° and h/C = 0.1. Under the conditions of α = 4° and h/C = 0.1, the effect of the Reynolds number on the aerodynamic characteristics of NACA 4406 is investigated in the range of 2× 10 5 ≤ Re ≤ 2× 109. As Re increases, Cl and Cd augments and decreases, respectively, and the lift-to-drag ratio increases linearly.

  12. Solutions to three-dimensional Navier-Stokes equations for incompressible fluids

    Directory of Open Access Journals (Sweden)

    Jorma Jormakka

    2010-07-01

    Full Text Available This article gives explicit solutions to the space-periodic Navier-Stokes problem with non-periodic pressure. These type of solutions are not unique and by using such solutions one can construct a periodic, smooth, divergence-free initial vector field allowing a space-periodic and time-bounded external force such that there exists a smooth solution to the 3-dimensional Navier-Stokes equations for incompressible fluid with those initial conditions, but the solution cannot be continued to the whole space.

  13. Development of One Dimensional Hyperbolic Coupled Solver for Two-Phase Flows

    International Nuclear Information System (INIS)

    Kim, Eoi Jin; Kim, Jong Tae; Jeong, Jae June

    2008-08-01

    The purpose of this study is a code development for one dimensional two-phase two-fluid flows. In this study, the computations of two-phase flow were performed by using the Roe scheme which is one of the upwind schemes. The upwind scheme is widely used in the computational fluid dynamics because it can capture discontinuities clearly such as a shock. And this scheme is applicable to multi-phase flows by the extension methods which were developed by Toumi, Stadtke, etc. In this study, the extended Roe upwind scheme by Toumi for two-phase flow was implemented in the one-dimensional code. The scheme was applied to a shock tube problem and a water faucet problem. This numerical method seems efficient for non oscillating solutions of two phase flow problems, and also capable for capturing discontinuities

  14. Development of One Dimensional Hyperbolic Coupled Solver for Two-Phase Flows

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Eoi Jin; Kim, Jong Tae; Jeong, Jae June

    2008-08-15

    The purpose of this study is a code development for one dimensional two-phase two-fluid flows. In this study, the computations of two-phase flow were performed by using the Roe scheme which is one of the upwind schemes. The upwind scheme is widely used in the computational fluid dynamics because it can capture discontinuities clearly such as a shock. And this scheme is applicable to multi-phase flows by the extension methods which were developed by Toumi, Stadtke, etc. In this study, the extended Roe upwind scheme by Toumi for two-phase flow was implemented in the one-dimensional code. The scheme was applied to a shock tube problem and a water faucet problem. This numerical method seems efficient for non oscillating solutions of two phase flow problems, and also capable for capturing discontinuities.

  15. Experimental study on two-dimensional film flow with local measurement methods

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Jin-Hwa, E-mail: evo03@snu.ac.kr [Nuclear Thermal-Hydraulic Engineering Laboratory, Seoul National University, Gwanak 599, Gwanak-ro, Gwanak-gu, Seoul 151-742 (Korea, Republic of); Korea Atomic Energy Research Institute, 989-111, Daedeok-daero, Yuseong-gu, Daejeon 305-600 (Korea, Republic of); Cho, Hyoung-Kyu [Nuclear Thermal-Hydraulic Engineering Laboratory, Seoul National University, Gwanak 599, Gwanak-ro, Gwanak-gu, Seoul 151-742 (Korea, Republic of); Kim, Seok [Korea Atomic Energy Research Institute, 989-111, Daedeok-daero, Yuseong-gu, Daejeon 305-600 (Korea, Republic of); Euh, Dong-Jin, E-mail: djeuh@kaeri.re.kr [Korea Atomic Energy Research Institute, 989-111, Daedeok-daero, Yuseong-gu, Daejeon 305-600 (Korea, Republic of); Park, Goon-Cherl [Nuclear Thermal-Hydraulic Engineering Laboratory, Seoul National University, Gwanak 599, Gwanak-ro, Gwanak-gu, Seoul 151-742 (Korea, Republic of)

    2015-12-01

    Highlights: • An experimental study on the two-dimensional film flow with lateral air injection was performed. • The ultrasonic thickness gauge was used to measure the local liquid film thickness. • The depth-averaged PIV (Particle Image Velocimetry) method was applied to measure the local liquid film velocity. • The uncertainty of the depth-averaged PIV was quantified with a validation experiment. • Characteristics of two-dimensional film flow were classified following the four different flow patterns. - Abstract: In an accident condition of a nuclear reactor, multidimensional two-phase flows may occur in the reactor vessel downcomer and reactor core. Therefore, those have been regarded as important issues for an advanced thermal-hydraulic safety analysis. In particular, the multi-dimensional two-phase flow in the upper downcomer during the reflood phase of large break loss of coolant accident appears with an interaction between a downward liquid and a transverse gas flow, which determines the bypass flow rate of the emergency core coolant and subsequently, the reflood coolant flow rate. At present, some thermal-hydraulic analysis codes incorporate multidimensional modules for the nuclear reactor safety analysis. However, their prediction capability for the two-phase cross flow in the upper downcomer has not been validated sufficiently against experimental data based on local measurements. For this reason, an experimental study was carried out for the two-phase cross flow to clarify the hydraulic phenomenon and provide local measurement data for the validation of the computational tools. The experiment was performed in a 1/10 scale unfolded downcomer of Advanced Power Reactor 1400 (APR1400). Pitot tubes, a depth-averaged PIV method and ultrasonic thickness gauge were applied for local measurement of the air velocity, the liquid film velocity and the liquid film thickness, respectively. The uncertainty of the depth-averaged PIV method for the averaged

  16. Experimental study on two-dimensional film flow with local measurement methods

    International Nuclear Information System (INIS)

    Yang, Jin-Hwa; Cho, Hyoung-Kyu; Kim, Seok; Euh, Dong-Jin; Park, Goon-Cherl

    2015-01-01

    Highlights: • An experimental study on the two-dimensional film flow with lateral air injection was performed. • The ultrasonic thickness gauge was used to measure the local liquid film thickness. • The depth-averaged PIV (Particle Image Velocimetry) method was applied to measure the local liquid film velocity. • The uncertainty of the depth-averaged PIV was quantified with a validation experiment. • Characteristics of two-dimensional film flow were classified following the four different flow patterns. - Abstract: In an accident condition of a nuclear reactor, multidimensional two-phase flows may occur in the reactor vessel downcomer and reactor core. Therefore, those have been regarded as important issues for an advanced thermal-hydraulic safety analysis. In particular, the multi-dimensional two-phase flow in the upper downcomer during the reflood phase of large break loss of coolant accident appears with an interaction between a downward liquid and a transverse gas flow, which determines the bypass flow rate of the emergency core coolant and subsequently, the reflood coolant flow rate. At present, some thermal-hydraulic analysis codes incorporate multidimensional modules for the nuclear reactor safety analysis. However, their prediction capability for the two-phase cross flow in the upper downcomer has not been validated sufficiently against experimental data based on local measurements. For this reason, an experimental study was carried out for the two-phase cross flow to clarify the hydraulic phenomenon and provide local measurement data for the validation of the computational tools. The experiment was performed in a 1/10 scale unfolded downcomer of Advanced Power Reactor 1400 (APR1400). Pitot tubes, a depth-averaged PIV method and ultrasonic thickness gauge were applied for local measurement of the air velocity, the liquid film velocity and the liquid film thickness, respectively. The uncertainty of the depth-averaged PIV method for the averaged

  17. Birds, magnets, soap, and sandblasting: surprising connections in the theory of incompressible flocks

    Science.gov (United States)

    Toner, John

    In this talk I'll describe the hydrodynamic theory of the motion of incompressible flocks: that is, collections of self-propelled entities (birds\\x9D) that are packed so tightly together that their density cannot change as they move. In two dimensions, this problem can be mapped onto an equilibrium magnet with a peculiar constraint. This problem, in turn, can be shown to be equivalent to a 2d smectic (soap\\x9D), with the flow lines of the flock playing the role of the smectic layers. Finally, this smectic problem can be mapped onto the 1+1 dimensional KPZ equation, which describes the growth or corrosion (sandblasting\\x9D) of a one dimensional interface. The scaling properties of this last system, which have been known exactly for a long time, can thereby be used to determine those of incompressible 2d flocks. One important implication of the resulting scaling laws is that such flocks can exhibit long-ranged order in two dimensions, unlike their equilibrium counterparts.

  18. Methods for the Determination of Currents and Fields in Steady Two-Dimensional MHD Flow With Tensor Conductivity

    International Nuclear Information System (INIS)

    Witalis, E.A.

    1965-12-01

    Rigorous derivations are given of the basic equations and methods available for the analysis of transverse MHD flow when Hall currents are not suppressed. The gas flow is taken to be incompressible and viscous with uniform tensor conductivity and arbitrary magnetic Reynold's number. The magnetic field is perpendicular to the flow and has variable strength. Analytical solutions can be obtained either in terms of the induced magnetic field or from two types of electric potential. The relevant set of suitable simplifications, restrictive conditions and boundary value considerations for each method is given

  19. Methods for the Determination of Currents and Fields in Steady Two-Dimensional MHD Flow With Tensor Conductivity

    Energy Technology Data Exchange (ETDEWEB)

    Witalis, E A

    1965-12-15

    Rigorous derivations are given of the basic equations and methods available for the analysis of transverse MHD flow when Hall currents are not suppressed. The gas flow is taken to be incompressible and viscous with uniform tensor conductivity and arbitrary magnetic Reynold's number. The magnetic field is perpendicular to the flow and has variable strength. Analytical solutions can be obtained either in terms of the induced magnetic field or from two types of electric potential. The relevant set of suitable simplifications, restrictive conditions and boundary value considerations for each method is given.

  20. Dynamics of lava flow - Thickness growth characteristics of steady two-dimensional flow

    Science.gov (United States)

    Park, S.; Iversen, J. D.

    1984-01-01

    The thickness growth characteristics of flowing lava are investigated using a heat balance model and a two-dimensional model for flow of a Bingham plastic fluid down an inclined plane. It is found that yield strength plays a crucial role in the thickening of a lava flow of given flow rate. To illustrate this point, downstream thickness profiles and yield strength distributions were calculated for flows with mass flow rates of 10,000 and 100,000 kg/m-sec. Higher flow rates led to slow cooling rates which resulted in slow rate of increase of yield strength and thus greater flow lengths.

  1. Structure-Preserving Variational Multiscale Modeling of Turbulent Incompressible Flow with Subgrid Vortices

    Science.gov (United States)

    Evans, John; Coley, Christopher; Aronson, Ryan; Nelson, Corey

    2017-11-01

    In this talk, a large eddy simulation methodology for turbulent incompressible flow will be presented which combines the best features of divergence-conforming discretizations and the residual-based variational multiscale approach to large eddy simulation. In this method, the resolved motion is represented using a divergence-conforming discretization, that is, a discretization that preserves the incompressibility constraint in a pointwise manner, and the unresolved fluid motion is explicitly modeled by subgrid vortices that lie within individual grid cells. The evolution of the subgrid vortices is governed by dynamical model equations driven by the residual of the resolved motion. Consequently, the subgrid vortices appropriately vanish for laminar flow and fully resolved turbulent flow. As the resolved velocity field and subgrid vortices are both divergence-free, the methodology conserves mass in a pointwise sense and admits discrete balance laws for energy, enstrophy, and helicity. Numerical results demonstrate the methodology yields improved results versus state-of-the-art eddy viscosity models in the context of transitional, wall-bounded, and rotational flow when a divergence-conforming B-spline discretization is utilized to represent the resolved motion.

  2. Analytic Approximate Solutions for Unsteady Two-Dimensional and Axisymmetric Squeezing Flows between Parallel Plates

    Directory of Open Access Journals (Sweden)

    Mohammad Mehdi Rashidi

    2008-01-01

    Full Text Available The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.

  3. Mathematical problems of the dynamics of incompressible fluid on a rotating sphere

    CERN Document Server

    Skiba, Yuri N

    2017-01-01

    This book presents selected mathematical problems involving the dynamics of a two-dimensional viscous and ideal incompressible fluid on a rotating sphere. In this case, the fluid motion is completely governed by the barotropic vorticity equation (BVE), and the viscosity term in the vorticity equation is taken in its general form, which contains the derivative of real degree of the spherical Laplace operator. This work builds a bridge between basic concepts and concrete outcomes by pursuing a rich combination of theoretical, analytical and numerical approaches, and is recommended for specialists developing mathematical methods for application to problems in physics, hydrodynamics, meteorology and geophysics, as well for upper undergraduate or graduate students in the areas of dynamics of incompressible fluid on a rotating sphere, theory of functions on a sphere, and flow stability.

  4. Lattice Boltzmann simulations of heat transfer in fully developed periodic incompressible flows

    Science.gov (United States)

    Wang, Zimeng; Shang, Helen; Zhang, Junfeng

    2017-06-01

    Flow and heat transfer in periodic structures are of great interest for many applications. In this paper, we carefully examine the periodic features of fully developed periodic incompressible thermal flows, and incorporate them in the lattice Boltzmann method (LBM) for flow and heat transfer simulations. Two numerical approaches, the distribution modification (DM) approach and the source term (ST) approach, are proposed; and they can both be used for periodic thermal flows with constant wall temperature (CWT) and surface heat flux boundary conditions. However, the DM approach might be more efficient, especially for CWT systems since the ST approach requires calculations of the streamwise temperature gradient at all lattice nodes. Several example simulations are conducted, including flows through flat and wavy channels and flows through a square array with circular cylinders. Results are compared to analytical solutions, previous studies, and our own LBM calculations using different simulation techniques (i.e., the one-module simulation vs. the two-module simulation, and the DM approach vs. the ST approach) with good agreement. These simple, however, representative simulations demonstrate the accuracy and usefulness of our proposed LBM methods for future thermal periodic flow simulations.

  5. Statistical mechanics of two-dimensional and geophysical flows

    International Nuclear Information System (INIS)

    Bouchet, Freddy; Venaille, Antoine

    2012-01-01

    The theoretical study of the self-organization of two-dimensional and geophysical turbulent flows is addressed based on statistical mechanics methods. This review is a self-contained presentation of classical and recent works on this subject; from the statistical mechanics basis of the theory up to applications to Jupiter’s troposphere and ocean vortices and jets. Emphasize has been placed on examples with available analytical treatment in order to favor better understanding of the physics and dynamics. After a brief presentation of the 2D Euler and quasi-geostrophic equations, the specificity of two-dimensional and geophysical turbulence is emphasized. The equilibrium microcanonical measure is built from the Liouville theorem. Important statistical mechanics concepts (large deviations and mean field approach) and thermodynamic concepts (ensemble inequivalence and negative heat capacity) are briefly explained and described. On this theoretical basis, we predict the output of the long time evolution of complex turbulent flows as statistical equilibria. This is applied to make quantitative models of two-dimensional turbulence, the Great Red Spot and other Jovian vortices, ocean jets like the Gulf-Stream, and ocean vortices. A detailed comparison between these statistical equilibria and real flow observations is provided. We also present recent results for non-equilibrium situations, for the studies of either the relaxation towards equilibrium or non-equilibrium steady states. In this last case, forces and dissipation are in a statistical balance; fluxes of conserved quantity characterize the system and microcanonical or other equilibrium measures no longer describe the system.

  6. Flow Analysis for the Falkner–Skan Wedge Flow

    DEFF Research Database (Denmark)

    Bararnia, H; Haghparast, N; Miansari, M

    2012-01-01

    In this article an analytical technique, namely the homotopy analysis method (HAM), is applied to solve the momentum and energy equations in the case of a two-dimensional incompressible flow passing over a wedge. The trail and error method and Padé approximation strategies have been used to obtai...

  7. Meshless Solution of Incompressible Flow Over Backward-Facing Step

    Directory of Open Access Journals (Sweden)

    Mužík Juraj

    2016-05-01

    Full Text Available Article presents the use of the meshless method for numerical simulation of incompressible fluid flow. The article presents the implementation of the meshless local Petrov-Galerkin method (MLPG, with Navier-Stokes equation formulated using the local weighted residual principle. The trial function construction process is the most important part of the meshless method implementation. In this article the radial basis functions (RBF are used for the process of the trial functions construction.

  8. Research on one-dimensional two-phase flow

    International Nuclear Information System (INIS)

    Adachi, Hiromichi

    1988-10-01

    In Part I the fundamental form of the hydrodynamic basic equations for a one-dimensional two-phase flow (two-fluid model) is described. Discussions are concentrated on the treatment of phase change inertial force terms in the equations of motion and the author's equations of motion which have a remarkable uniqueness on the following three points. (1) To express force balance of unit mass two-phase fluid instead of that of unit volume two-phase fluid. (2) To pick up the unit existing mass and the unit flowing mass as the unit mass of two-phase fluid. (3) To apply the kinetic energy principle instead of the momentum low in the evaluation of steady inertial force term. In these three, the item (1) is for excluding a part of momentum change or kinetic energy change due to mass change of the examined part of fluid, which is independent of force. The item (2) is not to introduce a phenomenological physical model into the evaluation of phase change inertial force term. And the item (3) is for correctly applying the momentum law taking into account the difference of representative velocities between the main flow fluid (vapor phase or liquid phase) and the phase change part of fluid. In Part II, characteristics of various kinds of high speed two-phase flow are clarified theoretically by the basic equations derived. It is demonstrated that the steam-water two-phase critical flow with violent flashing and the airwater two-phase critical flow without phase change can be described with fundamentally the same basic equations. Furthermore, by comparing the experimental data from the two-phase critical discharge test and the theoretical prediction, the two-phase discharge coefficient, C D , for large sharp-edged orifice is determined as the value which is not affected by the experimental facility characteristics, etc. (author)

  9. A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions

    Science.gov (United States)

    Liska, Sebastian; Colonius, Tim

    2017-02-01

    A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method, boundary forces are regarded as Lagrange multipliers that are used to satisfy the no-slip condition. The incompressible Navier-Stokes equations are discretized on an unbounded staggered Cartesian grid and are solved in a finite number of operations using lattice Green's function techniques. These techniques are used to automatically enforce the natural free-space boundary conditions and to implement a novel block-wise adaptive grid that significantly reduces the run-time cost of solutions by limiting operations to grid cells in the immediate vicinity and near-wake region of the immersed surface. These techniques also enable the construction of practical discrete viscous integrating factors that are used in combination with specialized half-explicit Runge-Kutta schemes to accurately and efficiently solve the differential algebraic equations describing the discrete momentum equation, incompressibility constraint, and no-slip constraint. Linear systems of equations resulting from the time integration scheme are efficiently solved using an approximation-free nested projection technique. The algebraic properties of the discrete operators are used to reduce projection steps to simple discrete elliptic problems, e.g. discrete Poisson problems, that are compatible with recent parallel fast multipole methods for difference equations. Numerical experiments on low-aspect-ratio flat plates and spheres at Reynolds numbers up to 3700 are used to verify the accuracy and physical fidelity of the formulation.

  10. On the Coupling of Incompressible Stokes or Navier–Stokes and Darcy Flows Through Porous Media

    KAUST Repository

    Girault, V.; Kanschat, G.; Riviè re, B.

    2012-01-01

    In this chapter, we present the theoretical analysis of coupled incompressible Navier-Stokes (or Stokes) flows and Darcy flows with the Beavers-Joseph-Saffman interface condition. We discuss alternative interface and porous media models. We review

  11. Magnetic field generation by pointwise zero-helicity three-dimensional steady flow of an incompressible electrically conducting fluid

    Science.gov (United States)

    Rasskazov, Andrey; Chertovskih, Roman; Zheligovsky, Vladislav

    2018-04-01

    We introduce six families of three-dimensional space-periodic steady solenoidal flows, whose kinetic helicity density is zero at any point. Four families are analytically defined. Flows in four families have zero helicity spectrum. Sample flows from five families are used to demonstrate numerically that neither zero kinetic helicity density nor zero helicity spectrum prohibit generation of large-scale magnetic field by the two most prominent dynamo mechanisms: the magnetic α -effect and negative eddy diffusivity. Our computations also attest that such flows often generate small-scale field for sufficiently small magnetic molecular diffusivity. These findings indicate that kinetic helicity and helicity spectrum are not the quantities controlling the dynamo properties of a flow regardless of whether scale separation is present or not.

  12. Dynamics of vortex interactions in two-dimensional flows

    DEFF Research Database (Denmark)

    Juul Rasmussen, J.; Nielsen, A.H.; Naulin, V.

    2002-01-01

    The dynamics and interaction of like-signed vortex structures in two dimensional flows are investigated by means of direct numerical solutions of the two-dimensional Navier-Stokes equations. Two vortices with distributed vorticity merge when their distance relative to their radius, d/R-0l. is below...... a critical value, a(c). Using the Weiss-field, a(c) is estimated for vortex patches. Introducing an effective radius for vortices with distributed vorticity, we find that 3.3 ... is effectively producing small scale structures and the relation to the enstrophy "cascade" in developed 2D turbulence is discussed. The influence of finite viscosity on the merging is also investigated. Additionally, we examine vortex interactions on a finite domain, and discuss the results in connection...

  13. Development of Modified Incompressible Ideal Gas Model for Natural Draft Cooling Tower Flow Simulation

    Science.gov (United States)

    Hyhlík, Tomáš

    2018-06-01

    The article deals with the development of incompressible ideal gas like model, which can be used as a part of mathematical model describing natural draft wet-cooling tower flow, heat and mass transfer. It is shown, based on the results of a complex mathematical model of natural draft wet-cooling tower flow, that behaviour of pressure, temperature and density is very similar to the case of hydrostatics of moist air, where heat and mass transfer in the fill zone must be taken into account. The behaviour inside the cooling tower is documented using density, pressure and temperature distributions. The proposed equation for the density is based on the same idea like the incompressible ideal gas model, which is only dependent on temperature, specific humidity and in this case on elevation. It is shown that normalized density difference of the density based on proposed model and density based on the nonsimplified model is in the order of 10-4. The classical incompressible ideal gas model, Boussinesq model and generalised Boussinesq model are also tested. These models show deviation in percentages.

  14. Development of Modified Incompressible Ideal Gas Model for Natural Draft Cooling Tower Flow Simulation

    Directory of Open Access Journals (Sweden)

    Hyhlík Tomáš

    2018-01-01

    Full Text Available The article deals with the development of incompressible ideal gas like model, which can be used as a part of mathematical model describing natural draft wet-cooling tower flow, heat and mass transfer. It is shown, based on the results of a complex mathematical model of natural draft wet-cooling tower flow, that behaviour of pressure, temperature and density is very similar to the case of hydrostatics of moist air, where heat and mass transfer in the fill zone must be taken into account. The behaviour inside the cooling tower is documented using density, pressure and temperature distributions. The proposed equation for the density is based on the same idea like the incompressible ideal gas model, which is only dependent on temperature, specific humidity and in this case on elevation. It is shown that normalized density difference of the density based on proposed model and density based on the nonsimplified model is in the order of 10-4. The classical incompressible ideal gas model, Boussinesq model and generalised Boussinesq model are also tested. These models show deviation in percentages.

  15. An efficient semi-implicit method for three-dimensional non-hydrostatic flows in compliant arterial vessels.

    Science.gov (United States)

    Fambri, Francesco; Dumbser, Michael; Casulli, Vincenzo

    2014-11-01

    Blood flow in arterial systems can be described by the three-dimensional Navier-Stokes equations within a time-dependent spatial domain that accounts for the elasticity of the arterial walls. In this article, blood is treated as an incompressible Newtonian fluid that flows through compliant vessels of general cross section. A three-dimensional semi-implicit finite difference and finite volume model is derived so that numerical stability is obtained at a low computational cost on a staggered grid. The key idea of the method consists in a splitting of the pressure into a hydrostatic and a non-hydrostatic part, where first a small quasi-one-dimensional nonlinear system is solved for the hydrostatic pressure and only in a second step the fully three-dimensional non-hydrostatic pressure is computed from a three-dimensional nonlinear system as a correction to the hydrostatic one. The resulting algorithm is robust, efficient, locally and globally mass conservative, and applies to hydrostatic and non-hydrostatic flows in one, two and three space dimensions. These features are illustrated on nontrivial test cases for flows in tubes with circular or elliptical cross section where the exact analytical solution is known. Test cases of steady and pulsatile flows in uniformly curved rigid and elastic tubes are presented. Wherever possible, axial velocity development and secondary flows are shown and compared with previously published results. Copyright © 2014 John Wiley & Sons, Ltd.

  16. A Rotational Pressure-Correction Scheme for Incompressible Two-Phase Flows with Open Boundaries

    Science.gov (United States)

    Dong, S.; Wang, X.

    2016-01-01

    Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present several new forms of open boundary conditions for two-phase outflow simulations within the phase field framework, as well as a rotational pressure correction based algorithm for numerically treating these open boundary conditions. Our algorithm gives rise to linear algebraic systems for the velocity and the pressure that involve only constant and time-independent coefficient matrices after discretization, despite the variable density and variable viscosity of the two-phase mixture. By comparing simulation results with theory and the experimental data, we show that the method produces physically accurate results. We also present numerical experiments to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows occur at the two-phase open boundaries. PMID:27163909

  17. Advanced numerical methods for three dimensional two-phase flow calculations

    Energy Technology Data Exchange (ETDEWEB)

    Toumi, I. [Laboratoire d`Etudes Thermiques des Reacteurs, Gif sur Yvette (France); Caruge, D. [Institut de Protection et de Surete Nucleaire, Fontenay aux Roses (France)

    1997-07-01

    This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.

  18. Advanced numerical methods for three dimensional two-phase flow calculations

    International Nuclear Information System (INIS)

    Toumi, I.; Caruge, D.

    1997-01-01

    This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe's method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations

  19. A Comparison of Simplified Two-dimensional Flow Models Exemplified by Water Flow in a Cavern

    Science.gov (United States)

    Prybytak, Dzmitry; Zima, Piotr

    2017-12-01

    The paper shows the results of a comparison of simplified models describing a two-dimensional water flow in the example of a water flow through a straight channel sector with a cavern. The following models were tested: the two-dimensional potential flow model, the Stokes model and the Navier-Stokes model. In order to solve the first two, the boundary element method was employed, whereas to solve the Navier-Stokes equations, the open-source code library OpenFOAM was applied. The results of numerical solutions were compared with the results of measurements carried out on a test stand in a hydraulic laboratory. The measurements were taken with an ADV probe (Acoustic Doppler Velocimeter). Finally, differences between the results obtained from the mathematical models and the results of laboratory measurements were analysed.

  20. Incompressible Steady Flow with Tensor Conductivity Leaving a Transverse Magnetic Field

    International Nuclear Information System (INIS)

    Witalis, E.A.

    1965-12-01

    The straight channel flow of an inviscid, incompressible fluid with tensor conductivity is considered when the flow leaves a region of constant transverse magnetic field. The channel walls are taken to be insulating, and an eddy current system arises. This is investigated by the method of magnetic field analysis as given by Witalis. The spatial distribution of magnetic field and ohmic power loss, both parallel and transverse to the flow, are given as functions of the Hall parameter with consideration also to the magnetic Reynolds number of the fluid. MHD power generator aspects of this problem and the results are discussed

  1. Incompressible Steady Flow with Tensor Conductivity Leaving a Transverse Magnetic Field

    Energy Technology Data Exchange (ETDEWEB)

    Witalis, E A

    1965-12-15

    The straight channel flow of an inviscid, incompressible fluid with tensor conductivity is considered when the flow leaves a region of constant transverse magnetic field. The channel walls are taken to be insulating, and an eddy current system arises. This is investigated by the method of magnetic field analysis as given by Witalis. The spatial distribution of magnetic field and ohmic power loss, both parallel and transverse to the flow, are given as functions of the Hall parameter with consideration also to the magnetic Reynolds number of the fluid. MHD power generator aspects of this problem and the results are discussed.

  2. Assessment of RELAP5-3D copyright using data from two-dimensional RPI flow tests

    International Nuclear Information System (INIS)

    Davis, C.B.

    1998-01-01

    The capability of the RELAP5-3D copyright computer code to perform multi-dimensional thermal-hydraulic analysis was assessed using data from steady-state flow tests conducted at Rensselaer Polytechnic Institute (RPI). The RPI data were taken in a two-dimensional test section in a low-pressure air/water loop. The test section consisted of a thin vertical channel that simulated a two-dimensional slice through the core of a pressurized water reactor. Single-phase and two-phase flows were supplied to the test section in an asymmetric manner to generate a two-dimensional flow field. A traversing gamma densitometer was used to measure void fraction at many locations in the test section. High speed photographs provided information on the flow patterns and flow regimes. The RPI test section was modeled using the multi-dimensional component in RELAP5-3D Version BF06. Calculations of three RPI experiments were performed. The flow regimes predicted by the base code were in poor agreement with those observed in the tests. The two-phase regions were observed to be in the bubbly and slug flow regimes in the test. However, nearly all of the junctions in the horizontal direction were calculated to be in the stratified flow regime because of the relatively low velocities in that direction. As a result, the void fraction predictions were also in poor agreement with the measured values. Significantly improved results were obtained in sensitivity calculations with a modified version of the code that prevented the horizontal junctions from entering the stratified flow regime. These results indicate that the code's logic in the determination of flow regimes in a multi-dimensional component must be improved. The results of the sensitivity calculations also indicate that RELAP5-3D will provide a significant multi-dimensional hydraulic analysis capability once the flow regime prediction is improved

  3. A mathematical model for turbulent incompressible flows through mixing grids

    International Nuclear Information System (INIS)

    Allaire, G.

    1989-01-01

    A mathematical model is proposed for the computation of turbulent incompressible flows through mixing grids. This model is obtained as follows: in a three-dimentional-domain we represent a mixing grid by small identical wings of size ε 2 periodically distributed at the nodes of a plane regular mesh of size ε, and we consider incompressible Navier-Stokes equations with a no-slip condition on the wings. Using an appropriate homogenization process we pass to the limit when ε tends to zero and we obtain a Brinkman equation, i.e. a Navier-Stokes equation plus a zero-order term for the velocity, in a homogeneous domain without anymore wings. The interest of this model is that the spatial discretization is simpler in a homogeneous domain, and, moreover, the new term, which expresses the grid's mixing effect, can be evaluated with a local computation around a single wing

  4. A meshless scheme for incompressible fluid flow using a velocity-pressure correction method

    KAUST Repository

    Bourantas, Georgios; Loukopoulos, Vassilios C.

    2013-01-01

    A meshless point collocation method is proposed for the numerical solution of the steady state, incompressible Navier-Stokes (NS) equations in their primitive u-v-p formulation. The flow equations are solved in their strong form using either a

  5. Diffusion in Poiseuille and Couette flows of binary mixtures of incompressible newtonian fluids

    International Nuclear Information System (INIS)

    Caetano Filho, E.; Qassim, R.Y.

    1981-07-01

    Using the continuum theory of binary mixtures of incompressible Newtonian fluids, Poiseuille and Couette flows are studied with a view to determining whether diffusion occurs in such flows. It is shown that diffusion is absent in the Couette case. However, in Poiseuille flow there are significant differences between the velocities of the species comprising the mixture. This result is in broad agreement with that of Mills for similar mixtures of nonuniform composition. (Author) [pt

  6. Three-dimensional investigation of the two-phase flow structure in a bubbly pipe flow

    International Nuclear Information System (INIS)

    Hassan, Y.A.; Schmidl, W.D.; Ortiz-Villafuerte, J.

    1997-01-01

    Particle Image Velocimetry (PIV) is a non-intrusive measurement technique, which can be used to study the structure of various fluid flows. PIV is used to measure the time varying full field velocity data of a particle-seeded flow field within either a two-dimensional plane or three-dimensional volume. PIV is a very efficient measurement technique since it can obtain both qualitative and quantitative spatial information about the flow field being studied. This information can be further processed into information such as vorticity and pathlines. Other flow measurement techniques (Laser Doppler Velocimetry, Hot Wire Anemometry, etc...) only provide quantitative information at a single point. PIV can be used to study turbulence structures if a sufficient amount of data can be acquired and analyzed, and it can also be extended to study two-phase flows if both phases can be distinguished. In this study, the flow structure around a bubble rising in a pipe filled with water was studied in three-dimensions. The velocity of the rising bubble and the velocity field of the surrounding water was measured. Then the turbulence intensities and Reynolds stresses were calculated from the experimental data. (author)

  7. Iterative and multigrid methods in the finite element solution of incompressible and turbulent fluid flow

    Science.gov (United States)

    Lavery, N.; Taylor, C.

    1999-07-01

    Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time-independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi-Babuska condition. The k-l model is used to complete the turbulence closure problem. The non-symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a V-cycling schedule. These methods are all compared to the non-symmetric frontal solver. Copyright

  8. On a modified form of navier-stokes equations for three-dimensional flows.

    Science.gov (United States)

    Venetis, J

    2015-01-01

    A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms of these fundamental equations, which are expressed in true vector form, and finally arrive at an equivalent system of three semilinear first order PDEs, which hold for a three-dimensional rectangular Cartesian coordinate system. Next, we present the related variational formulation of these modified equations as well as a general type of weak solutions which mainly concern Sobolev spaces.

  9. Large eddy simulation of new subgrid scale model for three-dimensional bundle flows

    International Nuclear Information System (INIS)

    Barsamian, H.R.; Hassan, Y.A.

    2004-01-01

    Having led to increased inefficiencies and power plant shutdowns fluid flow induced vibrations within heat exchangers are of great concern due to tube fretting-wear or fatigue failures. Historically, scaling law and measurement accuracy problems were encountered for experimental analysis at considerable effort and expense. However, supercomputers and accurate numerical methods have provided reliable results and substantial decrease in cost. In this investigation Large Eddy Simulation has been successfully used to simulate turbulent flow by the numeric solution of the incompressible, isothermal, single phase Navier-Stokes equations. The eddy viscosity model and a new subgrid scale model have been utilized to model the smaller eddies in the flow domain. A triangular array flow field was considered and numerical simulations were performed in two- and three-dimensional fields, and were compared to experimental findings. Results show good agreement of the numerical findings to that of the experimental, and solutions obtained with the new subgrid scale model represent better energy dissipation for the smaller eddies. (author)

  10. Two compressible and immiscible flow in porous media: mathematical and numerical analysis

    International Nuclear Information System (INIS)

    Khalil, Z.

    2010-01-01

    The aim of this thesis is the study of Cauchy problem (existence of weak solutions) for three degenerate highly coupled parabolic systems modeling compressible immiscible flow in porous media. The motivation of this work is a benchmark of the GNR MoMaS, to study the impact of the gas flow due to the corrosion of ferrous materials in a radioactive waste storage site. This thesis is divided into three independent chapters. Firstly, we look at a problem modeling the flow of two immiscible phases and considering one phase is compressible and the other is incompressible (water/gas). Secondly, we consider the problem modeling two-compressible immiscible flow in porous media. An existence results for both problems established by a semi-discretization method. Finally, The fourth chapter is devoted to the construction and convergence of a multi-dimensional finite volume method (upwind scheme) for the gas-water model under the assumption that the gas density is a function of a global pressure. (author)

  11. Stochastic modelling of two-phase flows including phase change

    International Nuclear Information System (INIS)

    Hurisse, O.; Minier, J.P.

    2011-01-01

    Stochastic modelling has already been developed and applied for single-phase flows and incompressible two-phase flows. In this article, we propose an extension of this modelling approach to two-phase flows including phase change (e.g. for steam-water flows). Two aspects are emphasised: a stochastic model accounting for phase transition and a modelling constraint which arises from volume conservation. To illustrate the whole approach, some remarks are eventually proposed for two-fluid models. (authors)

  12. Decaying quasi-two-dimensional viscous flow on a square domain

    DEFF Research Database (Denmark)

    Konijnenberg, J.A. van de; Flor, J.B.; Heijst, G.J.F. van

    1998-01-01

    A comparison is made between experimental, numerical and analytical results for the two-dimensional flow on a square domain. The experiments concern the flow at the interface of a two-layer stratified fluid, evoked by either stirring the fluid with a rake, or by injecting additional fluid...... at the interface. Two numerical simulations were performed with initial conditions and boundary conditions that correspond approximately with those met in the experiments. The analytical results concern the calculation of the lowest modes of a decaying Stokes flow on a square domain. At late times...... relationship between vorticity and stream function in the experiments and the simulations. (C) 1998 American Institute of Physics....

  13. Boundary-layer interactions in the plane-parallel incompressible flows

    International Nuclear Information System (INIS)

    Nguyen, Toan T; Sueur, Franck

    2012-01-01

    We study the inviscid limit problem of incompressible flows in the presence of both impermeable regular boundaries and a hypersurface transversal to the boundary across which the inviscid flow has a discontinuity jump. In the former case, boundary layers have been introduced by Prandtl as correctors near the boundary between the inviscid and viscous flows. In the latter case, the viscosity smoothes out the discontinuity jump by creating a transition layer which has the same amplitude and thickness as the Prandtl layer. In the neighbourhood of the intersection of the impermeable boundary and of the hypersurface, interactions between the boundary and the transition layers must then be considered. In this paper, we initiate a mathematical study of this interaction and carry out a strong convergence in the inviscid limit for the case of the plane-parallel flows introduced by Di Perna and Majda (1987 Commun. Math. Phys. 108 667–89). (paper)

  14. Two-dimensional analysis of motion artifacts, including flow effects

    International Nuclear Information System (INIS)

    Litt, A.M.; Brody, A.S.; Spangler, R.A.; Scott, P.D.

    1990-01-01

    The effects of motion on magnetic resonance images have been theoretically analyzed for the case of a point-like object in simple harmonic motion and for other one-dimensional trajectories. The authors of this paper extend this analysis to a generalized two-dimensional magnetization with an arbitrary motion trajectory. The authors provide specific solutions for the clinically relevant cases of the cross-sections of cylindrical objects in the body, such as the aorta, which has a roughly one-dimensional, simple harmonic motion during respiration. By extending the solution to include inhomogeneous magnetizations, the authors present a model which allows the effects of motion artifacts and flow artifacts to be analyzed simultaneously

  15. Numerical Study on Several Stabilized Finite Element Methods for the Steady Incompressible Flow Problem with Damping

    Directory of Open Access Journals (Sweden)

    Jilian Wu

    2013-01-01

    Full Text Available We discuss several stabilized finite element methods, which are penalty, regular, multiscale enrichment, and local Gauss integration method, for the steady incompressible flow problem with damping based on the lowest equal-order finite element space pair. Then we give the numerical comparisons between them in three numerical examples which show that the local Gauss integration method has good stability, efficiency, and accuracy properties and it is better than the others for the steady incompressible flow problem with damping on the whole. However, to our surprise, the regular method spends less CPU-time and has better accuracy properties by using Crout solver.

  16. Numerical solution of viscous and viscoelastic fluids flow through the branching channel by finite volume scheme

    Science.gov (United States)

    Keslerová, Radka; Trdlička, David

    2015-09-01

    This work deals with the numerical modelling of steady flows of incompressible viscous and viscoelastic fluids through the three dimensional channel with T-junction. The fundamental system of equations is the system of generalized Navier-Stokes equations for incompressible fluids. This system is based on the system of balance laws of mass and momentum for incompressible fluids. Two different mathematical models for the stress tensor are used for simulation of Newtonian and Oldroyd-B fluids flow. Numerical solution of the described models is based on cetral finite volume method using explicit Runge-Kutta time integration.

  17. Multi-dimensional two-fluid flow computation. An overview

    International Nuclear Information System (INIS)

    Carver, M.B.

    1992-01-01

    This paper discusses a repertoire of three-dimensional computer programs developed to perform critical analysis of single-phase, two-phase and multi-fluid flow in reactor components. The basic numerical approach to solving the governing equations common to all the codes is presented and the additional constitutive relationships required for closure are discussed. Particular applications are presented for a number of computer codes. (author). 12 refs

  18. A stable partitioned FSI algorithm for incompressible flow and deforming beams

    International Nuclear Information System (INIS)

    Li, L.; Henshaw, W.D.; Banks, J.W.; Schwendeman, D.W.; Main, A.

    2016-01-01

    An added-mass partitioned (AMP) algorithm is described for solving fluid–structure interaction (FSI) problems coupling incompressible flows with thin elastic structures undergoing finite deformations. The new AMP scheme is fully second-order accurate and stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The fluid, governed by the incompressible Navier–Stokes equations, is solved in velocity-pressure form using a fractional-step method; large deformations are treated with a mixed Eulerian-Lagrangian approach on deforming composite grids. The motion of the thin structure is governed by a generalized Euler–Bernoulli beam model, and these equations are solved in a Lagrangian frame using two approaches, one based on finite differences and the other on finite elements. The key AMP interface condition is a generalized Robin (mixed) condition on the fluid pressure. This condition, which is derived at a continuous level, has no adjustable parameters and is applied at the discrete level to couple the partitioned domain solvers. Special treatment of the AMP condition is required to couple the finite-element beam solver with the finite-difference-based fluid solver, and two coupling approaches are described. A normal-mode stability analysis is performed for a linearized model problem involving a beam separating two fluid domains, and it is shown that the AMP scheme is stable independent of the ratio of the mass of the fluid to that of the structure. A traditional partitioned (TP) scheme using a Dirichlet–Neumann coupling for the same model problem is shown to be unconditionally unstable if the added mass of the fluid is too large. A series of benchmark problems of increasing complexity are considered to illustrate the behavior of the AMP algorithm, and to compare the behavior with that of the TP scheme. The results of all these benchmark problems verify the stability and accuracy of the AMP scheme. Results for

  19. A stable partitioned FSI algorithm for incompressible flow and deforming beams

    Energy Technology Data Exchange (ETDEWEB)

    Li, L., E-mail: lil19@rpi.edu [Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180 (United States); Henshaw, W.D., E-mail: henshw@rpi.edu [Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180 (United States); Banks, J.W., E-mail: banksj3@rpi.edu [Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180 (United States); Schwendeman, D.W., E-mail: schwed@rpi.edu [Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180 (United States); Main, A., E-mail: amain8511@gmail.com [Department of Civil and Environmental Engineering, Duke University, Durham, NC 27708 (United States)

    2016-05-01

    An added-mass partitioned (AMP) algorithm is described for solving fluid–structure interaction (FSI) problems coupling incompressible flows with thin elastic structures undergoing finite deformations. The new AMP scheme is fully second-order accurate and stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The fluid, governed by the incompressible Navier–Stokes equations, is solved in velocity-pressure form using a fractional-step method; large deformations are treated with a mixed Eulerian-Lagrangian approach on deforming composite grids. The motion of the thin structure is governed by a generalized Euler–Bernoulli beam model, and these equations are solved in a Lagrangian frame using two approaches, one based on finite differences and the other on finite elements. The key AMP interface condition is a generalized Robin (mixed) condition on the fluid pressure. This condition, which is derived at a continuous level, has no adjustable parameters and is applied at the discrete level to couple the partitioned domain solvers. Special treatment of the AMP condition is required to couple the finite-element beam solver with the finite-difference-based fluid solver, and two coupling approaches are described. A normal-mode stability analysis is performed for a linearized model problem involving a beam separating two fluid domains, and it is shown that the AMP scheme is stable independent of the ratio of the mass of the fluid to that of the structure. A traditional partitioned (TP) scheme using a Dirichlet–Neumann coupling for the same model problem is shown to be unconditionally unstable if the added mass of the fluid is too large. A series of benchmark problems of increasing complexity are considered to illustrate the behavior of the AMP algorithm, and to compare the behavior with that of the TP scheme. The results of all these benchmark problems verify the stability and accuracy of the AMP scheme. Results for

  20. Mathematical aspects of finite element methods for incompressible viscous flows

    Science.gov (United States)

    Gunzburger, M. D.

    1986-01-01

    Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.

  1. A positivity preserving and conservative variational scheme for phase-field modeling of two-phase flows

    Science.gov (United States)

    Joshi, Vaibhav; Jaiman, Rajeev K.

    2018-05-01

    We present a positivity preserving variational scheme for the phase-field modeling of incompressible two-phase flows with high density ratio. The variational finite element technique relies on the Allen-Cahn phase-field equation for capturing the phase interface on a fixed Eulerian mesh with mass conservative and energy-stable discretization. The mass conservation is achieved by enforcing a Lagrange multiplier which has both temporal and spatial dependence on the underlying solution of the phase-field equation. To make the scheme energy-stable in a variational sense, we discretize the spatial part of the Lagrange multiplier in the phase-field equation by the mid-point approximation. The proposed variational technique is designed to reduce the spurious and unphysical oscillations in the solution while maintaining the second-order accuracy of both spatial and temporal discretizations. We integrate the Allen-Cahn phase-field equation with the incompressible Navier-Stokes equations for modeling a broad range of two-phase flow and fluid-fluid interface problems. The coupling of the implicit discretizations corresponding to the phase-field and the incompressible flow equations is achieved via nonlinear partitioned iterative procedure. Comparison of results between the standard linear stabilized finite element method and the present variational formulation shows a remarkable reduction of oscillations in the solution while retaining the boundedness of the phase-indicator field. We perform a standalone test to verify the accuracy and stability of the Allen-Cahn two-phase solver. We examine the convergence and accuracy properties of the coupled phase-field solver through the standard benchmarks of the Laplace-Young law and a sloshing tank problem. Two- and three-dimensional dam break problems are simulated to assess the capability of the phase-field solver for complex air-water interfaces involving topological changes on unstructured meshes. Finally, we demonstrate the phase

  2. Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations.

    Science.gov (United States)

    Miranda, Rodrigo A; Rempel, Erico L; Chian, Abraham C-L; Seehafer, Norbert; Toledo, Benjamin A; Muñoz, Pablo R

    2013-09-01

    We study a transition to hyperchaos in the two-dimensional incompressible Navier-Stokes equations with periodic boundary conditions and an external forcing term. Bifurcation diagrams are constructed by varying the Reynolds number, and a transition to hyperchaos (HC) is identified. Before the onset of HC, there is coexistence of two chaotic attractors and a hyperchaotic saddle. After the transition to HC, the two chaotic attractors merge with the hyperchaotic saddle, generating random switching between chaos and hyperchaos, which is responsible for intermittent bursts in the time series of energy and enstrophy. The chaotic mixing properties of the flow are characterized by detecting Lagrangian coherent structures. After the transition to HC, the flow displays complex Lagrangian patterns and an increase in the level of Lagrangian chaoticity during the bursty periods that can be predicted statistically by the hyperchaotic saddle prior to HC transition.

  3. On the Coupling of Incompressible Stokes or Navier–Stokes and Darcy Flows Through Porous Media

    KAUST Repository

    Girault, V.

    2012-11-03

    In this chapter, we present the theoretical analysis of coupled incompressible Navier-Stokes (or Stokes) flows and Darcy flows with the Beavers-Joseph-Saffman interface condition. We discuss alternative interface and porous media models. We review some finite element methods used by several authors in this coupling and present numerical experiments.

  4. Two-dimensional magnetohydrodynamic equilibria with flow and studies of equilibria fluctuations

    International Nuclear Information System (INIS)

    Agim, Y.Z.

    1989-08-01

    A set of reduced ideal MHD equations is derived to investigate equilibria of plasmas with mass flow in general two-dimensional geometry. These equations provide a means of investigating the effects of flow on self-consistent equilibria in a number of new two-dimensional configurations such as helically symmetric configurations with helical axis, which are relevant to stellarators, as well as axisymmetric configurations. It is found that as in the axisymmetric case, general two-dimensional flow equilibria are governed by a second-order quasi-linear partial differential equation for a magnetic flux function, which is coupled to a Bernoulli-type equation for the density. The equation for the magnetic flux function becomes hyperbolic at certain critical flow speeds which follow from its characteristic equation. When the equation is hyperbolic, shock phenomena may exist. As a particular example, unidirectional flow along the lines of symmetry is considered. In this case, the equation mentioned above is always elliptic. An exact solution for the case of helically symmetric unidirectional flow is found and studied to determine flow effects on the magnetic topology. In second part of this thesis, magnetic fluctuations due to the thermally excited MHD waves are investigated using fluid and kinetic models to describe stable, uniform, compressible plasma in the range above the drift wave frequency and below the ion cyclotron frequency. It is shown that the fluid model with resistivity yields spectral densities which are roughly Lorentzian, exhibit equipartition with no apparent cutoff in wavenumber space and a Bohm-type diffusion coefficient. Under certain conditions, the ensuing transport may be comparable to classical values. For a phenomenological cutoff imposed on the spectrum, the typical fluctuating-to-equilibrium magnetic field ratio is found to be of the order of 10 -10

  5. An Operator-Integration-Factor Splitting (OIFS) method for Incompressible Flows in Moving Domains

    Energy Technology Data Exchange (ETDEWEB)

    Patel, Saumil S. [Argonne National Lab. (ANL), Argonne, IL (United States); Fischer, Paul F. [Argonne National Lab. (ANL), Argonne, IL (United States); Univ. of Illinois, Urbana-Champaign, IL (United States); Min, Misun [Argonne National Lab. (ANL), Argonne, IL (United States); Tomboulides, Ananias G [Argonne National Lab. (ANL), Argonne, IL (United States); Aristotle Univ., Thessaloniki (Greece)

    2017-10-21

    In this paper, we present a characteristic-based numerical procedure for simulating incompressible flows in domains with moving boundaries. Our approach utilizes an operator-integration-factor splitting technique to help produce an effcient and stable numerical scheme. Using the spectral element method and an arbitrary Lagrangian-Eulerian formulation, we investigate flows where the convective acceleration effects are non-negligible. Several examples, ranging from laminar to turbulent flows, are considered. Comparisons with a standard, semi-implicit time-stepping procedure illustrate the improved performance of the scheme.

  6. Local lubrication model for spherical particles within incompressible Navier-Stokes flows

    Science.gov (United States)

    Lambert, B.; Weynans, L.; Bergmann, M.

    2018-03-01

    The lubrication forces are short-range hydrodynamic interactions essential to describe suspension of the particles. Usually, they are underestimated in direct numerical simulations of particle-laden flows. In this paper, we propose a lubrication model for a coupled volume penalization method and discrete element method solver that estimates the unresolved hydrodynamic forces and torques in an incompressible Navier-Stokes flow. Corrections are made locally on the surface of the interacting particles without any assumption on the global particle shape. The numerical model has been validated against experimental data and performs as well as existing numerical models that are limited to spherical particles.

  7. Local lubrication model for spherical particles within incompressible Navier-Stokes flows.

    Science.gov (United States)

    Lambert, B; Weynans, L; Bergmann, M

    2018-03-01

    The lubrication forces are short-range hydrodynamic interactions essential to describe suspension of the particles. Usually, they are underestimated in direct numerical simulations of particle-laden flows. In this paper, we propose a lubrication model for a coupled volume penalization method and discrete element method solver that estimates the unresolved hydrodynamic forces and torques in an incompressible Navier-Stokes flow. Corrections are made locally on the surface of the interacting particles without any assumption on the global particle shape. The numerical model has been validated against experimental data and performs as well as existing numerical models that are limited to spherical particles.

  8. Unsteady flow model for circulation-control airfoils

    Science.gov (United States)

    Rao, B. M.

    1979-01-01

    An analysis and a numerical lifting surface method are developed for predicting the unsteady airloads on two-dimensional circulation control airfoils in incompressible flow. The analysis and the computer program are validated by correlating the computed unsteady airloads with test data and also with other theoretical solutions. Additionally, a mathematical model for predicting the bending-torsion flutter of a two-dimensional airfoil (a reference section of a wing or rotor blade) and a computer program using an iterative scheme are developed. The flutter program has a provision for using the CC airfoil airloads program or the Theodorsen hard flap solution to compute the unsteady lift and moment used in the flutter equations. The adopted mathematical model and the iterative scheme are used to perform a flutter analysis of a typical CC rotor blade reference section. The program seems to work well within the basic assumption of the incompressible flow.

  9. Regularity criteria for incompressible magnetohydrodynamics equations in three dimensions

    International Nuclear Information System (INIS)

    Lin, Hongxia; Du, Lili

    2013-01-01

    In this paper, we give some new global regularity criteria for three-dimensional incompressible magnetohydrodynamics (MHD) equations. More precisely, we provide some sufficient conditions in terms of the derivatives of the velocity or pressure, for the global regularity of strong solutions to 3D incompressible MHD equations in the whole space, as well as for periodic boundary conditions. Moreover, the regularity criterion involving three of the nine components of the velocity gradient tensor is also obtained. The main results generalize the recent work by Cao and Wu (2010 Two regularity criteria for the 3D MHD equations J. Diff. Eqns 248 2263–74) and the analysis in part is based on the works by Cao C and Titi E (2008 Regularity criteria for the three-dimensional Navier–Stokes equations Indiana Univ. Math. J. 57 2643–61; 2011 Gobal regularity criterion for the 3D Navier–Stokes equations involving one entry of the velocity gradient tensor Arch. Rational Mech. Anal. 202 919–32) for 3D incompressible Navier–Stokes equations. (paper)

  10. Two-dimensional electron flow in pulsed power transmission lines and plasma opening switches

    International Nuclear Information System (INIS)

    Church, B.W.; Longcope, D.W.; Ng, C.K.; Sudan, R.N.

    1991-01-01

    The operation of magnetically insulated transmission lines (MITL) and the interruption of current in a plasma opening switch (POS) are determined by the physics of the electrons emitted by the cathode surface. A mathematical model describes the self-consistent two-dimensional flow of an electron fluid. A finite element code, FERUS, has been developed to solve the two equations which describe Poisson's and Ampere's law in two dimensions. The solutions from this code are obtained for parameters where the electron orbits are considerably modified by the self-magnetic field of the current. Next, the self-insulated electron flow in a MITL with a step change in cross-section is studied using a conventional two-dimensional fully electromagnetic particle-in-cell code, MASK. The equations governing two-dimensional quasi-static electron flow are solved numerically by a third technique which is suitable for predicting current interruption in a POS. The object of the study is to determine the critical load impedance, Z CL , required for current interruption for a given applied voltage, cathode voltage and plasma length. (author). 9 refs, 5 figs

  11. Numerical methods for limit problems in two-phase flow models

    International Nuclear Information System (INIS)

    Cordier, F.

    2011-01-01

    Numerical difficulties are encountered during the simulation of two-phase flows. Two issues are studied in this thesis: the simulation of phase transitions on one hand, and the simulation of both compressible and incompressible flows in the other hand. Un asymptotic study has shown that the loss of hyperbolicity of the bi fluid model was responsible for the difficulties encountered by the Roe scheme during the simulation of phase transitions. Robust and accurate polynomial schemes have thus been developed. To tackle the occasional lack of positivity of the solution, a numerical treatment based on adaptive diffusion was proposed and allowed to simulate with accuracy the test-cases of a boiling channel with creation of vapor and a tee-junction with separation of the phases. In a second part, an all-speed scheme for compressible and incompressible flows have been proposed. This pressure-based semi-implicit asymptotic preserving scheme is conservative, solves an elliptic equation on the pressure, and has been designed for general equations of state. The scheme was first developed for the full Euler equations and then extended to the Navier-Stokes equations. The good behaviour of the scheme in both compressible and incompressible regimes have been investigated. An extension of the scheme to the two-phase mixture model was implemented and demonstrated the ability of the scheme to simulate two-phase flows with phase change and a water-steam equation of state. (author) [fr

  12. Gravity Effect on Two-Phase Immiscible Flows in Communicating Layered Reservoirs

    DEFF Research Database (Denmark)

    Zhang, Xuan; Shapiro, Alexander; Stenby, Erling Halfdan

    2012-01-01

    An upscaling method is developed for two-phase immiscible incompressible flows in layered reservoirs with good communication between the layers. It takes the effect of gravity into consideration. Waterflooding of petroleum reservoirs is used as a basic example for application of this method....... An asymptotic analysis is applied to a system of 2D flow equations for incompressible fluids at high-anisotropy ratios, but low to moderate gravity ratios, which corresponds to the most often found reservoir conditions. The 2D Buckley–Leverett problem is reduced to a system of 1D parabolic equations...

  13. Improved flux calculations for viscous incompressible flow by the variable penalty method

    International Nuclear Information System (INIS)

    Kheshgi, H.; Luskin, M.

    1985-01-01

    The Navier-Stokes system for viscous, incompressible flow is considered, taking into account a replacement of the continuity equation by the perturbed continuity equation. The introduction of the approximation allows the pressure variable to be eliminated to obtain the system of equations for the approximate velocity. The penalty approximation is often applied to numerical discretizations since it provides a reduction in the size and band-width of the system of equations. Attention is given to error estimates, and to two numerical experiments which illustrate the error estimates considered. It is found that the variable penalty method provides an accurate solution for a much wider range of epsilon than the classical penalty method. 8 references

  14. Upscaling of Two-Phase Immiscible Flows in Communicating Stratified Reservoirs

    DEFF Research Database (Denmark)

    Zhang, Xuan; Shapiro, Alexander; Stenby, Erling Halfdan

    2011-01-01

    A semi-analytical method for upscaling two-phase immiscible flows in heterogeneous porous media is described. This method is developed for stratified reservoirs with perfect communication between layers (the case of vertical equilibrium), in a viscous dominant regime, where the effects of capillary...... forces and gravity may be neglected. The method is discussed on the example of its basic application: waterflooding in petroleum reservoirs. We apply asymptotic analysis to a system of two-dimensional (2D) mass conservation equations for incompressible fluids. For high anisotropy ratios, the pressure...... and piston-like displacement, and it presumes non-zero exchange between layers. The method generalizes also the study of Yortsos (Transp Porous Media 18:107–129, 1995), taking into account in a more consistent way the interactions between the layers....

  15. Modeling of Two-Phase Flow in Rough-Walled Fracture Using Level Set Method

    Directory of Open Access Journals (Sweden)

    Yunfeng Dai

    2017-01-01

    Full Text Available To describe accurately the flow characteristic of fracture scale displacements of immiscible fluids, an incompressible two-phase (crude oil and water flow model incorporating interfacial forces and nonzero contact angles is developed. The roughness of the two-dimensional synthetic rough-walled fractures is controlled with different fractal dimension parameters. Described by the Navier–Stokes equations, the moving interface between crude oil and water is tracked using level set method. The method accounts for differences in densities and viscosities of crude oil and water and includes the effect of interfacial force. The wettability of the rough fracture wall is taken into account by defining the contact angle and slip length. The curve of the invasion pressure-water volume fraction is generated by modeling two-phase flow during a sudden drainage. The volume fraction of water restricted in the rough-walled fracture is calculated by integrating the water volume and dividing by the total cavity volume of the fracture while the two-phase flow is quasistatic. The effect of invasion pressure of crude oil, roughness of fracture wall, and wettability of the wall on two-phase flow in rough-walled fracture is evaluated.

  16. Three-dimensional microbubble streaming flows

    Science.gov (United States)

    Rallabandi, Bhargav; Marin, Alvaro; Rossi, Massimiliano; Kaehler, Christian; Hilgenfeldt, Sascha

    2014-11-01

    Streaming due to acoustically excited bubbles has been used successfully for applications such as size-sorting, trapping and focusing of particles, as well as fluid mixing. Many of these applications involve the precise control of particle trajectories, typically achieved using cylindrical bubbles, which establish planar flows. Using astigmatic particle tracking velocimetry (APTV), we show that, while this two-dimensional picture is a useful description of the flow over short times, a systematic three-dimensional flow structure is evident over long time scales. We demonstrate that this long-time three-dimensional fluid motion can be understood through asymptotic theory, superimposing secondary axial flows (induced by boundary conditions at the device walls) onto the two-dimensional description. This leads to a general framework that describes three-dimensional flows in confined microstreaming systems, guiding the design of applications that profit from minimizing or maximizing these effects.

  17. Nearly incompressible fluids: Hydrodynamics and large scale inhomogeneity

    International Nuclear Information System (INIS)

    Hunana, P.; Zank, G. P.; Shaikh, D.

    2006-01-01

    A system of hydrodynamic equations in the presence of large-scale inhomogeneities for a high plasma beta solar wind is derived. The theory is derived under the assumption of low turbulent Mach number and is developed for the flows where the usual incompressible description is not satisfactory and a full compressible treatment is too complex for any analytical studies. When the effects of compressibility are incorporated only weakly, a new description, referred to as 'nearly incompressible hydrodynamics', is obtained. The nearly incompressible theory, was originally applied to homogeneous flows. However, large-scale gradients in density, pressure, temperature, etc., are typical in the solar wind and it was unclear how inhomogeneities would affect the usual incompressible and nearly incompressible descriptions. In the homogeneous case, the lowest order expansion of the fully compressible equations leads to the usual incompressible equations, followed at higher orders by the nearly incompressible equations, as introduced by Zank and Matthaeus. With this work we show that the inclusion of large-scale inhomogeneities (in this case time-independent and radially symmetric background solar wind) modifies the leading-order incompressible description of solar wind flow. We find, for example, that the divergence of velocity fluctuations is nonsolenoidal and that density fluctuations can be described to leading order as a passive scalar. Locally (for small lengthscales), this system of equations converges to the usual incompressible equations and we therefore use the term 'locally incompressible' to describe the equations. This term should be distinguished from the term 'nearly incompressible', which is reserved for higher-order corrections. Furthermore, we find that density fluctuations scale with Mach number linearly, in contrast to the original homogeneous nearly incompressible theory, in which density fluctuations scale with the square of Mach number. Inhomogeneous nearly

  18. K-FIX: a computer program for transient, two-dimensional, two-fluid flow

    International Nuclear Information System (INIS)

    Rivard, W.C.; Torrey, M.D.

    1976-11-01

    The transient dynamics of two-dimensional, two-phase flow with interfacial exchange are calculated at all flow speeds using the K-FIX program. Each phase is described in terms of its own density, velocity, and temperature. The six field equations for the two phases couple through mass, momentum, and energy exchange. The equations are solved using an Eulerian finite difference technique that implicitly couples the rates of phase transitions, momentum, and energy exchange to determination of the pressure, density, and velocity fields. The implicit solution is accomplished iteratively without linearizing the equations, thus eliminating the need for numerous derivative terms. K-FIX is written in a highly modular form to be easily adaptable to a variety of problems. It is applied to growth of an isolated steam bubble in a superheated water pool

  19. Stability of parallel flows

    CERN Document Server

    Betchov, R

    2012-01-01

    Stability of Parallel Flows provides information pertinent to hydrodynamical stability. This book explores the stability problems that occur in various fields, including electronics, mechanics, oceanography, administration, economics, as well as naval and aeronautical engineering. Organized into two parts encompassing 10 chapters, this book starts with an overview of the general equations of a two-dimensional incompressible flow. This text then explores the stability of a laminar boundary layer and presents the equation of the inviscid approximation. Other chapters present the general equation

  20. Diffusing passive tracers in random incompressible flows: Statistical topography aspects

    International Nuclear Information System (INIS)

    Klyatskin, V.I.; Woyczynski, W.A.; Gurarie, D.

    1996-01-01

    The paper studies statistical characteristics of the passive tracer concentrations and of its spatial gradient, in random incompressible velocity fields from the viewpoint of statistical topography. The statistics of interest include mean values, probability distributions, as well as various functionals characterizing topographic features of tracers. The functional approach is used. We consider the influence of the mean flow (the linear shear flow) and the molecular diffusion coefficient on the statistics of the tracer. Most of our analysis is carried out in the framework of the delta-correlated (in time) approximation and conditions for its applicability are established. But we also consider the diffusion approximation scheme for finite correlation radius. The latter is applied to a diffusing passive tracer that undergoes sedimentation in a random velocity field

  1. Dual plane problems for creeping flow of power-law incompressible medium

    Directory of Open Access Journals (Sweden)

    Dmitriy S. Petukhov

    2016-09-01

    Full Text Available In this paper, we consider the class of solutions for a creeping plane flow of incompressible medium with power-law rheology, which are written in the form of the product of arbitrary power of the radial coordinate by arbitrary function of the angular coordinate of the polar coordinate system covering the plane. This class of solutions represents the asymptotics of fields in the vicinity of singular points in the domain occupied by the examined medium. We have ascertained the duality of two problems for a plane with wedge-shaped notch, at which boundaries in one of the problems the vector components of the surface force vanish, while in the other—the vanishing components are the vector components of velocity, We have investigated the asymptotics and eigensolutions of the dual nonlinear eigenvalue problems in relation to the rheological exponent and opening angle of the notch for the branch associated with the eigenvalue of the Hutchinson–Rice–Rosengren problem learned from the problem of stress distribution over a notched plane for a power law medium. In the context of the dual problem we have determined the velocity distribution in the flow of power-law medium at the vertex of a rigid wedge, We have also found another two eigenvalues, one of which was determined by V. V. Sokolovsky for the problem of power-law fluid flow in a convergent channel.

  2. A sparse-mode spectral method for the simulation of turbulent flows

    International Nuclear Information System (INIS)

    Meneguzzi, M.; Politano, H.; Pouquet, A.; Zolver, M.

    1996-01-01

    We propose a new algorithm belonging to the family of the sparsemode spectral method to simulate turbulent flows. In this method the number of Fourier modes k increases with k more slowly than k D-1 in dimension D, while retaining the advantage of the fast Fourier transform. Examples of applications of the algorithm are given for the one-dimensional Burger's equation and two-dimensional incompressible MHD flows

  3. A Navier-Stokes/Cahn-Hilliard model for the simulation of three phase immiscible incompressible flows

    International Nuclear Information System (INIS)

    Celine Lapuerta; Bruno Piar; Franck Boyer; Philippe Angot; Michel Quintard

    2005-01-01

    This paper presents a Navier-Stokes/Cahn-Hilliard model designed for incompressible flows of three immiscible phases, characterized by different surface tensions and without phase change. This physical context is relevant to study the late phase of a hypothetical severe accident in a nuclear pressurized water reactor. Thanks to a suitable choice of a free energy and a particular form of the Cahn-Hilliard equation, the evolution of the three phases is described by only two order parameters. Moreover, this model allows the simulation of purely two phase flows as a limiting case: no artificial apparition of the third phase occurs if this later is physically absent which contrasts with others models of the literature. We examine the spreading of a liquid lens at the interface between two stratified phases. We present results showing that the method gives correct contact angles and pressure jumps, at equilibrium. (authors)

  4. Exact, rotational, infinite energy, blowup solutions to the 3-dimensional Euler equations

    International Nuclear Information System (INIS)

    Yuen, Manwai

    2011-01-01

    In this Letter, we construct a new class of blowup or global solutions with elementary functions to the 3-dimensional compressible or incompressible Euler and Navier-Stokes equations. And the corresponding blowup or global solutions for the incompressible Euler and Naiver-Stokes equations are also given. Our constructed solutions are similar to the famous Arnold-Beltrami-Childress (ABC) flow. The obtained solutions with infinite energy can exhibit the interesting behaviors locally. Furthermore, due to divu → =0 for the solutions, the solutions also work for the 3-dimensional incompressible Euler and Navier-Stokes equations. -- Highlights: → We construct a new class of solutions to the 3D compressible or incompressible Euler and Navier-Stokes equations. → The constructed solutions are similar to the famous Arnold-Beltrami-Childress flow. → The solutions with infinite energy can exhibit the interesting behaviors locally.

  5. NASA-VOF3D, 3-D Transient, Free Surface, Incompressible Fluid Dynamic

    International Nuclear Information System (INIS)

    Torrey, M.D.

    1992-01-01

    1 - Description of program or function: NASA-VOF3D is a three- dimensional, transient, free surface, incompressible fluid dynamics program. It is specifically designed to calculate confined flows in a low gravity environment in which surface physics must be accurately treated. It allows multiple free surfaces with surface tension and wall adhesion and includes a partial cell treatment that allows curved boundaries and internal obstacles. Variable mesh spacing is permitted in all three coordinate directions. Boundary conditions available are rigid free-slip wall, rigid no-slip, wall, continuative, periodic, and specified pressure outflow boundary. 2 - Method of solution: NASA-VOF3D simulates incompressible flows with free surfaces using the volume-of-fluid (VOF) algorithm. This technique is based on the use of donor-acceptor differencing to track the free surface across an Eulerian grid. The free surfaces are treated by introducing a function defined to be unity at any point occupied by the fluid and zero elsewhere. The complete Navier- Stokes equations for an incompressible fluid are solved by finite differences with surface tension effects included. Wall adhesion may be included or neglected as a user option. The pressures (and velocities) are advanced in time throughout the computing mesh by either a conjugate residual method or the successive over-relaxation (SOR) method. The conjugate residual method is vectorized for the Cray and uses a scaled coefficient matrix. 3 - Restrictions on the complexity of the problem: NASA-VOF3D is restricted to cylindrical coordinate representation of the geometry. A three-dimensional wall-adhesion procedure is available only for straight-walled containers

  6. Unstructured Cartesian refinement with sharp interface immersed boundary method for 3D unsteady incompressible flows

    Science.gov (United States)

    Angelidis, Dionysios; Chawdhary, Saurabh; Sotiropoulos, Fotis

    2016-11-01

    A novel numerical method is developed for solving the 3D, unsteady, incompressible Navier-Stokes equations on locally refined fully unstructured Cartesian grids in domains with arbitrarily complex immersed boundaries. Owing to the utilization of the fractional step method on an unstructured Cartesian hybrid staggered/non-staggered grid layout, flux mismatch and pressure discontinuity issues are avoided and the divergence free constraint is inherently satisfied to machine zero. Auxiliary/hanging nodes are used to facilitate the discretization of the governing equations. The second-order accuracy of the solver is ensured by using multi-dimension Lagrange interpolation operators and appropriate differencing schemes at the interface of regions with different levels of refinement. The sharp interface immersed boundary method is augmented with local near-boundary refinement to handle arbitrarily complex boundaries. The discrete momentum equation is solved with the matrix free Newton-Krylov method and the Krylov-subspace method is employed to solve the Poisson equation. The second-order accuracy of the proposed method on unstructured Cartesian grids is demonstrated by solving the Poisson equation with a known analytical solution. A number of three-dimensional laminar flow simulations of increasing complexity illustrate the ability of the method to handle flows across a range of Reynolds numbers and flow regimes. Laminar steady and unsteady flows past a sphere and the oblique vortex shedding from a circular cylinder mounted between two end walls demonstrate the accuracy, the efficiency and the smooth transition of scales and coherent structures across refinement levels. Large-eddy simulation (LES) past a miniature wind turbine rotor, parameterized using the actuator line approach, indicates the ability of the fully unstructured solver to simulate complex turbulent flows. Finally, a geometry resolving LES of turbulent flow past a complete hydrokinetic turbine illustrates

  7. Numerical simulation of 3-D incompressible, multi-phase flows over cavitating projectiles

    Energy Technology Data Exchange (ETDEWEB)

    Owis, F.M.; Nayfeh, A.H. [Blacksburg State University, Dept. of Engineering Science and Mechanics, MC 0219, Virginia Polytechnic Institute, VA (United States)

    2004-04-01

    The hydrodynamic cavitation over axisymmetric projectiles is computed using the unsteady incompressible Navier-Stokes equations for multi-fluid elements. The governing equations are discretized on a structured grid using an upwind difference scheme with flux limits. A preconditioning dual-time stepping method is used for the unsteady computations. The Eigen-system is derived for the Jacobian matrices. This Eigen-system is suitable for high-density ratio multi-fluid flows and it provides high numerical stability and fast convergence. This method can be used to compute single- as well as multi-phase flows. Cavitating flows over projectiles with different geometries are computed and the results are in good agreement with available experimental data and other published computations. (authors)

  8. Projection methods for the calculation of incompressible or dilatable flows; Methodes de projection pour le calcul d'ecoulements incompressibles ou dilatables

    Energy Technology Data Exchange (ETDEWEB)

    Jobelin, M

    2006-10-15

    This thesis treats of time resolution methods for the Navier-Stokes equations. Based on the well-known projection method of Chorin and Temam, an original pressure correction method, named 'projection-penalty' is developed. Its specificity concerns the addition of a penalty term in the prediction step, which constrains the predicted velocity to fit with the mass balance. The precision improvements added by this method are demonstrated by some analysis results and by some numerical experiments of incompressible or dilatable flows. Finally, the potentialities offered by the use of the joint finite elements method in this type of fractionary step scheme is studied. Two applications are presented, one for local refinement purpose, the other for the resolution of a multi-physics problem. (J.S.)

  9. Coupled incompressible Smoothed Particle Hydrodynamics model for continuum-based modelling sediment transport

    Science.gov (United States)

    Pahar, Gourabananda; Dhar, Anirban

    2017-04-01

    A coupled solenoidal Incompressible Smoothed Particle Hydrodynamics (ISPH) model is presented for simulation of sediment displacement in erodible bed. The coupled framework consists of two separate incompressible modules: (a) granular module, (b) fluid module. The granular module considers a friction based rheology model to calculate deviatoric stress components from pressure. The module is validated for Bagnold flow profile and two standardized test cases of sediment avalanching. The fluid module resolves fluid flow inside and outside porous domain. An interaction force pair containing fluid pressure, viscous term and drag force acts as a bridge between two different flow modules. The coupled model is validated against three dambreak flow cases with different initial conditions of movable bed. The simulated results are in good agreement with experimental data. A demonstrative case considering effect of granular column failure under full/partial submergence highlights the capability of the coupled model for application in generalized scenario.

  10. Numerical simulation of multi-dimensional two-phase flow based on flux vector splitting

    Energy Technology Data Exchange (ETDEWEB)

    Staedtke, H.; Franchello, G.; Worth, B. [Joint Research Centre - Ispra Establishment (Italy)

    1995-09-01

    This paper describes a new approach to the numerical simulation of transient, multidimensional two-phase flow. The development is based on a fully hyperbolic two-fluid model of two-phase flow using separated conservation equations for the two phases. Features of the new model include the existence of real eigenvalues, and a complete set of independent eigenvectors which can be expressed algebraically in terms of the major dependent flow parameters. This facilitates the application of numerical techniques specifically developed for high speed single-phase gas flows which combine signal propagation along characteristic lines with the conservation property with respect to mass, momentum and energy. Advantages of the new model for the numerical simulation of one- and two- dimensional two-phase flow are discussed.

  11. The horizontally homogeneous model equations of incompressible atmospheric flow in general orthogonal coordinates

    DEFF Research Database (Denmark)

    Jørgensen, Bo Hoffmann

    2003-01-01

    The goal of this brief report is to express the model equations for an incompressible flow which is horizontally homogeneous. It is intended as a computationally inexpensive starting point of a more complete solution for neutral atmospheric flow overcomplex terrain. This idea was set forth...... by Ayotte and Taylor (1995) and in the work of Beljaars et al. (1987). Unlike the previous models, the present work uses general orthogonal coordinates. Strong conservation form of the model equations is employedto allow a robust and consistent numerical procedure. An invariant tensor form of the model...

  12. Two dimensional numerical model for steam--water flow in a sudden contraction

    International Nuclear Information System (INIS)

    Crowe, C.T.; Choi, H.N.

    1976-01-01

    A computational model developed for two-dimensional dispersed two-phase flows is applied to steam--water flow in a sudden contraction. The calculational scheme utilizes the cellular approach in which each cell is regarded as a control volume and the droplets are regarded as sources of mass, momentum and energy to the conveying (steam) phase. The predictions show how droplets channel in the entry region and affect the velocity and pressure distributions along the duct

  13. Computation of two-dimensional isothermal flow in shell-and-tube heat exchangers

    International Nuclear Information System (INIS)

    Carlucci, L.N.; Galpin, P.F.; Brown, J.D.; Frisina, V.

    1983-07-01

    A computational procedure is outlined whereby two-dimensional isothermal shell-side flow distributions can be calculated for tube bundles having arbitrary boundaries and flow blocking devices, such as sealing strips, defined in arbitrary locations. The procedure is described in some detail and several computed results are presented to illustrate the robustness and generality of the method

  14. A parallel overset-curvilinear-immersed boundary framework for simulating complex 3D incompressible flows

    Science.gov (United States)

    Borazjani, Iman; Ge, Liang; Le, Trung; Sotiropoulos, Fotis

    2013-01-01

    We develop an overset-curvilinear immersed boundary (overset-CURVIB) method in a general non-inertial frame of reference to simulate a wide range of challenging biological flow problems. The method incorporates overset-curvilinear grids to efficiently handle multi-connected geometries and increase the resolution locally near immersed boundaries. Complex bodies undergoing arbitrarily large deformations may be embedded within the overset-curvilinear background grid and treated as sharp interfaces using the curvilinear immersed boundary (CURVIB) method (Ge and Sotiropoulos, Journal of Computational Physics, 2007). The incompressible flow equations are formulated in a general non-inertial frame of reference to enhance the overall versatility and efficiency of the numerical approach. Efficient search algorithms to identify areas requiring blanking, donor cells, and interpolation coefficients for constructing the boundary conditions at grid interfaces of the overset grid are developed and implemented using efficient parallel computing communication strategies to transfer information among sub-domains. The governing equations are discretized using a second-order accurate finite-volume approach and integrated in time via an efficient fractional-step method. Various strategies for ensuring globally conservative interpolation at grid interfaces suitable for incompressible flow fractional step methods are implemented and evaluated. The method is verified and validated against experimental data, and its capabilities are demonstrated by simulating the flow past multiple aquatic swimmers and the systolic flow in an anatomic left ventricle with a mechanical heart valve implanted in the aortic position. PMID:23833331

  15. Mixed finite element simulations in two-dimensional groundwater flow problems

    International Nuclear Information System (INIS)

    Kimura, Hideo

    1989-01-01

    A computer code of groundwater flow in two-dimensional porous media based on the mixed finite element method was developed for accurate approximations of Darcy velocities in safety evaluation of radioactive waste disposal. The mixed finite element procedure solves for both the Darcy velocities and pressure heads simultaneously in the Darcy equation and continuity equation. Numerical results of a single well pumping at a constant rate in a uniform flow field showed that the mixed finite element method gives more accurate Darcy velocities nearly 50 % on average error than standard finite element method. (author)

  16. Separation prediction in two dimensional boundary layer flows using artificial neural networks

    International Nuclear Information System (INIS)

    Sabetghadam, F.; Ghomi, H.A.

    2003-01-01

    In this article, the ability of artificial neural networks in prediction of separation in steady two dimensional boundary layer flows is studied. Data for network training is extracted from numerical solution of an ODE obtained from Von Karman integral equation with approximate one parameter Pohlhousen velocity profile. As an appropriate neural network, a two layer radial basis generalized regression artificial neural network is used. The results shows good agreements between the overall behavior of the flow fields predicted by the artificial neural network and the actual flow fields for some cases. The method easily can be extended to unsteady separation and turbulent as well as compressible boundary layer flows. (author)

  17. Slip-line field analysis of metal flow during two dimensional forging

    International Nuclear Information System (INIS)

    Fenton, R.G.; Khataan, H.A.

    1981-01-01

    A method of computation and a computer software package were developed for solving problems of two dimensional plastic flow between symmetrical dies of any specified shape. The load required to initiate plastic flow, the stress and velocity distributions in the plastic region of the metal, and the pressure distribution acting on the die are determined. The method can be used to solve any symmetrical plane strain flow problem regardless of the complexity of the die. The accurate solution obtained by this efficient method can provide valuable help to forging die designers. (Author) [pt

  18. Three-dimensional numerical modeling of turbulent single-phase and two-phase flow in curved pipes

    International Nuclear Information System (INIS)

    Xin, R.C.; Dong, Z.F.; Ebadian, M.A.

    1996-01-01

    In this study, three-dimensional single-phase and two-phase flows in curved pipes have been investigated numerically. Two different pipe configurations were computed. When the results of the single-phase flow simulation were compared with the experimental data, a fairly good agreement was achieved. A flow-developing process has been suggested in single-phase flow, in which the turbulence is stronger near the outer tube wall than near the inner tube wall. For two-phase flow, the Eulerian multiphase model was used to simulate the phase distribution of a three-dimensional gas-liquid bubble flow in curved pipe. The RNG/κ-ε turbulence model was used to determine the turbulence field. An inlet gas void fraction of 5 percent was simulated. The gas phase effects on the liquid phase flow velocity have been examined by comparing the results of single-phase flow and two-phase flow. The findings show that for the downward flow in the U bend, the gas concentrates at the inner portion of the cross section at φ = π/18 - π/6 in most cases. The results of the phase distribution simulation are compared to experimental observations qualitatively and topologically

  19. Boundary layers and the vanishing viscosity limit for incompressible 2D flow

    OpenAIRE

    Filho, Milton C. Lopes

    2007-01-01

    This manuscript is a survey on results related to boundary layers and the vanishing viscosity limit for incompressible flow. It is the lecture notes for a 10 hour minicourse given at the Morningside Center, Academia Sinica, Beijing, PRC from 11/28 to 12/07, 2007. The main topics covered are: a derivation of Prandtl's boundary layer equation; an outline of the rigorous theory of Prandtl's equation, without proofs; Kato's criterion for the vanishing viscosity limit; the vanishing viscosity limi...

  20. Hybrid-dimensional modelling of two-phase flow through fractured porous media with enhanced matrix fracture transmission conditions

    Science.gov (United States)

    Brenner, Konstantin; Hennicker, Julian; Masson, Roland; Samier, Pierre

    2018-03-01

    In this work, we extend, to two-phase flow, the single-phase Darcy flow model proposed in [26], [12] in which the (d - 1)-dimensional flow in the fractures is coupled with the d-dimensional flow in the matrix. Three types of so called hybrid-dimensional two-phase Darcy flow models are proposed. They all account for fractures acting either as drains or as barriers, since they allow pressure jumps at the matrix-fracture interfaces. The models also permit to treat gravity dominated flow as well as discontinuous capillary pressure at the material interfaces. The three models differ by their transmission conditions at matrix fracture interfaces: while the first model accounts for the nonlinear two-phase Darcy flux conservations, the second and third ones are based on the linear single phase Darcy flux conservations combined with different approximations of the mobilities. We adapt the Vertex Approximate Gradient (VAG) scheme to this problem, in order to account for anisotropy and heterogeneity aspects as well as for applicability on general meshes. Several test cases are presented to compare our hybrid-dimensional models to the generic equi-dimensional model, in which fractures have the same dimension as the matrix, leading to deep insight about the quality of the proposed reduced models.

  1. Study of two-dimensional flow by triangular unstructured grid around airfoil with dynamic ground effect

    International Nuclear Information System (INIS)

    Haghbin, S.; Farahat, S.

    2004-01-01

    In this paper, the numerical solution of two-dimensional incompressible viscid flow by triangular unstructured grid around airfoil with dynamic ground effect and by using geometric conservation law (GCL) has been represented. In this analysis, after the mesh generation for physical model, for the purpose of adaption of meshes with physical condition, the mesh adaption method has been used. Also, for increasing the speed of results convergence, the Multigrid method has been applied to the solver of governing equations. Because of the movement of meshes in this analysis, by using a spring simulation, the generated meshes have been moved and in every time step for the purpose of controlling the quality of meshes, by considering the EquiAngle Skew coefficient (EAS) and the volume of each mesh, the meshes that had a large EAS and a volume more than and less than defined maximum and minimum value, have been removed and then regenerated. Also, because the continuity and momentum conservations law were insufficient to work with these moving grids, the geometric conservation law was combined with the other conservation laws and a general equation was obtained for the dynamic meshes. For solving this general equation, the Simple Algorithm has been used. According to the results, the dynamic ground effect causes unsteadiness and also the Lift coefficient is increased vibrationally. And with respect to the type of airfoil, the Drag coefficient can decrease or increase vibrationally. (author)

  2. Study of two-dimensional flow by triangular unstructured grid around airfoil with dynamic ground effect

    Energy Technology Data Exchange (ETDEWEB)

    Haghbin, S.; Farahat, S. [Sistan and Baluchestan Univ., Dept. of Mechanical Engineering, Zahedan (Iran, Islamic Republic of)]. E-mail: sadegh_haghbin@yahoo.com

    2004-07-01

    In this paper, the numerical solution of two-dimensional incompressible viscid flow by triangular unstructured grid around airfoil with dynamic ground effect and by using geometric conservation law (GCL) has been represented. In this analysis, after the mesh generation for physical model, for the purpose of adaption of meshes with physical condition, the mesh adaption method has been used. Also, for increasing the speed of results convergence, the Multigrid method has been applied to the solver of governing equations. Because of the movement of meshes in this analysis, by using a spring simulation, the generated meshes have been moved and in every time step for the purpose of controlling the quality of meshes, by considering the EquiAngle Skew coefficient (EAS) and the volume of each mesh, the meshes that had a large EAS and a volume more than and less than defined maximum and minimum value, have been removed and then regenerated. Also, because the continuity and momentum conservations law were insufficient to work with these moving grids, the geometric conservation law was combined with the other conservation laws and a general equation was obtained for the dynamic meshes. For solving this general equation, the Simple Algorithm has been used. According to the results, the dynamic ground effect causes unsteadiness and also the Lift coefficient is increased vibrationally. And with respect to the type of airfoil, the Drag coefficient can decrease or increase vibrationally. (author)

  3. Accuracy and Numerical Stabilty Analysis of Lattice Boltzmann Method with Multiple Relaxation Time for Incompressible Flows

    Science.gov (United States)

    Pradipto; Purqon, Acep

    2017-07-01

    Lattice Boltzmann Method (LBM) is the novel method for simulating fluid dynamics. Nowadays, the application of LBM ranges from the incompressible flow, flow in the porous medium, until microflows. The common collision model of LBM is the BGK with a constant single relaxation time τ. However, BGK suffers from numerical instabilities. These instabilities could be eliminated by implementing LBM with multiple relaxation time. Both of those scheme have implemented for incompressible 2 dimensions lid-driven cavity. The stability analysis has done by finding the maximum Reynolds number and velocity for converged simulations. The accuracy analysis is done by comparing the velocity profile with the benchmark results from Ghia, et al and calculating the net velocity flux. The tests concluded that LBM with MRT are more stable than BGK, and have a similar accuracy. The maximum Reynolds number that converges for BGK is 3200 and 7500 for MRT respectively.

  4. The application of finite volume methods for modelling three-dimensional incompressible flow on an unstructured mesh

    Science.gov (United States)

    Lonsdale, R. D.; Webster, R.

    This paper demonstrates the application of a simple finite volume approach to a finite element mesh, combining the economy of the former with the geometrical flexibility of the latter. The procedure is used to model a three-dimensional flow on a mesh of linear eight-node brick (hexahedra). Simulations are performed for a wide range of flow problems, some in excess of 94,000 nodes. The resulting computer code ASTEC that incorporates these procedures is described.

  5. A boundary-fitted staggered difference method for incompressible flow using Riemann geometry

    International Nuclear Information System (INIS)

    Koshizuka, Seiichi; Kondo, Shunsuke; Oka, Yoshiaki.

    1990-01-01

    A boundary-fitted staggered difference method (BFSDM) is investigated for incompressible flow in nuclear plants. BFSDM employs control cells for scalars, staggered location of velocity components, and integrated formulation of div=0. Governing equations are written as coordinate-free forms using Riemann geometry. Flow velocity is represented with contravariant physical components in the present method. Connection terms emerge as source terms in the coordinate-free governing equations. These terms are studied from the viewpoints of physical meaning, numerical stability, and conservative property. Some flows on a round or slant boundary are solved using boundary-fitted curvilinear (BFC) grids and rectangular grids to compare the present method and the rectangular-type (R-type) staggered difference method (SDM). Supercomputing of the present method, including vector processing, is also discussed compared with the R-type method. (author)

  6. Robust boundary treatment for open-channel flows in divergence-free incompressible SPH

    Science.gov (United States)

    Pahar, Gourabananda; Dhar, Anirban

    2017-03-01

    A robust Incompressible Smoothed Particle Hydrodynamics (ISPH) framework is developed to simulate specified inflow and outflow boundary conditions for open-channel flow. Being purely divergence-free, the framework offers smoothed and structured pressure distribution. An implicit treatment of Pressure Poison Equation and Dirichlet boundary condition is applied on free-surface to minimize error in velocity-divergence. Beyond inflow and outflow threshold, multiple layers of dummy particles are created according to specified boundary condition. Inflow boundary acts as a soluble wave-maker. Fluid particles beyond outflow threshold are removed and replaced with dummy particles with specified boundary velocity. The framework is validated against different cases of open channel flow with different boundary conditions. The model can efficiently capture flow evolution and vortex generation for random geometry and variable boundary conditions.

  7. The incompressibility assumption in computational simulations of nasal airflow.

    Science.gov (United States)

    Cal, Ismael R; Cercos-Pita, Jose Luis; Duque, Daniel

    2017-06-01

    Most of the computational works on nasal airflow up to date have assumed incompressibility, given the low Mach number of these flows. However, for high temperature gradients, the incompressibility assumption could lead to a loss of accuracy, due to the temperature dependence of air density and viscosity. In this article we aim to shed some light on the influence of this assumption in a model of calm breathing in an Asian nasal cavity, by solving the fluid flow equations in compressible and incompressible formulation for different ambient air temperatures using the OpenFOAM package. At low flow rates and warm climatological conditions, similar results were obtained from both approaches, showing that density variations need not be taken into account to obtain a good prediction of all flow features, at least for usual breathing conditions. This agrees with most of the simulations previously reported, at least as far as the incompressibility assumption is concerned. However, parameters like nasal resistance and wall shear stress distribution differ for air temperatures below [Formula: see text]C approximately. Therefore, density variations should be considered for simulations at such low temperatures.

  8. Stochastic and collisional diffusion in two-dimensional periodic flows

    International Nuclear Information System (INIS)

    Doxas, I.; Horton, W.; Berk, H.L.

    1990-05-01

    The global effective diffusion coefficient D* for a two-dimensional system of convective rolls with a time dependent perturbation added, is calculated. The perturbation produces a background diffusion coefficient D, which is calculated analytically using the Menlikov-Arnold integral. This intrinsic diffusion coefficient is then enhanced by the unperturbed flow, to produce the global effective diffusion coefficient D*, which we can calculate theoretically for a certain range of parameters. The theoretical value agrees well with numerical simulations. 23 refs., 4 figs

  9. A general theory of two- and three-dimensional rotational flow in subsonic and transonic turbomachines

    Science.gov (United States)

    Wu, Chung-Hua

    1993-01-01

    This report represents a general theory applicable to axial, radial, and mixed flow turbomachines operating at subsonic and supersonic speeds with a finite number of blades of finite thickness. References reflect the evolution of computational methods used, from the inception of the theory in the 50's to the high-speed computer era of the 90's. Two kinds of relative stream surfaces, S(sub 1) and S(sub 2), are introduced for the purpose of obtaining a three-dimensional flow solution through the combination of two-dimensional flow solutions. Nonorthogonal curvilinear coordinates are used for the governing equations. Methods of computing transonic flow along S(sub 1) and S(sub 2) stream surfaces are given for special cases as well as for fully three-dimensional transonic flows. Procedures pertaining to the direct solutions and inverse solutions are presented. Information on shock wave locations and shapes needed for computations are discussed. Experimental data from a Deutsche Forschungs- und Versuchsanstalt fur Luft- und Raumfahrt e.V. (DFVLR) rotor and from a Chinese Academy of Sciences (CAS) transonic compressor rotor are compared with the computed flow properties.

  10. Two-dimensional steady unsaturated flow through embedded elliptical layers

    Science.gov (United States)

    Bakker, Mark; Nieber, John L.

    2004-12-01

    New analytic element solutions are presented for unsaturated, two-dimensional steady flow in vertical planes that include nonoverlapping impermeable elliptical layers and elliptical inhomogeneities. The hydraulic conductivity, which is represented by an exponential function of the pressure head, differs between the inside and outside of an elliptical inhomogeneity; both the saturated hydraulic conductivity and water retention parameters are allowed to differ between the inside and outside. The Richards equation is transformed, through the Kirchhoff transformation and a second standard transformation, into the modified Helmholtz equation. Analytic element solutions are obtained through separation of variables in elliptical coordinates. The resulting equations for the Kirchhoff potential consist of infinite sums of products of exponentials and modified Mathieu functions. In practical applications the series are truncated but still fulfill the differential equation exactly; boundary conditions are met approximately but up to machine accuracy, provided that enough terms are used. The pressure head, saturation, and flow may be computed analytically at any point in the vadose zone. Examples are given of the shadowing effect of an impermeable elliptical layer in a uniform flow field and funnel-type flow between two elliptical inhomogeneities. The presented solutions may be applied to study transport processes in vadose zones containing many impermeable elliptical layers or elliptical inhomogeneities.

  11. Two-phase flow models

    International Nuclear Information System (INIS)

    Delaje, Dzh.

    1984-01-01

    General hypothesis used to simplify the equations, describing two-phase flows, are considered. Two-component and one-component models of two-phase flow, as well as Zuber and Findlay model for actual volumetric steam content, and Wallis model, describing the given phase rates, are presented. The conclusion is made, that the two-component model, in which values averaged in time are included, is applicable for the solving of three-dimensional tasks for unsteady two-phase flow. At the same time, using the two-component model, including values, averaged in space only one-dimensional tasks for unsteady two-phase flow can be solved

  12. Hall-magnetohydrodynamic waves in flowing ideal incompressible solar-wind plasmas

    International Nuclear Information System (INIS)

    Zhelyazkov, I

    2010-01-01

    It is well established now that the solar atmosphere, from the photosphere to the corona and the solar wind, is a highly structured medium. Satellite observations have confirmed the presence of steady flows there. Here, we investigate the propagation of magnetohydrodynamic (MHD) eigenmodes (kink and sausage surface waves) travelling along an ideal incompressible flowing plasma cylinder (flux tube) surrounded by a flowing plasma environment in the framework of the Hall magnetohydrodynamics. The propagation characteristics of the waves are studied in a reference frame moving with the mass flow outside the tube. In general, the flows change the waves' phase velocities compared with their magnitudes in a static MHD flux tube and the Hall effect extends the number of the possible wave dispersion curves. It turns out that while the kink waves, considered in the context of the standard magnetohydrodynamics, are unstable against the Kelvin-Helmholtz instability, they become stable when the Hall term in the generalized Ohm's law is taken into account. The sausage waves are stable in both considerations. All results concerning the waves' propagation and their stability/instability status are obtained on the basis of the linearized Hall-magnetohydrodynamic equations and are applicable mainly to the solar wind plasmas.

  13. Mathematical modeling of turbulent stratified flows. Application of liquid metal fast breeders

    Energy Technology Data Exchange (ETDEWEB)

    Villand, M; Grand, D [CEA-Service des Transferts Thermiques, Grenoble (France)

    1983-07-01

    Mathematical model of turbulent stratified flow was proposed under the following assumptions: Newtonian fluid; incompressible fluid; coupling between temperature and momentum fields according to Boussinesq approximation; two-dimensional invariance for translation or rotation; coordinates cartesian or curvilinear. Solutions obtained by the proposed method are presented.

  14. One- and two-dimensional Stirling machine simulation using experimentally generated reversing flow turbuulence models

    International Nuclear Information System (INIS)

    Goldberg, L.F.

    1990-08-01

    The activities described in this report do not constitute a continuum but rather a series of linked smaller investigations in the general area of one- and two-dimensional Stirling machine simulation. The initial impetus for these investigations was the development and construction of the Mechanical Engineering Test Rig (METR) under a grant awarded by NASA to Dr. Terry Simon at the Department of Mechanical Engineering, University of Minnesota. The purpose of the METR is to provide experimental data on oscillating turbulent flows in Stirling machine working fluid flow path components (heater, cooler, regenerator, etc.) with particular emphasis on laminar/turbulent flow transitions. Hence, the initial goals for the grant awarded by NASA were, broadly, to provide computer simulation backup for the design of the METR and to analyze the results produced. This was envisaged in two phases: First, to apply an existing one-dimensional Stirling machine simulation code to the METR and second, to adapt a two-dimensional fluid mechanics code which had been developed for simulating high Rayleigh number buoyant cavity flows to the METR. The key aspect of this latter component was the development of an appropriate turbulence model suitable for generalized application to Stirling simulation. A final-step was then to apply the two-dimensional code to an existing Stirling machine for which adequate experimental data exist. The work described herein was carried out over a period of three years on a part-time basis. Forty percent of the first year's funding was provided as a match to the NASA funds by the Underground Space Center, University of Minnesota, which also made its computing facilities available to the project at no charge

  15. POST: a postprocessor computer code for producing three-dimensional movies of two-phase flow in a reactor vessel

    International Nuclear Information System (INIS)

    Taggart, K.A.; Liles, D.R.

    1977-08-01

    The development of the TRAC computer code for analysis of LOCAs in light-water reactors involves the use of a three-dimensional (r-theta-z), two-fluid hydrodynamics model to describe the two-phase flow of steam and water through the reactor vessel. One of the major problems involved in interpreting results from this code is the presentation of three-dimensional flow patterns. The purpose of the report is to present a partial solution to this data display problem. A first version of a code which produces three-dimensional movies of flow in the reactor vessel has been written and debugged. This code (POST) is used as a postprocessor in conjunction with a stand alone three-dimensional two-phase hydrodynamics code (CYLTF) which is a test bed for the three-dimensional algorithms to be used in TRAC

  16. Convective heat transfer from rough surfaces with two-dimensional ribs - transitional and laminar flow

    International Nuclear Information System (INIS)

    Dalle Donne, M.; Meyer, L.

    1978-01-01

    Measurements of friction factor and heat transfer coefficients for two rods of 18.9 mm 0.D. with two-dimensional roughness, each in two different outer smooth tubes have been performed in turbulent and laminar flow. The turbulent flow results indicate that the flow was not thermally fully established, the isothermal data however agree reasonably well with our previously obtained general correlation. Laminar flow results can be correlated best when the Reynolds and Greatz numbers are evaluated at the temperature average between the temperature of the inner rod surface and of the outer smooth surface of the annulus, the average being weighted over the two surfaces. (orig.) [de

  17. Transient response in granular quasi-two-dimensional bounded heap flow.

    Science.gov (United States)

    Xiao, Hongyi; Ottino, Julio M; Lueptow, Richard M; Umbanhowar, Paul B

    2017-10-01

    We study the transition between steady flows of noncohesive granular materials in quasi-two-dimensional bounded heaps by suddenly changing the feed rate. In both experiments and simulations, the primary feature of the transition is a wedge of flowing particles that propagates downstream over the rising free surface with a wedge front velocity inversely proportional to the square root of time. An additional longer duration transient process continues after the wedge front reaches the downstream wall. The entire transition is well modeled as a moving boundary problem with a diffusionlike equation derived from local mass balance and a local relation between the flux and the surface slope.

  18. Finite-time barriers to front propagation in two-dimensional fluid flows

    Science.gov (United States)

    Mahoney, John R.; Mitchell, Kevin A.

    2015-08-01

    Recent theoretical and experimental investigations have demonstrated the role of certain invariant manifolds, termed burning invariant manifolds (BIMs), as one-way dynamical barriers to reaction fronts propagating within a flowing fluid. These barriers form one-dimensional curves in a two-dimensional fluid flow. In prior studies, the fluid velocity field was required to be either time-independent or time-periodic. In the present study, we develop an approach to identify prominent one-way barriers based only on fluid velocity data over a finite time interval, which may have arbitrary time-dependence. We call such a barrier a burning Lagrangian coherent structure (bLCS) in analogy to Lagrangian coherent structures (LCSs) commonly used in passive advection. Our approach is based on the variational formulation of LCSs using curves of stationary "Lagrangian shear," introduced by Farazmand et al. [Physica D 278-279, 44 (2014)] in the context of passive advection. We numerically validate our technique by demonstrating that the bLCS closely tracks the BIM for a time-independent, double-vortex channel flow with an opposing "wind."

  19. Compressible flow modelling in unstructured mesh topologies using numerical methods developed for incompressible flows

    International Nuclear Information System (INIS)

    Caruso, A.; Mechitoua, N.; Duplex, J.

    1995-01-01

    The R and D thermal hydraulic codes, notably the finite difference codes Melodie (2D) and ESTET (3D) or the 2D and 3D versions of the finite element code N3S were initially developed for incompressible, possibly dilatable, turbulent flows, i.e. those where density is not pressure-dependent. Subsequent minor modifications to these finite difference code algorithms enabled extension of their scope to subsonic compressible flows. The first applications in both single-phase and two flow contexts have now been completed. This paper presents the techniques used to adapt these algorithms for the processing of compressible flows in an N3S type finite element code, whereby complex geometries normally difficult to model in finite difference meshes could be successfully dealt with. The development of version 3.0 of he N3S code led to dilatable flow calculations at lower cost. On this basis, a 2-D prototype version of N3S was programmed, tested and validated, drawing maximum benefit from Cray vectorization possibilities and from physical, numerical or data processing experience with other fluid dynamics codes, such as Melodie, ESTET or TELEMAC. The algorithms are the same as those used in finite difference codes, but their formulation is variational. The first part of the paper deals with the fundamental equations involved, expressed in basic form, together with the associated digital method. The modifications to the k-epsilon turbulence model extended to compressible flows are also described. THe second part presents the algorithm used, indicating the additional terms required by the extension. The third part presents the equations in integral form and the associated matrix systems. The solutions adopted for calculation of the compressibility related terms are indicated. Finally, a few representative applications and test cases are discussed. These include subsonic, but also transsonic and supersonic cases, showing the shock responses of the digital method. The application of

  20. Numerical simulations of the laminar-turbulent transition process in plane Poiseuille flow

    International Nuclear Information System (INIS)

    Kleiser, L.

    1982-04-01

    Laminar-turbulent transition in plane Poiseuille flow is simulated by numerical integration of the time-dependent three-dimensional Navier-Stokes equations for incompressible flow. The mathematical model of a spatially periodic, timewise developing flow in a moving frame of reference is used to match vibrating-ribbon experiments of Nishioka et al. The numerical discretisation is based on a spectral method with Fourier and Chebyshev polynomial expansions in space and second order finite differences in time. The pressure is calculated using a new method which enforces incompressibility and boundary conditions exactly. This is achieved by deriving the correct boundary conditions for the pressure Poisson equation. The numerical results obtained for two-dimensional finite amplitude disturbances are consistent with nonlinear stability theory. The time-periodic secondary flow is attained by the time-dependent calculation with reasonable accuracy after a long quasi-steady state. No sign of two-dimensional instability, but strong three-dimensional instability as well of the periodic secondary flow as of the quasi-steady state is found. This secondary three-dimensional instability is shown to be responsible for transition. It is shown that the three-dimensional simulations presented here reproduce the experimentally observed transition process up to the spike stage. Detailed comparisons with measurements of mean velocity, rms-values of fluctuation and instantaneous velocity distribution reveal very satisfactory agreement. The formation of peak-valley structure, longitudinal vortices, local high-shear layers and distinct spike-type signals is shown. In addition, the three-dimensional flow field structure before breakdown is investigated. An array of horseshoe vortices similar to those inferred from boundary layer flow visualization experiments is found. Spike signals are produced by local accumulations of low-speed fluid in the downstream loops of these vortices. (orig.) [de

  1. Ensemble distribution for immiscible two-phase flow in porous media.

    Science.gov (United States)

    Savani, Isha; Bedeaux, Dick; Kjelstrup, Signe; Vassvik, Morten; Sinha, Santanu; Hansen, Alex

    2017-02-01

    We construct an ensemble distribution to describe steady immiscible two-phase flow of two incompressible fluids in a porous medium. The system is found to be ergodic. The distribution is used to compute macroscopic flow parameters. In particular, we find an expression for the overall mobility of the system from the ensemble distribution. The entropy production at the scale of the porous medium is shown to give the expected product of the average flow and its driving force, obtained from a black-box description. We test numerically some of the central theoretical results.

  2. Comparison of 3-D finite elements for incompressible fluid flow

    International Nuclear Information System (INIS)

    Robichaud, M.; Tanguy, P.A.

    1985-01-01

    In recent years, the finite element method applied to the solution of incompressible fluid flow has been in constant evolution. In the present state-of-the-art, 2-D problems are solved routinely and reliable results are obtained at a reasonable cost. In 3-D the finite element method is still undergoing active research and many methods have been proposed to solve the Navier-Stokes equations at 'low cost'. These methods have in common the choice of the element which has a trilinear velocity and a discontinuous constant pressure (Q1-PO). The prohibitive cost of 3-D finite element method in fluid flow is the reason for this choice: the Q1-PO is the simplest and the cheapest 3-D element. However, as mentioned in (5) and (6), it generates 'spurious' pressure modes phenomenon called checkerboarding. On regular mesh these spurious modes can be filtered but on distorted mesh the pressure solution is meaningless. (author)

  3. Synchrotron 4-dimensional imaging of two-phase flow through porous media.

    Science.gov (United States)

    Kim, F H; Penumadu, D; Patel, P; Xiao, X; Garboczi, E J; Moylan, S P; Donmez, M A

    2016-01-01

    Near real-time visualization of complex two-phase flow in a porous medium was demonstrated with dynamic 4-dimensional (4D) (3D + time) imaging at the 2-BM beam line of the Advanced Photon Source (APS) at Argonne National Laboratory. Advancing fluid fronts through tortuous flow paths and their interactions with sand grains were clearly captured, and formations of air bubbles and capillary bridges were visualized. The intense X-ray photon flux of the synchrotron facility made 4D imaging possible, capturing the dynamic evolution of both solid and fluid phases. Computed Tomography (CT) scans were collected every 12 s with a pixel size of 3.25 µm. The experiment was carried out to improve understanding of the physics associated with two-phase flow. The results provide a source of validation data for numerical simulation codes such as Lattice-Boltzmann, which are used to model multi-phase flow through porous media.

  4. Comparative study of the two-fluid momentum equations for multi-dimensional bubbly flows: Modification of Reynolds stress

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Seung Jun; Park, Ik Kyu; Yoon, Han Young [Thermal-Hydraulic Safety Research Division, Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Jae, Byoung [School of Mechanical Engineering, Chungnam National University, Daejeon (Korea, Republic of)

    2017-01-15

    Two-fluid equations are widely used to obtain averaged behaviors of two-phase flows. This study addresses a problem that may arise when the two-fluid equations are used for multi-dimensional bubbly flows. If steady drag is the only accounted force for the interfacial momentum transfer, the disperse-phase velocity would be the same as the continuous-phase velocity when the flow is fully developed without gravity. However, existing momentum equations may show unphysical results in estimating the relative velocity of the disperse phase against the continuous-phase. First, we examine two types of existing momentum equations. One is the standard two-fluid momentum equation in which the disperse-phase is treated as a continuum. The other is the averaged momentum equation derived from a solid/ fluid particle motion. We show that the existing equations are not proper for multi-dimensional bubbly flows. To resolve the problem mentioned above, we modify the form of the Reynolds stress terms in the averaged momentum equation based on the solid/fluid particle motion. The proposed equation shows physically correct results for both multi-dimensional laminar and turbulent flows.

  5. On preconditioning incompressible non-Newtonian flow problems

    NARCIS (Netherlands)

    He, X.; Neytcheva, M.; Vuik, C.

    2013-01-01

    This paper deals with fast and reliable numerical solution methods for the incompressible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial differential equations. For space

  6. User's guide to HEATRAN: a computer program for three-dimensional transient fluid-flow and heat-transfer analysis

    International Nuclear Information System (INIS)

    Wong, C.N.C.; Cheng, S.K.; Todreas, N.E.

    1982-01-01

    This report provides the HEATRAN user with programming and input information. HEATRAN is a computer program which is written to analyze the transient three dimensional single phase incompressible fluid flow and heat transfer problem. In this report, the programming information is given first. This information includes details concerning the code and structure. The description of the required input variables is presented next. Following the input description, the sample problems are described and HEATRAN's results are presented

  7. High order spectral difference lattice Boltzmann method for incompressible hydrodynamics

    Science.gov (United States)

    Li, Weidong

    2017-09-01

    This work presents a lattice Boltzmann equation (LBE) based high order spectral difference method for incompressible flows. In the present method, the spectral difference (SD) method is adopted to discretize the convection and collision term of the LBE to obtain high order (≥3) accuracy. Because the SD scheme represents the solution as cell local polynomials and the solution polynomials have good tensor-product property, the present spectral difference lattice Boltzmann method (SD-LBM) can be implemented on arbitrary unstructured quadrilateral meshes for effective and efficient treatment of complex geometries. Thanks to only first oder PDEs involved in the LBE, no special techniques, such as hybridizable discontinuous Galerkin method (HDG), local discontinuous Galerkin method (LDG) and so on, are needed to discrete diffusion term, and thus, it simplifies the algorithm and implementation of the high order spectral difference method for simulating viscous flows. The proposed SD-LBM is validated with four incompressible flow benchmarks in two-dimensions: (a) the Poiseuille flow driven by a constant body force; (b) the lid-driven cavity flow without singularity at the two top corners-Burggraf flow; and (c) the unsteady Taylor-Green vortex flow; (d) the Blasius boundary-layer flow past a flat plate. Computational results are compared with analytical solutions of these cases and convergence studies of these cases are also given. The designed accuracy of the proposed SD-LBM is clearly verified.

  8. Point force singularities outside a drop covered with an incompressible surfactant: Image systems and their applications

    Science.gov (United States)

    Shaik, Vaseem A.; Ardekani, Arezoo M.

    2017-11-01

    In this work we derive the image flow fields for point force singularities placed outside a stationary drop covered with an insoluble, nondiffusing, and incompressible surfactant. We assume the interface to be Newtonian and use the Boussinesq-Scriven constitutive law for the interfacial stress tensor. We use this analytical solution to investigate two different problems. First, we derive the mobility matrix for two drops of arbitrary sizes covered with an incompressible surfactant. In the second example, we calculate the velocity of a swimming microorganism (modeled as a Stokes dipole) outside a drop covered with an incompressible surfactant.

  9. The Finite-Surface Method for incompressible flow: a step beyond staggered grid

    Science.gov (United States)

    Hokpunna, Arpiruk; Misaka, Takashi; Obayashi, Shigeru

    2017-11-01

    We present a newly developed higher-order finite surface method for the incompressible Navier-Stokes equations (NSE). This method defines the velocities as a surface-averaged value on the surfaces of the pressure cells. Consequently, the mass conservation on the pressure cells becomes an exact equation. The only things left to approximate is the momentum equation and the pressure at the new time step. At certain conditions, the exact mass conservation enables the explicit n-th order accurate NSE solver to be used with the pressure treatment that is two or four order less accurate without loosing the apparent convergence rate. This feature was not possible with finite volume of finite difference methods. We use Fourier analysis with a model spectrum to determine the condition and found that the range covers standard boundary layer flows. The formal convergence and the performance of the proposed scheme is compared with a sixth-order finite volume method. Finally, the accuracy and performance of the method is evaluated in turbulent channel flows. This work is partially funded by a research colloaboration from IFS, Tohoku university and ASEAN+3 funding scheme from CMUIC, Chiang Mai University.

  10. Advanced numerical methods for three dimensional two-phase flow calculations in PWR

    International Nuclear Information System (INIS)

    Toumi, I.; Gallo, D.; Royer, E.

    1997-01-01

    This paper is devoted to new numerical methods developed for three dimensional two-phase flow calculations. These methods are finite volume numerical methods. They are based on an extension of Roe's approximate Riemann solver to define convective fluxes versus mean cell quantities. To go forward in time, a linearized conservative implicit integrating step is used, together with a Newton iterative method. We also present here some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. This kind of numerical method, which is widely used for fluid dynamic calculations, is proved to be very efficient for the numerical solution to two-phase flow problems. This numerical method has been implemented for the three dimensional thermal-hydraulic code FLICA-4 which is mainly dedicated to core thermal-hydraulic transient and steady-state analysis. Hereafter, we will also find some results obtained for the EPR reactor running in a steady-state at 60% of nominal power with 3 pumps out of 4, and a thermal-hydraulic core analysis for a 1300 MW PWR at low flow steam-line-break conditions. (author)

  11. Statistical theory of turbulent incompressible multimaterial flow

    International Nuclear Information System (INIS)

    Kashiwa, B.

    1987-10-01

    Interpenetrating motion of incompressible materials is considered. ''Turbulence'' is defined as any deviation from the mean motion. Accordingly a nominally stationary fluid will exhibit turbulent fluctuations due to a single, slowly moving sphere. Mean conservation equations for interpenetrating materials in arbitrary proportions are derived using an ensemble averaging procedure, beginning with the exact equations of motion. The result is a set of conservation equations for the mean mass, momentum and fluctuational kinetic energy of each material. The equation system is at first unclosed due to integral terms involving unknown one-point and two-point probability distribution functions. In the mean momentum equation, the unclosed terms are clearly identified as representing two physical processes. One is transport of momentum by multimaterial Reynolds stresses, and the other is momentum exchange due to pressure fluctuations and viscous stress at material interfaces. Closure is approached by combining careful examination of multipoint statistical correlations with the traditional physical technique of κ-ε modeling for single-material turbulence. This involves representing the multimaterial Reynolds stress for each material as a turbulent viscosity times the rate of strain based on the mean velocity of that material. The multimaterial turbulent viscosity is related to the fluctuational kinetic energy κ, and the rate of fluctuational energy dissipation ε, for each material. Hence a set of κ and ε equations must be solved, together with mean mass and momentum conservation equations, for each material. Both κ and the turbulent viscosities enter into the momentum exchange force. The theory is applied to (a) calculation of the drag force on a sphere fixed in a uniform flow, (b) calculation of the settling rate in a suspension and (c) calculation of velocity profiles in the pneumatic transport of solid particles in a pipe

  12. A soap film shock tube to study two-dimensional compressible flows

    Energy Technology Data Exchange (ETDEWEB)

    Wen, C.Y.; Chen, Y.M.; Chang-Jian, S.K. [Dept. of Mechanical Engineering, Da-Yeh University Chang-Hwa (Taiwan)

    2001-07-01

    A new experimental approach to the study of the two-dimensional compressible flow phenomena is presented. In this technique, a variety of compressible flows were generated by bursting plane vertical soap films. An aureole and a ''shock wave'' preceding the rim of the expanding hole were clearly observed using traditional high-speed flash photography and a fast line-scan charge coupled device (CCD) camera. The moving shock wave images obtained from the line-scan CCD camera were similar to the x-t diagrams in gas dynamics. The moving shock waves cause thickness jumps and induce supersonic flows. Photographs of the supersonic flows over a cylinder and a wedge are presented. The results suggest clearly the feasibility of the ''soap film shock tube''. (orig.)

  13. Numerical simulation of transient, adiabatic, two-dimensional two-phase flow using the two-fluid model

    International Nuclear Information System (INIS)

    Neves Conti, T. das.

    1983-01-01

    A numerical method is developed to simulate adiabatic, transient, two-dimensional two-phase flow. The two-fluid model is used to obtain the mass and momentum conservation equations. These are solved by an iterative algorithm emphoying a time-marching scheme. Based on the corrective procedure of Hirt and Harlow a poisson equation is derived for the pressure field. This equation is finite-differenced and solved by a suitable matrix inversion technique. In the absence of experiment results several numerical tests were made in order to chec accuracy, convergence and stability of the proposed method. Several tests were also performed to check whether the behavior of void fraction and phasic velocities conforms with previous observations. (Author) [pt

  14. Mechanics of occurrence of critical flow in compressible two-phase flow

    International Nuclear Information System (INIS)

    Katto, Yoshiro; Sudo, Yukio

    1976-01-01

    Fundamental framework of mechanics for the occurrence of critical flow is investigated, following the principle that the critical flow appears as a limit in a continuous change of state of flow along a nozzle (or a pipe) and should be derived only from simultaneous mechanical equations concerned with the flow. Mathematical procedures with which the critical flow: (i) the single phase flow of an arbitrary fluid, unrestricted by the equation of state of ideal gas, where the number of simultaneous equations is equal to the number of independent variables, and (ii) the one-component, separated two-phase flow under saturated condition, where the number of equations exceeds that of variables. In each case, interesting mechanism of leading to the occurrence of a limiting state of flow at a definite cross-section in a nozzle (incl. a pipe) is clarified, and a definite state of flow at the critical cross-section is also determined. Then, the analysis is extended to the critical flow which should appear in the completely isolated and the homogeneously dispersed, two-component, two-phase flow (composed of a compressible and an incompressible substance). It is found that the analyses of these special flow patterns provide several supplementary information to the mechanics of critical flow. (auth.)

  15. POD-Galerkin Model for Incompressible Single-Phase Flow in Porous Media

    KAUST Repository

    Wang, Yi

    2017-01-25

    Fast prediction modeling via proper orthogonal decomposition method combined with Galerkin projection is applied to incompressible single-phase fluid flow in porous media. Cases for different configurations of porous media, boundary conditions and problem scales are designed to examine the fidelity and robustness of the model. High precision (relative deviation 1.0 x 10(-4)% similar to 2.3 x 10(-1)%) and large acceleration (speed-up 880 similar to 98454 times) of POD model are found in these cases. Moreover, the computational time of POD model is quite insensitive to the complexity of problems. These results indicate POD model is especially suitable for large-scale complex problems in engineering.

  16. Numerical prediction of augmented turbulent heat transfer in an annular fuel channel with repeated two-dimensional square ribs

    International Nuclear Information System (INIS)

    Takase, K.

    1996-01-01

    The square-ribbed fuel rod for high temperature gas-cooled reactors was designed and developed so as to enhance the turbulent heat transfer in comparison with the previous standard fuel rod. The turbulent heat transfer characteristics in an annular fuel channel with repeated two-dimensional square ribs were analysed numerically on a fully developed incompressible flow using the k-ε turbulence model and the two-dimensional axisymmetrical coordinate system. Numerical analyses were carried out under the conditions of Reynolds numbers from 3000 to 20000 and ratios of square-rib pitch to height of 10, 20 and 40 respectively. The predictions of the heat transfer coefficients agreed well within an error of 10% for the square-rib pitch to height ratio of 10, 20% for 20 and 25% for 40 respectively, with the heat transfer empirical correlations obtained from the experimental data due to the simulated square-ribbed fuel rods. Therefore it was found that the effect of heat transfer augmentation due to the square ribs could be predicted by the present numerical simulations and the mechanism could be explained by the change in the turbulence kinematic energy distribution along the flow direction. (orig.)

  17. Application of fast neutron radiography to three-dimensional visualization of steady two-phase flow in a rod bundle

    CERN Document Server

    Takenaka, N; Fujii, T; Mizubata, M; Yoshii, K

    1999-01-01

    Three-dimensional void fraction distribution of air-water two-phase flow in a 4x4 rod-bundle near a spacer was visualized by fast neutron radiography using a CT method. One-dimensional cross sectional averaged void fraction distribution was also calculated. The behaviors of low void fraction (thick water) two-phase flow in the rod bundle around the spacer were clearly visualized. It was shown that the void fraction distributions were visualized with a quality similar to those by thermal neutron radiography for low void fraction two-phase flow which is difficult to visualize by thermal neutron radiography. It is concluded that the fast neutron radiography is efficiently applicable to two-phase flow studies.

  18. Local invariants in non-ideal flows of neutral fluids and two-fluid plasmas

    Science.gov (United States)

    Zhu, Jian-Zhou

    2018-03-01

    The main objective is the locally invariant geometric object of any (magneto-)fluid dynamics with forcing and damping (nonideal), while more attention is paid to the untouched dynamical properties of two-fluid fashion. Specifically, local structures, beyond the well-known "frozen-in" to the barotropic flows of the generalized vorticities, of the two-fluid model of plasma flows are presented. More general non-barotropic situations are also considered. A modified Euler equation [T. Tao, "Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation," Ann. PDE 2, 9 (2016)] is also accordingly analyzed and remarked from the angle of view of the two-fluid model, with emphasis on the local structures. The local constraints of high-order differential forms such as helicity, among others, find simple formulation for possible practices in modeling the dynamics. Thus, the Cauchy invariants equation [N. Besse and U. Frisch, "Geometric formulation of the Cauchy invariants for incompressible Euler flow in flat and curved spaces," J. Fluid Mech. 825, 412 (2017)] may be enabled to find applications in non-ideal flows. Some formal examples are offered to demonstrate the calculations, and particularly interestingly the two-dimensional-three-component (2D3C) or the 2D passive scalar problem presents that a locally invariant Θ = 2θζ, with θ and ζ being, respectively, the scalar value of the "vertical velocity" (or the passive scalar) and the "vertical vorticity," may be used as if it were the spatial density of the globally invariant helicity, providing a Lagrangian prescription to control the latter in some situations of studying its physical effects in rapidly rotating flows (ubiquitous in atmosphere of astrophysical objects) with marked 2D3C vortical modes or in purely 2D passive scalars.

  19. Three-Dimensional Flow Generated by a Partially Penetrating Well in a Two-Aquifer System

    Science.gov (United States)

    Sepulveda, N.

    2007-12-01

    An analytical solution is presented for three-dimensional (3D) flow in a confined aquifer and the overlying storative semiconfining layer and unconfined aquifer. The equation describing flow caused by a partially penetrating production well is solved analytically to provide a method to accurately determine the hydraulic parameters in the confined aquifer, semiconfining layer, and unconfined aquifer from aquifer-test data. Previous solutions for a partially penetrating well did not account for 3D flow or storativity in the semiconfining unit. The 3D and two- dimensional (2D) flow solutions in the semiconfining layer are compared for various hydraulic conductivity ratios between the aquifer and the semiconfining layer. Analysis of the drawdown data from an aquifer test in central Florida showed that the 3D solution in the semiconfining layer provides a more unique identification of the hydraulic parameters than the 2D solution. The analytical solution could be used to analyze, with higher accuracy, the effect that pumping water from the lower aquifer in a two-aquifer system has on wetlands.

  20. The compactness of front tracking for chromatography electrophoresis and incompressible multiphase flow

    International Nuclear Information System (INIS)

    Wendroff, B.

    1992-01-01

    An analysis of the equations of chromatography from the point of view of hyperbolic conservation laws has been reviewed in recent literature. Serre was able to prove that the Lax-Friedrichs difference scheme, Godunov's method, and the viscosity method, have a subsequence converging to a weak solution of the chromatography equations, with no restriction on the size of the initial data. The purpose of this note is to announce that two versions of front tracking can be added to this list. After a brief description of the properties of the chromatography system and a definition of front tracking we give the basic steps of the proof. An example showing the quality of a front tracking solution is given. The equations of idealized electrophoresis and multiphase incompressible flow are very similar to the chromatography equations, but the former have linearly degenerate characteristic field, creating contact discontinuities. In the final section we briefly indicate how our result for chromatography carries over to this case

  1. A GPU-based incompressible Navier-Stokes solver on moving overset grids

    Science.gov (United States)

    Chandar, Dominic D. J.; Sitaraman, Jayanarayanan; Mavriplis, Dimitri J.

    2013-07-01

    In pursuit of obtaining high fidelity solutions to the fluid flow equations in a short span of time, graphics processing units (GPUs) which were originally intended for gaming applications are currently being used to accelerate computational fluid dynamics (CFD) codes. With a high peak throughput of about 1 TFLOPS on a PC, GPUs seem to be favourable for many high-resolution computations. One such computation that involves a lot of number crunching is computing time accurate flow solutions past moving bodies. The aim of the present paper is thus to discuss the development of a flow solver on unstructured and overset grids and its implementation on GPUs. In its present form, the flow solver solves the incompressible fluid flow equations on unstructured/hybrid/overset grids using a fully implicit projection method. The resulting discretised equations are solved using a matrix-free Krylov solver using several GPU kernels such as gradient, Laplacian and reduction. Some of the simple arithmetic vector calculations are implemented using the CU++: An Object Oriented Framework for Computational Fluid Dynamics Applications using Graphics Processing Units, Journal of Supercomputing, 2013, doi:10.1007/s11227-013-0985-9 approach where GPU kernels are automatically generated at compile time. Results are presented for two- and three-dimensional computations on static and moving grids.

  2. Experimental investigation of flow over two-dimensional multiple hill models.

    Science.gov (United States)

    Li, Qing'an; Maeda, Takao; Kamada, Yasunari; Yamada, Keisuke

    2017-12-31

    The aim of this study is to investigate the flow field characteristics in ABL (Atmospheric Boundary Layer) flow over multiple hills and valleys in two-dimensional models under neutral conditions. Active turbulence grids and boundary layer generation frame were used to simulate the natural winds in wind tunnel experiments. As a result, the mean wind velocity, the velocity vector diagram and turbulence intensity around the hills were investigated by using a PIV (Particle Image Velocimetry) system. From the measurement results, it was known that the average velocity was increased along the upstream slope of upside hill, and then separated at the top of the hills, the acceleration region of U/U ref >1 was generated at the downstream of the hill. Meanwhile, a large clockwise circulation flow was generated between the two hill models. Moreover, the turbulence intensity showed small value in the circulation flow regions. Compared to 1H model, the turbulence intensity in the mainstream direction showed larger value than that in the vertical direction. This paper provided a better understanding of the wind energy distribution on the terrain for proper selection of suitable sites for installing wind farms in the ABL. Copyright © 2017 Elsevier B.V. All rights reserved.

  3. Efficient Parallel Algorithms for Unsteady Incompressible Flows

    KAUST Repository

    Guermond, Jean-Luc; Minev, Peter D.

    2013-01-01

    The objective of this paper is to give an overview of recent developments on splitting schemes for solving the time-dependent incompressible Navier–Stokes equations and to discuss possible extensions to the variable density/viscosity case. A particular attention is given to algorithms that can be implemented efficiently on large parallel clusters.

  4. Numerical solutions of incompressible Navier-Stokes equations using modified Bernoulli's law

    Science.gov (United States)

    Shatalov, A.; Hafez, M.

    2003-11-01

    Simulations of incompressible flows are important for many practical applications in aeronautics and beyond, particularly in the high Reynolds number regime. The present formulation is based on Helmholtz velocity decomposition where the velocity is presented as the gradient of a potential plus a rotational component. Substituting in the continuity equation yields a Poisson equation for the potential which is solved with a zero normal derivative at solid surfaces. The momentum equation is used to update the rotational component with no slip/no penetration surface boundary conditions. The pressure is related to the potential function through a special relation which is a generalization of Bernoulli's law, with a viscous term included. Results of calculations for two- and three-dimensional problems prove that the present formulation is a valid approach, with some possible benefits compared to existing methods.

  5. Development of a Front Tracking Method for Two-Phase Micromixing of Incompressible Viscous Fluids with Interfacial Tension in Solvent Extraction

    Energy Technology Data Exchange (ETDEWEB)

    Zhou, Yijie [ORNL; Lim, Hyun-Kyung [ORNL; de Almeida, Valmor F [ORNL; Navamita, Ray [State University of New York, Stony Brook; Wang, Shuqiang [State University of New York, Stony Brook; Glimm, James G [ORNL; Li, Xiao-lin [State University of New York, Stony Brook; Jiao, Xiangmin [ORNL

    2012-06-01

    This progress report describes the development of a front tracking method for the solution of the governing equations of motion for two-phase micromixing of incompressible, viscous, liquid-liquid solvent extraction processes. The ability to compute the detailed local interfacial structure of the mixture allows characterization of the statistical properties of the two-phase mixture in terms of droplets, filaments, and other structures which emerge as a dispersed phase embedded into a continuous phase. Such a statistical picture provides the information needed for building a consistent coarsened model applicable to the entire mixing device. Coarsening is an undertaking for a future mathematical development and is outside the scope of the present work. We present here a method for accurate simulation of the micromixing dynamics of an aqueous and an organic phase exposed to intense centrifugal force and shearing stress. The onset of mixing is the result of the combination of the classical Rayleigh- Taylor and Kelvin-Helmholtz instabilities. A mixing environment that emulates a sector of the annular mixing zone of a centrifugal contactor is used for the mathematical domain. The domain is small enough to allow for resolution of the individual interfacial structures and large enough to allow for an analysis of their statistical distribution of sizes and shapes. A set of accurate algorithms for this application requires an advanced front tracking approach constrained by the incompressibility condition. This research is aimed at designing and implementing these algorithms. We demonstrate verification and convergence results for one-phase and unmixed, two-phase flows. In addition we report on preliminary results for mixed, two-phase flow for realistic operating flow parameters.

  6. Statistical Mechanics of the Geometric Control of Flow Topology in Two-Dimensional Turbulence

    Science.gov (United States)

    Nadiga, Balasubramanya; Loxley, Peter

    2013-04-01

    We apply the principle of maximum entropy to two dimensional turbulence in a new fashion to predict the effect of geometry on flow topology. We consider two prototypical regimes of turbulence that lead to frequently observed self-organized coherent structures. Our theory predicts bistable behavior that exhibits hysteresis and large abrupt changes in flow topology in one regime; the other regime is predicted to exhibit monstable behavior with a continuous change of flow topology. The predictions are confirmed in fully nonlinear numerical simulations of the two-dimensional Navier-Stokes equation. These results suggest an explanation of the low frequency regime transitions that have been observed in the non-equilibrium setting of this problem. Following further development in the non-equilibrium context, we expect that insights developed in this problem should be useful in developing a better understanding of the phenomenon of low frequency regime transitions that is a pervasive feature of the weather and climate systems. Familiar occurrences of this phenomenon---wherein extreme and abrupt qualitative changes occur, seemingly randomly, after very long periods of apparent stability---include blocking in the extra-tropical winter atmosphere, the bimodality of the Kuroshio extension system, the Dansgaard-Oeschger events, and the glacial-interglacial transitions.

  7. Alignment dynamics of diffusive scalar gradient in a two-dimensional model flow

    Science.gov (United States)

    Gonzalez, M.

    2018-04-01

    The Lagrangian two-dimensional approach of scalar gradient kinematics is revisited accounting for molecular diffusion. Numerical simulations are performed in an analytic, parameterized model flow, which enables considering different regimes of scalar gradient dynamics. Attention is especially focused on the influence of molecular diffusion on Lagrangian statistical orientations and on the dynamics of scalar gradient alignment.

  8. Analysis of one-dimensional nonequilibrium two-phase flow using control volume method

    International Nuclear Information System (INIS)

    Minato, Akihiko; Naitoh, Masanori

    1987-01-01

    A one-dimensional numerical analysis model was developed for prediction of rapid flow transient behavior involving boiling. This model was based on six conservation equations of time averaged parameters of gas and liquid behavior. These equations were solved by using a control volume method with an explicit time integration. This model did not use staggered mesh scheme, which had been commonly used in two-phase flow analysis. Because void fraction and velocity of each phase were defined at the same location in the present model, effects of void fraction on phase velocity calculation were treated directly without interpolation. Though non-staggered mesh scheme was liable to cause numerical instability with zigzag pressure field, stability was achieved by employing the Godunov method. In order to verify the present analytical model, Edwards' pipe blow down and Zaloudek's initially subcooled critical two-phase flow experiments were analyzed. Stable solutions were obtained for rarefaction wave propagation with boiling and transient two-phase flow behavior in a broken pipe by using this model. (author)

  9. Numerical method for three dimensional steady-state two-phase flow calculations

    International Nuclear Information System (INIS)

    Raymond, P.; Toumi, I.

    1992-01-01

    This paper presents the numerical scheme which was developed for the FLICA-4 computer code to calculate three dimensional steady state two phase flows. This computer code is devoted to steady state and transient thermal hydraulics analysis of nuclear reactor cores 1,3 . The first section briefly describes the FLICA-4 flow modelling. Then in order to introduce the numerical method for steady state computations, some details are given about the implicit numerical scheme based upon an approximate Riemann solver which was developed for calculation of flow transients. The third section deals with the numerical method for steady state computations, which is derived from this previous general scheme and its optimization. We give some numerical results for steady state calculations and comparisons on required CPU time and memory for various meshing and linear system solvers

  10. Numerical prediction of turbulent heat transfer augmentation in an annular fuel channel with two-dimensional square ribs

    International Nuclear Information System (INIS)

    Takase, Kazuyuki

    1996-01-01

    The square-ribbed fuel rod for high temperature gas-cooled reactors was developed in order to enhance the turbulent heat transfer in comparison with the standard fuel rod. To evaluate the heat transfer performance of the square-ribbed fuel rod, the turbulent heat transfer coefficients in an annular fuel channel with repeated two-dimensional square ribs were analyzed numerically on a fully developed incompressible flow using the k - ε turbulence model and the two-dimensional axisymmetrical coordinate system. Numerical analyses were carried out for a range of Reynolds numbers from 3000 to 20000 and ratios of square-rib pitch to height of 10, 20 and 40, respectively. The predicted values of the heat transfer coefficients agreed within an error of 10% for the square-rib pitch to height ratio of 10, 20% for 20 and 25% for 40, respectively, with the heat transfer empirical correlations obtained from the experimental data. It was concluded by the present study that the effect of the heat transfer augmentation by square ribs could be predicted sufficiently by the present numerical simulations and also a part of its mechanism could be explained by means of the change in the turbulence kinematic energy distribution along the flow direction. (author)

  11. Computational study of three-dimensional wake structure

    International Nuclear Information System (INIS)

    Himeno, R.; Shirayama, S.; Kamo, K.; Kuwahara, K.

    1986-01-01

    Three-dimensional wake structure is studied by numerically solving the incompressible Navier-Stokes equations. Results are visualized by a three-dimensional color graphic system. It was found that a pair of vortex tubes separated from a body plays the most important role in the wake. Near the body vortex tubes are rather stable, however, they gradually become unsteady as they flow down

  12. A Numerical Scheme Based on an Immersed Boundary Method for Compressible Turbulent Flows with Shocks: Application to Two-Dimensional Flows around Cylinders

    Directory of Open Access Journals (Sweden)

    Shun Takahashi

    2014-01-01

    Full Text Available A computational code adopting immersed boundary methods for compressible gas-particle multiphase turbulent flows is developed and validated through two-dimensional numerical experiments. The turbulent flow region is modeled by a second-order pseudo skew-symmetric form with minimum dissipation, while the monotone upstream-centered scheme for conservation laws (MUSCL scheme is employed in the shock region. The present scheme is applied to the flow around a two-dimensional cylinder under various freestream Mach numbers. Compared with the original MUSCL scheme, the minimum dissipation enabled by the pseudo skew-symmetric form significantly improves the resolution of the vortex generated in the wake while retaining the shock capturing ability. In addition, the resulting aerodynamic force is significantly improved. Also, the present scheme is successfully applied to moving two-cylinder problems.

  13. Unsteady Flow in a Horizontal Double-Sided Symmetric Thin Liquid Films

    Directory of Open Access Journals (Sweden)

    Joseph G. ABDULAHAD

    2017-06-01

    Full Text Available In this paper a mathematical model is constructed to describe a two dimensional incompressible flow in a symmetric horizontal thin liquid film for unsteadies flow. We apply the Navier-Stokes equations with specified boundary conditions and we obtain the equation of the film thickness by using the similarity method in which we can isolate the explicit time dependence and then the shape of the film will depend on one variable only.

  14. Finite element methods for viscous incompressible flows a guide to theory, practice, and algorithms

    CERN Document Server

    Gunzburger, Max D

    2012-01-01

    In this book, the author examines mathematical aspects of finite element methods for the approximate solution of incompressible flow problems. The principal goal is to present some of the important mathematical results that are relevant to practical computations. In so doing, useful algorithms are also discussed. Although rigorous results are stated, no detailed proofs are supplied; rather, the intention is to present these results so that they can serve as a guide for the selection and, in certain respects, the implementation of algorithms.

  15. NUMERICAL SIMULATION OF FLOW OVER TWO-DIMENSIONAL MOUNTAIN RIDGE USING SIMPLE ISENTROPIC MODEL

    Directory of Open Access Journals (Sweden)

    Siswanto Siswanto

    2009-07-01

    Full Text Available Model sederhana isentropis telah diaplikasikan untuk mengidentifikasi perilaku aliran masa udara melewati topografi sebuah gunung. Dalam model isentropis, temperature potensial θ digunakan sebagai koordinat vertikal dalam rezim aliran adiabatis. Medan angin dalam arah vertikal dihilangkan dalam koordinat isentropis sehingga mereduksi sistim tiga dimensi menjadi sistim dua dimensi lapisan θ. Skema komputasi beda hingga tengah telah digunakan untuk memformulasikan model adveksi. Paper ini membahas aplikasi sederhana dari model isentropis untuk mempelajari gelombang gravitasi dan fenomena angin gunung  dengan desain komputasi periodik dan kondisi batas lateral serta simulasi dengan topografi yang berbeda.   The aim of this work is to study turbulent flow over two-dimensional hill using a simple isentropic model. The isentropic model is represented by applying the potential temperature θ, as the vertical coordinate and is conversed in adiabatic flow regimes. This implies a vanishing vertical wind in isentropic coordinates which reduces the three dimensional system to a stack of two dimensional θ–layers. The equations for each isentropic layer are formally identical with the shallow water equation. A computational scheme of centered finite differences is used to formulate an advective model. This work reviews a simple isentropic model application to investigate gravity wave and mountain wave phenomena regard to different experimental design of computation and topographic height.

  16. Determination of the nuclear incompressibility from the rapidity-dependent elliptic flow in heavy-ion collisions at beam energies 0.4A–1.0A GeV

    Directory of Open Access Journals (Sweden)

    Yongjia Wang

    2018-03-01

    Full Text Available Background: The nuclear incompressibility (K0 plays a crucial role in understanding diverse phenomena in nuclear structure and reactions, as well as in astrophysics. Heavy-ion-collision measurements in combination with transport model simulations serve as important tools for extracting the nuclear incompressibility. However, uncertainties in transport models (or model dependence partly affect the reliability of the extracted result. Purpose: In the present work, by using the recently measured data of rapidity-dependent flows, we constrain the incompressibility of nuclear matter and analyze the impact of model uncertainties on the obtained value. Method: The method is based on the newly updated version of the ultrarelativistic quantum molecular dynamics (UrQMD model in which the Skyrme potential energy-density functional is introduced. Three different Skyrme interactions which give different incompressibilities varying from K0=201 to 271 MeV are adopted. The incompressibility is deduced from the comparison of the UrQMD model simulations and the FOPI data for rapidity-dependent elliptic flow in Au+Au collisions at beam energies 0.4A–1.0A GeV. Results: The elliptic flow v2 as a function of rapidity y0 can be well described by a quadratic fit v2=v20+v22⋅y02. It is found that the quantity v2n defined by v2n=|v20|+|v22| is quite sensitive to the incompressibility K0 and the in-medium nucleon–nucleon cross section, but not sensitive to the slope parameter L of the nuclear symmetry energy. Conclusions: With the FU3FP4 parametrization of the in-medium nucleon–nucleon cross section, an averaged K0=220±40 MeV is extracted from the v2n of free protons and deuterons. However, remaining systematic uncertainties, partly related to the choice of in-medium nucleon–nucleon cross sections, are of the same magnitude (±40 MeV. Overall, the rapidity dependent elliptic flow supports a soft symmetric-matter equation-of-state.

  17. Determination of the nuclear incompressibility from the rapidity-dependent elliptic flow in heavy-ion collisions at beam energies 0.4A-1.0A GeV

    Science.gov (United States)

    Wang, Yongjia; Guo, Chenchen; Li, Qingfeng; Le Fèvre, Arnaud; Leifels, Yvonne; Trautmann, Wolfgang

    2018-03-01

    Background: The nuclear incompressibility (K0) plays a crucial role in understanding diverse phenomena in nuclear structure and reactions, as well as in astrophysics. Heavy-ion-collision measurements in combination with transport model simulations serve as important tools for extracting the nuclear incompressibility. However, uncertainties in transport models (or model dependence) partly affect the reliability of the extracted result. Purpose: In the present work, by using the recently measured data of rapidity-dependent flows, we constrain the incompressibility of nuclear matter and analyze the impact of model uncertainties on the obtained value. Method: The method is based on the newly updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model in which the Skyrme potential energy-density functional is introduced. Three different Skyrme interactions which give different incompressibilities varying from K0 = 201 to 271 MeV are adopted. The incompressibility is deduced from the comparison of the UrQMD model simulations and the FOPI data for rapidity-dependent elliptic flow in Au + Au collisions at beam energies 0.4A-1.0A GeV. Results: The elliptic flow v2 as a function of rapidity y0 can be well described by a quadratic fit v2 =v20 +v22 ṡ y02 . It is found that the quantity v2n defined by v2n = |v20 | + |v22 | is quite sensitive to the incompressibility K0 and the in-medium nucleon-nucleon cross section, but not sensitive to the slope parameter L of the nuclear symmetry energy. Conclusions: With the FU3FP4 parametrization of the in-medium nucleon-nucleon cross section, an averaged K0 = 220 ± 40 MeV is extracted from the v2n of free protons and deuterons. However, remaining systematic uncertainties, partly related to the choice of in-medium nucleon-nucleon cross sections, are of the same magnitude (± 40 MeV). Overall, the rapidity dependent elliptic flow supports a soft symmetric-matter equation-of-state.

  18. Tensor formulation of the model equations on strong conservation form for an incompressible flow in general coordinates

    DEFF Research Database (Denmark)

    Jørgensen, Bo Hoffmann

    2003-01-01

    This brief report expresses the basic equations of an incompressible flow model in a form which can be translated easily into the form used by a numerical solver. The application of tensor notation makes is possible to effectively address the issue ofnumerical robustness and stating the model...... equations on a general form which accommodate curvilinear coordinates. Strong conservation form is obtained by formulating the equations so that the flow variables, velocity and pressure, are expressed in thephysical coordinate system while the location of evaluation is expressed within the transformed...... form of the equations is included which allows for special solutions to be developed in the transformedcoordinate system. Examples of applications are atmospheric flows over complex terrain, aerodynamically flows, industrial flows and environmental flows....

  19. INCOMPRESSIBLE LAMINAR BOUNDARY LAYER CONTROL BY BLOWING AND SUCTION

    OpenAIRE

    AZZEDINE NAHOUI; LAKHDAR BAHI

    2013-01-01

    A two-dimensional incompressible laminar boundary layer and its control using blowing and suction over a flat plate and around the NACA 0012 and 661012 profiles, is studied numerically. The study is based on the Prandtl boundary layer model using the finite differences method and the Crank-Nicolson scheme. The velocity distribution, the boundary layer thickness and the friction coefficient, are determined and presented with and without control. The application of the control technique, has de...

  20. A Finite Element Method for Free-Surface Flows of Incompressible Fluids in Three Dimensions, Part II: Dynamic Wetting Lines

    Energy Technology Data Exchange (ETDEWEB)

    Baer, T.A.; Cairncross, R.A.; Rao, R.R.; Sackinger, P.A.; Schunk, P.R.

    1999-01-29

    To date, few researchers have solved three-dimensional free-surface problems with dynamic wetting lines. This paper extends the free-surface finite element method described in a companion paper [Cairncross, R.A., P.R. Schunk, T.A. Baer, P.A. Sackinger, R.R. Rao, "A finite element method for free surface flows of incompressible fluid in three dimensions, Part I: Boundary-Fitted mesh motion.", to be published (1998)] to handle dynamic wetting. A generalization of the technique used in two dimensional modeling to circumvent double-valued velocities at the wetting line, the so-called kinematic paradox, is presented for a wetting line in three dimensions. This approach requires the fluid velocity normal to the contact line to be zero, the fluid velocity tangent to the contact line to be equal to the tangential component of web velocity, and the fluid velocity into the web to be zero. In addition, slip is allowed in a narrow strip along the substrate surface near the dynamic contact line. For realistic wetting-line motion, a contact angle which varies with wetting speed is required because contact lines in three dimensions typically advance or recede a different rates depending upon location and/or have both advancing and receding portions. The theory is applied to capillary rise of static fluid in a corner, the initial motion of a Newtonian droplet down an inclined plane, and extrusion of a Newtonian fluid from a nozzle onto a moving substrate. The extrusion results are compared to experimental visualization. Subject Categories

  1. Time-asymptotic interaction of flocking particles and an incompressible viscous fluid

    International Nuclear Information System (INIS)

    Bae, Hyeong-Ohk; Choi, Young-Pil; Ha, Seung-Yeal; Kang, Moon-Jin

    2012-01-01

    We present a new coupled kinetic-fluid model for the interactions between Cucker–Smale (C–S) flocking particles and incompressible fluid on the periodic spatial domain T d . Our coupled system consists of the kinetic C–S equation and the incompressible Navier–Stokes equations, and these two systems are coupled through the drag force. For the proposed model, we provide a global existence of weak solutions and a priori time-asymptotic exponential flocking estimates for any smooth flow, when the kinematic viscosity of the fluid is sufficiently large. The velocity of individual C–S particles and fluid velocity tend to the averaged time-dependent particle velocities exponentially fast

  2. Complex variable boundary elements for fluid flow; Robni elementi kompleksne spremenljivke za pretok fluidov

    Energy Technology Data Exchange (ETDEWEB)

    Bizjak, D; Alujevic, A [Institut ' Jozef Stefan' , Ljubljana (Yugoslavia)

    1988-07-01

    The Complex Variable Boundary Element Method is a numerical method for solving two-dimensional problems of Laplace or Poisson type. It is based on the theory of analytic functions. This paper resumes the basic facts about the method. Application of the method to the stationary incompressible irrotational flow is carried out after that. At the end, a sample problem of flow through an abrupt area change channel is shown. (author)

  3. Multi-dimensional two-phase flow measurements in a large-diameter pipe using wire-mesh sensor

    International Nuclear Information System (INIS)

    Kanai, Taizo; Furuya, Masahiro; Arai, Takahiro; Shirakawa, Kenetsu; Nishi, Yoshihisa; Ueda, Nobuyuki

    2011-01-01

    The authors developed a method of measurement to determine the multi-dimensionality of two phase flow. A wire-mesh sensor (WMS) can acquire a void fraction distribution at a high temporal and spatial resolution and also estimate the velocity of a vertical rising flow by investigating the signal time-delay of the upstream WMS relative to downstream. Previously, one-dimensional velocity was estimated by using the same point of each WMS at a temporal resolution of 1.0 - 5.0 s. The authors propose to extend this time series analysis to estimate the multi-dimensional velocity profile via cross-correlation analysis between a point of upstream WMS and multiple points downstream. Bubbles behave in various ways according to size, which is used to classify them into certain groups via wavelet analysis before cross-correlation analysis. This method was verified by air-water straight and swirl flows within a large-diameter vertical pipe. A high-speed camera is used to set the parameter of cross-correlation analysis. The results revealed that for the rising straight and swirl flows, large scale bubbles tend to move to the center, while the small bubble is pushed to the outside or sucked into the space where the large bubbles existed. Moreover, it is found that this method can estimate the rotational component of velocity of the swirl flow as well as measuring the multi-dimensional velocity vector at high temporal resolutions of 0.2 s. (author)

  4. Aeroacoustic modelling of low-speed flows

    Energy Technology Data Exchange (ETDEWEB)

    Wen Zhong Shen; Noerkaer Soerensen, Jens

    1998-08-01

    A new numerical algorithm for acoustic noise generation is developed. The approach involves two steps comprising an incompressible flow part and inviscid acoustic part. The acoustic part can be started at any time of the incompressible computation. The formulation can be applied both for isentropic flows and non-isentropic flows. The model is validated for the cases of an isentropic pulsating sphere and non-isentropic flows past a circular cylinder and a NACA 0015 airfoil. The computations show that the generated acoustic frequencies have the form 1/m of the basic frequency of incompressible flow. (au) 15 refs.

  5. A large-scale layered stationary convection of a incompressible viscous fluid under the action of shear stresses at the upper boundary. Temperature and presure field investigation

    Directory of Open Access Journals (Sweden)

    Natal'ya V. Burmasheva

    2017-12-01

    Full Text Available In this paper a new exact solution of an overdetermined system of Oberbeck–Boussinesq equations that describes a stationary shear flow of a viscous incompressible fluid in an infinite layer is under study. The given exact solution is a generalization of the Ostroumov–Birich class for a layered unidirectional flow. In the proposed solution, the horizontal velocities depend only on the transverse coordinate z. The temperature field and the pressure field are three-dimensional. In contradistinction to the Ostroumov–Birich solution, in the solution presented in the paper the horizontal temperature gradients are linear functions of the $z$ coordinate. This structure of the exact solution allows us to find a nontrivial solution of the Oberbeck–Boussinesq equations by means of the identity zero of the incompressibility equation. This exact solution is suitable for investigating large-scale flows of a viscous incompressible fluid by quasi-two-dimensional equations. Convective fluid motion is caused by the setting of tangential stresses on the free boundary of the layer. Inhomogeneous thermal sources are given on both boundaries. The pressure in the fluid at the upper boundary coincides with the atmospheric pressure. The paper focuses on the study of temperature and pressure fields, which are described by polynomials of three variables. The features of the distribution of the temperature and pressure profiles, which are polynomials of the seventh and eighth degree, respectively, are discussed in detail. To analyze the properties of temperature and pressure, algebraic methods are used to study the number of roots on a segment. It is shown that the background temperature and the background pressure are nonmonotonic functions. The temperature field is stratified into zones that form the thermocline and the thermal boundary layer near the boundaries of the fluid layer. Investigation of the properties of the pressure field showed that it is stratified

  6. Flow and Jamming of Granular Materials in a Two-dimensional Hopper

    Science.gov (United States)

    Tang, Junyao

    Flow in a hopper is both a fertile testing ground for understanding fundamental granular flow rheology and industrially highly relevant. Despite increasing research efforts in this area, a comprehensive physical theory is still lacking for both jamming and flow of granular materials in a hopper. In this work, I have designed a two dimensional (2D) hopper experiment using photoelastic particles (particles' shape: disk or ellipse), with the goal to build a bridge between macroscopic phenomenon of hopper flow and microscopic particle-scale dynamics. Through synchronized data of particle tracking and stress distributions in particles, I have shown differences between my data of the time-averaged velocity/stress profile of 2D hopper flow with previous theoretical predictions. I have also demonstrated the importance of a mechanical stable arch near the opening on controlling hopper flow rheology and suggested a heuristic phase diagram for the hopper flow/jamming transition. Another part of this thesis work is focused on studying the impact of particle shape of particles on hopper flow. By comparing particle-tracking and photoelastic data for ellipses and disks at the appropriate length scale, I have demonstrated an important role for the rotational freedom of elliptical particles in controlling flow rheology through particle tracking and stress analysis. This work has been supported by International Fine Particle Research Institute (IFPRI) .

  7. Three-dimensional visualization of material flow during friction stir welding by two pairs of X-ray transmission systems

    International Nuclear Information System (INIS)

    Morisada, Y.; Fujii, H.; Kawahito, Y.; Nakata, K.; Tanaka, M.

    2011-01-01

    Material flow during friction stir welding is crucial to obtaining sound joints. However, this phenomenon is still not fully understood despite many investigations and numerous models. In this study, the material flow is three-dimensionally visualized by X-ray radiography using a tiny spherical tungsten tracer. The movement of the tracer during the friction stir welding is observed by two pairs of X-ray transmission real-time imaging systems. The three-dimensional material flow is obtained by following the locus of the tracer.

  8. Direct calibration framework of triple-hole pressure probes for incompressible flow

    International Nuclear Information System (INIS)

    Díaz, K M Argüelles; Oro, J M Fernández; Marigorta, E Blanco

    2008-01-01

    This paper carries out a mathematical analysis of the limits and data reduction techniques of three-hole pressure (THP) probes operating in a 'non-nulling' mode for incompressible flow. As a result of this analysis, a direct procedure is advanced, based on the distinction of several zones within the angular range, where different relations can be applied to obtain the flow variables. This proposal provides a considerable increment of the operative angular range of THP probes: about ±70° instead of the typical ±35° for a cylindrical probe. This may extend the application of these probes in highly unsteady flows, or reduce the acquisition and data reduction effort minimizing the necessity of probe reorientation. The influence of the data reduction technique on the uncertainty transmission is also presented in the paper. From detailed considerations, it is demonstrated that the results uncertainty depends on the specific probe, but it is unaffected by the mathematical procedure employed to calculate the flow variables. Validation measurements with pneumatic probes have been made for Reynolds numbers from 4 × 10 3 to 3.5 × 10 4 . In addition, a highly unsteady measurement in a low-speed axial flow fan is succinctly analysed. Taking into account both attainable angular range and uncertainty, it is determined that the optimal construction angle for the holes of a low frequency response THP probe lies between 30° and 60°, while for fast response probes, in order to avoid the separated flow region, the optimal construction angle is around 30°

  9. Development of tearing instability in a current sheet forming by sheared incompressible flow

    Science.gov (United States)

    Tolman, Elizabeth A.; Loureiro, Nuno F.; Uzdensky, Dmitri A.

    2018-02-01

    Sweet-Parker current sheets in high Lundquist number plasmas are unstable to tearing, suggesting they will not form in physical systems. Understanding magnetic reconnection thus requires study of the stability of a current sheet as it forms. Formation can occur due to sheared, sub-Alfvénic incompressible flows which narrow the sheet. Standard tearing theory (Furth et al. Phys. Fluids, vol. 6 (4), 1963, pp. 459-484, Rutherford, Phys. Fluids, vol. 16 (11), 1973, pp. 1903-1908, Coppi et al. Fizika Plazmy, vol. 2, 1976, pp. 961-966) is not immediately applicable to such forming sheets for two reasons: first, because the flow introduces terms not present in the standard calculation; second, because the changing equilibrium introduces time dependence to terms which are constant in the standard calculation, complicating the formulation of an eigenvalue problem. This paper adapts standard tearing mode analysis to confront these challenges. In an initial phase when any perturbations are primarily governed by ideal magnetohydrodynamics, a coordinate transformation reveals that the flow compresses and stretches perturbations. A multiple scale formulation describes how linear tearing mode theory (Furth et al. Phys. Fluids, vol. 6 (4), 1963, pp. 459-484, Coppi et al. Fizika Plazmy, vol. 2, 1976, pp. 961-966) can be applied to an equilibrium changing under flow, showing that the flow affects the separable exponential growth only implicitly, by making the standard scalings time dependent. In the nonlinear Rutherford stage, the coordinate transformation shows that standard theory can be adapted by adding to the stationary rates time dependence and an additional term due to the strengthening equilibrium magnetic field. Overall, this understanding supports the use of flow-free scalings with slight modifications to study tearing in a forming sheet.

  10. Self-oscillations of a two-dimensional shear flow with forcing and dissipation

    Science.gov (United States)

    López Zazueta, A.; Zavala Sansón, L.

    2018-04-01

    Two-dimensional shear flows continuously forced in the presence of dissipative effects are studied by means of numerical simulations. In contrast with most previous studies, the forcing is confined in a finite region, so the behavior of the system is characterized by the long-term evolution of the global kinetic energy. We consider regimes with 1 limited to develop only one vortical instability by choosing an appropriate width of the forcing band. The most relevant regime is found for Reλ > 36, in which the energy maintains a regular oscillation around a reference value. The flow configuration is an elliptical vortex tilted with respect to the forcing axis, which oscillates steadily also. Second, the flow is allowed to develop two Kelvin-Helmholtz billows and eventually more complicated structures. The regimes of the one-vortex case are observed again, except for Reλ > 135. At these values, the energy oscillates chaotically as the two vortices merge, form dipolar structures, and split again, with irregular periodicity. The self-oscillations are explained as a result of the alternate competition between forcing and dissipation, which is verified by calculating the budget terms in the energy equation. The relevance of the forcing-vs.-dissipation competition is discussed for more general flow systems.

  11. STRUYA a code for two-dimensional fluid flow analysis with and without structure coupling

    International Nuclear Information System (INIS)

    Katz, F.W.; Schlechtendahl, E.G.; Stoelting, K.

    1979-11-01

    STRUYA is a code for two-dimensional subsonic and supersonic flow analysis. Both Eulerian and Lagrangian grids are allowed. In the third dimension the flow domain may be bounded by a moving wall. The wall movement may be prescribed in a time-and space varying way or computed by a structural model. STRUYA offers a general scheme for adapting various structural models. As a standard feature it includes a cylindrical shell model (CYLDY2). (orig.) [de

  12. Two-dimensional numerical experiments with DRIX-2D on two-phase-water-flows referring to the HDR-blowdown-experiments

    International Nuclear Information System (INIS)

    Moesinger, H.

    1979-08-01

    The computer program DRIX-2D has been developed from SOLA-DF. The essential elements of the program structure are described. In order to verify DRIX-2D an Edwards-Blowdown-Experiment is calculated and other numerical results are compared with steady state experiments and models. Numerical experiments on transient two-phase flow, occurring in the broken pipe of a PWR in the case of a hypothetic LOCA, are performed. The essential results of the two-dimensional calculations are: 1. The appearance of a radial profile of void-fraction, velocity, sound speed and mass flow-rate inside the blowdown nozzle. The reason for this is the flow contraction at the nozzle inlet leading to more vapour production in the vicinity of the pipe wall. 2. A comparison between modelling in axisymmetric and Cartesian coordinates and calculations with and without the core barrel show the following: a) The three-dimensional flow pattern at the nozzle inlet is poorly described using Cartesian coordinates. In consequence a considerable difference in pressure history results. b) The core barrel alters the reflection behaviour of the pressure waves oscillating in the blowdown-nozzle. Therefore, the core barrel should be modelled as a wall normal to the nozzle axis. (orig./HP) [de

  13. Final accepted paper. Effects of turbulence near a free surface on the dynamics of two-phase flow

    International Nuclear Information System (INIS)

    Uzawa, Ken; Watanabe, Tadashi

    2011-01-01

    The effect of turbulence on the dynamics of three-dimensional dam break flow is numerically investigated based on the incompressible Reynolds-averaged Navier- Stokes (RANS) equations with the Volume Of Fluid (VOF) function. It is found that the tip velocity over the ground and the impact pressure against the vertical wall in the Launder- Gibson (LG) model are in good agreement with experimental results. The dynamics of the dam break flow is subject to the viscous dissipation during the collapse of the flow, which is underestimated in the laminar model and overestimated in the realizable k - ε (RKE) model. The turbulent viscous dissipation near the free surface is comparable to that inside the water in the LG model. (author)

  14. Hermite-Pade approximation approach to hydromagnetic flows in convergent-divergent channels

    International Nuclear Information System (INIS)

    Makinde, O.D.

    2005-10-01

    The problem of two-dimensional, steady, nonlinear flow of an incompressible conducting viscous fluid in convergent-divergent channels under the influence of an externally applied homogeneous magnetic field is studied using a special type of Hermite-Pade approximation approach. This semi-numerical scheme offers some advantages over solutions obtained by using traditional methods such as finite differences, spectral method, shooting method, etc. It reveals the analytical structure of the solution function and the important properties of overall flow structure including velocity field, flow reversal control and bifurcations are discussed. (author)

  15. LLUVIA-II: A program for two-dimensional, transient flow through partially saturated porous media

    International Nuclear Information System (INIS)

    Eaton, R.R.; Hopkins, P.L.

    1992-08-01

    LLUVIA-II is a program designed for the efficient solution of two- dimensional transient flow of liquid water through partially saturated, porous media. The code solves Richards equation using the method-of-lines procedure. This document describes the solution procedure employed, input data structure, output, and code verification

  16. Exact partial solution to the compressible flow problems of jet formation and penetration in plane, steady flow

    International Nuclear Information System (INIS)

    Karpp, R.R.

    1984-01-01

    The particle solution of the problem of the symmetric impact of two compressible fluid stream is derived. The plane two-dimensional flow is assumed to be steady, and the inviscid compressible fluid is of the Chaplygin (tangent gas) type. The equations governing this flow are transformed to the hodograph plane where an exact, closed-form solution for the stream function is obtained. The distribution of fluid properties along the plane of symmetry and the shape of free surface streamlines are determined by transformation back to the physical plane. The problem of a compressible fluid jet penetrating an infinite target of similar material is also solved by considering a limiting case of this solution. Differences between compressible and incompressible flows of the type considered are illustrated

  17. Flow past a rotating cylinder

    Science.gov (United States)

    Mittal, Sanjay; Kumar, Bhaskar

    2003-02-01

    Flow past a spinning circular cylinder placed in a uniform stream is investigated via two-dimensional computations. A stabilized finite element method is utilized to solve the incompressible Navier Stokes equations in the primitive variables formulation. The Reynolds number based on the cylinder diameter and free-stream speed of the flow is 200. The non-dimensional rotation rate, [alpha] (ratio of the surface speed and freestream speed), is varied between 0 and 5. The time integration of the flow equations is carried out for very large dimensionless time. Vortex shedding is observed for [alpha] cylinder. The results from the stability analysis for the rotating cylinder are in very good agreement with those from direct numerical simulations. For large rotation rates, very large lift coefficients can be obtained via the Magnus effect. However, the power requirement for rotating the cylinder increases rapidly with rotation rate.

  18. On PDE analysis of flows of quasi-incompressible fluids

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Lu, Y.; Málek, J.

    2016-01-01

    Roč. 96, č. 4 (2016), s. 491-508 ISSN 0044-2267 Keywords : quasi-incompressible fluids * weak solution Subject RIV: BA - General Mathematics Impact factor: 1.332, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/zamm.201400229

  19. Pressure drop calculation using a one-dimensional mathematical model for two-phase flow through an orifice

    DEFF Research Database (Denmark)

    Petkov, K.P.; Puton, M; Madsen, Søren Peder

    2014-01-01

    are accounted for through both friction and acceleration as in a conventional formulation. However, in this analysis the acceleration term is both attributed geometrical effects through the area change and fluid dynamic effects through the expansion of the two-phase flow. The comparison of numerical...... is a one dimensional formulation in space and the equations incorporates the change in tubes and orifice diameter as formulated in (S. Madsen et.al., Dynamic Modeling of Phase Crossings in Two-Phase Flow, Communications in Computational Physics 12 (4), 1129-1147). The pressure changes in the flow...

  20. Unsteady flow of an incompressible fluid in a horizontal porous medium with suction

    International Nuclear Information System (INIS)

    Bestman, A.R.

    1988-04-01

    A theoretical analysis of two-dimensional unsteady flow in a porous medium bounded by a horizontal wall is presented as a perturbation on a basic flow. It is assumed that the perturbation is occasioned by a sudden suction at the wall. Even for a highly permeable medium the characteristic Reynolds number in porous media flow is usually small and asymptotic solutions are developed by the Laplace transform technique. It is observed that the perturbed shear stress at the wall decays exponentially with time. (author). 5 refs

  1. Existence and Stability of Spatial Plane Waves for the Incompressible Navier-Stokes in R^3

    Science.gov (United States)

    Correia, Simão; Figueira, Mário

    2018-03-01

    We consider the three-dimensional incompressible Navier-Stokes equation on the whole space. We observe that this system admits a L^∞ family of global spatial plane wave solutions, which are connected with the two-dimensional equation. We then proceed to prove local well-posedness over a space which includes L^3(R^3) and these solutions. Finally, we prove L^3-stability of spatial plane waves, with no condition on their size.

  2. Flow and Heat Transfer Characteristics of Turbulent Gas Flow in Microtube with Constant Heat Flux

    International Nuclear Information System (INIS)

    Hong, Chungpyo; Matsushita, Shinichi; Ueno, Ichiro; Asako, Yutaka

    2012-01-01

    Local friction factors for turbulent gas flows in circular microtubes with constant wall heat flux were obtained numerically. The numerical methodology is based on arbitrary-Lagrangian-Eulerian method to solve two-dimensional compressible momentum and energy equations. The Lam-Bremhorst's Low-Reynolds number turbulence model was employed to calculate eddy viscosity coefficient and turbulence energy. The simulations were performed for a wide flow range of Reynolds numbers and Mach numbers with different constant wall heat fluxes. The stagnation pressure was chosen in such a way that the outlet Mach number ranged from 0.07 to 1.0. Both Darcy friction factor and Fanning friction factor were locally obtained. The result shows that the obtained both friction factors were evaluated as a function of Reynolds number on the Moody chart. The values of Darcy friction factor differ from Blasius correlation due to the compressibility effects but the values of Fanning friction factor almost coincide with Blasius correlation. The wall heat flux varied from 100 to 10000 W/m 2 . The wall and bulk temperatures with positive heat flux are compared with those of incompressible flow. The result shows that the Nusselt number of turbulent gas flow is different from that of incompressible flow.

  3. Multigrid solution of incompressible turbulent flows by using two-equation turbulence models

    Energy Technology Data Exchange (ETDEWEB)

    Zheng, X.; Liu, C. [Front Range Scientific Computations, Inc., Denver, CO (United States); Sung, C.H. [David Taylor Model Basin, Bethesda, MD (United States)

    1996-12-31

    Most of practical flows are turbulent. From the interest of engineering applications, simulation of realistic flows is usually done through solution of Reynolds-averaged Navier-Stokes equations and turbulence model equations. It has been widely accepted that turbulence modeling plays a very important role in numerical simulation of practical flow problem, particularly when the accuracy is of great concern. Among the most used turbulence models today, two-equation models appear to be favored for the reason that they are more general than algebraic models and affordable with current available computer resources. However, investigators using two-equation models seem to have been more concerned with the solution of N-S equations. Less attention is paid to the solution method for the turbulence model equations. In most cases, the turbulence model equations are loosely coupled with N-S equations, multigrid acceleration is only applied to the solution of N-S equations due to perhaps the fact the turbulence model equations are source-term dominant and very stiff in sublayer region.

  4. Simulation of incompressible flows with heat and mass transfer using parallel finite element method

    Directory of Open Access Journals (Sweden)

    Jalal Abedi

    2003-02-01

    Full Text Available The stabilized finite element formulations based on the SUPG (Stream-line-Upwind/Petrov-Galerkin and PSPG (Pressure-Stabilization/Petrov-Galerkin methods are developed and applied to solve buoyancy-driven incompressible flows with heat and mass transfer. The SUPG stabilization term allows us to solve flow problems at high speeds (advection dominant flows and the PSPG term eliminates instabilities associated with the use of equal order interpolation functions for both pressure and velocity. The finite element formulations are implemented in parallel using MPI. In parallel computations, the finite element mesh is partitioned into contiguous subdomains using METIS, which are then assigned to individual processors. To ensure a balanced load, the number of elements assigned to each processor is approximately equal. To solve nonlinear systems in large-scale applications, we developed a matrix-free GMRES iterative solver. Here we totally eliminate a need to form any matrices, even at the element levels. To measure the accuracy of the method, we solve 2D and 3D example of natural convection flows at moderate to high Rayleigh numbers.

  5. An efficient implicit direct forcing immersed boundary method for incompressible flows

    International Nuclear Information System (INIS)

    Cai, S-G; Ouahsine, A; Smaoui, H; Favier, J; Hoarau, Y

    2015-01-01

    A novel efficient implicit direct forcing immersed boundary method for incompressible flows with complex boundaries is presented. In the previous work [1], the calculation is performed on the Cartesian grid regardless of the immersed object, with a fictitious force evaluated on the Lagrangian points to mimic the presence of the physical boundaries. However the explicit direct forcing method [1] fails to accurately impose the non-slip boundary condition on the immersed interface. In the present work, the calculation is based on the implicit treatment of the artificial force while in an effective way of system iteration. The accuracy is also improved by solving the Navier-Stokes equation with the rotational incremental pressure- correction projection method of Guermond and Shen [2]. Numerical simulations performed with the proposed method are in good agreement with those in the literature

  6. Triple-porosity/permeability flow in faulted geothermal reservoirs: Two-dimensional effects

    Energy Technology Data Exchange (ETDEWEB)

    Cesar Suarez Arriaga, M. [Michoacan Univ. & CFE, Mich. (Mexico); Samaniego Verduzco, F. [National Autonomous Univ. of Mexico, Coyoacan (Mexico)

    1995-03-01

    An essential characteristic of some fractured geothermal reservoirs is noticeable when the drilled wells intersect an open fault or macrofracture. Several evidences observed, suggest that the fluid transport into this type of systems, occurs at least in three stages: flow between rock matrix and microfractures, flow between fractures and faults and flow between faults and wells. This pattern flow could define, by analogy to the classical double-porosity model, a triple-porosity, triple-permeability concept. From a mathematical modeling point of view, the non-linearity of the heterogeneous transport processes, occurring with abrupt changes on the petrophysical properties of the rock, makes impossible their exact or analytic solution. To simulate this phenomenon, a detailed two-dimensional geometric model was developed representing the matrix-fracture-fault system. The model was solved numerically using MULKOM with a H{sub 2}O=CO{sub 2} equation of state module. This approach helps to understand some real processes involved. Results obtained from this study, exhibit the importance of considering the triple porosity/permeability concept as a dominant mechanism producing, for example, strong pressure gradients between the reservoir and the bottom hole of some wells.

  7. Unsteady free convection MHD flow between two heated vertical parallel conducting plates

    International Nuclear Information System (INIS)

    Sanyal, D.C.; Adhikari, A.

    2006-01-01

    Unsteady free convection flow of a viscous incompressible electrically conducting fluid between two heated conducting vertical parallel plates subjected to a uniform transverse magnetic field is considered. The approximate analytical solutions for velocity, induced field and temperature distribution are obtained for small and large values of magnetic Reynolds number. The problem is also extended to thermometric case. (author)

  8. Parallel Simulation of Three-Dimensional Free Surface Fluid Flow Problems

    International Nuclear Information System (INIS)

    BAER, THOMAS A.; SACKINGER, PHILIP A.; SUBIA, SAMUEL R.

    1999-01-01

    Simulation of viscous three-dimensional fluid flow typically involves a large number of unknowns. When free surfaces are included, the number of unknowns increases dramatically. Consequently, this class of problem is an obvious application of parallel high performance computing. We describe parallel computation of viscous, incompressible, free surface, Newtonian fluid flow problems that include dynamic contact fines. The Galerkin finite element method was used to discretize the fully-coupled governing conservation equations and a ''pseudo-solid'' mesh mapping approach was used to determine the shape of the free surface. In this approach, the finite element mesh is allowed to deform to satisfy quasi-static solid mechanics equations subject to geometric or kinematic constraints on the boundaries. As a result, nodal displacements must be included in the set of unknowns. Other issues discussed are the proper constraints appearing along the dynamic contact line in three dimensions. Issues affecting efficient parallel simulations include problem decomposition to equally distribute computational work among a SPMD computer and determination of robust, scalable preconditioners for the distributed matrix systems that must be solved. Solution continuation strategies important for serial simulations have an enhanced relevance in a parallel coquting environment due to the difficulty of solving large scale systems. Parallel computations will be demonstrated on an example taken from the coating flow industry: flow in the vicinity of a slot coater edge. This is a three dimensional free surface problem possessing a contact line that advances at the web speed in one region but transitions to static behavior in another region. As such, a significant fraction of the computational time is devoted to processing boundary data. Discussion focuses on parallel speed ups for fixed problem size, a class of problems of immediate practical importance

  9. Spatio-temporal organization of dynamics in a two-dimensional periodically driven vortex flow: A Lagrangian flow network perspective.

    Science.gov (United States)

    Lindner, Michael; Donner, Reik V

    2017-03-01

    We study the Lagrangian dynamics of passive tracers in a simple model of a driven two-dimensional vortex resembling real-world geophysical flow patterns. Using a discrete approximation of the system's transfer operator, we construct a directed network that describes the exchange of mass between distinct regions of the flow domain. By studying different measures characterizing flow network connectivity at different time-scales, we are able to identify the location of dynamically invariant structures and regions of maximum dispersion. Specifically, our approach allows us to delimit co-existing flow regimes with different dynamics. To validate our findings, we compare several network characteristics to the well-established finite-time Lyapunov exponents and apply a receiver operating characteristic analysis to identify network measures that are particularly useful for unveiling the skeleton of Lagrangian chaos.

  10. Unsteady free convection MHD flow between two heated vertical parallel plates in induced magnetic field

    International Nuclear Information System (INIS)

    Chakraborty, S.; Borkakati, A.K.

    1999-01-01

    An unsteady viscous incompressible free convection flow of an electrically conducting fluid between two heated vertical parallel plates is considered in presence of a uniform magnetic field applied transversely to the flow. The approximate analytical solutions for velocity, induced field and temperature distributions are obtained for small and large magnetic Reynolds number. The skin-friction on the two plates are obtained and plotted graphically. The problem is extended for thermometric case. (author)

  11. Wake structure and thrust generation of a flapping foil in two-dimensional flow

    DEFF Research Database (Denmark)

    Andersen, Anders Peter; Bohr, Tomas; Schnipper, Teis

    2017-01-01

    We present a combined numerical (particle vortex method) and experimental (soap film tunnel) study of a symmetric foil undergoing prescribed oscillations in a two-dimensional free stream. We explore pure pitching and pure heaving, and contrast these two generic types of kinematics. We compare...... measurements and simulations when the foil is forced with pitching oscillations, and we find a close correspondence between flow visualisations using thickness variations in the soap film and the numerically determined vortex structures. Numerically, we determine wake maps spanned by oscillation frequency...

  12. Discretizations in isogeometric analysis of Navier-Stokes flow

    DEFF Research Database (Denmark)

    Nielsen, Peter Nørtoft; Gersborg, Allan Roulund; Gravesen, Jens

    2011-01-01

    This paper deals with isogeometric analysis of 2-dimensional, steady state, incompressible Navier-Stokes flow subjected to Dirichlet boundary conditions. We present a detailed description of the numerical method used to solve the boundary value problem. Numerical inf-sup stability tests...

  13. Finite volume model for two-dimensional shallow environmental flow

    Science.gov (United States)

    Simoes, F.J.M.

    2011-01-01

    This paper presents the development of a two-dimensional, depth integrated, unsteady, free-surface model based on the shallow water equations. The development was motivated by the desire of balancing computational efficiency and accuracy by selective and conjunctive use of different numerical techniques. The base framework of the discrete model uses Godunov methods on unstructured triangular grids, but the solution technique emphasizes the use of a high-resolution Riemann solver where needed, switching to a simpler and computationally more efficient upwind finite volume technique in the smooth regions of the flow. Explicit time marching is accomplished with strong stability preserving Runge-Kutta methods, with additional acceleration techniques for steady-state computations. A simplified mass-preserving algorithm is used to deal with wet/dry fronts. Application of the model is made to several benchmark cases that show the interplay of the diverse solution techniques.

  14. Fluid flow and fuel-air mixing in a motored two-dimensional Wankel rotary engine

    Science.gov (United States)

    Shih, T. I.-P.; Nguyen, H. L.; Stegeman, J.

    1986-01-01

    The implicit-factored method of Beam and Warming was employed to obtain numerical solutions to the conservation equations of mass, species, momentum, and energy to study the unsteady, multidimensional flow and mixing of fuel and air inside the combustion chambers of a two-dimensional Wankel rotary engine under motored conditions. The effects of the following engine design and operating parameters on fluid flow and fuel-air mixing during the intake and compression cycles were studied: engine speed, angle of gaseous fuel injection during compression cycle, and speed of the fuel leaving fuel injector.

  15. A Variational Model for Two-Phase Immiscible Electroosmotic Flow at Solid Surfaces

    KAUST Repository

    Shao, Sihong

    2012-01-01

    We develop a continuum hydrodynamic model for two-phase immiscible flows that involve electroosmotic effect in an electrolyte and moving contact line at solid surfaces. The model is derived through a variational approach based on the Onsager principle of minimum energy dissipation. This approach was first presented in the derivation of a continuum hydrodynamic model for moving contact line in neutral two-phase immiscible flows (Qian, Wang, and Sheng, J. Fluid Mech. 564, 333-360 (2006)). Physically, the electroosmotic effect can be formulated by the Onsager principle as well in the linear response regime. Therefore, the same variational approach is applied here to the derivation of the continuum hydrodynamic model for charged two-phase immiscible flows where one fluid component is an electrolyte exhibiting electroosmotic effect on a charged surface. A phase field is employed to model the diffuse interface between two immiscible fluid components, one being the electrolyte and the other a nonconductive fluid, both allowed to slip at solid surfaces. Our model consists of the incompressible Navier-Stokes equation for momentum transport, the Nernst-Planck equation for ion transport, the Cahn-Hilliard phase-field equation for interface motion, and the Poisson equation for electric potential, along with all the necessary boundary conditions. In particular, all the dynamic boundary conditions at solid surfaces, including the generalized Navier boundary condition for slip, are derived together with the equations of motion in the bulk region. Numerical examples in two-dimensional space, which involve overlapped electric double layer fields, have been presented to demonstrate the validity and applicability of the model, and a few salient features of the two-phase immiscible electroosmotic flows at solid surface. The wall slip in the vicinity of moving contact line and the Smoluchowski slip in the electric double layer are both investigated. © 2012 Global-Science Press.

  16. Exact Solutions of Atmospheric (2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations

    Science.gov (United States)

    Liu, Ping; Wang, Ya-Xiong; Ren, Bo; Li, Jin-Hua

    2016-12-01

    Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. Supported by the National Natural Science Foundation of China under Grant Nos. 11305031 and 11305106, and Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No. Yq2013205

  17. A Weakly Nonlinear Model for Kelvin–Helmholtz Instability in Incompressible Fluids

    International Nuclear Information System (INIS)

    Li-Feng, Wang; Wen-Hua, Ye; Zheng-Feng, Fan; Chuang, Xue; Ying-Jun, Li

    2009-01-01

    A weakly nonlinear model is proposed for the Kelvin–Helmholtz instability in two-dimensional incompressible fluids by expanding the perturbation velocity potential to third order. The third-order harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The weakly nonlinear results are supported by numerical simulations. Density and resonance effects exist in the development of mode coupling. (fundamental areas of phenomenology (including applications))

  18. Multimode Coupling Theory for Kelvin–Helmholtz Instability in Incompressible Fluid

    International Nuclear Information System (INIS)

    Li-Feng, Wang; Ying-Jun, Li; Wen-Hua, Ye; Zheng-Feng, Fan

    2009-01-01

    A weakly nonlinear model is proposed for multimode Kelvin–Helmholtz instability. The second-order mode coupling formula for Kelvin–Helmholtz instability in two-dimensional incompressible fluid is presented by expanding the perturbation velocity potential to second order. It is found that there is an important resonance in the course of the sum frequency mode coupling but the difference frequency mode coupling does not have. This resonance makes the sum frequency mode coupling process relatively complex. The sum frequency mode coupling is strongly dependent on time especially when the density of the two fluids is adjacent and the difference frequency mode coupling is not

  19. A Two-Temperature Open-Source CFD Model for Hypersonic Reacting Flows, Part Two: Multi-Dimensional Analysis †

    Directory of Open Access Journals (Sweden)

    Vincent Casseau

    2016-12-01

    Full Text Available hy2Foam is a newly-coded open-source two-temperature computational fluid dynamics (CFD solver that has previously been validated for zero-dimensional test cases. It aims at (1 giving open-source access to a state-of-the-art hypersonic CFD solver to students and researchers; and (2 providing a foundation for a future hybrid CFD-DSMC (direct simulation Monte Carlo code within the OpenFOAM framework. This paper focuses on the multi-dimensional verification of hy2Foam and firstly describes the different models implemented. In conjunction with employing the coupled vibration-dissociation-vibration (CVDV chemistry–vibration model, novel use is made of the quantum-kinetic (QK rates in a CFD solver. hy2Foam has been shown to produce results in good agreement with previously published data for a Mach 11 nitrogen flow over a blunted cone and with the dsmcFoam code for a Mach 20 cylinder flow for a binary reacting mixture. This latter case scenario provides a useful basis for other codes to compare against.

  20. Unsteady flow around a two-dimensional section of a vertical axis turbine for tidal stream energy conversion

    Directory of Open Access Journals (Sweden)

    Hyun Ju Jung

    2009-12-01

    Full Text Available The two-dimensional unsteady flow around a vertical axis turbine for tidal stream energy conversion was investigated using a computational fluid dynamics tool solving the Reynolds-Averaged Navier-Stokes equations. The geometry of the turbine blade section was NACA653-018 airfoil. The computational analysis was done at several different angles of attack and the results were compared with the corresponding experimental data for validation and calibration. Simulations were then carried out for the two-dimensional cross section of a vertical axis turbine. The simulation results demonstrated the usefulness of the method for the typical unsteady flows around vertical axis turbines. The optimum turbine efficiency was achieved for carefully selected combinations of the number of blades and tip speed ratios.

  1. Flow Interactions of Two- and Three-Dimensional Networked Bio-Inspired Control Elements in an In-Line Arrangement.

    Science.gov (United States)

    Kurt, Melike; Moored, Keith

    2018-04-19

    We present experiments that examine the modes of interaction, the collective performance and the role of three-dimensionality in two pitching propulsors in an in-line arrangement. Both two-dimensional foils and three-dimensional rectangular wings of $AR = 2$ are examined. \\kwm{In contrast to previous work, two interaction modes distinguished as the coherent and branched wake modes are not observed to be directly linked to the propulsive efficiency, although they are linked to peak thrust performance and minimum power consumption as previously described \\cite[]{boschitsch2014propulsive}.} \\kwm{In fact, in closely-spaced propulsors peak propulsive efficiency of the follower occurs near its minimum power and this condition \\kwm{ reveals a} branched wake mode. Alternatively, for propulsors spaced far apart peak propulsive efficiency of the follower occurs near its peak thrust and this condition \\kwm{reveals a} coherent wake mode.} By examining the collective performance, it is discovered that there is an optimal spacing between the propulsors to maximize the collective efficiency. For two-dimensional foils the optimal spacing of $X^* = 0.75$ and the synchrony of $\\phi = 2\\pi /3$ leads to a collective efficiency and thrust enhancement of 50\\% and 32\\%, respectively, as compared to two isolated foils. In comparison, for $AR = 2$ wings the optimal spacing of $X^* = 0.25$ and the synchrony of $\\phi = 7\\pi /6$ leads to a collective efficiency and thrust enhancement of 30\\% and 22\\%, respectively. In addition, at the optimal conditions the collective lateral force coefficients in both the two- and three-dimensional cases are negligible, while operating off these conditions can lead to non-negligible lateral forces. Finally, the peak efficiency of the collective and the follower are shown to have opposite trends with increasing spacing in two- and three-dimensional flows. This is correlated to the breakdown of the impinging vortex on the follower wing in three

  2. Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

    KAUST Repository

    Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

    2017-01-01

    A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy

  3. Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

    KAUST Repository

    Destrade, M.

    2010-12-08

    We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then, we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov- Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics. © 2010 The Royal Society.

  4. Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

    KAUST Repository

    Destrade, M.; Goriely, A.; Saccomandi, G.

    2010-01-01

    We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then, we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov- Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics. © 2010 The Royal Society.

  5. Numerical solution of one-dimensional transient, two-phase flows with temporal fully implicit high order schemes: Subcooled boiling in pipes

    Energy Technology Data Exchange (ETDEWEB)

    López, R., E-mail: ralope1@ing.uc3m.es; Lecuona, A., E-mail: lecuona@ing.uc3m.es; Nogueira, J., E-mail: goriba@ing.uc3m.es; Vereda, C., E-mail: cvereda@ing.uc3m.es

    2017-03-15

    Highlights: • A two-phase flows numerical algorithm with high order temporal schemes is proposed. • Transient solutions route depends on the temporal high order scheme employed. • ESDIRK scheme for two-phase flows events exhibits high computational performance. • Computational implementation of the ESDIRK scheme can be done in a very easy manner. - Abstract: An extension for 1-D transient two-phase flows of the SIMPLE-ESDIRK method, initially developed for incompressible viscous flows by Ijaz is presented. This extension is motivated by the high temporal order of accuracy demanded to cope with fast phase change events. This methodology is suitable for boiling heat exchangers, solar thermal receivers, etc. The methodology of the solution consist in a finite volume staggered grid discretization of the governing equations in which the transient terms are treated with the explicit first stage singly diagonally implicit Runge-Kutta (ESDIRK) method. It is suitable for stiff differential equations, present in instant boiling or condensation processes. It is combined with the semi-implicit pressure linked equations algorithm (SIMPLE) for the calculation of the pressure field. The case of study consists of the numerical reproduction of the Bartolomei upward boiling pipe flow experiment. The steady-state validation of the numerical algorithm is made against these experimental results and well known numerical results for that experiment. In addition, a detailed study reveals the benefits over the first order Euler Backward method when applying 3rd and 4th order schemes, making emphasis in the behaviour when the system is subjected to periodic square wave wall heat function disturbances, concluding that the use of the ESDIRK method in two-phase calculations presents remarkable accuracy and computational advantages.

  6. Wind turbine aerodynamics using an incompressible overset grid method

    DEFF Research Database (Denmark)

    Zahle, Frederik; Johansen, Jeppe; Sørensen, Niels N.

    2007-01-01

    In this paper 3D Navier-Stokes simulations of the unsteady flow over the NREL Phase VI turbine are presented. The computations are carried out using the structured grid, incompressible, finite volume flow solver EllipSys3D, which has been extended to include the use of overset grids. Computations...

  7. Parallel simulation of two-phase incompressible and immiscible flows in porous media using a finite volume formulation and a modified IMPES approach

    International Nuclear Information System (INIS)

    Da Silva, R S; De Carvalho, D K E; Antunes, A R E; Lyra, P R M; Willmersdorf, R B

    2010-01-01

    In this paper a finite volume method with a 'Modified Implicit Pressure, Explicit Saturation' (MIMPES) approach is used to model the 3-D incompressible and immiscible two-phase flow of water and oil in heterogeneous and anisotropic porous media. A vertex centered finite volume method with an edge-based data structure is adopted to discretize both the elliptic pressure and the hyperbolic saturation equations using parallel computers with distributed memory. Due to the explicit solution of the saturation equation in the IMPES method, severe time step restrictions are imposed on the simulation. In order to circumvent this problem, an edge-based implementation of the MIMPES method was used. In this method, the pressure equation is solved and the velocity field is computed much less frequently than the saturation field. Following the work of Hurtado, a mean relative variation of the velocity field throughout the simulation is used to automatically control the updating process, allowing for much larger time-steps in a very simple way. In order to run large scale problems, we have developed a parallel implementation using clusters of PC's. The simulator uses open source parallel libraries like FMDB, ParMetis and PETSc. Results of speed-up and efficiency are presented to validate the performance of the parallel simulator.

  8. Finite element flow analysis; Proceedings of the Fourth International Symposium on Finite Element Methods in Flow Problems, Chuo University, Tokyo, Japan, July 26-29, 1982

    Science.gov (United States)

    Kawai, T.

    Among the topics discussed are the application of FEM to nonlinear free surface flow, Navier-Stokes shallow water wave equations, incompressible viscous flows and weather prediction, the mathematical analysis and characteristics of FEM, penalty function FEM, convective, viscous, and high Reynolds number FEM analyses, the solution of time-dependent, three-dimensional and incompressible Navier-Stokes equations, turbulent boundary layer flow, FEM modeling of environmental problems over complex terrain, and FEM's application to thermal convection problems and to the flow of polymeric materials in injection molding processes. Also covered are FEMs for compressible flows, including boundary layer flows and transonic flows, hybrid element approaches for wave hydrodynamic loadings, FEM acoustic field analyses, and FEM treatment of free surface flow, shallow water flow, seepage flow, and sediment transport. Boundary element methods and FEM computational technique topics are also discussed. For individual items see A84-25834 to A84-25896

  9. Numerical methods for incompressible viscous flows with engineering applications

    Science.gov (United States)

    Rose, M. E.; Ash, R. L.

    1988-01-01

    A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.

  10. Viscous and Joule heating effects on MHD free convection flow with variable plate temperature

    International Nuclear Information System (INIS)

    Hossain, M.A.

    1990-09-01

    A steady two-dimensional laminar boundary layer flow of a viscous incompressible and electrically conducting fluid past a vertical heated plate with variable temperature in the presence of a transverse uniform magnetic field has been investigated by bringing the effect of viscous and Joules heating. The non-dimensional boundary layer equations are solved using the implicit finite difference method along with Newton's approximation for small Prandtl number chosen as typical of coolant liquid metals at operating temperature. (author). 10 refs, 2 figs, 1 tab

  11. A continuum theory for two-phase flows of particulate solids: application to Poiseuille flows

    Science.gov (United States)

    Monsorno, Davide; Varsakelis, Christos; Papalexandris, Miltiadis V.

    2015-11-01

    In the first part of this talk, we present a novel two-phase continuum model for incompressible fluid-saturated granular flows. The model accounts for both compaction and shear-induced dilatancy and accommodates correlations for the granular rheology in a thermodynamically consistent way. In the second part of this talk, we exercise this two-phase model in the numerical simulation of a fully-developed Poiseuille flow of a dense suspension. The numerical predictions are shown to compare favorably against experimental measurements and confirm that the model can capture the important characteristics of the flow field, such as segregation and formation of plug zones. Finally, results from parametric studies with respect to the initial concentration, the magnitude of the external forcing and the width of the channel are presented and the role of these physical parameters is quantified. Financial Support has been provided by SEDITRANS, an Initial Training Network of the European Commission's 7th Framework Programme

  12. Exact integration of the unsteady incompressible Navier-Stokes equations, gauge criteria, and applications

    Science.gov (United States)

    Scholle, M.; Gaskell, P. H.; Marner, F.

    2018-04-01

    An exact first integral of the full, unsteady, incompressible Navier-Stokes equations is achieved in its most general form via the introduction of a tensor potential and parallels drawn with Maxwell's theory. Subsequent to this gauge freedoms are explored, showing that when used astutely they lead to a favourable reduction in the complexity of the associated equation set and number of unknowns, following which the inviscid limit case is discussed. Finally, it is shown how a change in gauge criteria enables a variational principle for steady viscous flow to be constructed having a self-adjoint form. Use of the new formulation is demonstrated, for different gauge variants of the first integral as the starting point, through the solution of a hierarchy of classical three-dimensional flow problems, two of which are tractable analytically, the third being solved numerically. In all cases the results obtained are found to be in excellent accord with corresponding solutions available in the open literature. Concurrently, the prescription of appropriate commonly occurring physical and necessary auxiliary boundary conditions, incorporating for completeness the derivation of a first integral of the dynamic boundary condition at a free surface, is established, together with how the general approach can be advantageously reformulated for application in solving unsteady flow problems with periodic boundaries.

  13. Lagrangian statistics and flow topology in forced two-dimensional turbulence.

    Science.gov (United States)

    Kadoch, B; Del-Castillo-Negrete, D; Bos, W J T; Schneider, K

    2011-03-01

    A study of the relationship between Lagrangian statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions. In the double periodic domain, the probability density function (pdf) of the Weiss field exhibits a negative skewness consistent with the fact that in periodic domains the flow is dominated by coherent vortex structures. On the other hand, in the circular domain, the elliptic and hyperbolic regions seem to be statistically similar. We follow a Lagrangian approach and obtain the statistics by tracking large ensembles of passively advected tracers. The pdfs of residence time in the topologically different regions are computed introducing the Lagrangian Weiss field, i.e., the Weiss field computed along the particles' trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf has exponential decaying tails. The conditional pdfs (with respect to the flow topology) of the Lagrangian velocity exhibit Gaussian-like behavior in the periodic and in the bounded domains. In contrast to the freely decaying turbulence case, the conditional pdfs of the Lagrangian acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the Lagrangian curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order -2.

  14. Three-dimensional fluctuating Couette flow through the porous plates with heat transfer

    Directory of Open Access Journals (Sweden)

    M. Guria

    2006-06-01

    Full Text Available Unsteady Couette flow of a viscous incompressible fluid between two horizontal porous flat plates is considered. The stationary plate is subjected to a periodic suction and the plate in uniform motion is subjected to uniform injection. Approximate solutions have been obtained for the velocity and the temperature fields, skin friction by using perturbation technique. The heat transfer characteristic has also been studied on taking viscous dissipation into account. It is found that the main flow velocity decreases with increase in frequency parameter. On the other hand, the magnitude of the cross-flow velocity increases with increase in frequency parameter. It is seen that the amplitude of the shear stress due to main flow decreases while that due to cross-flow increases with increase in frequency parameter. It is also seen that the tangent of phase shifts both due to the main and cross-flows decrease with increase in frequency parameter. It is observed that the temperature increases with increase in frequency parameter.

  15. Numerical analysis for two-dimensional compressible and two-phase flow fields of air-water in Eulerian grid framework

    International Nuclear Information System (INIS)

    Park, Chan Wook; Lee, Sung Su

    2008-01-01

    Two-phase compressible flow fields of air-water are investigated numerically in the fixed Eulerian grid framework. The phase interface is captured via volume fractions of ech phase. A way to model two phase compressible flows as a single phase one is found based on an equivalent equation of states of Tait's type for a multiphase cell. The equivalent single phase field is discretized using the Roe's approximate Riemann solver. Two approaches are tried to suppress the pressure oscillation phenomena at the phase interface, a passive advection of volume fraction and a direct pressure relaxation with the compressible form of volume fraction equation. The direct pressure equalizing method suppresses pressure oscillation successfully and generates sharp discontinuities, transmitting and reflecting acoustic waves naturally at the phase interface. In discretizing the compressible form of volume fraction equation, phase interfaces are geometrically reconstructed to minimize the numerical diffusion of volume fraction and relevant variables. The motion of a projectile in a water-filled tube which is fired by the release of highly pressurized air is simulated presuming the flow field as a two dimensional one, and several design factors affecting the projectile movement are investigated

  16. A Poisson equation formulation for pressure calculations in penalty finite element models for viscous incompressible flows

    Science.gov (United States)

    Sohn, J. L.; Heinrich, J. C.

    1990-01-01

    The calculation of pressures when the penalty-function approximation is used in finite-element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C0 velocity approximation using a least-squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.

  17. Large Eddy Simulation for Incompressible Flows An Introduction

    CERN Document Server

    Sagaut, P

    2005-01-01

    The first and most exhaustive work of its kind devoted entirely to the subject, Large Eddy Simulation presents a comprehensive account and a unified view of this young but very rich discipline. LES is the only efficient technique for approaching high Reynolds numbers when simulating industrial, natural or experimental configurations. The author concentrates on incompressible fluids and chooses his topics in treating with care both the mathematical ideas and their applications. The book addresses researchers as well as graduate students and engineers. The second edition was a greatly enriched version motivated both by the increasing theoretical interest in LES and the increasing number of applications. Two entirely new chapters were devoted to the coupling of LES with multiresolution multidomain techniques and to the new hybrid approaches that relate the LES procedures to the classical statistical methods based on the Reynolds-Averaged Navier-Stokes equations. This 3rd edition adds various sections to the text...

  18. Two dimensional MHD flows between porous boundaries

    International Nuclear Information System (INIS)

    Gratton, F.T.

    1994-01-01

    Similarity solutions of dissipative MHD equations representing conducting fluids injected through porous walls and flowing out in both directions from the center of the channel, are studied as a function of four non dimensional parameters, Reynolds number R e , magnetic Reynolds number R m , Alfvenic Mach number, M A , and pressure gradient coefficient, C. The effluence is restrained by an external magnetic field normal to the walls. When R m m >>1, the solution may model a collision of plasmas of astrophysical interest. In this case the magnetic field lines help to drive the outflow acting jointly with the pressure gradient. The law for C as a function of the other parameters is given for several asymptotic limits. (author). 3 refs, 6 figs

  19. Multiparticle imaging velocimetry measurements in two-phase flow

    International Nuclear Information System (INIS)

    Hassan, Y.A.

    1998-01-01

    The experimental flow visualization tool, Particle Image Velocimetry (PIV), is being extended to determine the velocity fields in two and three-dimensional, two-phase fluid flows. In the past few years, the technique has attracted quite a lot of interest. PIV enables fluid velocities across a region of a flow to be measured at a single instant in time in global domain. This instantaneous velocity profile of a given flow field is determined by digitally recording particle (microspheres or bubbles) images within the flow over multiple successive video frames and then conducting flow pattern identification and analysis of the data. This paper presents instantaneous velocity measurements in various two and three- dimensional, two-phase flow situations. (author)

  20. Three-dimensional attached viscous flow basic principles and theoretical foundations

    CERN Document Server

    Hirschel, Ernst Heinrich; Kordulla, Wilhelm

    2014-01-01

    Viscous flow is usually treated in the frame of boundary-layer theory and as a two-dimensional flow. At best, books on boundary layers provide the describing equations for three-dimensional boundary layers, and solutions only for certain special cases.   This book presents the basic principles and theoretical foundations of three-dimensional attached viscous flows as they apply to aircraft of all kinds. Though the primary flight speed range is that of civil air transport vehicles, flows past other flying vehicles up to hypersonic speeds are also considered. Emphasis is put on general three-dimensional attached viscous flows and not on three-dimensional boundary layers, as this wider scope is necessary in view of the theoretical and practical problems that have to be overcome in practice.   The specific topics covered include weak, strong, and global interaction; the locality principle; properties of three-dimensional viscous flows; thermal surface effects; characteristic properties; wall compatibility con...

  1. Active unsteady aerodynamic suppression of rotating stall in an incompressible flow centrifugal compressor with vaned diffuser

    Science.gov (United States)

    Lawless, Patrick B.; Fleeter, Sanford

    1991-01-01

    A mathematical model is developed to analyze the suppression of rotating stall in an incompressible flow centrifugal compressor with a vaned diffuser, thereby addressing the important need for centrifugal compressor rotating stall and surge control. In this model, the precursor to to instability is a weak rotating potential velocity perturbation in the inlet flow field that eventually develops into a finite disturbance. To suppress the growth of this potential disturbance, a rotating control vortical velocity disturbance is introduced into the impeller inlet flow. The effectiveness of this control is analyzed by matching the perturbation pressure in the compressor inlet and exit flow fields with a model for the unsteady behavior of the compressor. To demonstrate instability control, this model is then used to predict the control effectiveness for centrifugal compressor geometries based on a low speed research centrifugal compressor. These results indicate that reductions of 10 to 15 percent in the mean inlet flow coefficient at instability are possible with control waveforms of half the magnitude of the total disturbance at the inlet.

  2. Steady laminar flow of fractal fluids

    Energy Technology Data Exchange (ETDEWEB)

    Balankin, Alexander S., E-mail: abalankin@ipn.mx [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico); Mena, Baltasar [Laboratorio de Ingeniería y Procesos Costeros, Instituto de Ingeniería, Universidad Nacional Autónoma de México, Sisal, Yucatán, 97355 (Mexico); Susarrey, Orlando; Samayoa, Didier [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico)

    2017-02-12

    We study laminar flow of a fractal fluid in a cylindrical tube. A flow of the fractal fluid is mapped into a homogeneous flow in a fractional dimensional space with metric induced by the fractal topology. The equations of motion for an incompressible Stokes flow of the Newtonian fractal fluid are derived. It is found that the radial distribution for the velocity in a steady Poiseuille flow of a fractal fluid is governed by the fractal metric of the flow, whereas the pressure distribution along the flow direction depends on the fractal topology of flow, as well as on the fractal metric. The radial distribution of the fractal fluid velocity in a steady Couette flow between two concentric cylinders is also derived. - Highlights: • Equations of Stokes flow of Newtonian fractal fluid are derived. • Pressure distribution in the Newtonian fractal fluid is derived. • Velocity distribution in Poiseuille flow of fractal fluid is found. • Velocity distribution in a steady Couette flow is established.

  3. Étalement d'une goutte stratifiée incompressible

    Science.gov (United States)

    de Gennes, Pierre-Gilles; Cazabat, Anne-Marie

    L'étalement de films ultraminces de liquides simples sur une surface lisse horizontale conduit souvent à des gouttes à gradins d'une épaisseur moléculaire ([1]-[3]). Nous construisons ici un modèle pour la dynamique de l'étalement, en supposant que : (a) chaque gradin est un liquide bidimensionnel incompressible; (b) les molécules de la n-ième couche sont soumises à un potentiel (Wn) qui exprime leurs interactions à longue portée avec le solide; (c) on a un écoulement parallèle de cisaillement, et un écoulement normal de perméation. La perméation intervient seulement dans un certain « ruban » de largeur ξ sur le bord de chaque gradin. Dans le cas usuel, où le rayon du n-ième gradin Rn est trs supérieur à ξ, la dissipation est dominée par le cisaillement, et on arrive à des lois simples pour la vitesse de dilatation (ou de contraction) dotR_n. Very thin films of simple liquids often spread with well defined steps of molecular thickness ([1]-[3]). We construct a model for the dynamics of spreading assuming that: (a) each layer is an incompressible, 2 dimensional fluid; (b) the molecules in the (nth) layer experience a long range potential (e.g. Van der Waals) from the solid; (c) two types of flow occur: shear between layers and permeation normal to the layers. We find that permeation is important only in an annulus of small size ξ near each step. Between steps, the viscous effects in simple shear dominate, and this leads to simple laws for the dilation (or contraction) of the various layers.

  4. Topology optimization of Channel flow problems

    DEFF Research Database (Denmark)

    Gersborg-Hansen, Allan; Sigmund, Ole; Haber, R. B.

    2005-01-01

    function which measures either some local aspect of the velocity field or a global quantity, such as the rate of energy dissipation. We use the finite element method to model the flow, and we solve the optimization problem with a gradient-based math-programming algorithm that is driven by analytical......This paper describes a topology design method for simple two-dimensional flow problems. We consider steady, incompressible laminar viscous flows at low to moderate Reynolds numbers. This makes the flow problem non-linear and hence a non-trivial extension of the work of [Borrvall&Petersson 2002......]. Further, the inclusion of inertia effects significantly alters the physics, enabling solutions of new classes of optimization problems, such as velocity--driven switches, that are not addressed by the earlier method. Specifically, we determine optimal layouts of channel flows that extremize a cost...

  5. Goal-oriented model adaptivity for viscous incompressible flows

    KAUST Repository

    van Opstal, T. M.

    2015-04-04

    © 2015, Springer-Verlag Berlin Heidelberg. In van Opstal et al. (Comput Mech 50:779–788, 2012) airbag inflation simulations were performed where the flow was approximated by Stokes flow. Inside the intricately folded initial geometry the Stokes assumption is argued to hold. This linearity assumption leads to a boundary-integral representation, the key to bypassing mesh generation and remeshing. It therefore enables very large displacements with near-contact. However, such a coarse assumption cannot hold throughout the domain, where it breaks down one needs to revert to the original model. The present work formalizes this idea. A model adaptive approach is proposed, in which the coarse model (a Stokes boundary-integral equation) is locally replaced by the original high-fidelity model (Navier–Stokes) based on a-posteriori estimates of the error in a quantity of interest. This adaptive modeling framework aims at taking away the burden and heuristics of manually partitioning the domain while providing new insight into the physics. We elucidate how challenges pertaining to model disparity can be addressed. Essentially, the solution in the interior of the coarse model domain is reconstructed as a post-processing step. We furthermore present a two-dimensional numerical experiments to show that the error estimator is reliable.

  6. VNAP2: a computer program for computation of two-dimensional, time-dependent, compressible, turbulent flow

    Energy Technology Data Exchange (ETDEWEB)

    Cline, M.C.

    1981-08-01

    VNAP2 is a computer program for calculating turbulent (as well as laminar and inviscid), steady, and unsteady flow. VNAP2 solves the two-dimensional, time-dependent, compressible Navier-Stokes equations. The turbulence is modeled with either an algebraic mixing-length model, a one-equation model, or the Jones-Launder two-equation model. The geometry may be a single- or a dual-flowing stream. The interior grid points are computed using the unsplit MacCormack scheme. Two options to speed up the calculations for high Reynolds number flows are included. The boundary grid points are computed using a reference-plane-characteristic scheme with the viscous terms treated as source functions. An explicit artificial viscosity is included for shock computations. The fluid is assumed to be a perfect gas. The flow boundaries may be arbitrary curved solid walls, inflow/outflow boundaries, or free-jet envelopes. Typical problems that can be solved concern nozzles, inlets, jet-powered afterbodies, airfoils, and free-jet expansions. The accuracy and efficiency of the program are shown by calculations of several inviscid and turbulent flows. The program and its use are described completely, and six sample cases and a code listing are included.

  7. Bubbly flows around a two-dimensional circular cylinder

    Science.gov (United States)

    Lee, Jubeom; Park, Hyungmin

    2016-11-01

    Two-phase cross flows around a bluff body occur in many thermal-fluid systems like steam generators, heat exchangers and nuclear reactors. However, our current knowledge on the interactions among bubbles, bubble-induced flows and the bluff body are limited. In the present study, the gas-liquid bubbly flows around a solid circular cylinder are experimentally investigated while varying the mean void fraction from 5 to 27%. The surrounding liquid (water) is initially static and the liquid flow is only induced by the air bubbles. For the measurements, we use the high-speed two-phase particle image velocimetry techniques. First, depending on the mean void fraction, two regimes are classified with different preferential concentration of bubbles in the cylinder wake, which are explained in terms of hydrodynamic force balances acting on rising bubbles. Second, the differences between the two-phase and single-phase flows (while matching their Reynolds numbers) around a circular cylinder will be discussed in relation to effects of bubble dynamics and the bubble-induced turbulence on the cylinder wake. Supported by a Grant (MPSS-CG-2016-02) through the Disaster and Safety Management Institute funded by Ministry of Public Safety and Security of Korean government.

  8. Calculation of laminar incompressible fluid flow and heat transfer during spherical annulus filling

    International Nuclear Information System (INIS)

    Tuft, D.B.

    1979-04-01

    A method of computing laminar incompressible fluid-flow and heat transfer during the filling of a spherical annulus is presented. Transient fluid temperatures and heat flux rates in the spherical annulus are calculated for an insulated outer sphere and a constant temperature inner sphere with heated water filling the annulus from the bottom. To achieve a solution, laminar axially symmetric flow is assumed and the Marker-and-Cell (MAC) free surface computational method is applied to this problem in spherical coordinates. Changes in the standard MAC treatment are incorporated and special methods for handling the free surface are introduced. A variable mesh is used to improve resolution near the inner sphere where temperature and velocity gradients are steep and the governing equations are derived for variable fluid properties to allow an eddy viscosity turbulence model to be applied later. Calculations of velocity, temperature, and inner sphere heat flux in a spherical annulus of 139.7 mm inner radius, and 168.3 mm outer radius within an inlet tube diameter of 38.1 mm are presented

  9. A high-resolution code for large eddy simulation of incompressible turbulent boundary layer flows

    KAUST Repository

    Cheng, Wan

    2014-03-01

    We describe a framework for large eddy simulation (LES) of incompressible turbulent boundary layers over a flat plate. This framework uses a fractional-step method with fourth-order finite difference on a staggered mesh. We present several laminar examples to establish the fourth-order accuracy and energy conservation property of the code. Furthermore, we implement a recycling method to generate turbulent inflow. We use the stretched spiral vortex subgrid-scale model and virtual wall model to simulate the turbulent boundary layer flow. We find that the case with Reθ ≈ 2.5 × 105 agrees well with available experimental measurements of wall friction, streamwise velocity profiles and turbulent intensities. We demonstrate that for cases with extremely large Reynolds numbers (Reθ = 1012), the present LES can reasonably predict the flow with a coarse mesh. The parallel implementation of the LES code demonstrates reasonable scaling on O(103) cores. © 2013 Elsevier Ltd.

  10. A two-dimensional numerical study of the flow inside the combustion chamber of a motored rotary engine

    Science.gov (United States)

    Shih, T. I-P.; Yang, S. L.; Schock, H. J.

    1986-01-01

    A numerical study was performed to investigate the unsteady, multidimensional flow inside the combustion chambers of an idealized, two-dimensional, rotary engine under motored conditions. The numerical study was based on the time-dependent, two-dimensional, density-weighted, ensemble-averaged conservation equations of mass, species, momentum, and total energy valid for two-component ideal gas mixtures. The ensemble-averaged conservation equations were closed by a K-epsilon model of turbulence. This K-epsilon model of turbulence was modified to account for some of the effects of compressibility, streamline curvature, low-Reynolds number, and preferential stress dissipation. Numerical solutions to the conservation equations were obtained by the highly efficient implicit-factored method of Beam and Warming. The grid system needed to obtain solutions were generated by an algebraic grid generation technique based on transfinite interpolation. Results of the numerical study are presented in graphical form illustrating the flow patterns during intake, compression, gaseous fuel injection, expansion, and exhaust.

  11. A two-dimensional numerical study of the flow inside the combustion chambers of a motored rotary engine

    Science.gov (United States)

    Shih, T. I. P.; Yang, S. L.; Schock, H. J.

    1986-01-01

    A numerical study was performed to investigate the unsteady, multidimensional flow inside the combustion chambers of an idealized, two-dimensional, rotary engine under motored conditions. The numerical study was based on the time-dependent, two-dimensional, density-weighted, ensemble-averaged conservation equations of mass, species, momentum, and total energy valid for two-component ideal gas mixtures. The ensemble-averaged conservation equations were closed by a K-epsilon model of turbulence. This K-epsilon model of turbulence was modified to account for some of the effects of compressibility, streamline curvature, low-Reynolds number, and preferential stress dissipation. Numerical solutions to the conservation equations were obtained by the highly efficient implicit-factored method of Beam and Warming. The grid system needed to obtain solutions were generated by an algebraic grid generation technique based on transfinite interpolation. Results of the numerical study are presented in graphical form illustrating the flow patterns during intake, compression, gaseous fuel injection, expansion, and exhaust.

  12. Poiseuille equation for steady flow of fractal fluid

    Science.gov (United States)

    Tarasov, Vasily E.

    2016-07-01

    Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.

  13. Energy law preserving C0 finite element schemes for phase field models in two-phase flow computations

    International Nuclear Information System (INIS)

    Hua Jinsong; Lin Ping; Liu Chun; Wang Qi

    2011-01-01

    Highlights: → We study phase-field models for multi-phase flow computation. → We develop an energy-law preserving C0 FEM. → We show that the energy-law preserving method work better. → We overcome unphysical oscillation associated with the Cahn-Hilliard model. - Abstract: We use the idea in to develop the energy law preserving method and compute the diffusive interface (phase-field) models of Allen-Cahn and Cahn-Hilliard type, respectively, governing the motion of two-phase incompressible flows. We discretize these two models using a C 0 finite element in space and a modified midpoint scheme in time. To increase the stability in the pressure variable we treat the divergence free condition by a penalty formulation, under which the discrete energy law can still be derived for these diffusive interface models. Through an example we demonstrate that the energy law preserving method is beneficial for computing these multi-phase flow models. We also demonstrate that when applying the energy law preserving method to the model of Cahn-Hilliard type, un-physical interfacial oscillations may occur. We examine the source of such oscillations and a remedy is presented to eliminate the oscillations. A few two-phase incompressible flow examples are computed to show the good performance of our method.

  14. Application of Light Reflection Visualization for Measuring Organic-Liquid Saturation for Two-Phase Systems in Two-Dimensional Flow Cells.

    Science.gov (United States)

    DiFilippo, Erica L; Brusseau, Mark L

    2011-11-01

    A simple, noninvasive imaging technique was used to obtain in situ measurements of organic-liquid saturation in a two-phase system under dynamic conditions. Efficacy of the light reflection visualization (LRV) imaging method was tested through comparison of measured and known volumes of organic liquid for experiments conducted with a two-dimensional flow cell. Two sets of experiments were conducted, with source-zone configurations representing two archetypical residual-and-pool architectures. LRV measurements were collected during the injection of organic liquid and during a dissolution phase induced by water flushing. There was a strong correlation between measured and known organic-liquid volumes, with the LRV-measured values generally somewhat lower than the known volumes. Errors were greater for the system wherein organic liquid was present in multiple zones comprised of porous media of different permeabilities, and for conditions of multiphase flow. This method proved effective at determining organic-liquid distribution in a two-phase system using minimal specialized equipment.

  15. Dynamic response of a system with internal heat sources cooled by a flowing incompressible fluid

    International Nuclear Information System (INIS)

    Georgescu, R.; Dobrescu, C.

    1975-01-01

    The paper investigates the dynamic temperature response of an incompressible fluid which cools a duct with internal heat sources sinusoidally oscillated. The analytical results utilise the Laplace transformation technique. The experimental and calculated results are obtained by transfer function approach. Comparison of the calculated with the experimental data indicates agreement from 6 to 24 percent for the amplitude and up to 30 degree for the phase-shift. All the calculated data are below the experimental ones. The analytical method of transfer function approach presents interest and may be utilized for the initial calculations giving good results for flow rates above 1000 kg per hour

  16. The three-dimensional transient two-phase flow computer programme BACCHUS-3D/TP

    International Nuclear Information System (INIS)

    Bottoni, M.; Dorr, B.; Homann, C.

    1992-04-01

    The three-dimensional single-phase flow version of the BACCHUS code, which describes the thermal behaviour of a coolant in hexagonal bundle geometry, developed earlier, provided the basis for the development of the two-phase flow version documented in this report. A detailed description is given of the two-phase Slip Model (SM), and of the Homogeneous Equilibrium Model (HEM) as a subcase, which presents several improvements from both viewpoints of physical modelling and numerical treatment, with respect to usual models found in the literature. The most advanced Separated Phases Model (SPM) is then described in all analytical details necessary to fully understand its implementation in the code. Poblems related to the link between the two above models into an integrated code version are then discussed. The code provides an additional option for modelling of active or passive, permeable or impermeable blockages. This option is documented separately. New numerical methods for solving the algebraic systems of equations derived from the linearization of the fundamental equations have completely superseded previous ones and are explained in detail. Eventually a section is dedicated to an overview of the code verification, made over several years, which goes from steady state single-phase unheated bundle experiments up to fast transient two-phase flow experiments in electrically heated 37-pin bundles. (orig.) [de

  17. Statistical mechanics and correlation properties of a rotating two-dimensional flow of like-sign vortices

    International Nuclear Information System (INIS)

    Viecelli, J.A.

    1993-01-01

    The Hamiltonian flow of a set of point vortices of like sign and strength has a low-temperature phase consisting of a rotating triangular lattice of vortices, and a normal temperature turbulent phase consisting of random clusters of vorticity that orbit about a common center along random tracks. The mean-field flow in the normal temperature phase has similarities with turbulent quasi-two-dimensional rotating laboratory and geophysical flows, whereas the low-temperature phase displays effects associated with quantum fluids. In the normal temperature phase the vortices follow power-law clustering distributions, while in the time domain random interval modulation of the vortex orbit radii fluctuations produces singular fractional exponent power-law low-frequency spectra corresponding to time autocorrelation functions with fractional exponent power-law tails. Enhanced diffusion is present in the turbulent state, whereas in the solid-body rotation state vortices thermally diffuse across the lattice. Over the entire temperature range the interaction energy of a single vortex in the field of the rest of the vortices follows positive temperature Fermi--Dirac statistics, with the zero temperature limit corresponding to the rotating crystal phase, and the infinite temperature limit corresponding to a Maxwellian distribution. Analyses of weather records dependent on the large-scale quasi-two-dimensional atmospheric circulation suggest the presence of singular fractional exponent power-law spectra and fractional exponent power-law autocorrelation tails, consistent with the theory

  18. Spatial statistics of magnetic field in two-dimensional chaotic flow in the resistive growth stage

    Energy Technology Data Exchange (ETDEWEB)

    Kolokolov, I.V., E-mail: igor.kolokolov@gmail.com [Landau Institute for Theoretical Physics RAS, 119334, Kosygina 2, Moscow (Russian Federation); NRU Higher School of Economics, 101000, Myasnitskaya 20, Moscow (Russian Federation)

    2017-03-18

    The correlation tensors of magnetic field in a two-dimensional chaotic flow of conducting fluid are studied. It is shown that there is a stage of resistive evolution where the field correlators grow exponentially with time. The two- and four-point field correlation tensors are computed explicitly in this stage in the framework of Batchelor–Kraichnan–Kazantsev model. They demonstrate strong temporal intermittency of the field fluctuations and high level of non-Gaussianity in spatial field distribution.

  19. Effect of velocity boundary conditions on the heat transfer and flow topology in two-dimensional Rayleigh-Bénard convection.

    Science.gov (United States)

    van der Poel, Erwin P; Ostilla-Mónico, Rodolfo; Verzicco, Roberto; Lohse, Detlef

    2014-07-01

    The effect of various velocity boundary condition is studied in two-dimensional Rayleigh-Bénard convection. Combinations of no-slip, stress-free, and periodic boundary conditions are used on both the sidewalls and the horizontal plates. For the studied Rayleigh numbers Ra between 10(8) and 10(11) the heat transport is lower for Γ=0.33 than for Γ=1 in case of no-slip sidewalls. This is, surprisingly, the opposite for stress-free sidewalls, where the heat transport increases for a lower aspect ratio. In wider cells the aspect-ratio dependence is observed to disappear for Ra ≥ 10(10). Two distinct flow types with very different dynamics can be seen, mostly dependent on the plate velocity boundary condition, namely roll-like flow and zonal flow, which have a substantial effect on the dynamics and heat transport in the system. The predominantly horizontal zonal flow suppresses heat flux and is observed for stress-free and asymmetric plates. Low aspect-ratio periodic sidewall simulations with a no-slip boundary condition on the plates also exhibit zonal flow. In all the other cases, the flow is roll like. In two-dimensional Rayleigh-Bénard convection, the velocity boundary conditions thus have large implications on both roll-like and zonal flow that have to be taken into consideration before the boundary conditions are imposed.

  20. Inertia and compressibility effects on density waves and Ledinegg phenomena in two-phase flow systems

    International Nuclear Information System (INIS)

    Ruspini, L.C.

    2012-01-01

    Highlights: ► The stability influence of piping fluid inertia on two-phase instabilities is studied. ► Inlet inertia stabilizes the system while outlet inertia destabilizes it. ► High-order modes oscillations are found and analyzed. ► The effect of compressible volumes in the system is studied. ► Inlet compressibility destabilizes the system while outlet comp. stabilizes it. - Abstract: The most common kind of static and dynamic two-phase flow instabilities namely Ledinegg and density wave oscillations are studied. A new model to study two-phase flow instabilities taking into account general parameters from real systems is proposed. The stability influence of external parameters such as the fluid inertia and the presence of compressible gases in the system is analyzed. High-order oscillation modes are found to be related with the fluid inertia of external piping. The occurrence of high-order modes in experimental works is analyzed with focus on the results presented in this work. Moreover, both inertia and compressibility are proven to have a high impact on the stability limits of the systems. The performed study is done by modeling the boiling channel using a one dimensional equilibrium model. An incompressible transient model describes the evolution of the flow and pressure in the non-heated regions and an ideal gas model is used to simulate the compressible volumes in the system. The use of wavelet decomposition analysis is proven to be an efficient tool in stability analysis of several frequencies oscillations.

  1. Effective Rheology of Two-Phase Flow in Three-Dimensional Porous Media: Experiment and Simulation.

    Science.gov (United States)

    Sinha, Santanu; Bender, Andrew T; Danczyk, Matthew; Keepseagle, Kayla; Prather, Cody A; Bray, Joshua M; Thrane, Linn W; Seymour, Joseph D; Codd, Sarah L; Hansen, Alex

    2017-01-01

    We present an experimental and numerical study of immiscible two-phase flow of Newtonian fluids in three-dimensional (3D) porous media to find the relationship between the volumetric flow rate ( Q ) and the total pressure difference ([Formula: see text]) in the steady state. We show that in the regime where capillary forces compete with the viscous forces, the distribution of capillary barriers at the interfaces effectively creates a yield threshold ([Formula: see text]), making the fluids reminiscent of a Bingham viscoplastic fluid in the porous medium. In this regime, Q depends quadratically on an excess pressure drop ([Formula: see text]). While increasing the flow rate, there is a transition, beyond which the overall flow is Newtonian and the relationship is linear. In our experiments, we build a model porous medium using a column of glass beads transporting two fluids, deionized water and air. For the numerical study, reconstructed 3D pore networks from real core samples are considered and the transport of wetting and non-wetting fluids through the network is modeled by tracking the fluid interfaces with time. We find agreement between our numerical and experimental results. Our results match with the mean-field results reported earlier.

  2. Effects of flow shear and Alfven waves on two-dimensional magnetohydrodynamic turbulence

    International Nuclear Information System (INIS)

    Douglas, Jamie; Kim, Eun-jin; Thyagaraja, A.

    2008-01-01

    The suppression of turbulent transport by large scale mean shear flows and uniform magnetic fields is investigated in two-dimensional magnetohydrodynamic turbulence driven by a small-scale forcing with finite correlation time. By numerical integration the turbulent magnetic diffusivity D T is shown to be significantly quenched, with a scaling D T ∝B -2 Ω 0 -5/4 , which is much more severe than in the case of a short or delta correlated forcing typified by white noise, studied in E. Kim and B. Dubrulle [Phys. Plasmas 8, 813 (2001)]. Here B and Ω 0 are magnetic field strength and flow shear rate, respectively. The forcing with finite correlation time also leads to much stronger suppression of momentum transport through the cancellation of the Reynolds stress by the Maxwell stress with a positive small value of turbulent viscosity, ν T >0. While fluctuating kinetic and magnetic energies are unaffected by the magnetic field just as in the case of a delta correlated forcing, they are much more severely quenched by flow shear than in that of a delta correlated forcing. Underlying physical mechanisms for the reduction of turbulent transport and turbulence level by flow shear and magnetic field are discussed

  3. Surface Tension of Multi-phase Flow with Multiple Junctions Governed by the Variational Principle

    International Nuclear Information System (INIS)

    Matsutani, Shigeki; Nakano, Kota; Shinjo, Katsuhiko

    2011-01-01

    We explore a computational model of an incompressible fluid with a multi-phase field in three-dimensional Euclidean space. By investigating an incompressible fluid with a two-phase field geometrically, we reformulate the expression of the surface tension for the two-phase field found by Lafaurie et al. (J Comput Phys 113:134–147, 1994) as a variational problem related to an infinite dimensional Lie group, the volume-preserving diffeomorphism. The variational principle to the action integral with the surface energy reproduces their Euler equation of the two-phase field with the surface tension. Since the surface energy of multiple interfaces even with singularities is not difficult to be evaluated in general and the variational formulation works for every action integral, the new formulation enables us to extend their expression to that of a multi-phase (N-phase, N ≥ 2) flow and to obtain a novel Euler equation with the surface tension of the multi-phase field. The obtained Euler equation governs the equation for motion of the multi-phase field with different surface tension coefficients without any difficulties for the singularities at multiple junctions. In other words, we unify the theory of multi-phase fields which express low dimensional interface geometry and the theory of the incompressible fluid dynamics on the infinite dimensional geometry as a variational problem. We apply the equation to the contact angle problems at triple junctions. We computed the fluid dynamics for a two-phase field with a wall numerically and show the numerical computational results that for given surface tension coefficients, the contact angles are generated by the surface tension as results of balances of the kinematic energy and the surface energy.

  4. INCOMPRESSIBLE LAMINAR BOUNDARY LAYER CONTROL BY BLOWING AND SUCTION

    Directory of Open Access Journals (Sweden)

    AZZEDINE NAHOUI

    2013-12-01

    Full Text Available A two-dimensional incompressible laminar boundary layer and its control using blowing and suction over a flat plate and around the NACA 0012 and 661012 profiles, is studied numerically. The study is based on the Prandtl boundary layer model using the finite differences method and the Crank-Nicolson scheme. The velocity distribution, the boundary layer thickness and the friction coefficient, are determined and presented with and without control. The application of the control technique, has demonstrated its positive effect on the transition point and the friction coefficient. Both control procedures are compared for different lengths, speeds and angles of blowing and suction.

  5. Multi-dimensional rheology-based two-phase model for sediment transport and applications to sheet flow and pipeline scour

    International Nuclear Information System (INIS)

    Lee, Cheng-Hsien; Low, Ying Min; Chiew, Yee-Meng

    2016-01-01

    Sediment transport is fundamentally a two-phase phenomenon involving fluid and sediments; however, many existing numerical models are one-phase approaches, which are unable to capture the complex fluid-particle and inter-particle interactions. In the last decade, two-phase models have gained traction; however, there are still many limitations in these models. For example, several existing two-phase models are confined to one-dimensional problems; in addition, the existing two-dimensional models simulate only the region outside the sand bed. This paper develops a new three-dimensional two-phase model for simulating sediment transport in the sheet flow condition, incorporating recently published rheological characteristics of sediments. The enduring-contact, inertial, and fluid viscosity effects are considered in determining sediment pressure and stresses, enabling the model to be applicable to a wide range of particle Reynolds number. A k − ε turbulence model is adopted to compute the Reynolds stresses. In addition, a novel numerical scheme is proposed, thus avoiding numerical instability caused by high sediment concentration and allowing the sediment dynamics to be computed both within and outside the sand bed. The present model is applied to two classical problems, namely, sheet flow and scour under a pipeline with favorable results. For sheet flow, the computed velocity is consistent with measured data reported in the literature. For pipeline scour, the computed scour rate beneath the pipeline agrees with previous experimental observations. However, the present model is unable to capture vortex shedding; consequently, the sediment deposition behind the pipeline is overestimated. Sensitivity analyses reveal that model parameters associated with turbulence have strong influence on the computed results.

  6. Space-time coupled spectral/hp least-squares finite element formulation for the incompressible Navier-Stokes equations

    International Nuclear Information System (INIS)

    Pontaza, J.P.; Reddy, J.N.

    2004-01-01

    We consider least-squares finite element models for the numerical solution of the non-stationary Navier-Stokes equations governing viscous incompressible fluid flows. The paper presents a formulation where the effects of space and time are coupled, resulting in a true space-time least-squares minimization procedure, as opposed to a space-time decoupled formulation where a least-squares minimization procedure is performed in space at each time step. The formulation is first presented for the linear advection-diffusion equation and then extended to the Navier-Stokes equations. The formulation has no time step stability restrictions and is spectrally accurate in both space and time. To allow the use of practical C 0 element expansions in the resulting finite element model, the Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity as an additional independent variable and the least-squares method is used to develop the finite element model of the governing equations. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method in matrix-free form. Spectral convergence of the L 2 least-squares functional and L 2 error norms in space-time is verified using a smooth solution to the two-dimensional non-stationary incompressible Navier-Stokes equations. Numerical results are presented for impulsively started lid-driven cavity flow, oscillatory lid-driven cavity flow, transient flow over a backward-facing step, and flow around a circular cylinder; the results demonstrate the predictive capability and robustness of the proposed formulation. Even though the space-time coupled formulation is emphasized, we also present the formulation and numerical results for least

  7. Coupling Navier-stokes and Cahn-hilliard Equations in a Two-dimensional Annular flow Configuration

    KAUST Repository

    Vignal, Philippe

    2015-06-01

    In this work, we present a novel isogeometric analysis discretization for the Navier-Stokes- Cahn-Hilliard equation, which uses divergence-conforming spaces. Basis functions generated with this method can have higher-order continuity, and allow to directly discretize the higher- order operators present in the equation. The discretization is implemented in PetIGA-MF, a high-performance framework for discrete differential forms. We present solutions in a two- dimensional annulus, and model spinodal decomposition under shear flow.

  8. Three-dimensional groundwater velocity field in an unconfined aquifer under irrigation

    International Nuclear Information System (INIS)

    Zlotnik, V.

    1990-01-01

    A method for three-dimensional flow velocity calculation has been developed to evaluate unconfined aquifer sensitivity to areal agricultural contamination of groundwater. The methodology of Polubarinova-Kochina is applied to an unconfined homogeneous compressible or incompressible anisotropic aquifer. It is based on a three-dimensional groundwater flow model with a boundary condition on the moving surface. Analytical solutions are obtained for a hydraulic head under the influence of areal sources of circular and rectangular shape using integral transforms. Two-dimensional Hantush formulas result from the vertical averaging of the three-dimensional solutions, and the asymptotic behavior of solutions is analyzed. Analytical expressions for flow velocity components are obtained from the gradient of the hydraulic head field. Areal and temporal variability of specific yield in groundwater recharge areas is also taken into account. As a consequence of linearization of the boundary condition, the operation of any irrigation system with respect to groundwater is represented by superposition of the operating wells and circular and rectangular source influences. Combining the obtained solutions with Dagan or Neuman well functions, one can develop computer codes for the analytical computation of the three-dimensional groundwater hydraulic head and velocity component distributions. Methods for practical implementation are discussed. (Author) (20 refs., 4 figs.)

  9. A coupled three dimensional model of vanadium redox flow battery for flow field designs

    International Nuclear Information System (INIS)

    Yin, Cong; Gao, Yan; Guo, Shaoyun; Tang, Hao

    2014-01-01

    A 3D (three-dimensional) model of VRB (vanadium redox flow battery) with interdigitated flow channel design is proposed. Two different stack inlet designs, single-inlet and multi-inlet, are structured in the model to study the distributions of fluid pressure, electric potential, current density and overpotential during operation of VRB cell. Electrolyte flow rate and stack channel dimension are proved to be the critical factors affecting flow distribution and cell performance. The model developed in this paper can be employed to optimize both VRB stack design and system operation conditions. Further improvements of the model concerning current density and electrode properties are also suggested in the paper. - Highlights: • A coupled three-dimensional model of vanadium redox flow cell is proposed. • Interdigitated flow channels with two different manifold designs are simulated. • Manifold structure affects uniformity of distribution patterns significantly. • Increased electrolyte flow rate improves cell performance for both designs. • Decreased channel size and enlarged land width enhance cell voltage

  10. Effects of radiation and thermal conductivity on MHD boundary layer flow with heat transfer along a vertical stretching sheet in a porous medium

    KAUST Repository

    Ferdows, M.

    2017-03-10

    A steady two-dimensional free convective flow of a viscous incompressible fluid along a vertical stretching sheet with the effect of magnetic field, radiation and variable thermal conductivity in porous media is analyzed. The nonlinear partial differential equations, governing the flow field under consideration, have been transformed by a similarity transformation into a systemof nonlinear ordinary differential equations and then solved numerically. Resulting non-dimensional velocity and temperature profiles are then presented graphically for different values of the parameters. Finally, the effects of the pertinent parameters, which are of physical and engineering interest, are examined both in graphical and tabular form.

  11. Strong solutions for an incompressible Navier-Stokes/Allen-Cahn system with different densities

    Science.gov (United States)

    Li, Yinghua; Huang, Mingxia

    2018-06-01

    In this paper, we investigate a coupled Navier-Stokes/Allen-Cahn system describing a diffuse interface model for two-phase flow of viscous incompressible fluids with different densities in a bounded domain Ω \\subset R^N(N=2,3). We prove the existence and uniqueness of local strong solutions to the initial boundary value problem when the initial density function ρ _0 has a positive lower bound.

  12. Derivation of a correlation for Drag coefficient in two-dimensional bounded supercavitating flows, using artificial neural networks

    Energy Technology Data Exchange (ETDEWEB)

    Shafaghat, R.; Hosseinalipour, S.M.; Derakhshani, S.M.E. [Iran University of Science and Technology, Department of Mechanical Engineering, Tehran (Iran)

    2010-07-15

    Artificial neural networks (ANNs) are used as a new approach for the determination of the relations between drag coefficient and Cavitation Number with cavity geometry in supercavitating flows which have been most widely used in the hydrodynamics researches. Also the result of the ANNs as a cost function potentially will be used in an optimization algorithm. Instead of complex differential equations and limited experimental data, faster and simpler solutions were obtained using equations derived from the ANN model. For training of the ANN the numerical results are used that are obtained from a boundary element method (BEM). At this problem, a two-dimensional supercavitation potential inviscid flow pasts a symmetric two-dimensional cavitator, which is placed perpendicular to the flow in a channel of infinite width and immediately a cavity is formed behind the cavitator. It was found that the coefficient of multiple determination (R{sup 2}-value) between the actual and ANN predicted data is equal to about 0.9998 for the drag coefficient and Cavitation number. As seen from the obtained results, the calculated cavity geometry for all drag coefficients and Cavitation Numbers are obviously within acceptable limits. (orig.)

  13. A Three-Dimensional Model of Two-Phase Flows in a Porous Medium Accounting for Motion of the Liquid–Liquid Interface

    DEFF Research Database (Denmark)

    Shapiro, Alexander A.

    2018-01-01

    A new three-dimensional hydrodynamic model for unsteady two-phase flows in a porous medium, accounting for the motion of the interface between the flowing liquids, is developed. In a minimum number of interpretable geometrical assumptions, a complete system of macroscale flow equations is derived......, their expansion or contraction is also described, while rotation has been proven negligible. A detailed comparison with the previous studies for the two-phase flows accounting for propagation of the interface on micro- and macroscale has been carried out. A numerical algorithm has been developed allowing...

  14. Analysis of a fully developed laminar flow b/w two parallel plates ...

    African Journals Online (AJOL)

    ... Simulation Software Comsol Multiphysics. The flow behavior and the interaction with the boundary has been analysed. Wall no slip conditions were set for evaluation purpose. The analysis is a steady state analysis by using Incompressible Navier Stokes Model. Keywords: Steady state analysis, Velocity profile, Fluid flow.

  15. Numerical study on the two-dimensional flows of plasma and ionizing gas using trial particles

    International Nuclear Information System (INIS)

    Brushlinskij, K.V.; Kozlov, A.N.; Morozov, A.I.

    1985-01-01

    Two-dimensional flows of plasma and ionized αs in a channel between two coaxial electrodes are considered in the MHD-model with account of Hall effect. Stationary solutions of the problem on the flow are obtained either analytically in approximation of a ''smooth'' channel - for ideal conducting plasma, or numerically using the methos of establishment - in the ge-neral case of finite conductivity. A method of further numerical analysis of some peculiarities of flow is suggested in the paper. It is based on studying dynamics of single ''test'' particles in fields of the main MHD plasma flow. Trajectory of the test ion is calculated with account for interaction forces with earlier determined electromagentic field and friction responsible for Coulomb collisions with particles of the background flow. The calculations display trajectories of test particles with different masses, initial positions and initial rates. They are shown to be dose to current lines of background medium in plasma of finite conductivity, that testified to the virtue of effectiveness of the MHD-model. In case of ideal conductivity trajectories of test and background particles can noticeably differ from one another. Stabilization effects of motion of particles accidentally knocked out from the flow and separation of pariticles of different mass by electromao.netic forces are considered

  16. Energy transport in a shear flow of particles in a two-dimensional dusty plasma.

    Science.gov (United States)

    Feng, Yan; Goree, J; Liu, Bin

    2012-11-01

    A shear flow of particles in a laser-driven two-dimensional (2D) dusty plasma is observed in a study of viscous heating and thermal conduction. Video imaging and particle tracking yields particle velocity data, which we convert into continuum data, presented as three spatial profiles: mean particle velocity (i.e., flow velocity), mean-square particle velocity, and mean-square fluctuations of particle velocity. These profiles and their derivatives allow a spatially resolved determination of each term in the energy and momentum continuity equations, which we use for two purposes. First, by balancing these terms so that their sum (i.e., residual) is minimized while varying viscosity η and thermal conductivity κ as free parameters, we simultaneously obtain values for η and κ in the same experiment. Second, by comparing the viscous heating and thermal conduction terms, we obtain a spatially resolved characterization of the viscous heating.

  17. Hamiltonian formalism of two-dimensional Vlasov kinetic equation.

    Science.gov (United States)

    Pavlov, Maxim V

    2014-12-08

    In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.

  18. One-Dimensional, Two-Phase Flow Modeling Toward Interpreting Motor Slag Expulsion Phenomena

    Science.gov (United States)

    Kibbey, Timothy P.

    2012-01-01

    Aluminum oxide slag accumulation and expulsion was previously shown to be a player in various solid rocket motor phenomena, including the Space Shuttle's Reusable Solid Rocket Motor (RSRM) pressure perturbation, or "blip," and phantom moment. In the latter case, such un ]commanded side accelerations near the end of burn have also been identified in several other motor systems. However, efforts to estimate the mass expelled during a given event have come up short. Either bulk calculations are performed without enough physics present, or multiphase, multidimensional Computational Fluid Dynamic analyses are performed that give a snapshot in time and space but do not always aid in grasping the general principle. One ]dimensional, two ]phase compressible flow calculations yield an analytical result for nozzle flow under certain assumptions. This can be carried further to relate the bulk motor parameters of pressure, thrust, and mass flow rate under the different exhaust conditions driven by the addition of condensed phase mass flow. An unknown parameter is correlated to airflow testing with water injection where mass flow rates and pressure are known. Comparison is also made to full ]scale static test motor data where thrust and pressure changes are known and similar behavior is shown. The end goal is to be able to include the accumulation and flow of slag in internal ballistics predictions. This will allow better prediction of the tailoff when much slag is ejected and of mass retained versus time, believed to be a contributor to the widely-observed "flight knockdown" parameter.

  19. Wind turbine rotor-tower interaction using an incompressible overset grid method

    DEFF Research Database (Denmark)

    Zahle, Frederik; Johansen, Jeppe; Sørensen, Niels N.

    2007-01-01

    In this paper 3D Navier-Stokes simulations of the flow over the NREL Phase VI turbine are presented. The computations are carried out using the structured grid, incompressible, finite volume flow solver EllipSys3D, which has been extended to include the use of overset grids. Computations are pres...

  20. A six-mode truncation of the Navier-Stokes equations on a two-dimensional torus: a numerical study

    International Nuclear Information System (INIS)

    Angelo, P.M.; Riela, G.

    1981-01-01

    We study a model obtained from a six-mode truncation of the Navier-Stokes equations for a two-dimensional incompressible fluid on a torus. We find that at low values of the Reynolds number R the dynamics is characterized by fixed points and, at large values of R, by two stable periodic orbits; at intermediate values of R two infinite sequences of bifurcations of periodic orbits into periodic orbits of doubled period lead to two regions of ''turbulent'' or ''chaotic'' behaviour. The turbulent regions end up for values of R for which stable periodic orbits appear. (author)

  1. Edge instability in incompressible planar active fluids

    Science.gov (United States)

    Nesbitt, David; Pruessner, Gunnar; Lee, Chiu Fan

    2017-12-01

    Interfacial instability is highly relevant to many important biological processes. A key example arises in wound healing experiments, which observe that an epithelial layer with an initially straight edge does not heal uniformly. We consider the phenomenon in the context of active fluids. Improving upon the approximation used by Zimmermann, Basan, and Levine [Eur. Phys. J.: Spec. Top. 223, 1259 (2014), 10.1140/epjst/e2014-02189-7], we perform a linear stability analysis on a two-dimensional incompressible hydrodynamic model of an active fluid with an open interface. We categorize the stability of the model and find that for experimentally relevant parameters, fingering instability is always absent in this minimal model. Our results point to the crucial role of density variation in the fingering instability in tissue regeneration.

  2. Three-dimensional local ALE-FEM method for fluid flow in domains containing moving boundaries/objects interfaces

    Energy Technology Data Exchange (ETDEWEB)

    Carrington, David Bradley [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Monayem, A. K. M. [Univ. of New Mexico, Albuquerque, NM (United States); Mazumder, H. [Univ. of New Mexico, Albuquerque, NM (United States); Heinrich, Juan C. [Univ. of New Mexico, Albuquerque, NM (United States)

    2015-03-05

    A three-dimensional finite element method for the numerical simulations of fluid flow in domains containing moving rigid objects or boundaries is developed. The method falls into the general category of Arbitrary Lagrangian Eulerian methods; it is based on a fixed mesh that is locally adapted in the immediate vicinity of the moving interfaces and reverts to its original shape once the moving interfaces go past the elements. The moving interfaces are defined by separate sets of marker points so that the global mesh is independent of interface movement and the possibility of mesh entanglement is eliminated. The results is a fully robust formulation capable of calculating on domains of complex geometry with moving boundaries or devises that can also have a complex geometry without danger of the mesh becoming unsuitable due to its continuous deformation thus eliminating the need for repeated re-meshing and interpolation. Moreover, the boundary conditions on the interfaces are imposed exactly. This work is intended to support the internal combustion engines simulator KIVA developed at Los Alamos National Laboratories. The model's capabilities are illustrated through application to incompressible flows in different geometrical settings that show the robustness and flexibility of the technique to perform simulations involving moving boundaries in a three-dimensional domain.

  3. On the solvability of asymmetric quasilinear finite element approximate problems in nonlinear incompressible elasticity

    International Nuclear Information System (INIS)

    Ruas, V.

    1982-09-01

    A class of simplicial finite elements for solving incompressible elasticity problems in n-dimensional space, n=2 or 3, is presented. An asymmetric structure of the shape functions with respect to the centroid of the simplex, renders them particularly stable in the large strain case, in which the incompressibility condition is nonlinear. It is proved that under certain assembling conditions of the elements, there exists a solution to the corresponding discrete problems. Numerical examples illustrate the efficiency of the method. (Author) [pt

  4. An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids

    Science.gov (United States)

    English, R. Elliot; Qiu, Linhai; Yu, Yue; Fedkiw, Ronald

    2013-12-01

    We present a novel method for discretizing the incompressible Navier-Stokes equations on a multitude of moving and overlapping Cartesian grids each with an independently chosen cell size to address adaptivity. Advection is handled with first and second order accurate semi-Lagrangian schemes in order to alleviate any time step restriction associated with small grid cell sizes. Likewise, an implicit temporal discretization is used for the parabolic terms including Navier-Stokes viscosity which we address separately through the development of a method for solving the heat diffusion equations. The most intricate aspect of any such discretization is the method used in order to solve the elliptic equation for the Navier-Stokes pressure or that resulting from the temporal discretization of parabolic terms. We address this by first removing any degrees of freedom which duplicately cover spatial regions due to overlapping grids, and then providing a discretization for the remaining degrees of freedom adjacent to these regions. We observe that a robust second order accurate symmetric positive definite readily preconditioned discretization can be obtained by constructing a local Voronoi region on the fly for each degree of freedom in question in order to obtain both its stencil (logically connected neighbors) and stencil weights. Internal curved boundaries such as at solid interfaces are handled using a simple immersed boundary approach which is directly applied to the Voronoi mesh in both the viscosity and pressure solves. We independently demonstrate each aspect of our approach on test problems in order to show efficacy and convergence before finally addressing a number of common test cases for incompressible flow with stationary and moving solid bodies.

  5. Oberbeck-Bousinesq approximation for the motion of two incompressible fluids

    Czech Academy of Sciences Publication Activity Database

    Denisova, I.V.; Nečasová, Šárka

    2009-01-01

    Roč. 159, č. 4 (2009), s. 436-451 ISSN 1072-3374 R&D Projects: GA AV ČR IAA100190804; GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : surface tension * Oberbeck -Bousinesq approximation * incompressible fluids Subject RIV: BA - General Mathematics

  6. A computational model for viscous fluid flow, heat transfer, and melting in in situ vitrification melt pools

    International Nuclear Information System (INIS)

    McHugh, P.R.; Ramshaw, J.D.

    1991-11-01

    MAGMA is a FORTRAN computer code designed to viscous flow in in situ vitrification melt pools. It models three-dimensional, incompressible, viscous flow and heat transfer. The momentum equation is coupled to the temperature field through the buoyancy force terms arising from the Boussinesq approximation. All fluid properties, except density, are assumed variable. Density is assumed constant except in the buoyancy force terms in the momentum equation. A simple melting model based on the enthalpy method allows the study of the melt front progression and latent heat effects. An indirect addressing scheme used in the numerical solution of the momentum equation voids unnecessary calculations in cells devoid of liquid. Two-dimensional calculations can be performed using either rectangular or cylindrical coordinates, while three-dimensional calculations use rectangular coordinates. All derivatives are approximated by finite differences. The incompressible Navier-Stokes equations are solved using a new fully implicit iterative technique, while the energy equation is differenced explicitly in time. Spatial derivatives are written in conservative form using a uniform, rectangular, staggered mesh based on the marker and cell placement of variables. Convective terms are differenced using a weighted average of centered and donor cell differencing to ensure numerical stability. Complete descriptions of MAGMA governing equations, numerics, code structure, and code verification are provided. 14 refs

  7. A computational model for viscous fluid flow, heat transfer, and melting in in situ vitrification melt pools

    Energy Technology Data Exchange (ETDEWEB)

    McHugh, P.R.; Ramshaw, J.D.

    1991-11-01

    MAGMA is a FORTRAN computer code designed to viscous flow in in situ vitrification melt pools. It models three-dimensional, incompressible, viscous flow and heat transfer. The momentum equation is coupled to the temperature field through the buoyancy force terms arising from the Boussinesq approximation. All fluid properties, except density, are assumed variable. Density is assumed constant except in the buoyancy force terms in the momentum equation. A simple melting model based on the enthalpy method allows the study of the melt front progression and latent heat effects. An indirect addressing scheme used in the numerical solution of the momentum equation voids unnecessary calculations in cells devoid of liquid. Two-dimensional calculations can be performed using either rectangular or cylindrical coordinates, while three-dimensional calculations use rectangular coordinates. All derivatives are approximated by finite differences. The incompressible Navier-Stokes equations are solved using a new fully implicit iterative technique, while the energy equation is differenced explicitly in time. Spatial derivatives are written in conservative form using a uniform, rectangular, staggered mesh based on the marker and cell placement of variables. Convective terms are differenced using a weighted average of centered and donor cell differencing to ensure numerical stability. Complete descriptions of MAGMA governing equations, numerics, code structure, and code verification are provided. 14 refs.

  8. Two-dimensional flow characteristics of wave interactions with a free-rolling rectangular structure

    Energy Technology Data Exchange (ETDEWEB)

    Kwang Hyo Jung; Kuang-An Chang [Texas A and M University, College Station, TX (United States). Dept. of Civil Engineering; Huang, E.T. [Naval Facilities Engineering Service Center, Port Hueneme, CA (United States). Amphibious System Div.

    2005-01-01

    This paper presents laboratory observations of flow characteristics for regular waves passing a rectangular structure in a two-dimensional wave tank. The structure with a draft one-half of its height was hinged at the center of gravity and free to roll (one degree of freedom) by waves. Particle image velocimetry (PIV) was used to measure the velocity field in the vicinity of the structure. The mean velocity and turbulence properties were obtained by phase-averaging the PIV velocity maps from repeated test runs. Since the viscous damping (also called the eddy making damping) in a vortical flow affects the roll motion of a blunt body, the quantitative flow pattern was represented to elucidate the coupled interactions between the body motion and the waves. Additionally, the turbulence properties including the turbulence length scale and the turbulent kinetic energy budget were investigated to characterize the interactions. The results show that vortices were generated near the structure corners at locations opposing to that of the roll damping effect for waves with a period longer than the roll natural period of the structure. (Author)

  9. Additional band broadening of peptides in the first size-exclusion chromatographic dimension of an automated stop-flow two-dimensional high performance liquid chromatography.

    Science.gov (United States)

    Xu, Jucai; Sun-Waterhouse, Dongxiao; Qiu, Chaoying; Zhao, Mouming; Sun, Baoguo; Lin, Lianzhu; Su, Guowan

    2017-10-27

    The need to improve the peak capacity of liquid chromatography motivates the development of two-dimensional analysis systems. This paper presented a fully automated stop-flow two-dimensional liquid chromatography system with size exclusion chromatography followed by reversed phase liquid chromatography (SEC×RPLC) to efficiently separate peptides. The effects of different stop-flow operational parameters (stop-flow time, peak parking position, number of stop-flow periods and column temperature) on band broadening in the first dimension (1 st D) SEC column were quantitatively evaluated by using commercial small proteins and peptides. Results showed that the effects of peak parking position and the number of stop-flow periods on band broadening were relatively small. Unlike stop-flow analysis of large molecules with a long running time, additional band broadening was evidently observed for small molecule analytes due to the relatively high effective diffusion coefficient (D eff ). Therefore, shorter analysis time and lower 1 st D column temperature were suggested for analyzing small molecules. The stop-flow two-dimensional liquid chromatography (2D-LC) system was further tested on peanut peptides and an evidently improved resolution was observed for both stop-flow heart-cutting and comprehensive 2D-LC analysis (in spite of additional band broadening in SEC). The stop-flow SEC×RPLC, especially heart-cutting analysis with shorter analysis time and higher 1 st D resolution for selected fractions, offers a promising approach for efficient analysis of complex samples. Copyright © 2017 Elsevier B.V. All rights reserved.

  10. Characterization of the supersonic flowing microwave discharge using two dimensional plasma tomography

    Energy Technology Data Exchange (ETDEWEB)

    Nikolic, M.; Samolov, A.; Popovic, S.; Vuskovic, L.; Godunov, A. [Department of Physics, Center for Accelerator Science, Old Dominion University, Norfolk, Virginia 23529 (United States); Cuckov, F. [Department of Electrical and Computer Engineering, Old Dominion University, Norfolk, Virginia 23529 (United States)

    2013-03-14

    A tomographic numerical method based on the two-dimensional Radon formula for a cylindrical cavity has been employed for obtaining spatial distributions of the argon excited levels. The spectroscopy measurements were taken at different positions and directions to observe populations of excited species in the plasmoid region and the corresponding excitation temperatures. Excited argon states are concentrated near the tube walls, thus, confirming the assumption that the post discharge plasma is dominantly sustained by travelling surface wave. An automated optical measurement system has been developed for reconstruction of local plasma parameters of the plasmoid structure formed in an argon supersonic flowing microwave discharge. The system carries out angle and distance measurements using a rotating, flat mirror, as well as two high precision stepper motors operated by a microcontroller-based system and several sensors for precise feedback control.

  11. Topology of two-dimensional turbulent flows of dust and gas

    Science.gov (United States)

    Mitra, Dhrubaditya; Perlekar, Prasad

    2018-04-01

    We perform direct numerical simulations (DNS) of passive heavy inertial particles (dust) in homogeneous and isotropic two-dimensional turbulent flows (gas) for a range of Stokes number, StDNS confirms that the statistics of topological properties of B are the same in Eulerian and Lagrangian frames only if the Eulerian data are weighed by the dust density. We use this correspondence to study the statistics of topological properties of A in the Lagrangian frame from our Eulerian simulations by calculating density-weighted probability distribution functions. We further find that in the Lagrangian frame, the mean value of the trace of A is negative and its magnitude increases with St approximately as exp(-C /St) with a constant C ≈0.1 . The statistical distribution of different topological structures that appear in the dust flow is different in Eulerian and Lagrangian (density-weighted Eulerian) cases, particularly for St close to unity. In both of these cases, for small St the topological structures have close to zero divergence and are either vortical (elliptic) or strain dominated (hyperbolic, saddle). As St increases, the contribution to negative divergence comes mostly from saddles and the contribution to positive divergence comes from both vortices and saddles. Compared to the Eulerian case, the Lagrangian (density-weighted Eulerian) case has less outward spirals and more converging saddles. Inward spirals are the least probable topological structures in both cases.

  12. The Theory of Nearly Incompressible Magnetohydrodynamic Turbulence: Homogeneous Description

    Science.gov (United States)

    Zank, G. P.; Adhikari, L.; Hunana, P.; Shiota, D.; Bruno, R.; Telloni, D.; Avinash, K.

    2017-09-01

    The theory of nearly incompressible magnetohydrodynamics (NI MHD) was developed to understand the apparent incompressibility of the solar wind and other plasma environments, particularly the relationship of density fluctuations to incompressible manifestations of turbulence in the solar wind and interstellar medium. Of interest was the identification of distinct leading-order incompressible descriptions for plasma beta β ≫ 1 and β ∼ 1 or ≪ 1 environments. In the first case, the “dimensionality” of the MHD description is 3D whereas for the latter two, there is a collapse of dimensionality in that the leading-order incompressible MHD description is 2D in a plane orthogonal to the large-scale or mean magnetic field. Despite the success of NI MHD in describing fluctuations in a low-frequency plasma environment such as the solar wind, a basic turbulence description has not been developed. Here, we rewrite the NI MHD system in terms of Elsässer variables. We discuss the distinction that emerges between the three cases. However, we focus on the β ∼ 1 or ≪ 1 regimes since these are appropriate to the solar wind and solar corona. In both cases, the leading-order turbulence model describes 2D turbulence and the higher-order description corresponds to slab turbulence, which forms a minority component. The Elsäasser β ∼ 1 or ≪ 1 formulation exhibits the nonlinear couplings between 2D and slab components very clearly, and shows that slab fluctuations respond in a passive scalar sense to the turbulently evolving majority 2D component fluctuations. The coupling of 2D and slab fluctuations through the β ∼ 1 or ≪ 1 NI MHD description leads to a very natural emergence of the “Goldreich-Sridhar” critical balance scaling parameter, although now with a different interpretation. Specifically, the critical balance parameter shows that the energy flux in wave number space is a consequence of the intensity of Alfvén wave sweeping versus passive scalar

  13. Numerical simulations of natural or mixed convection in vertical channels: comparisons of level-set numerical schemes for the modeling of immiscible incompressible fluid flows

    International Nuclear Information System (INIS)

    Li, R.

    2012-01-01

    The aim of this research dissertation is at studying natural and mixed convections of fluid flows, and to develop and validate numerical schemes for interface tracking in order to treat incompressible and immiscible fluid flows, later. In a first step, an original numerical method, based on Finite Volume discretizations, is developed for modeling low Mach number flows with large temperature gaps. Three physical applications on air flowing through vertical heated parallel plates were investigated. We showed that the optimum spacing corresponding to the peak heat flux transferred from an array of isothermal parallel plates cooled by mixed convection is smaller than those for natural or forced convections when the pressure drop at the outlet keeps constant. We also proved that mixed convection flows resulting from an imposed flow rate may exhibit unexpected physical solutions; alternative model based on prescribed total pressure at inlet and fixed pressure at outlet sections gives more realistic results. For channels heated by heat flux on one wall only, surface radiation tends to suppress the onset of re-circulations at the outlet and to unify the walls temperature. In a second step, the mathematical model coupling the incompressible Navier-Stokes equations and the Level-Set method for interface tracking is derived. Improvements in fluid volume conservation by using high order discretization (ENO-WENO) schemes for the transport equation and variants of the signed distance equation are discussed. (author)

  14. Effects of Thermal Radiation and Chemical Reaction on MHD Free Convection Flow past a Flat Plate with Heat Source and Convective Surface Boundary Condition

    OpenAIRE

    E.Hemalatha; N. Bhaskar Reddy

    2015-01-01

    This paper analyzes the radiation and chemical reaction effects on MHD steady two-dimensional laminar viscous incompressible radiating boundary layer flow over a flat plate in the presence of internal heat generation and convective boundary condition. It is assumed that lower surface of the plate is in contact with a hot fluid while a stream of cold fluid flows steadily over the upper surface with a heat source that decays exponentially. The Rosseland approximation is used to desc...

  15. Hall effects on unsteady MHD flow between two rotating disks with non-coincident parallel axes

    Energy Technology Data Exchange (ETDEWEB)

    Barik, R.N., E-mail: barik.rabinarayan@rediffmail.com [Department of Mathematics, Trident Academy of Technology, Bhubaneswar (India); Dash, G.C., E-mail: gcdash@indiatimes.com [Department of Mathematics, S.O.A. University, Bhubaneswar (India); Rath, P.K., E-mail: pkrath_1967@yahoo.in [Department of Mathematics, B.R.M. International Institute of Technology, Bhubaneswar (India)

    2013-01-15

    Hall effects on the unsteady MHD rotating flow of a viscous incompressible electrically conducting fluid between two rotating disks with non-coincident parallel axes have been studied. There exists an axisymmetric solution to this problem. The governing equations are solved by applying Laplace transform method. It is found that the torque experienced by the disks decreases with an increase in either the Hall parameter, m or the rotation parameter, S{sup 2}. Further, the axis of rotation has no effect on the fluid flow. (author)

  16. Hall effects on unsteady MHD flow between two rotating disks with non-coincident parallel axes

    International Nuclear Information System (INIS)

    Barik, R.N.; Dash, G.C.; Rath, P.K.

    2013-01-01

    Hall effects on the unsteady MHD rotating flow of a viscous incompressible electrically conducting fluid between two rotating disks with non-coincident parallel axes have been studied. There exists an axisymmetric solution to this problem. The governing equations are solved by applying Laplace transform method. It is found that the torque experienced by the disks decreases with an increase in either the Hall parameter, m or the rotation parameter, S 2 . Further, the axis of rotation has no effect on the fluid flow. (author)

  17. On three-dimensional incompressible Navier-Stokes fluid on cantor sets in spherical Cantor type co-ordinate system

    Directory of Open Access Journals (Sweden)

    Meng Zhi-Jun

    2016-01-01

    Full Text Available This paper addresses the systems of the incompressible Navier-Stokes equations on Cantor sets without the external force involving the fractal heat-conduction problem vial local fractional derivative. The spherical Cantor type co-ordinate method is used to transfer the incompressible Navier-Stokes equation from the Cantorian co-ordinate system into the spherical Cantor type co-ordinate system.

  18. Two dimensional heat transfer problem in flow boiling in a rectangular minichannel

    Directory of Open Access Journals (Sweden)

    Hożejowska Sylwia

    2015-01-01

    Full Text Available The paper presents mathematical modelling of flow boiling heat transfer in a rectangular minichannel asymmetrically heated by a thin and one-sided enhanced foil. Both surfaces are available for observations due to the openings covered with glass sheets. Thus, changes in the colour of the plain foil surface can be registered and then processed. Plain side of the heating foil is covered with a base coat and liquid crystal paint. Observation of the opposite, enhanced surface of the minichannel allows for identification of the gas-liquid two-phase flow patterns and vapour quality. A two-dimensional mathematical model of heat transfer in three subsequent layers (sheet glass, heating foil, liquid was proposed. Heat transfer in all these layers was described with the respective equations: Laplace equation, Poisson equation and energy equation, subject to boundary conditions corresponding to the observed physical process. The solutions (temperature distributions in all three layers were obtained by Trefftz method. Additionally, the temperature of the boiling liquid was obtained by homotopy perturbation method (HPM combined with Trefftz method. The heat transfer coefficient, derived from Robin boundary condition, was estimated in both approaches. In comparison, the results by both methods show very good agreement especially when restricted to the thermal sublayer.

  19. Computational study of duct and pipe flows using the method of pseudocompressibility

    Science.gov (United States)

    Williams, Robert W.

    1991-01-01

    A viscous, three-dimensional, incompressible, Navier-Stokes Computational Fluid Dynamics code employing pseudocompressibility is used for the prediction of laminar primary and secondary flows in two 90-degree bends of constant cross section. Under study are a square cross section duct bend with 2.3 radius ratio and a round cross section pipe bend with 2.8 radius ratio. Sensitivity of predicted primary and secondary flow to inlet boundary conditions, grid resolution, and code convergence is investigated. Contour and velocity versus spanwise coordinate plots comparing prediction to experimental data flow components are shown at several streamwise stations before, within, and after the duct and pipe bends. Discussion includes secondary flow physics, computational method, computational requirements, grid dependence, and convergence rates.

  20. An efficient algorithm for incompressible N-phase flows

    International Nuclear Information System (INIS)

    Dong, S.

    2014-01-01

    We present an efficient algorithm within the phase field framework for simulating the motion of a mixture of N (N⩾2) immiscible incompressible fluids, with possibly very different physical properties such as densities, viscosities, and pairwise surface tensions. The algorithm employs a physical formulation for the N-phase system that honors the conservations of mass and momentum and the second law of thermodynamics. We present a method for uniquely determining the mixing energy density coefficients involved in the N-phase model based on the pairwise surface tensions among the N fluids. Our numerical algorithm has several attractive properties that make it computationally very efficient: (i) it has completely de-coupled the computations for different flow variables, and has also completely de-coupled the computations for the (N−1) phase field functions; (ii) the algorithm only requires the solution of linear algebraic systems after discretization, and no nonlinear algebraic solve is needed; (iii) for each flow variable the linear algebraic system involves only constant and time-independent coefficient matrices, which can be pre-computed during pre-processing, despite the variable density and variable viscosity of the N-phase mixture; (iv) within a time step the semi-discretized system involves only individual de-coupled Helmholtz-type (including Poisson) equations, despite the strongly-coupled phase–field system of fourth spatial order at the continuum level; (v) the algorithm is suitable for large density contrasts and large viscosity contrasts among the N fluids. Extensive numerical experiments have been presented for several problems involving multiple fluid phases, large density contrasts and large viscosity contrasts. In particular, we compare our simulations with the de Gennes theory, and demonstrate that our method produces physically accurate results for multiple fluid phases. We also demonstrate the significant and sometimes dramatic effects of the

  1. Fast chemical reaction in two-dimensional Navier-Stokes flow: initial regime.

    Science.gov (United States)

    Ait-Chaalal, Farid; Bourqui, Michel S; Bartello, Peter

    2012-04-01

    This paper studies an infinitely fast bimolecular chemical reaction in a two-dimensional biperiodic Navier-Stokes flow. The reactants in stoichiometric quantities are initially segregated by infinite gradients. The focus is placed on the initial stage of the reaction characterized by a well-defined one-dimensional material contact line between the reactants. Particular attention is given to the effect of the diffusion κ of the reactants. This study is an idealized framework for isentropic mixing in the lower stratosphere and is motivated by the need to better understand the effect of resolution on stratospheric chemistry in climate-chemistry models. Adopting a Lagrangian straining theory approach, we relate theoretically the ensemble mean of the length of the contact line, of the gradients along it, and of the modulus of the time derivative of the space-average reactant concentrations (here called the chemical speed) to the joint probability density function of the finite-time Lyapunov exponent λ with two times τ and τ[over ̃]. The time 1/λ measures the stretching time scale of a Lagrangian parcel on a chaotic orbit up to a finite time t, while τ measures it in the recent past before t, and τ[over ̃] in the early part of the trajectory. We show that the chemical speed scales like κ(1/2) and that its time evolution is determined by rare large events in the finite-time Lyapunov exponent distribution. The case of smooth initial gradients is also discussed. The theoretical results are tested with an ensemble of direct numerical simulations (DNSs) using a pseudospectral model.

  2. Turbulence prediction in two-dimensional bundle flows using large eddy simulation

    Energy Technology Data Exchange (ETDEWEB)

    Ibrahim, W.A.; Hassan, Y.A. [Texas A& M Univ., College Station, TX (United States)

    1995-09-01

    Turbulent flow is characterized by random fluctuations in the fluid velocity and by intense mixing of the fluid. Due to velocity fluctuations, a wide range of eddies exists in the flow field. Because these eddies carry mass, momentum, and energy, this enhanced mixing can sometimes lead to serious problems, such as tube vibrations in many engineering systems that include fluid-tube bundle combinations. Nuclear fuel bundles and PWR steam generators are existing examples in nuclear power plants. Fluid-induced vibration problems are often discovered during the operation of such systems because some of the fluid-tube interaction characteristics are not fully understood. Large Eddy Simulation, incorporated in a three dimensional computer code, became one of the promising techniques to estimate flow turbulence, predict and prevent of long-term tube fretting affecting PWR steam generators. the present turbulence investigations is a step towards more understanding of fluid-tube interaction characteristics by comparing the tube bundles with various pitch-to-diameter ratios were performed. Power spectral densities were used for comparison with experimental data. Correlations, calculations of different length scales in the flow domain and other important turbulent-related parameters were calculated. Finally, important characteristics of turbulent flow field were presented with the aid of flow visualization with tracers impeded in the flow field.

  3. CORPORATE VALUATION USING TWO-DIMENSIONAL MONTE CARLO SIMULATION

    Directory of Open Access Journals (Sweden)

    Toth Reka

    2010-12-01

    Full Text Available In this paper, we have presented a corporate valuation model. The model combine several valuation methods in order to get more accurate results. To determine the corporate asset value we have used the Gordon-like two-stage asset valuation model based on the calculation of the free cash flow to the firm. We have used the free cash flow to the firm to determine the corporate market value, which was calculated with use of the Black-Scholes option pricing model in frame of the two-dimensional Monte Carlo simulation method. The combined model and the use of the two-dimensional simulation model provides a better opportunity for the corporate value estimation.

  4. Two-dimensional heat flow analysis applied to heat sterilization of ponderosa pine and Douglas-fir square timbers

    Science.gov (United States)

    William T. Simpson

    2004-01-01

    Equations for a two-dimensional finite difference heat flow analysis were developed and applied to ponderosa pine and Douglas-fir square timbers to calculate the time required to heat the center of the squares to target temperature. The squares were solid piled, which made their surfaces inaccessible to the heating air, and thus surface temperatures failed to attain...

  5. Modeling water droplet condensation and evaporation in DNS of turbulent channel flow

    Energy Technology Data Exchange (ETDEWEB)

    Russo, E; Kuerten, J G M; Geld, C W M van der [Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven (Netherlands); Geurts, B J, E-mail: e.russo@tue.nl [Faculty EEMCS, University of Twente, PO Box 217, 7500 AE Enschede (Netherlands)

    2011-12-22

    In this paper a point particle model for two-way coupling in water droplet-laden incompressible turbulent flow of air is proposed. The model is based on conservation laws and semi-empirical correlations. It has been implemented and tested in a DNS code based for turbulent channel flow with an Eulerian-Lagrangian approach. The two-way coupling is investigated in terms of the effects of mass and heat transfer on the droplets distributions along the channel wall-normal direction and by comparison of the droplet temperature statistics with respect to the case without evaporation and condensation. A remarkable conclusion is that the presence of evaporating and condensing droplets results in an increase in the non-dimensional heat transfer coefficient of the channel flow represented by the Nusselt number.

  6. Methodology and optimization in the design and analysis of the efficiency of incompressible fluid turbomachines; Methodologie et optimisation dans la conception et l'analyse des performances des turbomachines a fluide incompressible

    Energy Technology Data Exchange (ETDEWEB)

    Asuaje, M.

    2003-07-15

    Faced with the problem of design in the pump industry, the main difficulty of manufacturers is to have fast, reliable and accurate methods. This research work involving, both theory and experiments deals, with this topic. We have developed a complete procedure for design, performance analysis and optimization of centrifugal and mixed incompressible flow turbomachinery. First of all, the definition of the pump geometry as well as the analysis of its global performance are carried out starting from the mean streamline method (1D), based on both ideal models and experimental correlations. A second stage of optimization is achieved from a quasi 3D method, by studying the meridional flow and blade to blade flow, using REMIX software developed by LEMFI. Finally, a three-dimensional flow study is performed by CFD tools from AEA-Technology group (CFX). The three-dimensional study provides the means to complete and validate the established procedure. To illustrate this procedure, a centrifugal machine with a volute was studied used. First, the analysis of the existing impeller was carried out to develop the various steps of the procedure. Then, the whole impeller-volute pump, was studied and compared with the previous trial runs. Special attention was paid to unsteady effects, resulting from impeller volute interaction. The results obtained are satisfactory. Finally, the integral method was applied to optimize a mixed flow pump equipped with a de-swirl. As it is a badly dimensioned pump, it is a good example of what this method can do. (author)

  7. A finite area scheme for shallow granular flows on three-dimensional surfaces

    Science.gov (United States)

    Rauter, Matthias

    2017-04-01

    Shallow granular flow models have become a popular tool for the estimation of natural hazards, such as landslides, debris flows and avalanches. The shallowness of the flow allows to reduce the three-dimensional governing equations to a quasi two-dimensional system. Three-dimensional flow fields are replaced by their depth-integrated two-dimensional counterparts, which yields a robust and fast method [1]. A solution for a simple shallow granular flow model, based on the so-called finite area method [3] is presented. The finite area method is an adaption of the finite volume method [4] to two-dimensional curved surfaces in three-dimensional space. This method handles the three dimensional basal topography in a simple way, making the model suitable for arbitrary (but mildly curved) topography, such as natural terrain. Furthermore, the implementation into the open source software OpenFOAM [4] is shown. OpenFOAM is a popular computational fluid dynamics application, designed so that the top-level code mimics the mathematical governing equations. This makes the code easy to read and extendable to more sophisticated models. Finally, some hints on how to get started with the code and how to extend the basic model will be given. I gratefully acknowledge the financial support by the OEAW project "beyond dense flow avalanches". Savage, S. B. & Hutter, K. 1989 The motion of a finite mass of granular material down a rough incline. Journal of Fluid Mechanics 199, 177-215. Ferziger, J. & Peric, M. 2002 Computational methods for fluid dynamics, 3rd edn. Springer. Tukovic, Z. & Jasak, H. 2012 A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow. Computers & fluids 55, 70-84. Weller, H. G., Tabor, G., Jasak, H. & Fureby, C. 1998 A tensorial approach to computational continuum mechanics using object-oriented techniques. Computers in physics 12(6), 620-631.

  8. INHOMOGENEOUS NEARLY INCOMPRESSIBLE DESCRIPTION OF MAGNETOHYDRODYNAMIC TURBULENCE

    International Nuclear Information System (INIS)

    Hunana, P.; Zank, G. P.

    2010-01-01

    The nearly incompressible theory of magnetohydrodynamics (MHD) is formulated in the presence of a static large-scale inhomogeneous background. The theory is an inhomogeneous generalization of the homogeneous nearly incompressible MHD description of Zank and Matthaeus and a polytropic equation of state is assumed. The theory is primarily developed to describe solar wind turbulence where the assumption of a composition of two-dimensional (2D) and slab turbulence with the dominance of the 2D component has been used for some time. It was however unclear, if in the presence of a large-scale inhomogeneous background, the dominant component will also be mainly 2D and we consider three distinct MHD regimes for the plasma beta β > 1. For regimes appropriate to the solar wind (β 2 s δp is not valid for the leading-order O(M) density fluctuations, and therefore in observational studies, the density fluctuations should not be analyzed through the pressure fluctuations. The pseudosound relation is valid only for higher order O(M 2 ) density fluctuations, and then only for short-length scales and fast timescales. The spectrum of the leading-order density fluctuations should be modeled as k -5/3 in the inertial range, followed by a Bessel function solution K ν (k), where for stationary turbulence ν = 1, in the viscous-convective and diffusion range. Other implications for solar wind turbulence with an emphasis on the evolution of density fluctuations are also discussed.

  9. Development of discrete gas kinetic scheme for simulation of 3D viscous incompressible and compressible flows

    Science.gov (United States)

    Yang, L. M.; Shu, C.; Wang, Y.; Sun, Y.

    2016-08-01

    The sphere function-based gas kinetic scheme (GKS), which was presented by Shu and his coworkers [23] for simulation of inviscid compressible flows, is extended to simulate 3D viscous incompressible and compressible flows in this work. Firstly, we use certain discrete points to represent the spherical surface in the phase velocity space. Then, integrals along the spherical surface for conservation forms of moments, which are needed to recover 3D Navier-Stokes equations, are approximated by integral quadrature. The basic requirement is that these conservation forms of moments can be exactly satisfied by weighted summation of distribution functions at discrete points. It was found that the integral quadrature by eight discrete points on the spherical surface, which forms the D3Q8 discrete velocity model, can exactly match the integral. In this way, the conservative variables and numerical fluxes can be computed by weighted summation of distribution functions at eight discrete points. That is, the application of complicated formulations resultant from integrals can be replaced by a simple solution process. Several numerical examples including laminar flat plate boundary layer, 3D lid-driven cavity flow, steady flow through a 90° bending square duct, transonic flow around DPW-W1 wing and supersonic flow around NACA0012 airfoil are chosen to validate the proposed scheme. Numerical results demonstrate that the present scheme can provide reasonable numerical results for 3D viscous flows.

  10. Direct numerical simulation of the passive scalar field in a two-dimensional turbulent channel flow

    International Nuclear Information System (INIS)

    Kasagi, N.; Tomita, Y.; Kuroda, A.

    1991-01-01

    This paper reports on a direct numerical simulation (DNS) of the fully developed thermal field in a two-dimensional turbulent channel flow of air that was carried out. The iso-flux condition is imposed on the walls so that the local mean temperature linearly increases in the streamwise direction. The computation was executed on 1,589,248 grid points by using a spectral method. The statistics obtained include rms velocity and temperature fluctuations, Reynolds stresses, turbulent heat fluxes and other higher order correlations. They are compared mainly with the DNS data obtained by Kim and Moin (1987) and Kim (1987) in a higher Reynolds number flow with isothermal walls. Agreement between these two results is generally good. Each term in the budget equations of temperature variance, its dissipation rate and turbulent heat fluxes is also calculated in order to establish a data base of convective heat transfer for thermal turbulence modeling

  11. Three Dimensional Viscous Flow Field in an Axial Flow Turbine Nozzle Passage

    Science.gov (United States)

    Ristic, D.; Lakshminarayana, B.

    1997-01-01

    The objective of this investigation is experimental and computational study of three dimensional viscous flow field in the nozzle passage of an axial flow turbine stage. The nozzle passage flow field has been measured using a two sensor hot-wire probe at various axial and radial stations. In addition, two component LDV measurements at one axial station (x/c(sum m) = 0.56) were performed to measure the velocity field. Static pressure measurements and flow visualization, using a fluorescent oil technique, were also performed to obtain the location of transition and the endwall limiting streamlines. A three dimensional boundary layer code, with a simple intermittency transition model, was used to predict the viscous layers along the blade and endwall surfaces. The boundary layers on the blade surface were found to be very thin and mostly laminar, except on the suction surface downstream of 70% axial chord. Strong radial pressure gradient, especially close to the suction surface, induces strong cross flow components in the trailing edge regions of the blade. On the end-walls the boundary layers were much thicker, especially near the suction corner of the casing surface, caused by secondary flow. The secondary flow region near the suction-casing surface corner indicates the presence of the passage vortex detached from the blade surface. The corner vortex is found to be very weak. The presence of a closely spaced rotor downstream (20% of the nozzle vane chord) introduces unsteadiness in the blade passage. The measured instantaneous velocity signal was filtered using FFT square window to remove the periodic unsteadiness introduced by the downstream rotor and fans. The filtering decreased the free stream turbulence level from 2.1% to 0.9% but had no influence on the computed turbulence length scale. The computation of the three dimensional boundary layers is found to be accurate on the nozzle passage blade surfaces, away from the end-walls and the secondary flow region. On

  12. A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows

    Science.gov (United States)

    Felici, Helene Marie

    1992-01-01

    A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.

  13. Two dimensional numerical analysis of aerodynamic characteristics for rotating cylinder on concentrated air flow

    Science.gov (United States)

    Alias, M. S.; Rafie, A. S. Mohd; Marzuki, O. F.; Hamid, M. F. Abdul; Chia, C. C.

    2017-12-01

    Over the years, many studies have demonstrated the feasibility of the Magnus effect on spinning cylinder to improve lift production, which can be much higher than the traditional airfoil shape. With this characteristic, spinning cylinder might be used as a lifting device for short take-off distance aircraft or unmanned aerial vehicle (UAV). Nonetheless, there is still a gap in research to explain the use of spinning cylinder as a good lifting device. Computational method is used for this study to analyse the Magnus effect, in which two-dimensional finite element numerical analysis method is applied using ANSYS FLUENT software to examine the coefficients of lift and drag, and to investigate the flow field around the rotating cylinder surface body. Cylinder size of 30mm is chosen and several configurations in steady and concentrated air flows have been evaluated. All in all, it can be concluded that, with the right configuration of the concentrated air flow setup, the rotating cylinder can be used as a lifting device for very short take-off since it can produce very high coefficient of lift (2.5 times higher) compared with steady air flow configuration.

  14. A form of MHD universal equations of unsteady incompressible fluid flow with variable elctroconductivity on heated moving plate

    Directory of Open Access Journals (Sweden)

    Boričić Zoran

    2005-01-01

    Full Text Available This paper deals with laminar, unsteady flow of viscous, incompressible and electro conductive fluid caused by variable motion of flat plate. Fluid electro conductivity is variable. Velocity of the plate is time function. Plate moves in its own plane and in "still" fluid. Present external magnetic filed is perpendicular to the plate. Plate temperature is a function of longitudinal coordinate and time. Viscous dissipation, Joule heat, Hole and polarization effects are neglected. For obtaining of universal equations system general similarity method is used as well as impulse and energy equation of described problem.

  15. Finite elements for the calculation of turbulent flows in three-dimensional complex geometries

    Science.gov (United States)

    Ruprecht, A.

    A finite element program for the calculation of incompressible turbulent flows is presented. In order to reduce the required storage an iterative algorithm is used which solves the necessary equations sequentially. The state of turbulence is defined by the k-epsilon model. In addition to the standard k-epsilon model, the modification of Bardina et al., taking into account the rotation of the mean flow, is investigated. With this program, the flow in the draft tube of a Kaplan turbine is examined. Calculations are carried out for swirling and nonswirling entrance flow. The results are compared with measurements.

  16. Numerical investigations of passive scalar transport in Taylor-Couette flows: Counter-rotation effect

    Science.gov (United States)

    Ouazib, Nabila; Salhi, Yacine; Si-Ahmed, El-Khider; Legrand, Jack; Degrez, G.

    2017-07-01

    Numerical methods for solving convection-diffusion-reaction (CDR) scalar transport equation in three-dimensional flow are used in the present investigation. The flow is confined between two concentric cylinders both the inner cylinder and the outer one are allowed to rotate. Direct numerical simulations (DNS) have been achieved to study the effects of the gravitational and the centrifugal potentials on the stability of incompressible Taylor-Couette flow. The Navier-Stokes equations and the uncoupled convection-diffusion-reaction equation are solved using a spectral development in one direction combined together with a finite element discretization in the two remaining directions. The complexity of the patterns is highlighted. Since, it increases as the rotation rates of the cylinders increase. In addition, the effect of the counter-rotation of the cylinders on the mass transfer is pointed out.

  17. One-dimensional GIS-based model compared with a two-dimensional model in urban floods simulation.

    Science.gov (United States)

    Lhomme, J; Bouvier, C; Mignot, E; Paquier, A

    2006-01-01

    A GIS-based one-dimensional flood simulation model is presented and applied to the centre of the city of Nîmes (Gard, France), for mapping flow depths or velocities in the streets network. The geometry of the one-dimensional elements is derived from the Digital Elevation Model (DEM). The flow is routed from one element to the next using the kinematic wave approximation. At the crossroads, the flows in the downstream branches are computed using a conceptual scheme. This scheme was previously designed to fit Y-shaped pipes junctions, and has been modified here to fit X-shaped crossroads. The results were compared with the results of a two-dimensional hydrodynamic model based on the full shallow water equations. The comparison shows that good agreements can be found in the steepest streets of the study zone, but differences may be important in the other streets. Some reasons that can explain the differences between the two models are given and some research possibilities are proposed.

  18. Effect of TIPS placement on portal and splanchnic arterial blood flow in 4-dimensional flow MRI

    Energy Technology Data Exchange (ETDEWEB)

    Stankovic, Zoran [Northwestern University, Department of Radiology, Feinberg School of Medicine, Chicago, IL (United States); University Medical Center Freiburg, Department of Diagnostic Radiology and Medical Physics, Freiburg (Germany); Roessle, Martin; Schultheiss, Michael [University Medical Center Freiburg, Department of Gastroenterology, Freiburg (Germany); Euringer, Wulf; Langer, Mathias [University Medical Center Freiburg, Department of Diagnostic Radiology and Medical Physics, Freiburg (Germany); Salem, Riad; Barker, Alex; Carr, James; Collins, Jeremy D. [Northwestern University, Department of Radiology, Feinberg School of Medicine, Chicago, IL (United States); Markl, Michael [Northwestern University, Department of Radiology, Feinberg School of Medicine, Chicago, IL (United States); Northwestern University, Department of Biomedical Engineering, McCormick School of Engineering, Chicago, IL (United States)

    2015-09-15

    To assess changes in portal and splanchnic arterial haemodynamics in patients undergoing transjugular intrahepatic portosystemic shunt (TIPS) using four-dimensional (4D) flow MRI, a non-invasive, non-contrast imaging technique. Eleven patients undergoing TIPS implantation were enrolled. K-t GRAPPA accelerated non-contrast 4D flow MRI of the liver vasculature was applied with acceleration factor R = 5 at 3Tesla. Flow analysis included three-dimensional (3D) blood flow visualization using time-resolved 3D particle traces and semi-quantitative flow pattern grading. Quantitative evaluation entailed peak velocities and net flows throughout the arterial and portal venous (PV) systems. MRI measurements were taken within 24 h before and 4 weeks after TIPS placement. Three-dimensional flow visualization with 4D flow MRI revealed good image quality with minor limitations in PV flow. Quantitative analysis revealed a significant increase in PV flow (562 ± 373 ml/min before vs. 1831 ± 965 ml/min after TIPS), in the hepatic artery (176 ± 132 ml/min vs. 354 ± 140 ml/min) and combined flow in splenic and superior mesenteric arteries (770 ml/min vs. 1064 ml/min). Shunt-flow assessment demonstrated stenoses in two patients confirmed and treated at TIPS revision. Four-dimensional flow MRI might have the potential to give new information about the effect of TIPS placement on hepatic perfusion. It may explain some unexpected findings in clinical observation studies. (orig.)

  19. A Three-Dimensional, Immersed Boundary, Finite Volume Method for the Simulation of Incompressible Heat Transfer Flows around Complex Geometries

    Directory of Open Access Journals (Sweden)

    Hassan Badreddine

    2017-01-01

    Full Text Available The current work focuses on the development and application of a new finite volume immersed boundary method (IBM to simulate three-dimensional fluid flows and heat transfer around complex geometries. First, the discretization of the governing equations based on the second-order finite volume method on Cartesian, structured, staggered grid is outlined, followed by the description of modifications which have to be applied to the discretized system once a body is immersed into the grid. To validate the new approach, the heat conduction equation with a source term is solved inside a cavity with an immersed body. The approach is then tested for a natural convection flow in a square cavity with and without circular cylinder for different Rayleigh numbers. The results computed with the present approach compare very well with the benchmark solutions. As a next step in the validation procedure, the method is tested for Direct Numerical Simulation (DNS of a turbulent flow around a surface-mounted matrix of cubes. The results computed with the present method compare very well with Laser Doppler Anemometry (LDA measurements of the same case, showing that the method can be used for scale-resolving simulations of turbulence as well.

  20. Pulsatile turbulent flow through pipe bends at high Dean and Womersley numbers

    Science.gov (United States)

    Kalpakli, Athanasia; Örlü, Ramis; Tillmark, Nils; Alfredsson, P. Henrik

    2011-12-01

    Turbulent pulsatile flows through pipe bends are prevalent in internal combustion engine components which consist of bent pipe sections and branching conduits. Nonetheless, most of the studies related to pulsatile flows in pipe bends focus on incompressible, low Womersley and low Dean number flows, primarily because they aim in modeling blood flow, while internal combustion engine related flows have mainly been addressed in terms of integral quantities and consist of single point measurements. The present study aims at bridging the gap between these two fields by means of time-resolved stereoscopic particle image velocimetry measurements in a pipe bend with conditions that are close to those encountered in exhaust manifolds. The time/phase-resolved three-dimensional cross-sectional flow-field 3 pipe diameters downstream the pipe bend is captured and the interplay between different secondary motions throughout a pulse cycle is discussed.

  1. Pulsatile turbulent flow through pipe bends at high Dean and Womersley numbers

    International Nuclear Information System (INIS)

    Kalpakli, Athanasia; Örlü, Ramis; Tillmark, Nils; Alfredsson, P Henrik

    2011-01-01

    Turbulent pulsatile flows through pipe bends are prevalent in internal combustion engine components which consist of bent pipe sections and branching conduits. Nonetheless, most of the studies related to pulsatile flows in pipe bends focus on incompressible, low Womersley and low Dean number flows, primarily because they aim in modeling blood flow, while internal combustion engine related flows have mainly been addressed in terms of integral quantities and consist of single point measurements. The present study aims at bridging the gap between these two fields by means of time-resolved stereoscopic particle image velocimetry measurements in a pipe bend with conditions that are close to those encountered in exhaust manifolds. The time/phase-resolved three-dimensional cross-sectional flow-field 3 pipe diameters downstream the pipe bend is captured and the interplay between different secondary motions throughout a pulse cycle is discussed.

  2. Lyapunov stability of ideal compressible and incompressible fluid equilibria in three dimensions

    International Nuclear Information System (INIS)

    Holm, D.D.

    1985-08-01

    Linearized stability of ideal compressible and incompressible fluid equilibria in three dimensions is analyzed using Lyapunov's direct method. An action principle is given for the Eulerian and Lagrangian fluid descriptions and the family of constants of motion due to symmetry under fluid-particle relabelling is derived in the form of Ertel's theorem for each description. In an augmented Euleriah description, the steady equilibrium flows of these two fluids theories are identified as critical points of the conserved Lyapunov functionals defined by the sum, H + C, of the energy H, and the Ertel constants of motion, C. It turns out that unconditional linear Lyapunov stability of these flows in the norm provided by the second variation of H + C is precluded by vortex-particle stretching, even for otherwise shear-stable flows. Conditional Lyapunov stability of these flows is discussed. 24 refs

  3. Dissipation, intermittency, and singularities in incompressible turbulent flows

    Science.gov (United States)

    Debue, P.; Shukla, V.; Kuzzay, D.; Faranda, D.; Saw, E.-W.; Daviaud, F.; Dubrulle, B.

    2018-05-01

    We examine the connection between the singularities or quasisingularities in the solutions of the incompressible Navier-Stokes equation (INSE) and the local energy transfer and dissipation, in order to explore in detail how the former contributes to the phenomenon of intermittency. We do so by analyzing the velocity fields (a) measured in the experiments on the turbulent von Kármán swirling flow at high Reynolds numbers and (b) obtained from the direct numerical simulations of the INSE at a moderate resolution. To compute the local interscale energy transfer and viscous dissipation in experimental and supporting numerical data, we use the weak solution formulation generalization of the Kármán-Howarth-Monin equation. In the presence of a singularity in the velocity field, this formulation yields a nonzero dissipation (inertial dissipation) in the limit of an infinite resolution. Moreover, at finite resolutions, it provides an expression for local interscale energy transfers down to the scale where the energy is dissipated by viscosity. In the presence of a quasisingularity that is regularized by viscosity, the formulation provides the contribution to the viscous dissipation due to the presence of the quasisingularity. Therefore, our formulation provides a concrete support to the general multifractal description of the intermittency. We present the maps and statistics of the interscale energy transfer and show that the extreme events of this transfer govern the intermittency corrections and are compatible with a refined similarity hypothesis based on this transfer. We characterize the probability distribution functions of these extreme events via generalized Pareto distribution analysis and find that the widths of the tails are compatible with a similarity of the second kind. Finally, we make a connection between the topological and the statistical properties of the extreme events of the interscale energy transfer field and its multifractal properties.

  4. K-FIX: a computer program for transient, two-dimensional, two-fluid flow. THREED: an extension of the K-FIX code for three-dimensional calculations

    International Nuclear Information System (INIS)

    Rivard, W.C.; Torrey, M.D.

    1978-10-01

    The transient, two-dimensional, two-fluid code K-FIX has been extended to perform three-dimensional calculations. This capability is achieved by adding five modification sets of FORTRAN statements to the basic two-dimensional code. The modifications are listed and described, and a complete listing of the three-dimensional code is provided. Results of an example problem are provided for verification

  5. Non-linear instability analysis of the two-dimensional Navier-Stokes equation: The Taylor-Green vortex problem

    Science.gov (United States)

    Sengupta, Tapan K.; Sharma, Nidhi; Sengupta, Aditi

    2018-05-01

    An enstrophy-based non-linear instability analysis of the Navier-Stokes equation for two-dimensional (2D) flows is presented here, using the Taylor-Green vortex (TGV) problem as an example. This problem admits a time-dependent analytical solution as the base flow, whose instability is traced here. The numerical study of the evolution of the Taylor-Green vortices shows that the flow becomes turbulent, but an explanation for this transition has not been advanced so far. The deviation of the numerical solution from the analytical solution is studied here using a high accuracy compact scheme on a non-uniform grid (NUC6), with the fourth-order Runge-Kutta method. The stream function-vorticity (ψ, ω) formulation of the governing equations is solved here in a periodic square domain with four vortices at t = 0. Simulations performed at different Reynolds numbers reveal that numerical errors in computations induce a breakdown of symmetry and simultaneous fragmentation of vortices. It is shown that the actual physical instability is triggered by the growth of disturbances and is explained by the evolution of disturbance mechanical energy and enstrophy. The disturbance evolution equations have been traced by looking at (a) disturbance mechanical energy of the Navier-Stokes equation, as described in the work of Sengupta et al., "Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003), and (b) the creation of rotationality via the enstrophy transport equation in the work of Sengupta et al., "Diffusion in inhomogeneous flows: Unique equilibrium state in an internal flow," Comput. Fluids 88, 440-451 (2013).

  6. A new approach for solving the three-dimensional steady Euler equations. I - General theory

    Science.gov (United States)

    Chang, S.-C.; Adamczyk, J. J.

    1986-01-01

    The present iterative procedure combines the Clebsch potentials and the Munk-Prim (1947) substitution principle with an extension of a semidirect Cauchy-Riemann solver to three dimensions, in order to solve steady, inviscid three-dimensional rotational flow problems in either subsonic or incompressible flow regimes. This solution procedure can be used, upon discretization, to obtain inviscid subsonic flow solutions in a 180-deg turning channel. In addition to accurately predicting the behavior of weak secondary flows, the algorithm can generate solutions for strong secondary flows and will yield acceptable flow solutions after only 10-20 outer loop iterations.

  7. A Semi-implicit Numerical Scheme for a Two-dimensional, Three-field Thermo-Hydraulic Modeling

    International Nuclear Information System (INIS)

    Hwang, Moonkyu; Jeong, Jaejoon

    2007-07-01

    The behavior of two-phase flow is modeled, depending on the purpose, by either homogeneous model, drift flux model, or separated flow model, Among these model, in the separated flow model, the behavior of each flow phase is modeled by its own governing equation, together with the interphase models which describe the thermal and mechanical interactions between the phases involved. In this study, a semi-implicit numerical scheme for two-dimensional, transient, two-fluid, three-field is derived. The work is an extension to the previous study for the staggered, semi-implicit numerical scheme in one-dimensional geometry (KAERI/TR-3239/2006). The two-dimensional extension is performed by specifying a relevant governing equation set and applying the related finite differencing method. The procedure for employing the semi-implicit scheme is also described in detail. Verifications are performed for a 2-dimensional vertical plate for a single-phase and two-phase flows. The calculations verify the mass and energy conservations. The symmetric flow behavior, for the verification problem, also confirms the momentum conservation of the numerical scheme

  8. Numerical approximation of flow in a symmetric channel with vibrating walls

    Directory of Open Access Journals (Sweden)

    Sváček P.

    2010-12-01

    Full Text Available In this paper the numerical solution of two dimensional fluid-structure interaction problem is addressed. The fluid motion is modelled by the incompressible unsteady Navier-Stokes equations. The spatial discretization by stabilized finite element method is used. The motion of the computational domain is treated with the aid of Arbitrary Lagrangian Eulerian (ALE method. The time-space problem is solved with the aid of multigrid method. The method is applied onto a problem of interaction of channel flow with moving walls, which models the air flow in the glottal region of the human vocal tract. The pressure boundary conditions and the effects of the isotropic and anisotropic mesh refinement are discussed. The numerical results are presented.

  9. Iterative methods for the detection of Hopf bifurcations in finite element discretisation of incompressible flow problems

    International Nuclear Information System (INIS)

    Cliffe, K.A.; Garratt, T.J.; Spence, A.

    1992-03-01

    This paper is concerned with the problem of computing a small number of eigenvalues of large sparse generalised eigenvalue problems arising from mixed finite element discretisations of time dependent equations modelling viscous incompressible flow. The eigenvalues of importance are those with smallest real part and can be used in a scheme to determine the stability of steady state solutions and to detect Hopf bifurcations. We introduce a modified Cayley transform of the generalised eigenvalue problem which overcomes a drawback of the usual Cayley transform applied to such problems. Standard iterative methods are then applied to the transformed eigenvalue problem to compute approximations to the eigenvalue of smallest real part. Numerical experiments are performed using a model of double diffusive convection. (author)

  10. Study on numerical methods for transient flow induced by speed-changing impeller of fluid machinery

    International Nuclear Information System (INIS)

    Wu, Dazhuan; Chen, Tao; Wang, Leqin; Cheng, Wentao; Sun, Youbo

    2013-01-01

    In order to establish a reliable numerical method for solving the transient rotating flow induced by a speed-changing impeller, two numerical methods based on finite volume method (FVM) were presented and analyzed in this study. Two-dimensional numerical simulations of incompressible transient unsteady flow induced by an impeller during starting process were carried out respectively by using DM and DSR methods. The accuracy and adaptability of the two methods were evaluated by comprehensively comparing the calculation results. Moreover, an intensive study on the application of DSR method was conducted subsequently. The results showed that transient flow structure evolution and transient characteristics of the starting impeller are obviously affected by the starting process. The transient flow can be captured by both two methods, and the DSR method shows a higher computational efficiency. As an application example, the starting process of a mixed-flow pump was simulated by using DSR method. The calculation results were analyzed by comparing with the experiment data.

  11. Multiple-relaxation-time lattice Boltzmann model for incompressible miscible flow with large viscosity ratio and high Péclet number

    Science.gov (United States)

    Meng, Xuhui; Guo, Zhaoli

    2015-10-01

    A lattice Boltzmann model with a multiple-relaxation-time (MRT) collision operator is proposed for incompressible miscible flow with a large viscosity ratio as well as a high Péclet number in this paper. The equilibria in the present model are motivated by the lattice kinetic scheme previously developed by Inamuro et al. [Philos. Trans. R. Soc. London, Ser. A 360, 477 (2002), 10.1098/rsta.2001.0942]. The fluid viscosity and diffusion coefficient depend on both the corresponding relaxation times and additional adjustable parameters in this model. As a result, the corresponding relaxation times can be adjusted in proper ranges to enhance the performance of the model. Numerical validations of the Poiseuille flow and a diffusion-reaction problem demonstrate that the proposed model has second-order accuracy in space. Thereafter, the model is used to simulate flow through a porous medium, and the results show that the proposed model has the advantage to obtain a viscosity-independent permeability, which makes it a robust method for simulating flow in porous media. Finally, a set of simulations are conducted on the viscous miscible displacement between two parallel plates. The results reveal that the present model can be used to simulate, to a high level of accuracy, flows with large viscosity ratios and/or high Péclet numbers. Moreover, the present model is shown to provide superior stability in the limit of high kinematic viscosity. In summary, the numerical results indicate that the present lattice Boltzmann model is an ideal numerical tool for simulating flow with a large viscosity ratio and/or a high Péclet number.

  12. Suitable weak solutions: from compressible viscous to incompressible inviscid fluid flows

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Novotný, A.; Petzeltová, Hana

    2013-01-01

    Roč. 356, č. 2 (2013), s. 683-702 ISSN 0025-5831 R&D Projects: GA ČR GA201/09/0917 Institutional research plan: CEZ:AV0Z10190503 Keywords : relative entropy * incompressible limit * inviscid limit Subject RIV: BA - General Mathematics Impact factor: 1.201, year: 2013 http://link.springer.com/article/10.1007%2Fs00208-012-0862-5

  13. Direct differentiation of the quasi-incompressible fluid formulation of fluid-structure interaction using the PFEM

    Science.gov (United States)

    Zhu, Minjie; Scott, Michael H.

    2017-07-01

    Accurate and efficient response sensitivities for fluid-structure interaction (FSI) simulations are important for assessing the uncertain response of coastal and off-shore structures to hydrodynamic loading. To compute gradients efficiently via the direct differentiation method (DDM) for the fully incompressible fluid formulation, approximations of the sensitivity equations are necessary, leading to inaccuracies of the computed gradients when the geometry of the fluid mesh changes rapidly between successive time steps or the fluid viscosity is nonzero. To maintain accuracy of the sensitivity computations, a quasi-incompressible fluid is assumed for the response analysis of FSI using the particle finite element method and DDM is applied to this formulation, resulting in linearized equations for the response sensitivity that are consistent with those used to compute the response. Both the response and the response sensitivity can be solved using the same unified fractional step method. FSI simulations show that although the response using the quasi-incompressible and incompressible fluid formulations is similar, only the quasi-incompressible approach gives accurate response sensitivity for viscous, turbulent flows regardless of time step size.

  14. Effects of irregular two-dimensional and three-dimensional surface roughness in turbulent channel flows

    International Nuclear Information System (INIS)

    De Marchis, M.; Napoli, E.

    2012-01-01

    Highlights: ► 3D irregular rough surfaces produce higher effects than those observed over 2D. ► Effective slope is a geometrical parameter representative of the roughness effects. ► 3D rough surfaces enhance the turbulence isotropization. ► 2D and 3D irregular roughness partially support the wall similarity. ► Irregular rough surfaces shear some features with regular rough walls. - Abstract: Wall-resolved Large Eddy Simulation of fully developed turbulent channel flows over two different rough surfaces is performed to investigate on the effects of irregular 2D and 3D roughness on the turbulence. The two geometries are obtained through the superimposition of sinusoidal functions having random amplitudes and different wave lengths. In the 2D configuration the irregular shape in the longitudinal direction is replicated in the transverse one, while in the 3D case the sinusoidal functions are generated both in streamwise and spanwise directions. Both channel walls are roughened in such a way as to obtain surfaces with statistically equivalent roughness height, but different shapes. In order to compare the turbulence properties over the two rough walls and to analyse the differences with a smooth wall, the simulations are performed at the same Reynolds number Re τ = 395. The same mean roughness height h = 0.05δ (δ the half channel height) is used for the rough walls. The roughness function obtained with the 3D roughness is larger than in the 2D case, although the two walls share the same mean height. Thus, the considered irregular 3D roughness is more effective in reducing the flow velocity with respect to the 2D roughness, coherently with the literature results that identified a clear dependence of the roughness function on the effective slope (see ), higher in the generated 3D rough wall. The analysis of higher-order statistics shows that the effects of the roughness, independently on its two- or three-dimensional shape, are mainly confined in the inner

  15. Numerical modelling of two phase flow with hysteresis in heterogeneous porous media

    Energy Technology Data Exchange (ETDEWEB)

    Abreu, E. [Instituto Nacional de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, RJ (Brazil); Furtado, F.; Pereira, F. [University of Wyoming, Laramie, WY (United States). Dept. of Mathematicsatics; Souza, G. [Universidade do Estado do Rio de Janeiro (UERJ), RJ (Brazil)

    2008-07-01

    Numerical simulators are necessary for the understanding of multiphase flow in porous media in order to optimize hydrocarbon recovery. In this work, the immiscible flow of two incompressible phases, a problem very common in waterflooding of petroleum reservoirs, is considered and numerical simulation techniques are presented. The system of equations which describe this type of flow form a coupled, highly nonlinear system of time-dependent partial differential equations (PDEs). The equation for the saturation of the invading fluid is a convection-dominated, degenerate parabolic PDE whose solutions typically exhibit sharp fronts (i.e., internal layers with strong gradients) and is very difficult to approximate numerically. It is well known that accurate modeling of convective and diffusive processes is one of the most daunting tasks in the numerical approximation of PDEs. Particularly difficult is the case where convection dominates diffusion. Specifically, we consider the injection problem for a model of two-phase (water/oil) flow in a core sample of porous rock, taking into account hysteresis effects in the relative permeability of the oil phase. (author)

  16. Predicted macroinvertebrate response to water diversion from a montane stream using two-dimensional hydrodynamic models and zero flow approximation

    Science.gov (United States)

    Holmquist, Jeffrey G.; Waddle, Terry J.

    2013-01-01

    We used two-dimensional hydrodynamic models for the assessment of water diversion effects on benthic macroinvertebrates and associated habitat in a montane stream in Yosemite National Park, Sierra Nevada Mountains, CA, USA. We sampled the macroinvertebrate assemblage via Surber sampling, recorded detailed measurements of bed topography and flow, and coupled a two-dimensional hydrodynamic model with macroinvertebrate indicators to assess habitat across a range of low flows in 2010 and representative past years. We also made zero flow approximations to assess response of fauna to extreme conditions. The fauna of this montane reach had a higher percentage of Ephemeroptera, Plecoptera, and Trichoptera (%EPT) than might be expected given the relatively low faunal diversity of the study reach. The modeled responses of wetted area and area-weighted macroinvertebrate metrics to decreasing discharge indicated precipitous declines in metrics as flows approached zero. Changes in area-weighted metrics closely approximated patterns observed for wetted area, i.e., area-weighted invertebrate metrics contributed relatively little additional information above that yielded by wetted area alone. Loss of habitat area in this montane stream appears to be a greater threat than reductions in velocity and depth or changes in substrate, and the modeled patterns observed across years support this conclusion. Our models suggest that step function losses of wetted area may begin when discharge in the Merced falls to 0.02 m3/s; proportionally reducing diversions when this threshold is reached will likely reduce impacts in low flow years.

  17. Advances in Spectral Methods for UQ in Incompressible Navier-Stokes Equations

    KAUST Repository

    Le Maitre, Olivier

    2014-01-06

    In this talk, I will present two recent contributions to the development of efficient methodologies for uncertainty propagation in the incompressible Navier-Stokes equations. The first one concerns the reduced basis approximation of stochastic steady solutions, using Proper Generalized Decompositions (PGD). An Arnoldi problem is projected to obtain a low dimensional Galerkin problem. The construction then amounts to the resolution of a sequence of uncoupled deterministic Navier-Stokes like problem and simple quadratic stochastic problems, followed by the resolution of a low-dimensional coupled quadratic stochastic problem, with a resulting complexity which has to be contrasted with the dimension of the whole Galerkin problem for classical spectral approaches. An efficient algorithm for the approximation of the stochastic pressure field is also proposed. Computations are presented for uncertain viscosity and forcing term to demonstrate the effectiveness of the reduced method. The second contribution concerns the computation of stochastic periodic solutions to the Navier-Stokes equations. The objective is to circumvent the well-known limitation of spectral methods for long-time integration. We propose to directly determine the stochastic limit-cycles through the definition of its stochastic period and an initial condition over the cycle. A modified Newton method is constructed to compute iteratively both the period and initial conditions. Owing to the periodic character of the solution, and by introducing an appropriate time-scaling, the solution can be approximated using low-degree polynomial expansions with large computational saving as a result. The methodology is illustrated for the von-Karman flow around a cylinder with stochastic inflow conditions.

  18. Advances in Spectral Methods for UQ in Incompressible Navier-Stokes Equations

    KAUST Repository

    Le Maitre, Olivier

    2014-01-01

    In this talk, I will present two recent contributions to the development of efficient methodologies for uncertainty propagation in the incompressible Navier-Stokes equations. The first one concerns the reduced basis approximation of stochastic steady solutions, using Proper Generalized Decompositions (PGD). An Arnoldi problem is projected to obtain a low dimensional Galerkin problem. The construction then amounts to the resolution of a sequence of uncoupled deterministic Navier-Stokes like problem and simple quadratic stochastic problems, followed by the resolution of a low-dimensional coupled quadratic stochastic problem, with a resulting complexity which has to be contrasted with the dimension of the whole Galerkin problem for classical spectral approaches. An efficient algorithm for the approximation of the stochastic pressure field is also proposed. Computations are presented for uncertain viscosity and forcing term to demonstrate the effectiveness of the reduced method. The second contribution concerns the computation of stochastic periodic solutions to the Navier-Stokes equations. The objective is to circumvent the well-known limitation of spectral methods for long-time integration. We propose to directly determine the stochastic limit-cycles through the definition of its stochastic period and an initial condition over the cycle. A modified Newton method is constructed to compute iteratively both the period and initial conditions. Owing to the periodic character of the solution, and by introducing an appropriate time-scaling, the solution can be approximated using low-degree polynomial expansions with large computational saving as a result. The methodology is illustrated for the von-Karman flow around a cylinder with stochastic inflow conditions.

  19. Asymptotic stability of shear-flow solutions to incompressible viscous free boundary problems with and without surface tension

    Science.gov (United States)

    Tice, Ian

    2018-04-01

    This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a rigid plane and with an upper boundary given by a free surface. The fluid is subject to a constant external force with a horizontal component, which arises in modeling the motion of such a fluid down an inclined plane, after a coordinate change. We consider the problem both with and without surface tension for horizontally periodic flows. This problem gives rise to shear-flow equilibrium solutions, and the main thrust of this paper is to study the asymptotic stability of the equilibria in certain parameter regimes. We prove that there exists a parameter regime in which sufficiently small perturbations of the equilibrium at time t=0 give rise to global-in-time solutions that return to equilibrium exponentially in the case with surface tension and almost exponentially in the case without surface tension. We also establish a vanishing surface tension limit, which connects the solutions with and without surface tension.

  20. Shape sensitivity analysis of time-dependent flows of incompressible non-Newtonian fluids

    Czech Academy of Sciences Publication Activity Database

    Sokolowski, J.; Stebel, Jan

    2011-01-01

    Roč. 40, č. 4 (2011), s. 1077-1097 ISSN 0324-8569 R&D Projects: GA ČR GA201/09/0917 Institutional research plan: CEZ:AV0Z10190503 Keywords : shape optimization * shape gradient * incompressible viscous fluid Subject RIV: BA - General Mathematics Impact factor: 0.300, year: 2010

  1. Development and assessment of multi-dimensional flow model in MARS compared with the RPI air-water experiment

    International Nuclear Information System (INIS)

    Lee, Seok Min; Lee, Un Chul; Bae, Sung Won; Chung, Bub Dong

    2004-01-01

    The Multi-Dimensional flow models in system code have been developed during the past many years. RELAP5-3D, CATHARE and TRACE has its specific multi-dimensional flow models and successfully applied it to the system safety analysis. In KAERI, also, MARS(Multi-dimensional Analysis of Reactor Safety) code was developed by integrating RELAP5/MOD3 code and COBRA-TF code. Even though COBRA-TF module can analyze three-dimensional flow models, it has a limitation to apply 3D shear stress dominant phenomena or cylindrical geometry. Therefore, Multi-dimensional analysis models are newly developed by implementing three-dimensional momentum flux and diffusion terms. The multi-dimensional model has been assessed compared with multi-dimensional conceptual problems and CFD code results. Although the assessment results were reasonable, the multi-dimensional model has not been validated to two-phase flow using experimental data. In this paper, the multi-dimensional air-water two-phase flow experiment was simulated and analyzed

  2. A new approach to flow through a region bounded by two ellipses of the same ellipticity

    Science.gov (United States)

    Lal, K.; Chorlton, F.

    1981-05-01

    A new approach is presented to calculate steady flow of a laminar viscous incompressible fluid through a channel whose cross section is bounded by two ellipses with the same ellipticity. The Milne-Thomas approach avoids the stream function and is similar to the Rayleigh-Ritz approximation process of the calculus of variations in its first satisfying boundary conditions and then adjusting constants or multiplying functions to fit the differential equation.

  3. A model to analyse the flow of an incompressible Newtonian fluid through a rigid, homogeneous, isotropic and infinite porous medium

    International Nuclear Information System (INIS)

    Gama, R.M.S. da; Sampaio, R.

    1985-01-01

    The flow of an incompressible Newtonian fluid through a rigid, homogeneous, isotropic and infinite porous medium which has a given inicial distribuition of the mentioned fluid, is analyzed. It is proposed a model that assumes that the motion is caused by concentration gradient, but it does not consider the friction between the porous medium and the fluid. We solve an onedimensional case where the mathematical problem is reduced to the solution of a non-linear hyperbolic system of differential equations, subjected to an inicial condition given by a step function, called 'Riemann Problem'. (Author) [pt

  4. Pressure-driven peristaltic flow

    International Nuclear Information System (INIS)

    Mingalev, S V; Lyubimov, D V; Lyubimova, T P

    2013-01-01

    The peristaltic motion of an incompressible fluid in two-dimensional channel is investigated. Instead of fixing the law of wall's coordinate variation, the law of pressure variation on the wall is fixed and the border's coordinate changes to provide the law of pressure variation on the wall. In case of small amplitude of pressure-variation on the wall A, expansion wave propagates along the length of channel and the wave results in the peristaltic transport of fluid. In the case of large A, the channel divides into two parts. The small pulsating part in the end of the tube creates the flow as a human heart, while the other big part loses this function. The solution of problem for the first peristaltic mode is stable, while the solution for the second 'heart' mode is unstable and depends heavily on boundary conditions.

  5. Effects of Ramped Wall Temperature on Unsteady Two-Dimensional Flow Past a Vertical Plate with Thermal Radiation and Chemical Reaction

    Directory of Open Access Journals (Sweden)

    V. Rajesh

    2014-08-01

    Full Text Available The interaction of free convection with thermal radiation of a viscous incompressible unsteady flow past a vertical plate with ramped wall temperature and mass diffusion is presented here, taking into account the homogeneous chemical reaction of first order. The fluid is gray, absorbing-emitting but non-scattering medium and the Rosseland approximation is used to describe the radiative flux in the energy equation. The dimensionless governing equations are solved using an implicit finite-difference method of the Crank-Nicolson type, which is stable and convergent. The velocity profiles are compared with the available theoretical solution and are found to be in good agreement. Numerical results for the velocity, the temperature, the concentration, the local and average skin friction, the Nusselt number and Sherwood number are shown graphically. This work has wide application in chemical and power engineering and also in the study of vertical air flow into the atmosphere. The present results can be applied to an important class of flows in which the driving force for the flow is provided by combination of the thermal and chemical species diffusion effects.

  6. Flow of miscible and immiscible hydrocarbons in heterogeneous porous media

    Energy Technology Data Exchange (ETDEWEB)

    Butts, M.B.

    1996-12-31

    A series of large-scale two-dimensional physical model studies has been carried out in order to better understand and predict the multiphase flow of hydrocarbon contaminants and the release of the water-soluble fraction of such contaminants into the groundwater stream. The detailed measurements of the fluid saturations within the bulk hydrocarbon plume as well as the aqueous concentrations recorded downstream should provide a useful data set for testing and improving numerical models of both multiphase flow and transport. Predictions of a numerical model of immiscible multiphase flow developed in the petroleum industry were found to compare favourably with the observed oil plume for the case of an immiscible oil spill. Nevertheless, subtle layering within the experimental flume altered the long-term development of the oil plume in a manner not predicted by the numerical model. A stochastic model for three-dimensional, two-phase incompressible flow in heterogeneous soil and rock formations is developed. Analytical solutions for the resulting stochastic differential equations are derived for asymptotic flows using a perturbation approach. These solutions were used to derive general expressions for the large-scale (effective) properties for large-scale two-phase flow in porous media. An important observation from this analysis is that general large-scale flow in heterogeneous soils cannot be predicted on the basis of simple averages of the soil hydraulic properties alone. The large-scale capillary pressure saturation relation is evaluated for imbibition into a wet soil or rock formation. (EG) 194 refs.

  7. Flow of miscible and immiscible hydrocarbons in heterogeneous porous media

    Energy Technology Data Exchange (ETDEWEB)

    Butts, M B

    1997-12-31

    A series of large-scale two-dimensional physical model studies has been carried out in order to better understand and predict the multiphase flow of hydrocarbon contaminants and the release of the water-soluble fraction of such contaminants into the groundwater stream. The detailed measurements of the fluid saturations within the bulk hydrocarbon plume as well as the aqueous concentrations recorded downstream should provide a useful data set for testing and improving numerical models of both multiphase flow and transport. Predictions of a numerical model of immiscible multiphase flow developed in the petroleum industry were found to compare favourably with the observed oil plume for the case of an immiscible oil spill. Nevertheless, subtle layering within the experimental flume altered the long-term development of the oil plume in a manner not predicted by the numerical model. A stochastic model for three-dimensional, two-phase incompressible flow in heterogeneous soil and rock formations is developed. Analytical solutions for the resulting stochastic differential equations are derived for asymptotic flows using a perturbation approach. These solutions were used to derive general expressions for the large-scale (effective) properties for large-scale two-phase flow in porous media. An important observation from this analysis is that general large-scale flow in heterogeneous soils cannot be predicted on the basis of simple averages of the soil hydraulic properties alone. The large-scale capillary pressure saturation relation is evaluated for imbibition into a wet soil or rock formation. (EG) 194 refs.

  8. The Three Dimensional Flow Field at the Exit of an Axial-Flow Turbine Rotor

    Science.gov (United States)

    Lakshminarayana, B.; Ristic, D.; Chu, S.

    1998-01-01

    A systematic and comprehensive investigation was performed to provide detailed data on the three dimensional viscous flow phenomena downstream of a modem turbine rotor and to understand the flow physics such as origin, nature, development of wakes, secondary flow, and leakage flow. The experiment was carried out in the Axial Flow Turbine Research Facility (AFTRF) at Penn State, with velocity measurements taken with a 3-D LDV System. Two radial traverses at 1% and 10% of chord downstream of the rotor have been performed to identify the three-dimensional flow features at the exit of the rotor blade row. Sufficient spatial resolution was maintained to resolve blade wake, secondary flow, and tip leakage flow. The wake deficit is found to be substantial, especially at 1% of chord downstream of the rotor. At this location, negative axial velocity occurs near the tip, suggesting flow separation in the tip clearance region. Turbulence intensities peak in the wake region, and cross- correlations are mainly associated with the velocity gradient of the wake deficit. The radial velocities, both in the wake and in the endwall region, are found to be substantial. Two counter-rotating secondary flows are identified in the blade passage, with one occupying the half span close to the casino and the other occupying the half span close to the hub. The tip leakage flow is well restricted to 10% immersion from the blade tip. There are strong vorticity distributions associated with these secondary flows and tip leakage flow. The passage averaged data are in good agreement with design values.

  9. Laboratory setup and results of experiments on two-dimensional multiphase flow in porous media

    International Nuclear Information System (INIS)

    McBride, J.F.; Graham, D.N.

    1990-10-01

    In the event of an accidental release into earth's subsurface of an immiscible organic liquid, such as a petroleum hydrocarbon or chlorinated organic solvent, the spatial and temporal distribution of the organic liquid is of great interest when considering efforts to prevent groundwater contamination or restore contaminated groundwater. An accurate prediction of immiscible organic liquid migration requires the incorporation of relevant physical principles in models of multiphase flow in porous media; these physical principles must be determined from physical experiments. This report presents a series of such experiments performed during the 1970s at the Swiss Federal Institute of Technology (ETH) in Zurich, Switzerland. The experiments were designed to study the transient, two-dimensional displacement of three immiscible fluids in a porous medium. This experimental study appears to be the most detailed published to date. The data obtained from these experiments are suitable for the validation and test calibration of multiphase flow codes. 73 refs., 140 figs

  10. PELE-IC, 2-D Eulerian Incompressible Hydrodynamic and Bubble Dynamic after LWR LOCA

    International Nuclear Information System (INIS)

    McMaster, W.H.; Gong, E.Y.

    1981-01-01

    1 - Description of problem or function: PELE-IC is a two-dimensional semi-implicit Eulerian hydrodynamics program for the solution of incompressible flow coupled to flexible structures. The code was developed to calculate fluid-structure interactions and bubble dynamics of a pressure-suppression system following a loss-of- coolant accident (LOCA). The fluid, structure, and coupling algorithms have been verified by calculation of benchmark problems and air and steam blowdown experiments. The code is written for both plane and cylindrical coordinates. The coupling algorithm is general enough to handle a wide variety of structural shapes. The concepts of void fractions and interface orientation are used to track the movement of free surfaces, allowing great versatility in following fluid-gas interfaces both for bubble definition and water surface motion without the use of marker particles. 2 - Method of solution: The solution strategy is to first solve the Navier-Stokes equations explicitly using values from the previous time-step. Since these values do not necessarily satisfy the continuity equation, the pressure field is iterated upon until the incompressibility condition for each computational cell is satisfied within prescribed limits. The structural motion is computed by a finite element code from the applied pressure at the fluid-structure interface. The shell structure algorithm uses conventional thin-shell theory with transverse shear. The finite-element spatial discretization employs piecewise-linear interpolation functions and one-point quadrature applied to conical frustra. The Newmark implicit time integration method is used as a one-step module. The fluid code then uses the structure's position and velocity as boundary conditions. The fluid pressure field and the structure's response are corrected iteratively until the normal velocities of fluid and structure are equal. The effects of steam condensation and oscillatory chugging on structures are

  11. New techniques for experimental generation of two-dimensional blade-vortex interaction at low Reynolds numbers

    Science.gov (United States)

    Booth, E., Jr.; Yu, J. C.

    1986-01-01

    An experimental investigation of two dimensional blade vortex interaction was held at NASA Langley Research Center. The first phase was a flow visualization study to document the approach process of a two dimensional vortex as it encountered a loaded blade model. To accomplish the flow visualization study, a method for generating two dimensional vortex filaments was required. The numerical study used to define a new vortex generation process and the use of this process in the flow visualization study were documented. Additionally, photographic techniques and data analysis methods used in the flow visualization study are examined.

  12. Numerical simulation of interior flow field of nuclear model pump

    International Nuclear Information System (INIS)

    Wang Chunlin; Peng Na; Kang Can; Zhao Baitong; Zhang Hao

    2009-01-01

    Reynolds time-averaged N-S equations and the standard k-ε turbulent model were adopted, and three-dimensional non-structural of tetrahedral mesh division was used for modeling. Multiple reference frame model of rotating fluid mechanical model was used, under the design condition, the three-dimensional incompressible turbulent flow of nuclear model pump was simulated, and the results preferably post the characteristics of the interior flow field. This paper first analyzes the total pressure and velocity distribution in the flow field, and then describes the interior flow field characteristics of each part such as the impeller, diffuser and spherical shell, and also discusses the reasons that cause these characteristics. The study results can be used to estimate the performance of nuclear model pump, and will provide some useful references for its hydraulic optimized design. (authors)

  13. A linearized system describing stationary incompressible viscous flow around rotating and translating bodies: improved decay estimates of the velocity and its gradient

    Czech Academy of Sciences Publication Activity Database

    Deuring, P.; Kračmar, S.; Nečasová, Šárka

    2011-01-01

    Roč. 2011, - (2011), s. 351-361 ISSN 1078-0947. [8th AIMS International Conference. Dresden, 25.05.2010-28.05.2010] R&D Projects: GA AV ČR IAA100190804; GA ČR(CZ) GAP201/11/1304 Institutional research plan: CEZ:AV0Z10190503 Keywords : viscous incompressible flow * rotating body * fundamental solution Subject RIV: BA - General Mathematics Impact factor: 0.913, year: 2011 http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=6978

  14. Determination of two-dimensional correlation lengths in an anisotropic two-component flow

    International Nuclear Information System (INIS)

    Thomson, O.

    1994-05-01

    Former studies have shown that correlation methods can be used for determination of various two-component flow parameters, among these the correlation length. In cases where the flow can be described as a mixture, in which the minority component forms spatially limited perturbations within the majority component, this parameter gives a good indication of the maximum extension of these perturbations. In the former studies, spherical symmetry of the perturbations has been assumed, and the correlation length has been measured in the direction of the flow (axially) only. However, if the flow structure is anisotropic, the correlation length will be different in different directions. In the present study, the method has been developed further, allowing also measurements perpendicular to the flow direction (radially). The measurements were carried out using laser beams and the two-component flows consisted of either glass beads and air or air and water. In order to make local measurements of both the axial and radial correlation length simultaneously, it is necessary to use 3 laser beams and to form the triple cross-covariance. This lead to some unforeseen complications, due to the character of this function. The experimental results are generally positive and size determinations with an accuracy of better than 10% have been achieved in most cases. Less accurate results appeared only for difficult conditions (symmetrical signals), when 3 beams were used. 5 refs, 13 figs, 3 tabs

  15. Stabilizing local boundary conditions for two-dimensional shallow water equations

    KAUST Repository

    Dia, Ben Mansour; Oppelstrup, Jesper

    2018-01-01

    In this article, we present a sub-critical two-dimensional shallow water flow regulation. From the energy estimate of a set of one-dimensional boundary stabilization problems, we obtain a set of polynomial equations with respect to the boundary

  16. Waves in separated two-phase flow

    International Nuclear Information System (INIS)

    Pols, R.M.

    1998-06-01

    This dissertation presents an integral approach to the modelling of co-current flow of liquid and gas for a class of non-linear wave problems. Typically the liquid phase and the gas phase are decoupled and the liquid is depth averaged. The resulting non-linear shallow water equations are solved to predict the behaviour of the finite amplitude waves. The integral approach is applied to the modelling of two-dimensional waves in a horizontal and slightly inclined rectangular channel, two-dimensional waves in a vertical pipe and three-dimensional waves in a horizontal tube. For flow in a horizontal or slightly inclined channel the liquid is driven by the interfacial shear from the gas phase and the surface is subject to extensive wave action. For thin liquid films the pressure in the liquid may be taken as hydrostatic and gravity acts as a restoring force on the liquid. Roll wave solutions to the non-linear shallow water equations are sought corresponding to an interfacial shear stress dependent on the liquid film height. Wave solutions are shown to exist but only for parameters within a defined range dependent on the channel inclination, interfacial roughness and linear dependence on the liquid film height of the shear stresses. Such solutions are discontinuous and are pieced together by a jump where mass and momentum are conserved. The model calculations on wave height and wave velocity are compared with experimental data. The essentially two-dimensional analysis developed for stratified horizontal flow can be extended to quasi three-dimensional flow in the case of shallow liquid depth for a circular pipe. In this case the liquid depth changes with circumferential position and consequently modifies the interfacial shear exerted on the liquid surface creating a wave spreading mechanism alongside changing the wave profile across the pipe. The wave spreading mechanism supposes a wave moving in axial direction at a velocity faster than the liquid thereby sweeping liquid

  17. Numerical method for two-phase flow discontinuity propagation calculation

    International Nuclear Information System (INIS)

    Toumi, I.; Raymond, P.

    1989-01-01

    In this paper, we present a class of numerical shock-capturing schemes for hyperbolic systems of conservation laws modelling two-phase flow. First, we solve the Riemann problem for a two-phase flow with unequal velocities. Then, we construct two approximate Riemann solvers: an one intermediate-state Riemann solver and a generalized Roe's approximate Riemann solver. We give some numerical results for one-dimensional shock-tube problems and for a standard two-phase flow heat addition problem involving two-phase flow instabilities

  18. The effects of axis ratio on laminar fluid flow around an elliptical cylinder

    International Nuclear Information System (INIS)

    Faruquee, Zakir; Ting, David S-K.; Fartaj, Amir; Barron, Ronald M.; Carriveau, Rupp

    2007-01-01

    An elliptical cylinder is a generic shape which represents a flat plate at its minor to major axis ratio (AR) limits of zero and infinity, and a circular cylinder at AR of unity. While incompressible flows over a streamwise flat plate (AR = 0), a cross-stream flat plate (AR = ∞), and a circular cylinder have been studied extensively, the role of AR on the detailed flow structure is still not well understood. Therefore, a numerical study was conducted to examine the flow field around an elliptical cylinder over a range of ARs from 0.3 to 1, with the major axis parallel to the free-stream, at a Reynolds number of 40 based on the hydraulic diameter. The control volume approach of FLUENT was used to solve the fluid flow equations, assuming the flow over the cylinder is unbounded, steady, incompressible and two-dimensional. It has been found that a pair of steady vortices forms when AR reaches a critical value of 0.34; below this value no vortices are formed behind the elliptical cylinder. Various wake parameters, drag coefficient, pressure and velocity distributions, have been characterized as functions of AR. The wake size and the drag coefficient are found to increase with the increase of AR. Quadratic correlations have been obtained to describe the relations of wake length and drag coefficient with axis ratio

  19. Three-dimensional features on oscillating microbubbles streaming flows

    Science.gov (United States)

    Rossi, Massimiliano; Marin, Alvaro G.; Wang, Cheng; Hilgenfeldt, Sascha; Kähler, Christian J.

    2013-11-01

    Ultrasound-driven oscillating micro-bubbles have been used as active actuators in microfluidic devices to perform manifold tasks such as mixing, sorting and manipulation of microparticles. A common configuration consists in side-bubbles, created by trapping air pockets in blind channels perpendicular to the main channel direction. This configuration results in bubbles with a semi-cylindrical shape that creates a streaming flow generally considered quasi two-dimensional. However, recent experiments performed with three-dimensional velocimetry methods have shown how microparticles can present significant three-dimensional trajectories, especially in regions close to the bubble interface. Several reasons will be discussed such as boundary effects of the bottom/top wall, deformation of the bubble interface leading to more complex vibrational modes, or bubble-particle interactions. In the present investigation, precise measurements of particle trajectories close to the bubble interface will be performed by means of 3D Astigmatic Particle Tracking Velocimetry. The results will allow us to characterize quantitatively the three-dimensional features of the streaming flow and to estimate its implications in practical applications as particle trapping, sorting or mixing.

  20. The linearized pressure Poisson equation for global instability analysis of incompressible flows

    Science.gov (United States)

    Theofilis, Vassilis

    2017-12-01

    The linearized pressure Poisson equation (LPPE) is used in two and three spatial dimensions in the respective matrix-forming solution of the BiGlobal and TriGlobal eigenvalue problem in primitive variables on collocated grids. It provides a disturbance pressure boundary condition which is compatible with the recovery of perturbation velocity components that satisfy exactly the linearized continuity equation. The LPPE is employed to analyze instability in wall-bounded flows and in the prototype open Blasius boundary layer flow. In the closed flows, excellent agreement is shown between results of the LPPE and those of global linear instability analyses based on the time-stepping nektar++, Semtex and nek5000 codes, as well as with those obtained from the FreeFEM++ matrix-forming code. In the flat plate boundary layer, solutions extracted from the two-dimensional LPPE eigenvector at constant streamwise locations are found to be in very good agreement with profiles delivered by the NOLOT/PSE space marching code. Benchmark eigenvalue data are provided in all flows analyzed. The performance of the LPPE is seen to be superior to that of the commonly used pressure compatibility (PC) boundary condition: at any given resolution, the discrete part of the LPPE eigenspectrum contains converged and not converged, but physically correct, eigenvalues. By contrast, the PC boundary closure delivers some of the LPPE eigenvalues and, in addition, physically wrong eigenmodes. It is concluded that the LPPE should be used in place of the PC pressure boundary closure, when BiGlobal or TriGlobal eigenvalue problems are solved in primitive variables by the matrix-forming approach on collocated grids.

  1. An investigation of two-dimensional, two-phase flow of steam in a cascade of turbine blading by the time-marching method

    International Nuclear Information System (INIS)

    Teymourtash, A. R.; Mahpeykar, M. R.

    2003-01-01

    During the course of expansion in turbines, the steam at first super cools and then nucleated to become a two-phase mixture. This is an area where greater understanding can lead to improved design. This paper describes a numerical method for the solution of two-dimensional two-phase flow of steam in a cascade of turbine blading; the unsteady euler equations governing the overall behaviour of the fluid are combined with equations describing droplet behaviour and treated by Jasmine fourth order runge Kutta time marching scheme which modified to allow for two-phase effects. The theoretical surface pressure distributions, droplet radii and contours of constant wetness fraction are presented and results are discussed in the light of knowledge of actual surface pressure distributions

  2. Analysis of the one-dimensional transient compressible vapor flow in heat pipes

    Science.gov (United States)

    Jang, Jong H.; Faghri, Amir; Chang, Won S.

    1991-01-01

    The transient compressible one-dimensional vapor flow dynamics in a heat pipe is modeled. The numerical results are obtained by using the implicit non-iterative Beam-Warming finite difference method. The model is tested for simulated heat pipe vapor flow and actual vapor flow in cylindrical heat pipes. A good comparison of the present transient results for the simulated heat pipe vapor flow with the previous results of a two-dimensional numerical model is achieved and the steady state results are in agreement with the existing experimental data. The transient behavior of the vapor flow under subsonic, sonic, and supersonic speeds as well as high mass flow rates are successfully predicted.

  3. Transport behavior of water molecules through two-dimensional nanopores

    International Nuclear Information System (INIS)

    Zhu, Chongqin; Li, Hui; Meng, Sheng

    2014-01-01

    Water transport through a two-dimensional nanoporous membrane has attracted increasing attention in recent years thanks to great demands in water purification and desalination applications. However, few studies have been reported on the microscopic mechanisms of water transport through structured nanopores, especially at the atomistic scale. Here we investigate the microstructure of water flow through two-dimensional model graphene membrane containing a variety of nanopores of different size by using molecular dynamics simulations. Our results clearly indicate that the continuum flow transits to discrete molecular flow patterns with decreasing pore sizes. While for pores with a diameter ≥15 Å water flux exhibits a linear dependence on the pore area, a nonlinear relationship between water flux and pore area has been identified for smaller pores. We attribute this deviation from linear behavior to the presence of discrete water flow, which is strongly influenced by the water-membrane interaction and hydrogen bonding between water molecules

  4. Mechanistic multidimensional analysis of horizontal two-phase flows

    International Nuclear Information System (INIS)

    Tselishcheva, Elena A.; Antal, Steven P.; Podowski, Michael Z.

    2010-01-01

    The purpose of this paper is to discuss the results of analysis of two-phase flow in horizontal tubes. Two flow situations have been considered: gas/liquid flow in a long straight pipe, and similar flow conditions in a pipe with 90 deg. elbow. The theoretical approach utilizes a multifield modeling concept. A complete three-dimensional two-phase flow model has been implemented in a state-of-the-art computational multiphase fluid dynamics (CMFD) computer code, NPHASE. The overall model has been tested parametrically. Also, the results of NPHASE simulations have been compared against experimental data for a pipe with 90 deg. elbow.

  5. Critical pressure of non-equilibrium two-phase critical flow

    Energy Technology Data Exchange (ETDEWEB)

    Minzer, U [Israel Electric Corp. Ltd., Haifa (Israel)

    1996-12-01

    Critical pressure is defined as the pressure existing at the exit edge of the piping, when it remains constant despite a decrease in the back. According to this definition the critical pressure is larger than the back pressure and for two-phase conditions below saturation pressure. The two-phase critical pressure has a major influence on the two-phase critical flow characteristics. Therefore it is of High significance in calculations of critical mass flux and critical depressurization rate, which are important in the fields of Nuclear Reactor Safety and Industrial Safety. At the Nuclear Reactor Safety field is useful for estimations of the Reactor Cooling System depressurization, the core coolant level, and the pressure build-up in the containment. In the Industrial Safety field it is helpful for estimating the leakage rate of toxic gases Tom liquefied gas pressure vessels, depressurization of pressure vessels, and explosion conditions due to liquefied gas release. For physical description of non-equilibrium two-phase critical flow it would be convenient to divide the flow into two stages. The first stage is the flow of subcooled liquid at constant temperature and uniform pressure drop (i.e., the case of incompressible fluid and uniform piping cross section). The rapid flow of the liquid causes a delay in the boiling of the liquid, which begins to boil below saturation pressure, at thermal non-equilibrium. The boiling is the beginning of the second stage, characterized by a sharp increase of the pressure drop. The liquid temperature on the second stage is almost constant because most of the energy for vaporization is supplied from the large pressure drop The present work will focus on the two-phase critical pressure of water, since water serves as coolant in the vast majority of nuclear power reactors throughout the world. (author).

  6. Critical pressure of non-equilibrium two-phase critical flow

    International Nuclear Information System (INIS)

    Minzer, U.

    1996-01-01

    Critical pressure is defined as the pressure existing at the exit edge of the piping, when it remains constant despite a decrease in the back. According to this definition the critical pressure is larger than the back pressure and for two-phase conditions below saturation pressure. The two-phase critical pressure has a major influence on the two-phase critical flow characteristics. Therefore it is of High significance in calculations of critical mass flux and critical depressurization rate, which are important in the fields of Nuclear Reactor Safety and Industrial Safety. At the Nuclear Reactor Safety field is useful for estimations of the Reactor Cooling System depressurization, the core coolant level, and the pressure build-up in the containment. In the Industrial Safety field it is helpful for estimating the leakage rate of toxic gases Tom liquefied gas pressure vessels, depressurization of pressure vessels, and explosion conditions due to liquefied gas release. For physical description of non-equilibrium two-phase critical flow it would be convenient to divide the flow into two stages. The first stage is the flow of subcooled liquid at constant temperature and uniform pressure drop (i.e., the case of incompressible fluid and uniform piping cross section). The rapid flow of the liquid causes a delay in the boiling of the liquid, which begins to boil below saturation pressure, at thermal non-equilibrium. The boiling is the beginning of the second stage, characterized by a sharp increase of the pressure drop. The liquid temperature on the second stage is almost constant because most of the energy for vaporization is supplied from the large pressure drop The present work will focus on the two-phase critical pressure of water, since water serves as coolant in the vast majority of nuclear power reactors throughout the world. (author)

  7. Toward two-dimensional search engines

    International Nuclear Information System (INIS)

    Ermann, L; Shepelyansky, D L; Chepelianskii, A D

    2012-01-01

    We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way, the ranking of nodes becomes two dimensional which paves the way for the development of two-dimensional search engines of a new type. Statistical properties of information flow on the PageRank–CheiRank plane are analyzed for networks of British, French and Italian universities, Wikipedia, Linux Kernel, gene regulation and other networks. A special emphasis is done for British universities networks using the large database publicly available in the UK. Methods of spam links control are also analyzed. (paper)

  8. Application of a two-dimensional model for predicting the pressure-flow and compression properties during column packing scale-up.

    Science.gov (United States)

    McCue, Justin T; Cecchini, Douglas; Chu, Cathy; Liu, Wei-Han; Spann, Andrew

    2007-03-23

    A two-dimensional model was formulated to describe the pressure-flow behavior of compressible stationary phases for protein chromatography at different temperatures and column scales. The model was based on the assumption of elastic deformation of the solid phase and steady-state Darcy flow. Using a single fitted value for the empirical modulus parameters, the model was applied to describe the pressure-flow behavior of several adsorbents packed using both fluid flow and mechanical compression. Simulations were in agreement with experimental data and accurately predicted the pressure-flow and compression behavior of three adsorbents over a range of column scales and operating temperatures. Use of the described theoretical model potentially improves the accuracy of the column scale-up process, allowing the use of limited laboratory scale data to predict column performance in large scale applications.

  9. Micromachined two dimensional resistor arrays for determination of gas parameters

    NARCIS (Netherlands)

    van Baar, J.J.J.; Verwey, Willem B.; Dijkstra, Mindert; Dijkstra, Marcel; Wiegerink, Remco J.; Lammerink, Theodorus S.J.; Krijnen, Gijsbertus J.M.; Elwenspoek, Michael Curt

    A resistive sensor array is presented for two dimensional temperature distribution measurements in a micromachined flow channel. This allows simultaneous measurement of flow velocity and fluid parameters, like thermal conductivity, diffusion coefficient and viscosity. More general advantages of

  10. End Effects on the Linear Induction MHD Generator Calculated by Two-Sided Laplace Transform

    Energy Technology Data Exchange (ETDEWEB)

    Engeln, F.; Peschka, W. [Deutsche Versuchsanstalt fuer Luft- und Raumfahrt e.V., Institut fuer Energiewandlung und Elektrische Antriebe, Stuttgart, Federal Republic of Germany (Germany)

    1966-11-15

    In induction MHD systems special problems occur where the flow enters or leaves the magnetic field. These problems are generally described as end effects. Large gradients of the magnetic field are present at the inlet and also at the outlet of an MHD induction engine, these generating electric current systems in the fluid which may spoil the performance characteristics of the generator due to the interaction with the primary field of the engine. The two-dimensional induction MHD generator of finite length, using a polyphase winding system to obtain a travelling magnetic field, is treated as a boundary value problem by two-sided Laplace transform. For simplicity incompressibility is assumed. The two- dimensional boundary value problem of the induction engine is solved for - {infinity} Less-Than-Over-Equal-To x Less-Than-Over-Equal-To {infinity}. x is parallel to the flow direction of the linear MHD generator. In the region 0 Less-Than-Over-Equal-To x Less-Than-Over-Equal-To L the magnetic travelling wave is sinusoidal with a cyclical frequency {omega} and a phase-velocity v{sub s}. At x = 0 the conducting incompressible working fluid enters the field region and leaves it at the point-x = L. Two mathematical methods can be used to solve the boundary value problem, the Fourier transform or the two-sided Laplace transform. The latter offers the advantage of representing a complex analytical function in the image space. Moreover, it is possible to obtain the characteristics of the generator in the image space (e. g. field configuration, power flow function, etc.). That implies a large simplification of mathematical treatment. The solution in the original space then is given by asymptotic expansion of the known image function. (author)

  11. Evaporation effect on two-dimensional wicking in porous media.

    Science.gov (United States)

    Benner, Eric M; Petsev, Dimiter N

    2018-03-15

    We analyze the effect of evaporation on expanding capillary flow for losses normal to the plane of a two-dimensional porous medium using the potential flow theory formulation of the Lucas-Washburn method. Evaporation induces a finite steady state liquid flux on capillary flows into fan-shaped domains which is significantly greater than the flux into media of constant cross section. We introduce the evaporation-capillary number, a new dimensionless quantity, which governs the frontal motion when multiplied by the scaled time. This governing product divides the wicking behavior into simple regimes of capillary dominated flow and evaporative steady state, as well as the intermediate regime of evaporation influenced capillary driven motion. We also show flow dimensionality and evaporation reduce the propagation rate of the wet front relative to the Lucas-Washburn law. Copyright © 2017 Elsevier Inc. All rights reserved.

  12. Three dimensional computations of the flow around a LM19 rotor

    Energy Technology Data Exchange (ETDEWEB)

    Hambraeus, T. [FFA, Bromma (Sweden)

    1997-12-31

    To achieve insight in the flow phenomenon occurring in wind power engineering modeling of the flow through the basic governing equations, Navier-Stokes and Euler, can be a great complement to experiments and other computational methods such as the BEM (Blade Element Momentum). Navier-Stokes methods is regularly used in prediction of air-foil flows but then mostly under attached flow conditions. One of the main differences between air-foil computations for aircraft industry and computations for wind turbine applications is that the former is not very interested in separated flow while for the latter case this is part of the operating conditions. It has been noted that separated flow poses problems since the most popular turbulence models such as Baldwin-Lomax and the {kappa}-{epsilon} model seems to over estimate the amount of turbulent viscosity produced and thus suppressing the separation. The work with finding better turbulence models is presently an area with large amount of research offering improved models. However, in the present report only the two mentioned turbulence models have been used. The present report shows computational results obtained with the Navier-Stokes solver EU-RANUS. First the results from a two-dimensional verification cases are shown to verify that the solver produces results comparable with other solvers. The flow computed is attached flow and slightly separated flow over the so called Profile-A. Secondly three dimensional computations of the flow over a full three dimensional rotor at attached and stalled conditions is shown. The computed results are compared with measured power data from field experiments. (EG)

  13. Analysis Of Convective Plane Stagnation Point Chemically Reactive Mhd Flow Past A Vertical Porous Plate With A Convective Boundary Condition In The Presence Of A Uniform Magnetic Field.

    OpenAIRE

    Adeniyan, A.,

    2013-01-01

    The numerical investigation of a stagnation point boundary layer flow , mass and heat transfer of a steady two dimensional , incompressible , viscous electrically conducting, chemically reacting laminar fluid over a vertical convectively heated , electrically neutral flat plate exposed to a transverse uniform magnetic field has been carried out to examine the influence of the simultaneous presence of the effects of a convective boundary condition, chemical reaction, heat transfer and suctio...

  14. Nearly incompressible MHD turbulence in the solar wind

    International Nuclear Information System (INIS)

    Matthaeus, W.H.; Zhou, Y.

    1989-01-01

    Observational studies indicate that solar wind plasma and magnetic field fluctuations may be meaningfully viewed as an example of magnetohydrodynamic turbulence. This paper presents a brief summary of some relevant results of turbulence theory and reviews a turbulence style description of 'typical' solar wind conditions. Recent results, particularly those regarding the radial evolution of inertial range cross helicity, support the viewpoint that interplanetary turbulence is active and evolving with heliocentric distance. A number of observed properties can be understood by appeal to incompressible turbulence mechanisms. This connection may be understood by appeal to incompressible turbulence mechanisms. This connection may be understood in terms of theories of pseudosound density fluctuations and nearly incompressible magnetohydrodynamics, which are also reviewed here. Finally, we summarize a recent two-scale dynamical theory of the radial and temporal evolution of the turbulence, which may provide an additional framework for understanding the observations. (author). 49 refs

  15. Study of two-phase flow redistribution between two passes of a heat exchanger

    International Nuclear Information System (INIS)

    Mendes de Moura, L.F.

    1989-04-01

    The object of the present thesis deals with the study of two-phase flow redistribution between two passes of a heat exchanger. Mass flow rate measurements of each component performed at each channel outlet of the second pass allowed us to determine the influence of mass flow, gas quality, flow direction (upward or downward) and common header geometry upon flow redistribution. Local void fraction inside common header was measured with an optical probe. A two-dimensional two-phase flow computational code was developed from a two-fluid model. Modelling of interfacial momentum transfer was used in order to take into account twp-phase flow patterns in common headers. Numerical simulation results show qualitative agreement with experimental results. Present theoretical model limitations are analysed and future improvements are proposed [fr

  16. COMPUTATIONAL ANALYSIS OF BACKWARD-FACING STEP FLOW

    Directory of Open Access Journals (Sweden)

    Erhan PULAT

    2001-01-01

    Full Text Available In this study, backward-facing step flow that are encountered in electronic systems cooling, heat exchanger design, and gas turbine cooling are investigated computationally. Steady, incompressible, and two-dimensional air flow is analyzed. Inlet velocity is assumed uniform and it is obtained from parabolic profile by using maximum velocity. In the analysis, the effects of channel expansion ratio and Reynolds number to reattachment length are investigated. In addition, pressure distribution throughout the channel length is also obtained and flow is analyzed for the Reynolds number values of 50 and 150 and channel expansion ratios of 1.5 and 2. Governing equations are solved by using Galerkin finite element mothod of ANSYS-FLOTRAN code. Obtained results are compared with the solutions of lattice BGK method that is relatively new method in fluid dynamics and other numerical and experimental results. It is concluded that reattachment length increases with increasing Reynolds number and at the same Reynolds number it decreases with increasing channel expansion ratio.

  17. Universal equations of unsteady two-dimensional MHD boundary layer whose temperature varies with time

    Directory of Open Access Journals (Sweden)

    Boričić Zoran

    2009-01-01

    Full Text Available This paper concerns with unsteady two-dimensional temperature laminar magnetohydrodynamic (MHD boundary layer of incompressible fluid. It is assumed that induction of outer magnetic field is function of longitudinal coordinate with force lines perpendicular to the body surface on which boundary layer forms. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in inductionless approximation. Characteristic properties of fluid are constant because velocity of flow is much lower than speed of light and temperature difference is small enough (under 50ºC . Introduced assumptions simplify considered problem in sake of mathematical solving, but adopted physical model is interesting from practical point of view, because its relation with large number of technically significant MHD flows. Obtained partial differential equations can be solved with modern numerical methods for every particular problem. Conclusions based on these solutions are related only with specific temperature MHD boundary layer problem. In this paper, quite different approach is used. First new variables are introduced and then sets of similarity parameters which transform equations on the form which don't contain inside and in corresponding boundary conditions characteristics of particular problems and in that sense equations are considered as universal. Obtained universal equations in appropriate approximation can be solved numerically once for all. So-called universal solutions of equations can be used to carry out general conclusions about temperature MHD boundary layer and for calculation of arbitrary particular problems. To calculate any particular problem it is necessary also to solve corresponding momentum integral equation.

  18. Three-dimensional numerical study of heat transfer enhancement in separated flows

    Science.gov (United States)

    Kumar, Saurav; Vengadesan, S.

    2017-11-01

    The flow separation appears in a wide range of heat transfer applications and causes poor heat transfer performance. It motivates the study of heat transfer enhancement in laminar as well as turbulent flows over a backward facing step by means of an adiabatic fin mounted on the top wall. Recently, we have studied steady, 2-D numerical simulations in laminar flow and investigated the effect of fin length, location, and orientation. It revealed that the addition of fin causes enhancement of heat transfer and it is very effective to control the flow and thermal behavior. The fin is most effective and sensitive when it is placed exactly above the step. A slight displacement of the fin in upstream of the step causes the complete change of flow and thermal behavior. Based on the obtained 2-D results it is interesting to investigate the side wall effect in three-dimensional simulations. The comparison of two-dimensional and three-dimensional numerical simulations with the available experimental results will be presented. Special attention has to be given to capture unsteadiness in the flow and thermal field.

  19. Analytical simulation of two dimensional advection dispersion ...

    African Journals Online (AJOL)

    The study was designed to investigate the analytical simulation of two dimensional advection dispersion equation of contaminant transport. The steady state flow condition of the contaminant transport where inorganic contaminants in aqueous waste solutions are disposed of at the land surface where it would migrate ...

  20. Analytical Simulation of Two Dimensional Advection Dispersion ...

    African Journals Online (AJOL)

    ADOWIE PERE

    ABSTRACT: The study was designed to investigate the analytical simulation of two dimensional advection dispersion equation of contaminant transport. The steady state flow condition of the contaminant transport where inorganic contaminants in aqueous waste solutions are disposed of at the land surface where it would ...

  1. Three-Dimensional Flows

    CERN Document Server

    Araujo, Vitor; Viana, Marcelo

    2010-01-01

    In this book, the authors present the elements of a general theory for flows on three-dimensional compact boundaryless manifolds, encompassing flows with equilibria accumulated by regular orbits. The book aims to provide a global perspective of this theory and make it easier for the reader to digest the growing literature on this subject. This is not the first book on the subject of dynamical systems, but there are distinct aspects which together make this book unique. Firstly, this book treats mostly continuous time dynamical systems, instead of its discrete counterpart, exhaustively treated

  2. Experimental investigation on flow and heat transfer for cooling flush-mounted ribbons in a channel: Application of an EHD active enhancement method

    OpenAIRE

    Alami Nia Amin; Campo Antonio

    2016-01-01

    In the present study, the heat transfer enhancement of a bundle of flush-mounted ribbons placed on the floor of a rectangular duct was investigated experimentally. The flush-mounted ribbons act as heat sources and the cooling happens with air. The air flow was two-dimensional, steady, viscous and incompressible under either laminar (500 ≤ ReDh < 2000) and turbulent (2000 ≤ Re Dh ≤ 4500) conditions. The hydrodynamics and heat transfer behavior of the air flo...

  3. A two-dimensional analytical model for groundwater flow in a leaky aquifer extending finite distance under the estuary

    Science.gov (United States)

    Chuang, Mo-Hsiung; Hung, Chi-Tung; -Yen Lin, Wen; Ma, Kuo-chen

    2017-04-01

    In recent years, cities and industries in the vicinity of the estuarine region have developed rapidly, resulting in a sharp increase in the population concerned. The increasing demand for human activities, agriculture irrigation, and aquaculture relies on massive pumping of water in estuarine area. Since the 1950s, numerous studies have focused on the effects of tidal fluctuations on groundwater flow in the estuarine area. Tide-induced head fluctuation in a two-dimensional estuarine aquifer system is complicated and rather important in dealing with many groundwater management or remediation problems. The conceptual model of the aquifer system considered is multi-layered with estuarine bank and the leaky aquifer extend finite distance under the estuary. The solution of the model describing the groundwater head distribution in such an estuarine aquifer system and subject to the tidal fluctuation effects from estuarine river is developed based on the method of separation of variables along with river boundary. The solutions by Sun (Sun H. A two-dimensional analytical solution of groundwater response to tidal loading in an estuary, Water Resour. Res. 1997; 33:1429-35) as well as Tang and Jiao (Tang Z. and J. J. Jiao, A two-dimensional analytical solution for groundwater flow in a leaky confined aquifer system near open tidal water, Hydrological Processes, 2001; 15: 573-585) can be shown to be special cases of the present solution. On the basis of the analytical solution, the groundwater head distribution in response to estuarine boundary is examined and the influences of leakage, hydraulic parameters, and loading effect on the groundwater head fluctuation due to tide are investigated and discussed. KEYWORDS: analytical model, estuarine river, groundwater fluctuation, leaky aquifer.

  4. Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction

    Science.gov (United States)

    Sid, S.; Terrapon, V. E.; Dubief, Y.

    2018-02-01

    The goal of the present study is threefold: (i) to demonstrate the two-dimensional nature of the elasto-inertial instability in elasto-inertial turbulence (EIT), (ii) to identify the role of the bidimensional instability in three-dimensional EIT flows, and (iii) to establish the role of the small elastic scales in the mechanism of self-sustained EIT. Direct numerical simulations of viscoelastic fluid flows are performed in both two- and three-dimensional straight periodic channels using the Peterlin finitely extensible nonlinear elastic model (FENE-P). The Reynolds number is set to Reτ=85 , which is subcritical for two-dimensional flows but beyond the transition for three-dimensional ones. The polymer properties selected correspond to those of typical dilute polymer solutions, and two moderate Weissenberg numbers, Wiτ=40 ,100 , are considered. The simulation results show that sustained turbulence can be observed in two-dimensional subcritical flows, confirming the existence of a bidimensional elasto-inertial instability. The same type of instability is also observed in three-dimensional simulations where both Newtonian and elasto-inertial turbulent structures coexist. Depending on the Wi number, one type of structure can dominate and drive the flow. For large Wi values, the elasto-inertial instability tends to prevail over the Newtonian turbulence. This statement is supported by (i) the absence of typical Newtonian near-wall vortices and (ii) strong similarities between two- and three-dimensional flows when considering larger Wi numbers. The role of small elastic scales is investigated by introducing global artificial diffusion (GAD) in the hyperbolic transport equation for polymers. The aim is to measure how the flow reacts when the smallest elastic scales are progressively filtered out. The study results show that the introduction of large polymer diffusion in the system strongly damps a significant part of the elastic scales that are necessary to feed

  5. Stability of interfacial waves in two-phase flows

    Energy Technology Data Exchange (ETDEWEB)

    Liu, W S [Ontario Hydro, Toronto, ON (Canada)

    1996-12-31

    The influence of the interfacial pressure and the flow distribution in the one-dimensional two-fluid model on the stability problems of interfacial waves is discussed. With a proper formulation of the interfacial pressure, the following two-phase phenomena can be predicted from the stability and stationary criteria of the interfacial waves: onset of slug flow, stationary hydraulic jump in a stratified flow, flooding in a vertical pipe, and the critical void fraction of a bubbly flow. It can be concluded that the interfacial pressure plays an important role in the interfacial wave propagation of the two-fluid model. The flow distribution parameter may enhance the flow stability range, but only plays a minor role in the two-phase characteristics. (author). 20 refs., 3 tabs., 4 figs.

  6. Characteristics and stability analyses of transient one-dimensional two-phase flow equations and their finite difference approximations

    International Nuclear Information System (INIS)

    Lyczkowski, R.W.; Gidaspow, D.; Solbrig, C.W.; Hughes, E.D.

    1975-01-01

    Equation systems describing one-dimensional, transient, two-phase flow with separate continuity, momentum, and energy equations for each phase are classified by use of the method of characteristics. Little attempt is made to justify the physics of these equations. Many of the equation systems possess complex-valued characteristics and hence, according to well-known mathematical theorems, are not well-posed as initial-value problems (IVPs). Real-valued characteristics are necessary but not sufficient to insure well-posedness. In the absence of lower order source or sink terms (potential type flows), which can affect the well-posedness of IVPs, the complex characteristics associated with these two-phase flow equations imply unbounded exponential growth for disturbances of all wavelengths. Analytical and numerical examples show that the ill-posedness of IVPs for the two-phase flow partial differential equations which possess complex characteristics produce unstable numerical schemes. These unstable numerical schemes can produce apparently stable and even accurate results if the growth rate resulting from the complex characteristics remains small throughout the time span of the numerical experiment or if sufficient numerical damping is present for the increment size used. Other examples show that clearly nonphysical numerical instabilities resulting from the complex characteristics can be produced. These latter types of numerical instabilities are shown to be removed by the addition of physically motivated differential terms which eliminate the complex characteristics. (auth)

  7. The Three-Dimensional Velocity Distribution of Wide Gap Taylor-Couette Flow Modelled by CFD

    Directory of Open Access Journals (Sweden)

    David Shina Adebayo

    2016-01-01

    Full Text Available A numerical investigation is conducted for the flow between two concentric cylinders with a wide gap, relevant to bearing chamber applications. This wide gap configuration has received comparatively less attention than narrow gap journal bearing type geometries. The flow in the gap between an inner rotating cylinder and an outer stationary cylinder has been modelled as an incompressible flow using an implicit finite volume RANS scheme with the realisable k-ε model. The model flow is above the critical Taylor number at which axisymmetric counterrotating Taylor vortices are formed. The tangential velocity profiles at all axial locations are different from typical journal bearing applications, where the velocity profiles are quasilinear. The predicted results led to two significant findings of impact in rotating machinery operations. Firstly, the axial variation of the tangential velocity gradient induces an axially varying shear stress, resulting in local bands of enhanced work input to the working fluid. This is likely to cause unwanted heat transfer on the surface in high torque turbomachinery applications. Secondly, the radial inflow at the axial end-wall boundaries is likely to promote the transport of debris to the junction between the end-collar and the rotating cylinder, causing the build-up of fouling in the seal.

  8. Numerical and dimensional analysis of nanoparticles transport with two-phase flow in porous media

    KAUST Repository

    El-Amin, Mohamed

    2015-04-01

    In this paper, a mathematical model and numerical simulation are developed to describe the imbibition of nanoparticles-water suspension into two-phase flow in a porous medium. The flow system may be changed from oil-wet to water-wet due to nanoparticles (which are also water-wet) deposition on surface of the pores. So, the model is extended to include the negative capillary pressure and mixed-wet relative permeability correlations to fit with the mixed-wet system. Moreover, buoyancy and capillary forces as well as Brownian diffusion and mechanical dispersion are considered in the mathematical model. An example of countercurrent imbibition in a core of small scale is considered. A dimensional analysis of the governing equations is introduced to examine contributions of each term of the model. Several important dimensionless numbers appear in the dimensionless equations, such as Darcy number Da, capillary number Ca, and Bond number Bo. Throughout this investigation, we monitor the changing of the fluids and solid properties due to addition of the nanoparticles using numerical experiments.

  9. Two-phase flow characteristics analysis code: MINCS

    International Nuclear Information System (INIS)

    Watanabe, Tadashi; Hirano, Masashi; Akimoto, Masayuki; Tanabe, Fumiya; Kohsaka, Atsuo.

    1992-03-01

    Two-phase flow characteristics analysis code: MINCS (Modularized and INtegrated Code System) has been developed to provide a computational tool for analyzing two-phase flow phenomena in one-dimensional ducts. In MINCS, nine types of two-phase flow models-from a basic two-fluid nonequilibrium (2V2T) model to a simple homogeneous equilibrium (1V1T) model-can be used under the same numerical solution method. The numerical technique is based on the implicit finite difference method to enhance the numerical stability. The code structure is highly modularized, so that new constitutive relations and correlations can be easily implemented into the code and hence evaluated. A flow pattern can be fixed regardless of flow conditions, and state equations or steam tables can be selected. It is, therefore, easy to calculate physical or numerical benchmark problems. (author)

  10. A two-dimensional, two-phase mass transport model for liquid-feed DMFCs

    International Nuclear Information System (INIS)

    Yang, W.W.; Zhao, T.S.

    2007-01-01

    A two-dimensional, isothermal two-phase mass transport model for a liquid-feed direct methanol fuel cell (DMFC) is presented in this paper. The two-phase mass transport in the anode and cathode porous regions is formulated based on the classical multiphase flow in porous media without invoking the assumption of constant gas pressure in the unsaturated porous medium flow theory. The two-phase flow behavior in the anode flow channel is modeled by utilizing the drift-flux model, while in the cathode flow channel the homogeneous mist-flow model is used. In addition, a micro-agglomerate model is developed for the cathode catalyst layer. The model also accounts for the effects of both methanol and water crossover through the membrane. The comprehensive model formed by integrating those in the different regions is solved numerically using a home-written computer code and validated against the experimental data in the literature. The model is then used to investigate the effects of various operating and structural parameters, such as methanol concentration, anode flow rate, porosities of both anode and cathode electrodes, the rate of methanol crossover, and the agglomerate size, on cell performance

  11. Three-Dimensional Mapping of Air Flow at an Urban Canyon Intersection

    Science.gov (United States)

    Carpentieri, Matteo; Robins, Alan G.; Baldi, Sandro

    2009-11-01

    In this experimental work both qualitative (flow visualisation) and quantitative (laser Doppler anemometry) methods were applied in a wind tunnel in order to describe the complex three-dimensional flow field in a real environment (a street canyon intersection). The main aim was an examination of the mean flow, turbulence and flow pathlines characterising a complex three-dimensional urban location. The experiments highlighted the complexity of the observed flows, particularly in the upwind region of the intersection. In this complex and realistic situation some details of the upwind flow, such as the presence of two tall towers, play an important role in defining the flow field within the intersection, particularly at roof level. This effect is likely to have a strong influence on the mass exchange mechanism between the canopy flow and the air aloft, and therefore the distribution of pollutants. This strong interaction between the flows inside and outside the urban canopy is currently neglected in most state-of-the-art local scale dispersion models.

  12. Asymptotic structure of viscous incompressible flow around a rotating body, with nonvanishing flow field at infinity

    Czech Academy of Sciences Publication Activity Database

    Deuring, P.; Kračmar, S.; Nečasová, Šárka

    2017-01-01

    Roč. 68, č. 1 (2017), č. článku 16. ISSN 0044-2275 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : asymptotic profile * Pointwise decay * rotating body * stationary incompressible Navier–Stokes system Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.687, year: 2016 http://link.springer.com/article/10.1007%2Fs00033-016-0760-x

  13. Asymptotic structure of viscous incompressible flow around a rotating body, with nonvanishing flow field at infinity

    Czech Academy of Sciences Publication Activity Database

    Deuring, P.; Kračmar, S.; Nečasová, Šárka

    2017-01-01

    Roč. 68, č. 1 (2017), č. článku 16. ISSN 0044-2275 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : asymptotic profile * Pointwise decay * rotating body * stationary incompressible Navier–Stokes system Subject RIV: BA - General Math ematics OBOR OECD: Pure math ematics Impact factor: 1.687, year: 2016 http://link.springer.com/article/10.1007%2Fs00033-016-0760-x

  14. Turbine endwall two-cylinder program. [wind tunnel and water tunnel investigation of three dimensional separation of fluid flow

    Science.gov (United States)

    Langston, L. S.

    1980-01-01

    Progress is reported in an effort to study the three dimensional separation of fluid flow around two isolated cylinders mounted on an endwall. The design and performance of a hydrogen bubble generator for water tunnel tests to determine bulk flow properties and to measure main stream velocity and boundary layer thickness are described. Although the water tunnel tests are behind schedule because of inlet distortion problems, tests are far enough along to indicate cylinder spacing, wall effects and low Reynolds number behavior, all of which impacted wind tunnel model design. The construction, assembly, and operation of the wind tunnel and the check out of its characteristics are described. An off-body potential flow program was adapted to calculate normal streams streamwise pressure gradients at the saddle point locations.

  15. A multidomain chebyshev pseudo-spectral method for fluid flow and heat transfer from square cylinders

    KAUST Repository

    Wang, Zhiheng

    2015-01-01

    A simple multidomain Chebyshev pseudo-spectral method is developed for two-dimensional fluid flow and heat transfer over square cylinders. The incompressible Navier-Stokes equations with primitive variables are discretized in several subdomains of the computational domain. The velocities and pressure are discretized with the same order of Chebyshev polynomials, i.e., the PN-PN method. The Projection method is applied in coupling the pressure with the velocity. The present method is first validated by benchmark problems of natural convection in a square cavity. Then the method based on multidomains is applied to simulate fluid flow and heat transfer from square cylinders. The numerical results agree well with the existing results. © Taylor & Francis Group, LLC.

  16. Flow predictions for MHD channels with an approximation for three-dimensional effects

    International Nuclear Information System (INIS)

    Blottner, F.G.

    1978-01-01

    A finite-difference procedure has been formulated for predicting the flow properties across channels. A quasi-two-dimensional approach has been developed which allows the three-dimensional channel effects to be taken into account. Comparison of the numerical solutions with experimental results show that this approach is a reasonable approximation for MHD flow conditions if there is not significant merging of the wall boundary layers. The resulting code provides a technique to obtain the flow details in the symmetry plane of the channel and requires only a small amount of computer time

  17. Two-dimensional model of coupled heat and moisture transport in frost-heaving soils

    International Nuclear Information System (INIS)

    Guymon, G.L.; Berg, R.L.; Hromadka, T.V.

    1984-01-01

    A two-dimensional model of coupled heat and moisture flow in frost-heaving soils is developed based upon well known equations of heat and moisture flow in soils. Numerical solution is by the nodal domain integration method which includes the integrated finite difference and the Galerkin finite element methods. Solution of the phase change process is approximated by an isothermal approach and phenomenological equations are assumed for processes occurring in freezing or thawing zones. The model has been verified against experimental one-dimensional freezing soil column data and experimental two-dimensional soil thawing tank data as well as two-dimensional soil seepage data. The model has been applied to several simple but useful field problems such as roadway embankment freezing and frost heaving

  18. Theory and Transport of Nearly Incompressible Magnetohydrodynamic Turbulence

    Energy Technology Data Exchange (ETDEWEB)

    Zank, G. P.; Adhikari, L.; Hunana, P. [Center for Space Plasma and Aeronomic Research (CSPAR), University of Alabama in Huntsville, Huntsville, AL 35805 (United States); Shiota, D. [Institute for Space-Earth Environmental Research, Nagoya University, Nagoya, Aichi 464-8601 (Japan); Bruno, R. [INAF-IAPS Istituto di Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere 100, I-00133 Roma (Italy); Telloni, D. [INAF—Astrophysical Observatory of Torino, Via Osservatorio 20, I-10025 Pino Torinese (Italy)

    2017-02-01

    The theory of nearly incompressible magnetohydrodynamics (NI MHD) was developed largely in the early 1990s, together with an important extension to inhomogeneous flows in 2010. Much of the focus in the earlier work was to understand the apparent incompressibility of the solar wind and other plasma environments, and the relationship of density fluctuations to apparently incompressible manifestations of turbulence in the solar wind and interstellar medium. Further important predictions about the “dimensionality” of solar wind turbulence and its relationship to the plasma beta were made and subsequently confirmed observationally. However, despite the initial success of NI MHD in describing fluctuations in the solar wind, a detailed application to solar wind turbulence has not been undertaken. Here, we use the equations of NI MHD to describe solar wind turbulence, rewriting the NI MHD system in terms of Elsässer variables. Distinct descriptions of 2D and slab turbulence emerge naturally from the Elsässer formulation, as do the nonlinear couplings between 2D and slab components. For plasma beta order 1 or less regions, predictions for 2D and slab spectra result from the NI MHD description, and predictions for the spectral characteristics of density fluctuations can be made. We conclude by presenting a NI MHD formulation describing the transport of majority 2D and minority slab turbulence throughout the solar wind. A preliminary comparison of theory and observations is presented.

  19. Effect of slip on existence, uniqueness, and behavior of similarity solutions for steady incompressible laminar flow in porous tubes and channels

    Science.gov (United States)

    Chellam, Shankararaman; Liu, Mei

    2006-08-01

    The existence and multiplicity of similarity solutions for steady, fully developed, incompressible laminar flow in uniformly porous tubes and channels with one or two permeable walls is investigated from first principles. A fourth-order ordinary differential equation obtained by simplifying the Navier-Stokes equations by introducing Berman's stream function [A. S. Berman, J. Appl. Phys. 24, 1232 (1953)] and Terrill's transformation [R. M. Terrill, Aeronaut. Q. 15, 299 (1964)] is probed analytically. In this work that considers only symmetric flows for symmetric ducts; the no-slip boundary condition at porous walls is relaxed to account for momentum transfer within the porous walls. By employing the Saffman [P. G. Saffman, Stud. Appl. Math. 50, 93 (1971)] form of the slip boundary condition, the uniqueness of similarity solutions is investigated theoretically in terms of the signs of the guesses for the missing initial conditions. Solutions were obtained for all wall Reynolds numbers for channel flows whereas no solutions existed for intermediate values for tube flows. Introducing slip did not fundamentally change the number or the character of solutions corresponding to different sections. However, the range of wall Reynolds numbers for which similarity solutions are theoretically impossible in tube flows was found to be a weak function of the slip coefficient. Slip also weakly influenced the transition wall Reynolds number corresponding to flow in the direction of a favorable axial pressure gradient to one in the direction of an adverse pressure gradient. Momentum transfer from the longitudinal axis to the walls appears to occur more efficiently in porous channels compared to porous tubes even in the presence of slip.

  20. On the Stability of Three-Dimensional Boundary Layers. Part 1; Linear and Nonlinear Stability

    Science.gov (United States)

    Janke, Erik; Balakumar, Ponnampalam

    1999-01-01

    The primary stability of incompressible three-dimensional boundary layers is investigated using the Parabolized Stability Equations (PSE). We compute the evolution of stationary and traveling disturbances in the linear and nonlinear region prior to transition. As model problems, we choose Swept Hiemenz Flow and the DLR Transition Experiment. The primary stability results for Swept Hiemenz Flow agree very well with computations by Malik et al. For the DLR Experiment, the mean flow profiles are obtained by solving the boundary layer equations for the measured pressure distribution. Both linear and nonlinear results show very good agreement with the experiment.

  1. Numerical analysis of temperature and flow effects in a dry, two-dimensional, porous-media reservoir used for compressed air energy storage

    Energy Technology Data Exchange (ETDEWEB)

    Wiles, L.E.

    1979-10-01

    The purpose of the work is to define the hydrodynamic and thermodynamic response of a CAES dry porous media reservoir subjected to simulated air mass cycling. The knowledge gained will provide, or will assist in providing, design guidelines for the efficient and stable operation of the air storage reservoir. The analysis and results obtained by two-dimensional modeling of dry reservoirs are presented. While the fluid/thermal response of the underground system is dependent on many parameters, the two-dimensional model was applied only to those parameters that entered the analysis by virtue of inclusion of the vertical dimension. In particular, the parameters or responses that were quantified or characterized include wellbore heat transfer, heat losses to the vertical boundaries of the porous zone, gravitationally induced flows, producing length of the wellbore, and the effects of nonuniform permeability. The analysis of the wellbore heat transfer included consideration of insulation, preheating (bubble development with heated air), and air mass flow rate.

  2. Linearized stationary incompressible flow around rotating and translating bodies: Asymptotic profile of the velocity gradient and decay estimate of the second derivatives of the velocity

    Czech Academy of Sciences Publication Activity Database

    Deuring, P.; Kračmar, S.; Nečasová, Šárka

    2012-01-01

    Roč. 252, č. 1 (2012), s. 459-476 ISSN 0022-0396 R&D Projects: GA AV ČR IAA100190804; GA ČR(CZ) GAP201/11/1304 Institutional research plan: CEZ:AV0Z10190503 Keywords : viscous incompressible flow * rotating body * rundamental solution * decay * asymptotic profile * Navier-Stokes system Subject RIV: BA - General Mathematics Impact factor: 1.480, year: 2012 http://www.sciencedirect.com/science/article/pii/S0022039611003573

  3. Numerical study of Free Convective Viscous Dissipative flow along Vertical Cone with Influence of Radiation using Network Simulation method

    Science.gov (United States)

    Kannan, R. M.; Pullepu, Bapuji; Immanuel, Y.

    2018-04-01

    A two dimensional mathematical model is formulated for the transient laminar free convective flow with heat transfer over an incompressible viscous fluid past a vertical cone with uniform surface heat flux with combined effects of viscous dissipation and radiation. The dimensionless boundary layer equations of the flow which are transient, coupled and nonlinear Partial differential equations are solved using the Network Simulation Method (NSM), a powerful numerical technique which demonstrates high efficiency and accuracy by employing the network simulator computer code Pspice. The velocity and temperature profiles have been investigated for various factors, namely viscous dissipation parameter ε, Prandtl number Pr and radiation Rd are analyzed graphically.

  4. Numerical solver for compressible two-fluid flow

    NARCIS (Netherlands)

    J. Naber (Jorick)

    2005-01-01

    textabstractThis report treats the development of a numerical solver for the simulation of flows of two non-mixing fluids described by the two-dimensional Euler equations. A level-set equation in conservative form describes the interface. After each time step the deformed level-set function is

  5. A two-dimensional continuum model of biofilm growth incorporating fluid flow and shear stress based detachment

    KAUST Repository

    Duddu, Ravindra

    2009-05-01

    We present a two-dimensional biofilm growth model in a continuum framework using an Eulerian description. A computational technique based on the eXtended Finite Element Method (XFEM) and the level set method is used to simulate the growth of the biofilm. The model considers fluid flow around the biofilm surface, the advection-diffusion and reaction of substrate, variable biomass volume fraction and erosion due to the interfacial shear stress at the biofilm-fluid interface. The key assumptions of the model and the governing equations of transport, biofilm kinetics and biofilm mechanics are presented. Our 2D biofilm growth results are in good agreement with those obtained by Picioreanu et al. (Biotechnol Bioeng 69(5):504-515, 2000). Detachment due to erosion is modeled using two continuous speed functions based on: (a) interfacial shear stress and (b) biofilm height. A relation between the two detachment models in the case of a 1D biofilm is established and simulated biofilm results with detachment in 2D are presented. The stress in the biofilm due to fluid flow is evaluated and higher stresses are observed close to the substratum where the biofilm is attached. © 2008 Wiley Periodicals, Inc.

  6. New non-structured discretizations for fluid flows with reinforced incompressibility

    International Nuclear Information System (INIS)

    Heib, S.

    2003-01-01

    This work deals with the discretization of Stokes and Navier-Stokes equations modeling the flow of incompressible fluids on 2-D or 3-D non-structured meshes. Triangles and tetrahedrons are used for 2-D and 3-D meshes, respectively. The developments and calculations are performed with the code Priceles (fast CEA-EdF industrial platform for large Eddy simulation). This code allows to perform simulations both on structured and non-structured meshes. A finite-volume resolution method is used: a finite difference volume (FDV) method is used for the structured meshes and a finite element volume (FEV) method is used for the non-structured meshes. The finite element used in the beginning of this work has several defects. Starting from this situation, the discretization is improved by adding modifications to this element and the new elements introduced are analyzed theoretically. In parallel to these analyses, the new discretizations are implemented in order to test them numerically and to confirm the theoretical analyses. The first chapter presents the physical and mathematical modeling used in this work. The second chapter treats of the discretization of Stokes equations and presents the FEV resolution method. Chapter 3 presents a first attempt of improvement of this finite element and leads to the proposal of a new element which is presented in details. The problem encountered with the new discretization leads to a modification presented in chapter 4. This new discretization gives all the expected convergence results and sometimes shows super-convergence properties. Chapter 5 deals with the study and discretization of the Navier-Stokes equations. The study of the filtered Navier-Stokes equations, used for large Eddy simulations, requires to give a particular attention to the discretization of the diffusive terms. Then, the convective terms are considered. The effects of the convective terms in the initial discretization and in the improved method are compared. The use of

  7. Sensitivity analysis explains quasi-one-dimensional current transport in two-dimensional materials

    DEFF Research Database (Denmark)

    Boll, Mads; Lotz, Mikkel Rønne; Hansen, Ole

    2014-01-01

    We demonstrate that the quasi-one-dimensional (1D) current transport, experimentally observed in graphene as measured by a collinear four-point probe in two electrode configurations A and B, can be interpreted using the sensitivity functions of the two electrode configurations (configurations...... A and B represents different pairs of electrodes chosen for current sources and potential measurements). The measured sheet resistance in a four-point probe measurement is averaged over an area determined by the sensitivity function. For a two-dimensional conductor, the sensitivity functions for electrode...... configurations A and B are different. But when the current is forced to flow through a percolation network, e.g., graphene with high density of extended defects, the two sensitivity functions become identical. This is equivalent to a four-point measurement on a line resistor, hence quasi-1D transport...

  8. Probing temperature-driven flow lines in a gated two-dimensional electron gas with tunable spin-splitting

    International Nuclear Information System (INIS)

    Wang, Yi-Ting; Huang, C F; Chen, Wei-Jen; Chang, Y H; Liang, C-T; Kim, Gil-Ho; Lo, Shun-Tsung; Nicholls, J T; Lin, Li-Hung; Ritchie, D A; Dolan, B P

    2012-01-01

    We study the temperature flow of conductivities in a gated GaAs two-dimensional electron gas (2DEG) containing self-assembled InAs dots and compare the results with recent theoretical predictions. By changing the gate voltage, we are able to tune the 2DEG density and thus vary disorder and spin-splitting. Data for both the spin-resolved and spin-degenerate phase transitions are presented, the former collapsing to the latter with decreasing gate voltage and/or decreasing spin-splitting. The experimental results support a recent theory, based on modular symmetry, which predicts how the critical Hall conductivity varies with spin-splitting.

  9. One-dimensional two-fluid model for wavy flow beyond the Kelvin–Helmholtz instability: Limit cycles and chaos

    Energy Technology Data Exchange (ETDEWEB)

    Lopez de Bertodano, Martín, E-mail: bertodan@purdue.edu [School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907 (United States); Fullmer, William D. [Department of Chemical and Biological Engineering, U. of Colorado, Boulder, CO 80309 (United States); Clausse, Alejandro [CNEA-CONICET and Universidad Nacional del Centro, 7000 Tandil (Argentina)

    2016-12-15

    A 1D TFM numerical simulation of near horizontal stratified two-phase flow is performed where the TFM, including surface tension and viscous stresses, is simplified to a two-equation model using the fixed-flux approximation. As the angle of inclination of the channel increases so does the driving body force, so the flow becomes KH unstable, and waves grow and develop nonlinearities. It is shown that these waves grow until they reach a limit cycle due to viscous dissipation at wave fronts. Upon further inclination of the channel, chaos is observed. The appearance of chaos in a 1D TFM implies a nonlinear process that transfers energy intermittently from long wavelengths where energy is produced to short wavelengths where energy is dissipated by viscosity, so that an averaged energy equilibrium in frequency space is attained. This is comparable to the well-known turbulent stability mechanism of the multi-dimensional Navier–Stokes equations, i.e., chaos implies Lyapunov stability, but in this case it is strictly a two-phase phenomenon.

  10. Assessment of wall friction model in multi-dimensional component of MARS with air–water cross flow experiment

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Jin-Hwa [Nuclear Thermal-Hydraulic Engineering Laboratory, Seoul National University, Gwanak 599, Gwanak-ro, Gwanak-gu, Seoul 151-742 (Korea, Republic of); Korea Atomic Energy Research Institute, 989-111, Daedeok-daero, Yuseong-gu, Daejeon 305-600 (Korea, Republic of); Choi, Chi-Jin [Nuclear Thermal-Hydraulic Engineering Laboratory, Seoul National University, Gwanak 599, Gwanak-ro, Gwanak-gu, Seoul 151-742 (Korea, Republic of); Cho, Hyoung-Kyu, E-mail: chohk@snu.ac.kr [Nuclear Thermal-Hydraulic Engineering Laboratory, Seoul National University, Gwanak 599, Gwanak-ro, Gwanak-gu, Seoul 151-742 (Korea, Republic of); Euh, Dong-Jin [Korea Atomic Energy Research Institute, 989-111, Daedeok-daero, Yuseong-gu, Daejeon 305-600 (Korea, Republic of); Park, Goon-Cherl [Nuclear Thermal-Hydraulic Engineering Laboratory, Seoul National University, Gwanak 599, Gwanak-ro, Gwanak-gu, Seoul 151-742 (Korea, Republic of)

    2017-02-15

    Recently, high precision and high accuracy analysis on multi-dimensional thermal hydraulic phenomena in a nuclear power plant has been considered as state-of-the-art issues. System analysis code, MARS, also adopted a multi-dimensional module to simulate them more accurately. Even though it was applied to represent the multi-dimensional phenomena, but implemented models and correlations in that are one-dimensional empirical ones based on one-dimensional pipe experimental results. Prior to the application of the multi-dimensional simulation tools, however, the constitutive models for a two-phase flow need to be carefully validated, such as the wall friction model. Especially, in a Direct Vessel Injection (DVI) system, the injected emergency core coolant (ECC) on the upper part of the downcomer interacts with the lateral steam flow during the reflood phase in the Large-Break Loss-Of-Coolant-Accident (LBLOCA). The interaction between the falling film and lateral steam flow induces a multi-dimensional two-phase flow. The prediction of ECC flow behavior plays a key role in determining the amount of coolant that can be used as core cooling. Therefore, the wall friction model which is implemented to simulate the multi-dimensional phenomena should be assessed by multidimensional experimental results. In this paper, the air–water cross film flow experiments simulating the multi-dimensional phenomenon in upper part of downcomer as a conceptual problem will be introduced. The two-dimensional local liquid film velocity and thickness data were used as benchmark data for code assessment. And then the previous wall friction model of the MARS-MultiD in the annular flow regime was modified. As a result, the modified MARS-MultiD produced improved calculation result than previous one.

  11. Turbulence modelling for incompressible flows

    International Nuclear Information System (INIS)

    Rodi, W.

    1985-12-01

    EUROMECH colloquium 180 was held at Karlsruhe from 4-6 July, 1984, with the aim of bringing together specialists working in the area of turbulence modelling and of reviewing the state-of-the-art in this field. 44 scientists from 12 countries participated and 28 papers were presented. The meeting started with a review of the performance of two-equation turbulence models employing transport equations for both the velocity and the length scale of turbulence. These models are now generally well established, but it was found that their application to certain flow situations remains problematic. The modelling assumptions involved in Reynolds stress-equation models were reviewed next, and new assumptions were proposed. It was generally agreed that, as computing power increases, these more complex models will become more popular also for practical applications. The increase in computing power also allows more and more to resolve the viscous sublayer with low Reynolds numbers models, and the capabilities and problems of these models were discussed. In this connection, special aspects of boundary layer calculations were also discussed, namely those associated with 3D boundary layers, converging and diverging flow and slightly detached boundary layers. The complex physical phenomena prevalent in situations under the influence of buoyancy and rotation were reviewed, and several papers were presented on models for simulating these effects. (orig./HP) [de

  12. Two dimensional radial gas flows in atmospheric pressure plasma-enhanced chemical vapor deposition

    Science.gov (United States)

    Kim, Gwihyun; Park, Seran; Shin, Hyunsu; Song, Seungho; Oh, Hoon-Jung; Ko, Dae Hong; Choi, Jung-Il; Baik, Seung Jae

    2017-12-01

    Atmospheric pressure (AP) operation of plasma-enhanced chemical vapor deposition (PECVD) is one of promising concepts for high quality and low cost processing. Atmospheric plasma discharge requires narrow gap configuration, which causes an inherent feature of AP PECVD. Two dimensional radial gas flows in AP PECVD induces radial variation of mass-transport and that of substrate temperature. The opposite trend of these variations would be the key consideration in the development of uniform deposition process. Another inherent feature of AP PECVD is confined plasma discharge, from which volume power density concept is derived as a key parameter for the control of deposition rate. We investigated deposition rate as a function of volume power density, gas flux, source gas partial pressure, hydrogen partial pressure, plasma source frequency, and substrate temperature; and derived a design guideline of deposition tool and process development in terms of deposition rate and uniformity.

  13. Geometrical effects on the airfoil flow separation and transition

    KAUST Repository

    Zhang, Wei; Cheng, Wan; Gao, Wei; Qamar, Adnan; Samtaney, Ravi

    2015-01-01

    We present results from direct numerical simulations (DNS) of incompressible flow over two airfoils, NACA-4412 and NACA-0012-64, to investigate the effects of the airfoil geometry on the flow separation and transition patterns at Re=104 and 10

  14. Numerical Simulation of Two Dimensional Flows in Yazidang Reservoir

    Science.gov (United States)

    Huang, Lingxiao; Liu, Libo; Sun, Xuehong; Zheng, Lanxiang; Jing, Hefang; Zhang, Xuande; Li, Chunguang

    2018-01-01

    This paper studied the problem of water flow in the Yazid Ang reservoir. It built 2-D RNG turbulent model, rated the boundary conditions, used the finite volume method to discrete equations and divided the grid by the advancing-front method. It simulated the two conditions of reservoir flow field, compared the average vertical velocity of the simulated value and the measured value nearby the water inlet and the water intake. The results showed that the mathematical model could be applied to the similar industrial water reservoir.

  15. Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations

    OpenAIRE

    Destrade, Michel; Goriely, Alain; Saccomandi, Giuseppe

    2011-01-01

    We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent, and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation c...

  16. Calculation of large Reynolds number two-dimensional flow using discrete vortices with random walk

    International Nuclear Information System (INIS)

    Milinazzo, F.; Saffman, P.G.

    1977-01-01

    The numerical calculation of two-dimensional rotational flow at large Reynolds number is considered. The method of replacing a continuous distribution of vorticity by a finite number, N, of discrete vortices is examined, where the vortices move under their mutually induced velocities plus a random component to simulate effects of viscosity. The accuracy of the method is studied by comparison with the exact solution for the decay of a circular vortex. It is found, and analytical arguments are produced in support, that the quantitative error is significant unless N is large compared with a characteristic Reynolds number. The mutually induced velocities are calculated by both direct summation and by the ''cloud in cell'' technique. The latter method is found to produce comparable error and to be much faster

  17. Numerical simulation of countercurrent flow based on two-fluid model

    Energy Technology Data Exchange (ETDEWEB)

    Chen, H.D. [Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai 519082 (China); School of Electric Power, South China University of Technology, Guangzhou 510640 (China); Zhang, X.Y., E-mail: zxiaoying@mail.sysu.edu.cn [Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai 519082 (China)

    2017-03-15

    Highlights: • Using one-dimensional two-fluid model to help understanding counter-current flow two-phase flows. • Using surface tension model to make the one-dimensional two-fluid flow model well-posed. • Solving the governing equations with a modified SIMPLE algorithm. • Validating code with experimental data and applying it to vertical air/steam countercurrent flow condition - Abstract: In order to improve the understanding of counter-current two-phase flows, a transient analysis code is developed based on one-dimensional two-fluid model. A six equation model has been established and a two phase pressure model with surface tension term, wall drag force and interface shear terms have been used. Taking account of transport phenomenon, heat and mass transfer models of interface were incorporated. The staggered grids have been used in discretization of equations. For validation of the model and code, a countercurrent air-water problem in one experimental horizontal stratified flow has been considered firstly. Comparison of the computed results and the experimental one shows satisfactory agreement. As the full problem for investigation, one vertical pipe with countercurrent flow of steam-water and air-water at same boundary condition has been taken for study. The transient distribution of liquid fraction, liquid velocity and gas velocity for selected positions of steam-water and air-water problem were presented and discussed. The results show that these two simulations have similar transient behavior except that the distribution of gas velocity for steam-water problem have larger oscillation than the one for air-water. The effect of mesh size on wavy characteristics of interface surface was also investigated. The mesh size has significant influence on the simulated results. With the increased refinement, the oscillation gets stronger.

  18. Pointwise decay of stationary rotational viscous incompressible flows with nonzero velocity at infinity

    Czech Academy of Sciences Publication Activity Database

    Deuring, P.; Kračmar, S.; Nečasová, Šárka

    2013-01-01

    Roč. 255, č. 7 (2013), s. 1576-1606 ISSN 0022-0396 R&D Projects: GA ČR(CZ) GAP201/11/1304 Institutional support: RVO:67985840 Keywords : stationary incompressible Navier-Stokes system * rotating body * fundamental solution Subject RIV: BA - General Mathematics Impact factor: 1.570, year: 2013 http://www.sciencedirect.com/science/article/pii/S0022039613002106

  19. Modelling of two-phase flow based on separation of the flow according to velocity

    International Nuclear Information System (INIS)

    Narumo, T.

    1997-01-01

    The thesis concentrates on the development work of a physical one-dimensional two-fluid model that is based on Separation of the Flow According to Velocity (SFAV). The conventional way to model one-dimensional two-phase flow is to derive conservation equations for mass, momentum and energy over the regions occupied by the phases. In the SFAV approach, the two-phase mixture is divided into two subflows, with as distinct average velocities as possible, and momentum conservation equations are derived over their domains. Mass and energy conservation are treated equally with the conventional model because they are distributed very accurately according to the phases, but momentum fluctuations follow better the flow velocity. Submodels for non-uniform transverse profile of velocity and density, slip between the phases within each subflow and turbulence between the subflows have been derived. The model system is hyperbolic in any sensible flow conditions over the whole range of void fraction. Thus, it can be solved with accurate numerical methods utilizing the characteristics. The characteristics agree well with the used experimental data on two-phase flow wave phenomena Furthermore, the characteristics of the SFAV model are as well in accordance with their physical counterparts as of the best virtual-mass models that are typically optimized for special flow regimes like bubbly flow. The SFAV model has proved to be applicable in describing two-phase flow physically correctly because both the dynamics and steady-state behaviour of the model has been considered and found to agree well with experimental data This makes the SFAV model especially suitable for the calculation of fast transients, taking place in versatile form e.g. in nuclear reactors

  20. Mixed convective thermally radiative micro nanofluid flow in a stretchable channel with porous medium and magnetic field

    Energy Technology Data Exchange (ETDEWEB)

    Rauf, A., E-mail: raufamar@ciitsahiwal.edu.pk; Shahzad, S. A.; Meraj, M. A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Siddiq, M. K. [Department of CASPAM, Bahauddin Zakariya University, Multan 63000 (Pakistan); Raza, J. [School of Quantitative Sciences, Universiti Utara Malaysia, 06010, Sintok, Kedah (Malaysia)

    2016-03-15

    A numerical study is carried out for two dimensional steady incompressible mixed convective flow of electrically conductive micro nanofluid in a stretchable channel. The flow is generated due to the stretching walls of the channel immersed in a porous medium. The magnetic field is applied perpendicular to the walls. The impact of radiation, viscous dissipation, thermophoretic and Brownian motion of nanoparticles appear in the energy equation. A numerical technique based on Runge-Kutta-Fehlberg fourth-fifth order (RFK45) method is used to express the solutions of velocity, microrotation, temperature and concentration fields. The dimensionless physical parameters are discussed both in tabular and graphical forms. The results are also found in a good agreement with previously published literature work.