Free-Surface Viscous Flow Solution Methods for Ship Hydrodynamics
Wackers, J.; Koren, B.; Raven, H.C.; Ploeg, A. van der; Starke, A.R.; Deng, G.B.; Queutey, P.; Visonneau, M.; Hino, T.; Ohashi, K.
2011-01-01
The simulation of viscous free-surface water flow is a subject that has reached a certain maturity and is nowadays used in industrial applications, like the simulation of the flow around ships. While almost all methods used are based on the Navier-Stokes equations, the discretisation methods for the
Free-Surface Viscous Flow Solution Methods for Ship Hydrodynamics
WACKERS, Jeroen; Koren, Barry; Raven, H.C.; Van Der Ploeg,, Atze; Starke, A.R.; Deng, G.B.; Queutey, P.; VISONNEAU, Michel; Hino, T.; Ohashi, K
2011-01-01
The simulation of viscous free-surface water flow is a subject that has reached a certain maturity and is nowadays used in industrial applications, like the simulation of the flow around ships. While almost all methods used are based on the Navier-Stokes equations, the discretisation methods for the water surface differ widely. Many of these highly different methods are being used with success. We review three of these methods, by describing in detail their implementation in one particular co...
Viscous flows stretching and shrinking of surfaces
Mehmood, Ahmer
2017-01-01
This authored monograph provides a detailed discussion of the boundary layer flow due to a moving plate. The topical focus lies on the 2- and 3-dimensional case, considering axially symmetric and unsteady flows. The author derives a criterion for the self-similar and non-similar flow, and the turbulent flow due to a stretching or shrinking sheet is also discussed. The target audience primarily comprises research experts in the field of boundary layer flow, but the book will also be beneficial for graduate students.
Ferromagnetic Flow of Viscous Fluid in a Slot between Fixed Surfaces of Revolution
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Jerzy Sawicki
2016-12-01
Full Text Available In this paper the steady laminar flow of viscous incompressible ferromagnetic fluid is considered in a slot between fixed surfaces of revolution having a common axis of symmetry. The boundary layer ferromagnetic equations for axial symmetry are expressed in terms of the intrinsic curvilinear orthogonal coordinate system x, θ ,y.The method of perturbation is used to solve the boundary layer equations. As a result, the formulae defining such parameters of the flow as the velocity components vx, vy, and the pressure , were obtained.
Lubricant-impregnated surfaces for drag reduction in viscous laminar flow
Solomon, Brian; Khalil, Karim; Varanasi, Kripa; MIT Team
2013-11-01
For the first time, we explore the potential of lubricant impregnated surfaces (LIS) in reducing drag. LIS, inspired by the surface of the Nepenthes pitcher plant, have been introduced as a novel way of functionalizing a surface. LIS are characterized by extremely low contact angle hysteresis and have been show to effectively repel various liquids including water, oils, ketchup and blood. Motivated by the slippery nature of such surfaces, we explore the potential of LIS to reduce drag in internal flows. We observe a reduction in drag for LIS surfaces in a viscous laminar drag flow and model the impact of relevant system parameters (lubricant viscosity, working fluid viscosity, solid fraction, depth of texture, etc.).
Stability and accuracy of free surface time integration in viscous flows
Rose, Ian; Buffett, Bruce; Heister, Timo
2017-01-01
Geodynamic simulations increasingly rely on models with a true free surface to investigate questions of dynamic topography, tectonic deformation, gravity perturbations, and global mantle convection. However, implementations of free surface boundary conditions have proven challenging from a standpoint of accuracy, robustness, and stability. In particular, time integration of a free surface tends to suffer from a numerical instability that manifests as sloshing surface motions, also known as the "drunken sailor" instability. This instability severely limits stable timestep sizes to those much smaller than can be used in geodynamic simulations without a free surface. Several schemes have been proposed in the literature to deal with these instabilities. Here we analyze the problem of creeping viscous flow with a free surface and discuss the origin of these instabilities. We demonstrate their cause and how existing stabilization schemes work to damp them out. We also propose a new scheme for removing instabilities from free surface calculations. It does not require modifications to the system matrix, nor additional variables, but is instead an explicit scheme based on nonstandard finite differences. It relies on a single stabilization parameter which may be identified with the smallest relaxation timescale of the free surface. Finally, we present numerical results to show the effectiveness of the new approach and discuss the free surface implementation in the open source, community based mantle convection software ASPECT.
Langlois, William E
2014-01-01
Leonardo wrote, 'Mechanics is the paradise of the mathematical sciences, because by means of it one comes to the fruits of mathematics' ; replace 'Mechanics' by 'Fluid mechanics' and here we are." - from the Preface to the Second Edition Although the exponential growth of computer power has advanced the importance of simulations and visualization tools for elaborating new models, designs and technologies, the discipline of fluid mechanics is still large, and turbulence in flows remains a challenging problem in classical physics. Like its predecessor, the revised and expanded Second Edition of this book addresses the basic principles of fluid mechanics and solves fluid flow problems where viscous effects are the dominant physical phenomena. Much progress has occurred in the nearly half a century that has passed since the edition of 1964. As predicted, aspects of hydrodynamics once considered offbeat have risen to importance. For example, the authors have worked on problems where variations in viscosity a...
An orthogonal coordinate grid following the three-dimensional viscous flow over a concave surface
Dagenhart, J. R; Saric, W. S.
1983-01-01
Swept wings designed for laminar flow control exhibit both centrifugal and crossflow instabilities which produce streamwise vortices that can lead to early transition from laminar to turbulent flow in the presence of Tollmien-Schlichting waves. This paper outlines an iterative algorithm for generation of an orthogonal, curvilinear, coordinate grid following the streamlines of the three-dimensional viscous flow over a swept, concave surface. The governing equations for the metric tensor are derived from the Riemann-Christoffel tensor for an Euclidian geometry. Unit vectors along streamline, normal and binormal directions are determined. The governing equations are not solved directly, but are employed only as compatibility equations. The scale factor for the streamline coordinate is obtained by an iterative integration scheme on a 200 x 100 x 5 grid, while the other two scale factors are determined from definitions. Sample results are obtained which indicate that the compatibility equation error decreases linearly with grid step size. Grids smaller than 200 x 100 x 5 are found to be inadequate to resolve the grid curvature.
Frequency-dependent viscous flow in channels with fractal rough surfaces
Energy Technology Data Exchange (ETDEWEB)
Cortis, A.; Berryman, J.G.
2010-05-01
The viscous dynamic permeability of some fractal-like channels is studied. For our particular class of geometries, the ratio of the pore surface area-to-volume tends to {infinity} (but has a finite cutoff), and the universal scaling of the dynamic permeability, k({omega}), needs modification. We performed accurate numerical computations of k({omega}) for channels characterized by deterministic fractal wall surfaces, for a broad range of fractal dimensions. The pertinent scaling model for k({omega}) introduces explicitly the fractal dimension of the wall surface for a range of frequencies across the transition between viscous and inertia dominated regimes. The new model provides excellent agreement with our numerical simulations.
The flow and heat transfer in a viscous fluid over an unsteady stretching surface
Ene, Remus-Daniel; Marinca, Bogdan
2015-01-01
In this paper we have studied the flow and heat transfer in a viscous fluid by a horizontal sheet. The stretching rate and temperature of the sheet vary with time. The governing equations for momentum and thermal energy are reduced to ordinary differential equations by means of similarity transformation. These equations are solved approximately by means of the Optimal Homotopy Asymptotic Method (OHAM) which provides us with a convenient way to control the convergence of approximation solutions and adjust convergence rigorous when necessary. Some examples are given and the results obtained reveal that the proposed method is effective and easy to use.
Computation of Viscous Incompressible Flows
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...
Magnetohydrodynamic viscous flow over a nonlinearly moving surface: Closed-form solutions
Fang, Tiegang
2014-05-01
In this paper, the magnetohydrodynamic (MHD) flow over a nonlinearly (power-law velocity) moving surface is investigated analytically and solutions are presented for a few special conditions. The solutions are obtained in closed forms with hyperbolic functions. The effects of the magnetic, the wall moving, and the mass transpiration parameters are discussed. These solutions are important to show the flow physics as well as to be used as bench mark problems for numerical validation and development of new solution schemes.
Sharma, Kalpna; Gupta, Sumit
2017-06-01
This paper investigates steady two dimensional flow of an incompressible magnetohydrodynamic (MHD) boundary layer flow and heat transfer of nanofluid over an impermeable surface in presence of thermal radiation and viscous dissipation. By using similarity transformation, the arising governing equations of momentum, energy and nanoparticle concentration are transformed into coupled nonlinear ordinary differential equations, which are than solved by homotopy analysis method (HAM). The effect of different physical parameters, namely, Prandtl number Pr, Eckert number Ec, Magnetic parameter M, Brownian motion parameter Nb, Thermophoresis parameter Nt, Lewis parameter Le and Radiation parameter Rd on the velocity, temperature and concentration profiles along with the Nusselt number and skin friction coefficient are discussed graphically and in tabular form in details. The present results are also compared with existing limiting solutions.
Rotationally symmetric viscous gas flows
Weigant, W.; Plotnikov, P. I.
2017-03-01
The Dirichlet boundary value problem for the Navier-Stokes equations of a barotropic viscous compressible fluid is considered. The flow region and the data of the problem are assumed to be invariant under rotations about a fixed axis. The existence of rotationally symmetric weak solutions for all adiabatic exponents from the interval (γ*,∞) with a critical exponent γ* < 4/3 is proved.
A 3D Simulation of a Moving Solid in Viscous Free-Surface Flows by Coupling SPH and DEM
Directory of Open Access Journals (Sweden)
Liu-Chao Qiu
2017-01-01
Full Text Available This work presents a three-dimensional two-way coupled method to simulate moving solids in viscous free-surface flows. The fluid flows are solved by weakly compressible smoothed particle hydrodynamics (SPH and the displacement and rotation of the solids are calculated using the multisphere discrete element method (DEM allowing for the contact mechanics theories to be used in arbitrarily shaped solids. The fluid and the solid phases are coupled through Newton’s third law of motion. The proposed method does not require a computational mesh, nor does it rely on empirical models to couple the fluid and solid phases. To verify the numerical model, the floating and sinking processes of a rectangular block in a water tank are simulated, and the numerical results are compared with experimental results reported in published literatures. The results indicate that the method presented in this paper is accurate and is capable of modelling fluid-solid interactions with a free-surface.
Mean Velocity Estimation of Viscous Debris Flows
Institute of Scientific and Technical Information of China (English)
Hongjuan Yang; Fangqiang Wei; Kaiheng Hu
2014-01-01
The mean velocity estimation of debris flows, especially viscous debris flows, is an impor-tant part in the debris flow dynamics research and in the design of control structures. In this study, theoretical equations for computing debris flow velocity with the one-phase flow assumption were re-viewed and used to analyze field data of viscous debris flows. Results show that the viscous debris flow is difficult to be classified as a Newtonian laminar flow, a Newtonian turbulent flow, a Bingham fluid, or a dilatant fluid in the strict sense. However, we can establish empirical formulas to compute its mean velocity following equations for Newtonian turbulent flows, because most viscous debris flows are tur-bulent. Factors that potentially influence debris flow velocity were chosen according to two-phase flow theories. Through correlation analysis and data fitting, two empirical formulas were proposed. In the first one, velocity is expressed as a function of clay content, flow depth and channel slope. In the second one, a coefficient representing the grain size nonuniformity is used instead of clay content. Both formu-las can give reasonable estimate of the mean velocity of the viscous debris flow.
Directory of Open Access Journals (Sweden)
K. GANGADHAR
2015-01-01
Full Text Available This study is devoted to investigate the radiation, heat generation viscous dissipation and magnetohydrodynamic effects on the laminar boundary layer about a flat-plate in a uniform stream of fluid (Blasius flow, and about a moving plate in a quiescent ambient fluid (Sakiadis flow both under a convective surface boundary condition. Using a similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically by using shooting technique alongside with the forth order of Runge-Kutta method and the variations of dimensionless surface temperature and fluid-solid interface characteristics for different values of Magnetic field parameter M, Grashof number Gr, Prandtl number Pr, radiation parameter NR, Heat generation parameter Q, Convective parameter and the Eckert number Ec, which characterizes our convection processes are graphed and tabulated. Quite different and interesting behaviors were encountered for Blasius flow compared with a Sakiadis flow. A comparison with previously published results on special cases of the problem shows excellent agreement.
Directory of Open Access Journals (Sweden)
K. Gangadhar
2016-01-01
Full Text Available The problem of laminar radiation and viscous dissipation effects on laminar boundary layer flow over a vertical plate with a convective surface boundary condition is studied using different types of nanoparticles. The general governing partial differential equations are transformed into a set of two nonlinear ordinary differential equations using unique similarity transformation. Numerical solutions of the similarity equations are obtained using the Nachtsheim-Swigert Shooting iteration technique along with the fourth order Runga Kutta method. Two different types of nanoparticles copper water nanofluid and alumina water nanofluid are studied. The effects of radiation and viscous dissipation on the heat transfer characteristics are discussed in detail. It is observed that as Radiation parameter increases, temperature decreases for copper water and alumina water nanofluid and the heat transfer coefficient of nanofluids increases with the increase of convective heat transfer parameter for copper water and alumina water nanofluids.
Sekhar, G P Raja; Rohde, Christian
2016-01-01
The motion of a viscous drop is investigated when the interface is fully covered with a stagnant layer of surfactant in an arbitrary unsteady Stokes flow for the low surface P\\'eclet number limit. The effect of the interfacial slip coefficient on the behavior of the flow field is also considered. The hydrodynamic problem is solved by the solenoidal decomposition method and the drag force is computed in terms of Faxen's laws using a perturbation ansatz in powers of the surface P\\'eclet number. The analytical expressions for the migration velocity of the drop are also obtained in powers of the surface P\\'eclet number. Further instances corresponding to a given ambient flow as uniform flow, Couette flow, Poiseuille flow are analyzed. Moreover, it is observed that, a surfactant-induced cross-stream migration of the drop occur towards the centre-line in both Couette flow and Poiseuille flow cases. The variation of the drag force and migration velocity is computed for different parameters such as P\\'eclet number, M...
Gravel Accumulation in Deposits of Viscous Debris Flows with Hyper-concentration
Institute of Scientific and Technical Information of China (English)
WANG Yuyi; TAN Rongzhi; JAN Chyandeng; TIAN Bing
2009-01-01
According to the observational data of viscous debris flows with hyper-concentration, debris flows can be classified into three types: high-viscous, viscous, and sub-viscous debris flows. Distinct formation mechanism of different graded bedding structures in deposits of viscous debris flows was analyzed in this paper by using their yield-stress ratio and flow plug ratio. This paper specially analyzed the effect of Weissenberg which the gravels in squirm condition of hyper-concentration viscous flows would tend to move vertically, and the formation mechanism of the gravels accumulated at surface was also studied. The analysis in this paper can establish a foundation for the studies on differentiation of bedding structures of debris flow deposits and studies on dynamic parameters of debris flows.
Viscous flows the practical use of theory
Brenner, Howard
1988-01-01
Representing a unique approach to the study of fluid flows, Viscous Flows demonstrates the utility of theoretical concepts and solutions for interpreting and predicting fluid flow in practical applications. By critically comparing all relevant classes of theoretical solutions with experimental data and/or general numerical solutions, it focuses on the range of validity of theoretical expressions rather than on their intrinsic character.This book features extensive use of dimensional analysis on both models and variables, and extensive development of theoretically based correlating equations.
Directory of Open Access Journals (Sweden)
Machireddy Gnaneswara Reddy
2014-01-01
Full Text Available A two-dimensional mathematical model is presented for the laminar heat and mass transfer of an electrically-conducting, viscous and Joule (Ohmic heating fluid over an inclined radiate isothermal permeable surface in the presence of the variable thermal conductivity, thermophoresis and heat generation. The Talbot- Cheng-Scheffer-Willis formulation (1980 is used to introduce a thermophoretic coefficient into the concentration boundary layer equation. The governing partial differential equations are non-dimensionalized and transformed into a system of nonlinear ordinary differential similarity equations, in a single independent variable . The resulting coupled nonlinear equations are solved under appropriate transformed boundary conditions using the Runge-Kutta fourth order along with shooting method. Comparisons with previously published work are performed and the results are found to be in very good agreement. Computations are performed for a wide range of the governing flow parameters, viz., magnetic field parameter, thermophoretic coefficient (a function of Knudsen number, Eckert number (viscous heating effect, angle of inclination, thermal conductivity parameter, heat generation parameter and Schmidt number. The present problem finds applications in optical fiber fabrication, aerosol filter precipitators, particle deposition on hydronautical blades, semiconductor wafer design, thermo-electronics and magnetohydrodynamic energy generators.
Topological Fluid Dynamics For Free and Viscous Surfaces
DEFF Research Database (Denmark)
Balci, Adnan
In an incompressible fluid flow, streamline patterns and their bifurcations are investigated close to wall for two-dimensional system and close to free and viscous surfaces in three-dimensional system. Expanding the velocity field in a Taylor series, we conduct a local analysis at the given...
Directory of Open Access Journals (Sweden)
Khilap Singh
2016-01-01
Full Text Available A numerical model is developed to examine the effects of thermal radiation on unsteady mixed convection flow of a viscous dissipating incompressible micropolar fluid adjacent to a heated vertical stretching surface in the presence of the buoyancy force and heat generation/absorption. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The model contains nonlinear coupled partial differential equations which have been converted into ordinary differential equation by using the similarity transformations. The dimensionless governing equations for this investigation are solved by Runge-Kutta-Fehlberg fourth fifth-order method with shooting technique. Numerical solutions are then obtained and investigated in detail for different interesting parameters such as the local skin-friction coefficient, wall couple stress, and Nusselt number as well as other parametric values such as the velocity, angular velocity, and temperature.
Directory of Open Access Journals (Sweden)
Kishan N.
2014-05-01
Full Text Available A fluid flow and heat transfer analysis of an electrically conducting non-Newtonian power law fluid flowing over a non-linear stretching surface in the presence of a transverse magnetic field taking into consideration viscous dissipation effects is investigated. The stretching velocity, the temperature and the transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The flow is induced due to an infinite elastic sheet which is stretched in its own plane. The governing equations are reduced to non-linear ordinary differential equations by means of similarity transformations. By using quasi-linearization techniques first linearize the non linear momentum equation is linearized and then the coupled ordinary differential equations are solved numerically by an implicit finite difference scheme. The numerical solution is found to be dependent on several governing parameters, including the magnetic field parameter, power-law index, Eckert number, velocity exponent parameter, temperature exponent parameter, modified Prandtl number and heat source/sink parameter. A systematic study is carried out to illustrate the effects of these parameters on the fluid velocity and the temperature distribution in the boundary layer. The results for the local skin-friction coefficient and the local Nusselt number are tabulated and discussed.
Viscous Swirling Flow over a Stretching Cylinder
Institute of Scientific and Technical Information of China (English)
Tiegang FANG; ShanshanYAO
2011-01-01
We investigate a viscous How over a cylinder with stretching and torsional motion. There is an exact solution to the Navier-Stokes equations and there exists a unique solution for all the given values of the flow Reynolds number. The results show that velocity decays faster for a higher Reynolds number and the How penetrates shallower into the ambient Huid. All the velocity proHles decay algebraically to the ambient zero velocity.%We investigate a viscous flow over a cylinder with stretching and torsional motion.There is an exact solution to the Navier-Stokes equations and there exists a unique solution for all the given values of the flow Reynolds number.The results show that velocity decays faster for a higher Reynolds number and the flow penetrates shallower into the ambient fluid.All the velocity profiles decay algebraically to the ambient zero velocity.Exact solutions of the Navier-Stokes (NS) equations play important roles in the development of fluid mechanics.In the review articles,[1,2] Wang summarized the available exact solutions of the unsteady state and of the steady-state NS equations.Swirl flows have important engineering applications in many fields such as the cyclone for separation of solid,liquid and gas,swirl atomizers,swirl combustion devices,heat transfer enhancement and others.[3,4] A famous example of flows involving rotation or swirl is the rotating disk problem studied by von Karman.[5-8] The flow induced by a stretching boundary is also important in the extrusion processes in plastic and metal industries.[9-11] Crane[12] presented an exact solution of the two-dimensional NS equations for a stretching sheet problem with a closed analytical form.The stretching wall problem was extended by Wang[13]to a three-dimensional setting.The flow between two stretching disks was studied by Fang and Zhang recently.[14] The combined effects of disk stretching and rotation on the von Karman flow was investigated by Fang.[15] The flow inside a channel or a
Studies in the Computation of Compressible Viscous Flows.
1987-02-01
singular solutions have been found which may bridge the gap between smooth shock free flow and the flow with embedded shocks. Keywords: Transonic flow; Computational aerodynamics; Viscous inviscid interactions.
Viscous Flow over an Unsteady Shrinking Sheet with Mass Transfer
Institute of Scientific and Technical Information of China (English)
FANG Tie-Gang; ZHANG Ji; YAO Shan-Shan
2009-01-01
The unsteady viscous flow over a continuously shrinking surface with mass suction is studied. The solution is fortunately an exact solution of the unsteady Navier-Stokes equations. Similarity equations are obtained through the application of similarity transformation techniques. Numerical techniques are used to solve the similarity equations for different values of the mass suction parameters" and the unsteadiness parameters. Results show that multiple solutions exist for a certain range of mass suction and unsteadiness parameters. Quite different flow behaviour is observed for an unsteady shrinking sheet from an unsteady stretching sheet.
潜艇水面与水下粘性绕流数值模拟%Numerical Simulation of Free Surface Viscous Flow Around Submarine
Institute of Scientific and Technical Information of China (English)
张楠; 应良镁; 姚惠之; 沈泓萃; 高秋新
2005-01-01
The flow fields of SUBOFF hull with various appendages are numerically simulated by solving RANS equations with four turbulence models.Numerical predictions of the axial velocities for given radii at the propeller plane are compared with experimental data. Comparison shows that turbulence model plays an important role in numerical simulation. The performance of submarine at full surface condition is important. Computational study of free surface flow around submarine is a focus of attention in ship hydrodynamics. In this paper,the numerical simulations of free surface flow around two submarine models at different Froude numbers are carried out with Volume of Fluid (VOF) algorithm which is an interface-capturing method. Computational results including resistances,wave profiles and wave patterns are analyzed and compared with experimental data. The comparison between the prediction and the model test measurement shows fairly good agreement. Some generic features of submarine hydrodynamics with free surface are discussed. The capability of the CFD approach to the prediction of viscous flow of submarine is validated.%本文采用求解RANS方程的方法结合四种湍流模型,对于带有不同附体的SUBOFF模型尾流场进行了数值模拟.数值预报的桨盘面处不同半径上的轴向无量纲速度与试验结果进行了对比,结果表明湍流模型在数值模拟中起到重要作用.潜艇水面航行性能十分重要,因而对于潜艇自由液面绕流的数值模拟备受关注.本文采用VOF方法对于两条潜艇模型在不同傅汝德数下的自由液面绕流进行了数值模拟.计算得到的阻力、波形与试验结果吻合较好.文中也探讨了潜艇自由液面绕流的一般特性.并验证了用CFD手段预报潜艇粘性流场的能力.
Polynomial interpolation methods for viscous flow calculations
Rubin, S. G.; Khosla, P. K.
1977-01-01
Higher-order collocation procedures which result in block-tridiagonal matrix systems are derived from (1) Taylor series expansions and from (2) polynomial interpolation, and the relationships between the two formulations, called respectively Hermite and spline collocation, are investigated. A Hermite block-tridiagonal system for a nonuniform mesh is derived, and the Hermite approach is extended in order to develop a variable-mesh sixth-order block-tridiagonal procedure. It is shown that all results obtained by Hermite development can be recovered by appropriate spline polynomial interpolation. The additional boundary conditions required for these higher-order procedures are also given. Comparative solutions using second-order accurate finite difference and spline and Hermite formulations are presented for the boundary layer on a flat plate, boundary layers with uniform and variable mass transfer, and the viscous incompressible Navier-Stokes equations describing flow in a driven cavity.
Polynomial interpolation methods for viscous flow calculations
Rubin, S. G.; Khosla, P. K.
1977-01-01
Higher-order collocation procedures which result in block-tridiagonal matrix systems are derived from (1) Taylor series expansions and from (2) polynomial interpolation, and the relationships between the two formulations, called respectively Hermite and spline collocation, are investigated. A Hermite block-tridiagonal system for a nonuniform mesh is derived, and the Hermite approach is extended in order to develop a variable-mesh sixth-order block-tridiagonal procedure. It is shown that all results obtained by Hermite development can be recovered by appropriate spline polynomial interpolation. The additional boundary conditions required for these higher-order procedures are also given. Comparative solutions using second-order accurate finite difference and spline and Hermite formulations are presented for the boundary layer on a flat plate, boundary layers with uniform and variable mass transfer, and the viscous incompressible Navier-Stokes equations describing flow in a driven cavity.
DEFF Research Database (Denmark)
Sheikholeslami, R; Ashorynejad, H.R; Barari, Amin
2013-01-01
Purpose – The purpose of this paper is to analyze hydromagnetic flow between two horizontal plates in a rotating system. The bottom plate is a stretching sheet and the top one is a solid porous plate. Heat transfer in an electrically conducting fluid bounded by two parallel plates is also studied...
INTERACTION OF VISCOUS WAKES WITH A FREE SURFACE
Institute of Scientific and Technical Information of China (English)
卢东强
2004-01-01
The interaction of laminar wakes with free-surface waves generated by a moving body beneath the surface of an incompressible viscous fluid of infinite depth was investigated analytically.The analysis was based on the steady Oseen equations for disturbed flows.The kinematic and dynamic boundary conditions were linearized for the small-amplitude free-surface waves.The effect of the moving body was mathematically modeled as an Oseenlet.The disturbed flow was regarded as the sum of an unbounded singular Oseen flow which represents the effect of the viscous wake and a bounded regular Oseen flow which represents the influence of the free surface.The exact solution for the free-surface waves was obtained by the method of integral transforms.The asymptotic representation with additive corrections for the free-surface waves was derived by means of Lighthill's two-stage scheme.The symmetric solution obtained shows that the amplitudes of the free-surface waves are exponentially damped by the presences of viscosity and submergence depth.
Impact of Viscous Droplets on Superamphiphobic Surfaces
Zhao, Binyu; Chen, Longquan; Deng, Xu
2016-11-01
Superamphiphobic coating is promising for various applications in industry, e.g. self-cleaning windows, where the impingement of droplets on surfaces is commonly encountered. In this work, we experimentally investigated the impact of droplets with similar surface tension (63-72 mN/m) but much different viscosity (1-150 mPa s) on superamphiphobic surfaces. We found that droplets can rebound from the superamphiphobic surfaces when the impact velocity is larger than a critical value, which linearly increases with the liquid viscosity. Droplet with higher viscosity spreads, retracts slower, and eventually rebounds lower and fewer times than that of low viscous droplet. These findings have important implications for surface engineers to use superamphiphobic coatings. Furthermore, we measured the maximum spreading factors for droplet impact on superamphiphobic surfaces and proposed a simple model based on energy conversation to describe its relationship to the Weber number and Reynolds number.
Capillary and viscous perturbations to Helmholtz flows
Moore, M. R.
2014-02-21
Inspired by recent calculations by Thoraval et al. (Phys. Rev. Lett., vol. 108, 2012, p.Â 264506) relating to droplet impact, this paper presents an analysis of the perturbations to the free surface caused by small surface tension and viscosity in steady Helmholtz flows. In particular, we identify the regimes in which appreciable vorticity can be shed from the boundary layer to the bulk flow. © 2014 Cambridge University Press.
Foam rheology: A model of viscous effects in shear flow
Kraynik, Andrew M.; Reinelt, Douglas A.
Foams consisting of gas bubbles dispersed in a continuous network of thin liquid films display a remarkable range of rheological characteristics that include a finite shear modulus, yield stress, non-Newtonian viscosity, and slip at the wall. Progress in developing micromechanical theories to describe foam rheology has depended upon two-dimensional models, which in most cases are assumed to have perfectly ordered structure. Princen accounted for surface tension and geometrical effects, and analyzed the nonlinear elastic response of a spatially periodic foam in simple shear. His analysis has been extended to account for more general deformations. Khan and Armstrong and Kraynik and Hansen have proposed ad hoc models for viscous effects in foam rheology. Their models capture numerous qualitative phenomena but incorporate relaxation mechanisms based upon overly simplified assumptions of liquid flow in the thin films. Mysels, Shinoda, and Frankel considered soap films with interfaces that are inextensible due to the presence of surfactants. They analyzed the primary flow that occurs when such films are slowly withdrawn from or recede into essentially static junction regions such as the Plateau borders in a foam. Adopting this mechanism, Schwartz and Princen considered small periodic deformations of a foam and calculated the energy dissipation due to viscous flow in the thin films. In the following, we also adopt the basic interfacial and viscous mechanisms introduced by Mysels et al. and analyze simple shearing deformations of finite amplitude. The configuration and effective stress of the foam are determined. Under these deformation conditions, the foam is a nonlinear viscoelastic material. Results for the uniform expansion of a foam are also presented.
Noncircular converging flows in viscous gravity currents
Diez, J. A.; Thomas, L. P.; Betelú, S.; Gratton, R.; Marino, B.; Gratton, J.; Aronson, D. G.; Angenent, S. B.
1998-11-01
We study the filling of a dry region (cavity) within a viscous liquid layer on a horizontal plane. In our experiments the cavities are created by removable dams of various shapes surrounded by a silicon oil, and we measure the evolution of the cavity's boundaries after removal of the dams. Experimental runs with circular, equilateral triangular, and square dams result in circular collapse of the cavities. However, dams whose shapes lack these discrete rotational symmetries, for example, ellipses, rectangles, or isosceles triangles, do not lead to circular collapses. Instead, we find that near collapse the cavities have elongated oval shapes. The axes of these ovals shrink according to different power laws, so that while the cavity collapses to a point, the aspect ratio is increasing. The experimental setup is modeled within the lubrication approximation. As long as capillarity is negligible, the evolution of the fluid height is governed by a nonlinear diffusion equation. Numerical simulations of the experiments in this approximation show good agreement up to the time where the cavity is so small that surface tension can no longer be ignored. Nevertheless, the noncircular shape of the collapsing cavity cannot be due to surface tension which would tend to round the contours. These results are supplemented by numerical simulations of the evolution of contours which are initially circles distorted by small sinusoidal perturbations with wave numbers k>=2. These nonlinear stability calculations show that the circle is unstable in the presence of the mode k=2 and stable in its absence. The same conclusion is obtained from the linearized stability analysis of the front for the known self-similar solution for a circular cavity.
Bulk flow coupled to a viscous interfacial film sheared by a rotating knife edge
Raghunandan, Aditya; Rasheed, Fayaz; Hirsa, Amir; Lopez, Juan
2015-11-01
The measurement of the interfacial properties of highly viscous biofilms, such as DPPC (the primary component of lung surfactant), present on the surface of liquids (bulk phase) continues to attract significant attention. Most measurement techniques rely on shearing the interfacial film and quantifying its viscous response in terms of a surface (excess) viscosity at the air-liquid interface. The knife edge viscometer offers a significant advantage over other approaches used to study highly viscous films as the film is directly sheared by a rotating knife edge in direct contact with the film. However, accurately quantifying the viscous response is non-trivial and involves accounting for the coupled interfacial and bulk phase flows. Here, we examine the nature of the viscous response of water insoluble DPPC films sheared in a knife edge viscometer over a range of surface packing, and its influence on the strength of the coupled bulk flow. Experimental results, obtained via Particle Image Velocimetry in the bulk and at the surface (via Brewster Angle Microscopy), are compared with numerical flow predictions to quantify the coupling across hydrodynamic flow regimes, from the Stokes flow limit to regimes where flow inertia is significant. Supported by NNX13AQ22G, National Aeronautics and Space Administration.
Unsteady Viscous Flow Past an Impulsively Started Porous Vertical ...
African Journals Online (AJOL)
Journal of the Nigerian Association of Mathematical Physics ... Open Access DOWNLOAD FULL TEXT ... Past an Impulsively Started Porous Vertical Surface with Variable Viscosity Fluid in the Presence of Viscous Dissipation: BSRM Approach.
Special-relativistic model flows of viscous fluid
Rogava, A D
1996-01-01
Two, the most simple cases of special-relativistic flows of a viscous, incompressible fluid are considered: plane Couette flow and plane Poiseuille flow. Considering only the regular motion of the fluid we found the distribution of velocity in the fluid (velocity profiles) and the friction force, acting on immovable wall. The results are expressed through simple analytical functions for the Couette flow, while for the Poiseiulle flow they are expressed by higher transcendental functions (Jacobi's elliptic functions).
Viscous flow modelling using unstructured meshes for aeronautical applications
Szmelter, J.; Pagano, A.
The novel application of viscous coupling to unstructured meshes has been proposed and developed. The method allows fro viscous flows modelling and avoids the difficulty of generating highly stretched tetrahedral in 3D or triangular in 2D elements required for Navier-Stokes solvers. The time step allowed by the explicit euler solver is limited by the size of the "Euler" mesh, resulting in faster algorithms than standard explicit Navier-Stokes solvers.
Perdigou, C.; Audoly, B.
2016-11-01
The stability of thin viscous sheets has been studied so far in the special case where the base flow possesses a direction of invariance: the linear stability is then governed by an ordinary differential equation. We propose a mathematical formulation and a numerical method of solution that are applicable to the linear stability analysis of viscous sheets possessing no particular symmetry. The linear stability problem is formulated as a non-Hermitian eigenvalue problem in a 2D domain and is solved numerically using the finite-element method. Specifically, we consider the case of a viscous sheet in an open flow, which falls in a bath of fluid; the sheet is mildly stretched by gravity and the flow can become unstable by 'curtain' modes. The growth rates of these modes are calculated as a function of the fluid parameters and of the geometry, and a phase diagram is obtained. A transition is reported between a buckling mode (static bifurcation) and an oscillatory mode (Hopf bifurcation). The effect of surface tension is discussed.
Development of a surface micromachined spiral-channel viscous pump
Kilani, Mohammad Ibrahim
This work introduces a new pump, called the spiral pump, which targets the surface micromachining technology. We demonstrate the possibility of realizing the spiral pump geometry in standard surface micromachining, lay out the theoretical foundation for its operation, and conduct an objective assessment for its practicality. The spiral pump is a shear-driven viscous pump, which works by rotating a disk with a spiral groove at a close proximity over a stationary plate. Fluid contained in the spiral groove between the stationary plate and the rotating disk, is subject to a net tangential viscous stress, which allows it to be transported against an imposed pressure difference. A number of spiral pumps were fabricated in 5 levels of polysilicon using Sandia's Ultraplanar Multilevel Surface Micromachining Technology, SUMMiT, and the fabricated micropump were tested in dry-run mode using electrostatic probing and optical microscopy. To achieve a more comprehensive understanding of the spiral micropump operation, an analytical model was developed for the flow field in the spiral channel of the pump using an approximation which replaces the spiral channel with an equivalent straight channel with appropriate dimensions and boundary conditions. An analytical solution for this model at the lubrication limit relates the flow rate, torque and power consumption of the spiral pump to the pressure difference and rotation rate. The model was validated using macroscale experiments conducted on a scaled up spiral pump model, which involved a quantitative characterization of the spiral pump performance. Those experiments validate the developed theory and help assess the practicality of the spiral pump concept. In addition to the spiral pump, two positive-displacement ring-gear pumps were designed and fabricated in this work. The feasibility of surface micromachined ring-gear pumps is briefly investigated in this work, and compare to that of the spiral micropump.
Viscous Flow over Nonlinearly Stretching Sheet with Effects of Viscous Dissipation
Directory of Open Access Journals (Sweden)
Javad Alinejad
2012-01-01
Full Text Available The flow and heat transfer characteristics of incompressible viscous flow over a nonlinearly stretching sheet with the presence of viscous dissipation is investigated numerically. The similarity transformation reduces the time-independent boundary layer equations for momentum and thermal energy into a set of coupled ordinary differential equations. The obtained equations, including nonlinear equation for the velocity field and differential equation by variable coefficient for the temperature field , are solved numerically by using the fourth order of Runge-Kutta integration scheme accompanied by shooting technique with Newton-Raphson iteration method. The effect of various values of Prandtl number, Eckert number and nonlinear stretching parameter are studied. The results presented graphically show some behaviors such as decrease in dimensionless temperature due to increase in Pr number, and curve relocations are observed when heat dissipation is considered.
Magnetohydrodynamic Viscous Flow Over a Shrinking Sheet With Second Order Slip Flow Model
Mahmood, T; Abbas, G
2014-01-01
In this paper, we investigate the magnetohydrodynamic viscous flow with second order slip flow model over a permeable shrinking surface. We have obtained the closed form of exact solution of Navier-Stokes equations by using similarity variable technique. The effects of slip, suction and magnetic parameter have been investigated in detail. The results show that there are two solution branches, namely lower and upper solution branch. The behavior of velocity and shear stress profiles for different values of slip, suction and magnetic parameters has been discussed through graphs.
UNSTEADY FREE-SURFACE WAVES GENERATED BY BODIES IN A VISCOUS FLUID
Institute of Scientific and Technical Information of China (English)
LU Dong-qiang
2004-01-01
The interaction of laminar flows with free sur face waves generated by submerged bodies in an incompressible viscous fluid of infinite depth is investigated analytically.The analysis is based on the linearized Navier-Stokes equations for disturbed flows. The kinematic and dynamic boundary conditions are linearized for the small amplitude free-surface waves, and the initial values of the flow are taken to be those of the steady state cases. The submerged bodies are mathematically represented by fundamental singularities of viscous flows. The asymptotic representations for unsteady free-surface waves produced by the Stokeslets and Oseenlets are derived analytically. It is found that the unsteady waves generated by a body consist of steady-state and transient responses.As time tends to infinity, the transient waves vanish due to the presence of a viscous decay factor. Thus. an ultimate steady state can be attained.
Directory of Open Access Journals (Sweden)
Kishore P.M.
2012-01-01
Full Text Available This investigation is undertaken to study the hydromagnetic flow of a viscous incompressible fluid past an oscillating vertical plate embedded in a porous medium with radiation, viscous dissipation and variable heat and mass diffusion. Governing equations are solved by unconditionally stable explicit finite difference method of DuFort - Frankel’s type for concentration, temperature, vertical velocity field and skin - friction and they are presented graphically for different values of physical parameters involved. It is observed that plate oscillation, variable mass diffusion, radiation, viscous dissipation and porous medium affect the flow pattern significantly.
Creeping Viscous Flow around a Heat-Generating Solid Sphere
DEFF Research Database (Denmark)
Krenk, Steen
1981-01-01
The velocity field for creeping viscous flow around a solid sphere due to a spherically symmetric thermal field is determined and a simple thermal generalization of Stokes' formula is obtained. The velocity field due to an instantaneous heat source at the center of the sphere is obtained in close...... form and an application to the storage of heat-generating nuclear waste is discussed....
Anisotropic plastic deformation by viscous flow in ion tracks
van Dillen, T; Polman, A; Onck, PR; van der Giessen, E
2005-01-01
A model describing the origin of ion beam-induced anisotropic plastic deformation is derived and discussed. It is based on a viscoelastic thermal spike model for viscous flow in single ion tracks derived by Trinkaus and Ryazanov. Deviatoric (shear) stresses, brought about by the rapid thermal expans
An update on projection methods for transient incompressible viscous flow
Energy Technology Data Exchange (ETDEWEB)
Gresho, P.M.; Chan, S.T.
1995-07-01
Introduced in 1990 was the biharmonic equation (for the pressure) and the concomitant biharmonic miracle when transient incompressible viscous flow is solved approximately by a projection method. Herein is introduced the biharmonic catastrophe that sometimes occurs with these same projection methods.
Numerical Solution of Boundary Layer MHD Flow with Viscous Dissipation
Directory of Open Access Journals (Sweden)
S. R. Mishra
2014-01-01
Full Text Available The present paper deals with a steady two-dimensional laminar flow of a viscous incompressible electrically conducting fluid over a shrinking sheet in the presence of uniform transverse magnetic field with viscous dissipation. Using suitable similarity transformations the governing partial differential equations are transformed into ordinary differential equations and then solved numerically by fourth-order Runge-Kutta method with shooting technique. Results for velocity and temperature profiles for different values of the governing parameters have been discussed in detail with graphical representation. The numerical evaluation of skin friction and Nusselt number are also given in this paper.
An Iterative Stabilized Scheme for Unsteady Incompressible Viscous Flow
Institute of Scientific and Technical Information of China (English)
BAO Yan; ZHOU Dai; LI Hua-feng
2009-01-01
An efficient iterative algorithm is presented for the numerical solution of viscous incompressible NavierStokes equations based on Taylor-Galerkin like split and pressure correction method in this paper. Taylor-Hood element is introduced to overcome the numerical difficulties arising from the fluid incompressibility. In order to confirm the properties of the algorithm, the numerical simulation on plane Poisseuille flow problem and liddriven cavity flow problem with different Reynolds numbers is presented. The numerical results indicate that the proposed iterative version can be effectively applied to the simulation of viscous incompressible flows. Moreover, the proposed iterative version has a better overall performance in maximum time step size allowed, under comparable convergence rate, stability and accuracy, than other tested versions in numerical solutions of the plane PoisseuiUe flow with different Reynolds numbers ranging from low to high viscosities.
The Finiteness of vortices in steady incompressible viscous fluid flow
Kalita, Jiten C; Panda, Swapnendu
2016-01-01
In this work, we provide two novel approaches to show that incompressible fluid flow in a finite domain contains at most a finite number vortices. We use a recently developed geometric theory of incompressible viscous flows along with an existing mathematical analysis concept to establish the finiteness. We also offer a second proof of finiteness by roping in the Kolmogorov's length scale criterion in conjunction with the notion of diametric disks.
Standing Shocks in Viscous Accretion Flows around Black Holes
Institute of Scientific and Technical Information of China (English)
GU Wei-Min; LU Ju-Fu
2005-01-01
@@ We study the problem of standing shocks in viscous accretion flows around black holes.We parameterize such a flow with two physical constants, namely the specific angular momentum accreted by the black hole j and the energy quantity K.By providing the global dependence of shock formation in the j - K parameter space, we show that a significant parameter region can ensure solutions with shocks of different types, namely Rankine-Hugoniot shocks, isothermal shocks, and more realistically, mixed shocks.
Numerical Study of Two-Dimensional Viscous Flow over Dams
Institute of Scientific and Technical Information of China (English)
王利兵; 刘宇陆; 涂敏杰
2003-01-01
In this paper, the characteristics of two-dimensional viscous flow over two dams were numerically investigated. The results show that the behavior of the vortices is closely related to the space between two dams, water depth, Fr number and Reynolds number. In addition, the flow properties behind each dam are different, and the changes over two dams are more complex than over one dam. Finally, the relevant turbulent characteristics were analyzed.
Adaptive mesh generation for viscous flows using Delaunay triangulation
Mavriplis, Dimitri J.
1990-01-01
A method for generating an unstructured triangular mesh in two dimensions, suitable for computing high Reynolds number flows over arbitrary configurations is presented. The method is based on a Delaunay triangulation, which is performed in a locally stretched space, in order to obtain very high aspect ratio triangles in the boundary layer and the wake regions. It is shown how the method can be coupled with an unstructured Navier-Stokes solver to produce a solution adaptive mesh generation procedure for viscous flows.
Passive swimming in viscous oscillatory flows
Jo, Ikhee; Huang, Yangyang; Zimmermann, Walter; Kanso, Eva
2016-12-01
Fluid-based locomotion at low Reynolds number is subject to the constraints of Purcell's scallop theorem: reciprocal shape kinematics identical under a time-reversal symmetry cannot cause locomotion. In particular, a single degree-of-freedom scallop undergoing opening and closing motions cannot swim. Most strategies for symmetry breaking and locomotion rely on direct control of the swimmer's shape kinematics. Less is known about indirect control via actuation of the fluid medium. To address how such indirect actuation strategies can lead to locomotion, we analyze a Λ -shaped model system analogous to Purcell's scallop but able to deform passively in oscillatory flows. Neutrally buoyant scallops undergo no net locomotion. We show that dense, elastic scallops can exhibit passive locomotion in zero-mean oscillatory flows. We examine the efficiency of swimming parallel to the background flow and analyze the stability of these motions. We observe transitions from stable to unstable swimming, including ordered transitions from fluttering to chaoticlike motions and tumbling. Our results demonstrate that flow oscillations can be used to passively actuate and control the motion of microswimmers, which may be relevant to applications such as surgical robots and cell sorting and manipulation in microfluidic devices.
Three-dimensional attached viscous flow basic principles and theoretical foundations
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...
Longitudinal Viscous Flow in Granular Gases
Santos, Andres
2008-01-01
The flow characterized by a linear longitudinal velocity field $u_x(x,t)=a(t)x$, where $a(t)={a_0}/({1+a_0t})$, a uniform density $n(t)\\propto a(t)$, and a uniform temperature $T(t)$ is analyzed for dilute granular gases by means of a BGK-like model kinetic equation in $d$ dimensions. For a given value of the coefficient of normal restitution $\\alpha$, the relevant control parameter of the problem is the reduced deformation rate $a^*(t)=a(t)/\
Numerical solution of inviscid and viscous flow around the profile
Slouka, Martin; Kozel, Karel; Prihoda, Jaromir
2015-05-01
This work deals with the 2D numerical solution of inviscid compressible flow and viscous compressible laminar and turbulent flow around the profile. In a case of turbulent flow algebraic Baldwin-Lomax model is used and compared with Wilcox's k-ω model. Calculations are done in GAMM channel computational domain with 10% DCA profile and in turbine cascade computational domain with 8% DCA profile. Numerical methods are based on a finite volume solution and compared with experimental measurements for 8% DCA profile.
Properties of Accretion Shocks in Viscous Flows with Cooling Effects
Das, S; Das, Santabrata; Chakrabarti, Sandip K.
2004-01-01
Low angular momentum accretion flows can have standing and oscillating shock waves. We study the region of the parameter space in which multiple sonic points occur in viscous flows in presence of various cooling effects such as bremsstrahlung and Comptonization. We also quantify the parameter space in which shocks are steady or oscillating. We find that cooling induces effects opposite to heating by viscosity even in modifying the topology of the solutions, though one can never be exactly balanced by the other due to their dissimilar dependence on dynamic and thermodynamic parameters. We show that beyond a critical value of cooling, the flow ceases to contain a shock wave.
Viscous and gravitational fingering in multiphase compositional and compressible flow
Moortgat, Joachim
2016-03-01
Viscous and gravitational fingering refer to flow instabilities in porous media that are triggered by adverse mobility or density ratios, respectively. These instabilities have been studied extensively in the past for (1) single-phase flow (e.g., contaminant transport in groundwater, first-contact-miscible displacement of oil by gas in hydrocarbon production), and (2) multi-phase immiscible and incompressible flow (e.g., water-alternating-gas (WAG) injection in oil reservoirs). Fingering in multiphase compositional and compressible flow has received much less attention, perhaps due to its high computational complexity. However, many important subsurface processes involve multiple phases that exchange species. Examples are carbon sequestration in saline aquifers and enhanced oil recovery (EOR) by gas or WAG injection below the minimum miscibility pressure. In multiphase flow, relative permeabilities affect the mobility contrast for a given viscosity ratio. Phase behavior can also change local fluid properties, which can either enhance or mitigate viscous and gravitational instabilities. This work presents a detailed study of fingering behavior in compositional multiphase flow in two and three dimensions and considers the effects of (1) Fickian diffusion, (2) mechanical dispersion, (3) flow rates, (4) domain size and geometry, (5) formation heterogeneities, (6) gravity, and (7) relative permeabilities. Results show that fingering in compositional multiphase flow is profoundly different from miscible conditions and upscaling techniques used for the latter case are unlikely to be generalizable to the former.
Numerical calculation of periodic viscous flow through a circular hole
Notomi, T.; Namba, M.
1992-08-01
Periodic viscous flows through a circular hole driven by fluctuating far field pressure are studied numerically. The time dependent incompressible Navier-Stokes equations formulated with orthogonal curvilinear co-ordinates are solved by using a finite difference method. The flow patterns and acoustic impedance of the circular hole are investigated for various combinations of the pressure/viscous force ratio, frequency and hole edge thickness. Numerical calculations revealed some interesting facts, as follows. First, the flow patterns are classified into three regimes by fluctuating pressure amplitude and frequency: flows with no laminar separation (high-frequency-low-pressure range), flows with attached separation bubble (intermediate frequency and pressure range) and flows with detached vortex rings (low-frequency-high-pressure range). Second, the flow resistance of the circular hole is proportional to the acoustic particle velocity but independent of the viscosity of the fluid, and almost invariant with the frequency for the low-frequency-high-pressure range. On the other hand, for the high-frequency-low-pressure range, the flow resistance is independent of the periodic pressure amplitude and varies directly with the 2/3 power of the frequency. Finally, the predicted circular hole impedance is in good agreement with the experimental data for the orifice impedance of Ingard and Ising.
Flow harmonics within an analytically solvable viscous hydrodynamic model
Hatta, Yoshitaka; Torrieri, Giorgio; Xiao, Bo-Wen
2014-01-01
Based on a viscous hydrodynamic model with anisotropically perturbed Gubser flow and isothermal Cooper-Frye freezeout, we analytically compute the flow harmonics $v_n(p_T)$ and study how they scale with the harmonic number $n$ and transverse momentum, as well as the system size, shear and bulk viscosity coefficients, and collision energy. In particular, we find that the magnitude of shear viscous corrections grows linearly with $n$. The mixing between different harmonics is also discussed. While this model is rather simple as compared to realistic heavy-ion collisions, we argue that the scaling results presented here may be meaningfully compared to experimental data collected over many energies, system sizes, and geometries.
Unsteady Viscous Dissipative Dusty Nanofluid Flow Over a Vertical Plate
Directory of Open Access Journals (Sweden)
D.R.V.S.R.K. Sastry
2016-10-01
Full Text Available The flow past an infinite vertical isothermal plate started impulsively in its own plane in a viscous incompressible two-phase nanofluid has been considered by taking into account the viscous dissipative heat. Two nano particles Copper (Cu and Alumina (Al2O3 are submerged in a base fluid, Water (H20. The coupled non-linear partial differential equations which govern the flow are solved for nanofluid and dust particle phases by finite difference method. The velocity and temperature fields have been shown graphically for various parameters. Here Grashof number, (Gr being positive (cooling of the plate for dusty air. Also the effects of Eckert number on heat transfer and skin friction coefficient for various parameters are represented graphically. It is observed that dusty nanofluid enhances both skin friction and heat transfer rate in the case of cooling.
Unsteady Axisymmetric Rotational Flow of Dusty Elastico Viscous Liquid
Directory of Open Access Journals (Sweden)
G. C. Mandal
1990-04-01
Full Text Available This paper reports the flow of elastico-viscous liquid embedded with particles in an oscillating cylinder. Explicit expressions are obtained for the velocities of liquid and dust particles by the technique of Laplace transforms. Numerical computations of the velocity fields are carried out for different values of mass concentration and relaxation time of the dust particles and varying elastic elements in the liquid.
Small-amplitude viscous motion on arbitrary potential flows
Goldstein, M. E.
1984-02-01
This paper is concerned with small-amplitude, unsteady, vortical and entropic motion imposed on steady potential flows. It is restricted to the case where the spatial scale of the unsteady motion is small compared to that of the mean flow. Under such conditions, the unsteady motion may be influenced by viscosity even if the mean flow is not. An exact high-frequency (small-wavelength) solution is obtained for the small-amplitude viscous motion imposed on a steady potential flow. It generalizes the one obtained by Pearson (1959) for the homogeneous-strain case to the case of quasi-homogeneous strain. This result is used to study the effect of viscosity on rapidly distorted turbulent flows. Specific numerical results are given for a turbulent flow near a two-dimensional stagnation point.
A calculation procedure for viscous flow in turbomachines, volume 1
Khalil, I.; Tabakoff, W.
1979-01-01
A method for analyzing the nonadiabatic viscous flow through turbomachine rotors is presented. The field analysis is based upon the numerical integration of the full incompressible stream function vorticity form of the Navier-Stokes equations, together with the energy equation, over the rotor blade-to-blade stream channels. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system that suits the most complicated blade geometries. A numerical scheme is used to carry out the necessary integration of the elliptic governing equations. The flow characteristics within the rotor of a radial inflow turbine are investigated over a wide range of operating conditions. The calculated results are compared to existing experimental data. The flow in a radial compressor is analyzed in order to study the behavior of viscous flow in diffusing cascades. The results are compared qualitatively to known experimental trends. The solution obtained provides insight into the flow phenomena in this type of turbomachine. It is concluded that the method of analysis is quite general and gives a good representation of the actual flow behavior within turbomachine passages.
Decay of viscous surface waves without surface tension
Guo, Yan
2010-01-01
Consider a viscous fluid of finite depth below the air. In the absence of the surface tension effect at the air-fluid interface, the long time behavior of a free surface with small amplitude has been an intriguing question since the work of Beale \\cite{beale_1}. In this monograph, we develop a new mathematical framework to resolve this question. If the free interface is horizontally infinite, we establish that it decays to a flat surface at an algebraic rate. On the other hand, if the free interface is periodic, we establish that it decays at an almost exponential rate, i.e. at an arbitrarily fast algebraic rate determined by the smallness of the data. Our framework contains several novel techniques, which include: (1) a local well-posed theory of the Navier-Stokes equations in the presence of a moving boundary; (2) a two-tier energy method that couples the boundedness of high-order energy to the decay of low-order energy, the latter of which is necessary to balance out the growth of the highest derivatives o...
A calculation procedure for viscous flow in turbomachines, volume 2
Khalil, J.; Tabakoff, W.
1980-01-01
Turbulent flow within turbomachines having arbitrary blade geometries is examined. Effects of turbulence are modeled using two equations, one expressing the development of the turbulence kinetic energy and the other its dissipation rate. To account for complicated blade geometries, the flow equations are formulated in terms of a nonorthogonal boundary fitted coordinate system. The analysis is applied to a radial inflow turbine. The solution obtained indicates the severity of the complex interaction mechanism that occurs between the different flow regimes (i.e., boundary layers, recirculating eddies, separation zones, etc.). Comparison with nonviscous flow solutions tend to justify strongly the inadequacy of using the latter with standard boundary layer techniques to obtain viscous flow details within turbomachine rotors. Capabilities and limitations of the present method of analysis are discussed.
Viscous and Gravitational Fingering in Multiphase Compositional and Compressible Flow
Moortgat, Joachim
2016-01-01
Viscous and gravitational fingering refer to flow instabilities in porous media that are triggered by adverse mobility or density ratios, respectively. These instabilities have been studied extensively in the past for 1) single-phase flow (e.g., contaminant transport in groundwater, first-contact-miscible displacement of oil by gas in hydrocarbon production), and 2) multi-phase immiscible and incompressible flow (e.g., water-alternating-gas (WAG) injection in oil reservoirs). Fingering in multiphase compositional and compressible flow has received much less attention, perhaps due to its high computational complexity. However, many important subsurface processes involve multiple phases that exchange species. Examples are carbon sequestration in saline aquifers and enhanced oil recovery (EOR) by gas or WAG injection below the minimum miscibility pressure. In multiphase flow, relative permeabilities affect the mobility contrast for a given viscosity ratio. Phase behavior can also change local fluid properties, w...
Numerical Simulations of Viscous Accretion Flow around Black Holes
Lee, Seong-Jae; Chattopadhyay, Indranil; Kumar, Rajiv; Hyung, Siek; Ryu, Dongsu
2016-06-01
We present shocked viscous accretion flow onto a black hole in a two dimensional cylindrical geometry, where initial conditions were chosen from analytical solutions. The simulation code used the Lagrangian Total Variation Diminishing (LTVD) and remap routine, which enabled us to attain high accuracy in capturing shocks and to handle the angular momentum distribution correctly. The steady state shocked solution in the inviscid, as well as in the viscous regime, matched theoretical predictions well, but increasing viscosity renders the accretion shock unstable. Large amplitude shock oscillation is accompanied by intermittent, transient inner multiple shocks. Such oscillation of the inner part of disk is interpreted as the source of QPO in hard X-rays observed in microquasars; and strong shock oscillation induces strong episodic jet emission. The periodicity of jets and shock oscillation are similar. Our simulation shows that the jets for higher viscosity parameter are evidently stronger and faster than that for lower viscosity.
Effects of Joule Heating and Viscous Dissipation on MHD Marangoni Convection Boundary Layer Flow
Directory of Open Access Journals (Sweden)
Rohana Abdul Hamid
2011-09-01
Full Text Available An analysis is performed to study the effects of the Joule heating and viscous dissipation on the magnetohydrodynamics (MHD Marangoni convection boundary layer flow. The governing partial differential equations are reduced to a system of ordinary differential equations via the similarity transformations. Numerical results of the similarity equations are obtained using the Runge-Kutta-Fehlberg method. Effects of the magnetic field parameter, and the combined effects of the Joule heating and the viscous dissipation are investigated and the numerical results are tabulated in tables and figures. It is found that the magnetic field reduces the fluid velocity but increases the fluid temperature. On the other hand, the combined effects of the Joule heating and viscous dissipation have significantly influenced the surface temperature gradient.
Visualization of bacterial flagella dynamics in a viscous shear flow
Ali, Jamel; Kim, Minjun
2016-11-01
We report on the dynamics of tethered bacterial flagella in an applied viscous shear flow and analyze their behavior using image processing. Flagellin proteins were repolymerized into flagellar filaments functionalized with biotin at their proximal end, and allowed to self-assemble within a micro channel coated with streptavidin. It was observed that all attached flagellar filaments aligned with the steady shear flow of various polymeric solutions. Furthermore it was observed that many of the filaments were stretched, and at elevated flow rates began to undergo polymorphic transformations, which were initiated at one end of the flagellum. When undergoing a change to a different helical form the flagellum was observed to transform to an oppositely handed helix, as to counteract the viscous torque imparted by the shear flow. It was also observed that some flagellar filaments did not undergo polymorphic transformations, but rotated about their helical axis. The rate of this rotation appears to be a function of the applied flow rate. These results expand on previous experimental work and aid in the development of a novel platform that harnesses the autonomic response of a 'forest' of bacterial flagella for engineering applications. This work was funded by NSF Grant CMMI-1000255, KEIT MOTIE Grant No. 10052980, and with Government support under and awarded by DoD, Air Force Office of Scientific Research, National Defense Science and Engineering Graduate (NDSEG) Fellowship, 32 CFR 168a.
2006-03-01
COUETTE & POISEUILLE FLOWS OF NEMATIC POLYMERS IN VISCOUS SOLVENTS: MORPHOLOGY IN MOLECULAR ORIENTATION, STRESS & FLOW Hong Zhou...viscoelastic stresses, and flow feedback. Pre- vious studies in plane Couette & Poiseuille flow (with the exception of [7]) have focused on the coupling between...with Plane Couette & Poiseuille Flows of Nematic Polymers in Viscous Solvents: Morphology in Molecular Orientation, Stress & Flow 5a. CONTRACT
Thermal stability for a reactive viscous flow in a slab
Okoya, S S
2002-01-01
The paper deals with the effect of dimensionless non - Newtonian coefficient on the thermal stability of a reactive viscous liquid in steady flow between parallel heated plates. It is assumed that the liquid is symmetrically heated and the flow fully developed. Approximate analytical solution is obtained for the velocity of the flow and the criterion for which this solution is valid is determined. After the velocity distribution is known, the temperature distribution may be calculated. Criticality and disappearance of criticality (transition values) are obtained in the following cases: (i) Bimolecular (ii) Arrhenius and (iii) Sensitized temperature dependence. We have observed that nonlinear effect from velocity and temperature fields introduced decaying for the transitional values of the dimensionless central temperature. Other effects of this nonlinearity are reported. We also give results for the plane - Couette flow problem. The results help to enhance understanding of the interplay between Newtonian and ...
The surface tension effect on viscous liquid spreading along a superhydrophobic surface
Aksenov, A. V.; Sudarikova, A. D.; Chicherin, I. S.
2017-01-01
Within the Stokes film approximation, unsteady plane-parallel spreading of a thin layer of a heavy viscous fluid along a horizontal superhydrophobic surface is studied. The forced spreading regimes induced by the mass supply are considered. Plane-parallel flow along the principal direction of the slip tensor of the superhydrophobic surface is studied in case that the corresponding slip tensor component is a power function of the spatial coordinate. An evolution equation for the film thickness is derived taking into account surface tension that is dependent on the spatial coordinate. The group classification problem is solved. Self-similar and invariant solutions are constructed for power and exponent time dependences on mass supply respectively at a special form of the surface tension coefficient. Surface tension is shown to have a significant influence on the character of the liquid spreading.
Viscously driven plasma flows in the deep geomagnetic tail
Energy Technology Data Exchange (ETDEWEB)
Owen, C.J.; Slavin, J.A. (NASA/Goddard Space Flight Center, Greenbelt, MD (United States))
1992-07-24
The authors present an analysis, based on the principles of stress balance in a 1-dimensional current sheet, which considers the problem of closed magnetic flux transport into the deep tail by a viscous'-like interaction between the solar wind and the magnetosphere. They illustrate the analysis with an example of ISEE-3 data showing strong tailward plasma sheet flows on apparently closed field lines in the deep tail. Apart from narrow regions adjacent to the magnetopause, these flows are not driven by the scattering of magnetosheath plasma into the magnetosphere. They estimate the fraction of the magnetosheath momentum flux needed to be anomalously transferred into the plasma sheet to drive the flows. In their example this is [approximately] 6%. No previously suggested mechanism (e.g., the Kelvin-Helmholtz Instability) has been shown capable of providing anomalous momentum transport of this magnitude. Their current understanding of the viscous' interaction between the solar wind and magnetosphere is thus insufficient to explain these observations.
Unsteady Viscous Flow over an Expanding Stretching Cylinder
Institute of Scientific and Technical Information of China (English)
方铁钢; 章骥; 钟永芳; 陶华
2011-01-01
We study the viscous How over an expanding stretching cylinder. The solution is exact to the Navier-Stokes equations. The stretching velocity of the cylinder is proportional to the axial distance from the origin and decreases with time. There exists a unique solution for the How with all the studied values of Reynolds number and the unsteadiness parameter. Reversal Hows exist for an expanding stretching cylinder. The velocity decays faster for a larger Reynolds number and a more rapidly expanding cylinder.%We study the viscous flow over an expanding stretching cylinder.The solution is exact to the Navier-Stokes equations.The stretching velocity of the cylinder is proportional to the axial distance from the origin and decreases with time.There exists a unique solution for the flow with all the studied values of Reynolds number and the unsteadiness parameter.Reversal flows exist for an expanding stretching cylinder.The velocity decays faster for a larger Reynolds number and a more rapidly expanding cylinder.
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.
Aminated Copolymers as Flow Improvers for Super-viscous Crude Oils
Institute of Scientific and Technical Information of China (English)
Zhang Hong; Shen Benxian
2007-01-01
The new flow improvers for super-viscous crude oils were developed via esterification of polybasic high carbon alcohol with methacrylate and copolymerization of monomers followed by amination of copolymers.The structure of the synthesized polymer flow improver additive was confirmed by IR spectroscopy and the crystal structure of the flow improver additives were determined by X-ray diffraction analysis.The structure of wax crystals was also studied at the same time.The results showed that the wax crystal structure was closely related with the crystal structure of the flow improver,which could change the pour point depression and viscosity reduction behavior of the crude oil.When the wax crystal structure matched well with that of the additive,the Wax crystals were dispersed satisfactorily,resulting in favorable effects in terms of pour point depression and viscosity reduction.The new synthesized aminated polymer flow improver additive was most efficient for treating super-viscous crude oils.The super-viscous crude oil had a high content of resins and asphaltenes,which might aggregate onto the surface of wax crystals to form blocks to limit the crude oil fluidity.However,amination of copolymers having similar structure with the resins and asphaltenes contained in crude oil could dissolve the huge polar groups to make the deposit formation difficult.
Numerical study of viscous starting flow past a flat plate
Xu, Ling
2014-01-01
Viscous flow past a finite plate which is impulsively started in direction normal to itself is studied numerically using a high order mixed finite difference and semi-Lagrangian scheme. The goal is to resolve details of the vorticity generation at early times, and to determine the effect of viscosity on flow quantities such as the core trajectory and vorticity, and the shed circulation. Vorticity contours, streaklines and streamlines are presented for a range of Reynolds numbers $Re \\in [250, 2000]$ and a range of times $t \\in[0. 0002, 5]$. At early times, most of the vorticity is attached to the plate. The paper proposes a definition for the shed circulation at early as well as late times, and shows that it indeed represents vorticity that separates from the plate without reattaching. The contribution of viscous diffusion to the circulation shedding rate is found to be significant, but, interestingly, to depend only slightly on the value of the Reynolds number. The shed circulation and the vortex core trajec...
Angular dynamics of small crystals in viscous flows
Fries, Johan; Einarsson, Jonas; Mehlig, Bernhard
2016-11-01
The angular dynamics of a very small ellipsoidal particle in a viscous flow decouples from its translational dynamics, and the particle angular velocity is given by Jeffery's theory. It is known that cuboid particles share these properties. In the literature a special case is most frequently discussed, that of axisymmetric particles, with a continuous rotational symmetry. Here we compute the angular dynamics of crystals that possess a discrete rotational symmetry and certain mirror symmetries, but that do not have a continuous rotational symmetry. We give examples of such particles that nevertheless obey Jeffery's theory. But there are other examples where the angular dynamics is determined by a more general equation of motion. Vetenskapsrådet [Grant Number 2013-3992], Formas [Grant Number 2014-585], "Bottlenecks for particle growth in turbulent aerosols" from the Knut and Alice Wallenberg Foundation, Dnr. KAW 2014.0048, MPNS COST Action MP1305 "Flowing matter".
Hady, Fekry M; Ibrahim, Fouad S; Abdel-Gaied, Sahar M; Eid, Mohamed R
2012-04-22
In this work, we study the flow and heat transfer characteristics of a viscous nanofluid over a nonlinearly stretching sheet in the presence of thermal radiation, included in the energy equation, and variable wall temperature. A similarity transformation was used to transform the governing partial differential equations to a system of nonlinear ordinary differential equations. An efficient numerical shooting technique with a fourth-order Runge-Kutta scheme was used to obtain the solution of the boundary value problem. The variations of dimensionless surface temperature, as well as flow and heat-transfer characteristics with the governing dimensionless parameters of the problem, which include the nanoparticle volume fraction ϕ, the nonlinearly stretching sheet parameter n, the thermal radiation parameter NR, and the viscous dissipation parameter Ec, were graphed and tabulated. Excellent validation of the present numerical results has been achieved with the earlier nonlinearly stretching sheet problem of Cortell for local Nusselt number without taking the effect of nanoparticles.
Asghar, S.; Hussain, Q.; Hayat, T.; Alsaedi, A.
2015-07-01
This article addresses the heat transfer in a peristaltic flow of a reactive combustible viscous fluid through a porous saturated medium. The flow here is induced because of travelling waves along the channel walls. It is assumed that exothermic chemical reactions take place within the channel under the Arrhenius kinetics and the convective heat exchange with the ambient medium at the surfaces of the channel walls follows Newton's law of cooling. The analysis is carried out in the presence of viscous dissipation and without consumption of the material. The governing equations are formulated by employing the long-wavelength approximation. Closed-form solutions for the stream function, axial velocity, and axial pressure gradient are obtained. It is found that the temperature decreases at high Biot numbers, and the Nusselt number increases with increasing reaction parameter. The Biot number and reaction parameter produce the opposite effects on the Nusselt number.
Highly viscous fluid flow in a spinning and nutating cylinder
Herbert, T.
1985-02-01
Spin-stabilized projectiles with liquid payloads can experience a severe flight instability characterized by a rapid yaw angle growth and a simultaneous loss in spin rate. Laboratory experiments and field tests have shown that this instability originates from the internal fluid motion in the range of high viscosity. Evaluation of the experimental data and analysis of the equations for the fluid motion in a spinning and nutating cylinder suggest a theoretical approach in three major steps: (1) analysis of the steady viscous flow in an infinitely long cylinder, (2) hydrodynamic stability analysis of this basic flow, and (3) analysis of the end effects. The basic flow has been found in analytical form. At low Reynolds number, this flow agrees well with computational results for the center section of a cylinder of aspect ratio 4.3. The despin moment caused by this flow largely agrees with experimental data for a wide range of Reynolds numbers. Current work aims at the stability of this flow.
Flow of a viscous nematic fluid around a sphere
Gómez-González, Manuel
2013-01-01
We analyze the creeping flow generated by a spherical particle moving through a viscous fluid with nematic directional order, in which momentum diffusivity is anisotropic and which opposes resistance to bending. Specifically, we provide closed-form analytical expressions for the response function, i.e. the equivalent to Stokes's drag formula for nematic fluids. Particular attention is given to the rotationally pseudo-isotropic condition defined by zero resistance to bending, and to the strain pseudo-isotropic condition defined by isotropic momentum diffusivity. We find the former to be consistent with the rheology of biopolymer networks and the latter to be closer to the rheology of nematic liquid crystals. These "pure" anisotropic conditions are used to benchmark existing particle tracking microrheology methods that provide effective directional viscosities by applying Stokes's drag law separately in different directions. We find that the effective viscosity approach is phenomenologically justified in rotati...
Characteristic analysis of unsteady viscous flow around a cavitating propeller
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Based on viscous multiphase flow theory, this paper presents some recent validation results with a hybrid grid and sliding mesh solving Unsteady Navier-Stokes (N-S) and Bubble Dynamics equations as applied to prediction of pressure, velocity and vapor volume fraction in the wake in an uniform inflow. Comparable to experimental results, numerical predictions of sheet cavitation, tip vortex cavitation and hub vortex cavitation are in agreement with the corresponding experimental data, the same as numerical predictions of pressure in wake. Tip vortex cavitation is the most important to generate the pressure fluctuation within the near wake. The characteristics such as blade and shaft rate frequency of propeller pressure in wake coincide with its geometric model and parameters. With increasing distance from propeller disk, the pressure signals at blade frequency de-crease. The process of attenuation becomes fast with the decreased advance coefficient and cavitation number.
Disappearance of a spout: singular surface in viscous withdrawal
Zhang, Wendy
2003-03-01
Inspired by recent experiments (Cohen & Nagel, PRL 2002) showing steady flow past an interface between two viscous but immiscible fluids can create sharp features on the interface as the interface transforms from a hump to a spout, we present a model for the formation of a steady-state singularity on the fluid interface. We show the topological transition from a spout to a hump is continuous, with the interface approaching a singularity, in the limit of vanishing lower-layer viscosity. For small lower-layer viscosity, the transition is weakly discontinous, with a cut-off which decreases exponentially with the viscosity contrast.
Directory of Open Access Journals (Sweden)
Norfifah Bachok
Full Text Available The steady boundary layer flow of a viscous and incompressible fluid over a moving vertical flat plate in an external moving fluid with viscous dissipation is theoretically investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary (similarity differential equations, which is then solved numerically using a Maple software. Results for the skin friction or shear stress coefficient, local Nusselt number, velocity and temperature profiles are presented for different values of the governing parameters. It is found that the set of the similarity equations has unique solutions, dual solutions or no solutions, depending on the values of the mixed convection parameter, the velocity ratio parameter and the Eckert number. The Eckert number significantly affects the surface shear stress as well as the heat transfer rate at the surface.
Periodic massloss from viscous accretion flows around black holes
Das, Santabrata; Nandi, Anuj; Molteni, Diego
2014-01-01
We investigate the behaviour of low angular momentum viscous accretion flows around black holes using Smooth Particle Hydrodynamics (SPH) method. Earlier, it has been observed that in a significant part of the energy and angular momentum parameter space, rotating transonic accretion flow undergoes shock transition before entering in to the black hole and a part of the post-shock matter is ejected as bipolar outflows, which are supposed to be the precursor of relativistic jets. In this work, we simulate accretion flows having injection parameters from the inviscid shock parameter space, and study the response of viscosity on them. With the increase of viscosity, shock becomes time dependent and starts to oscillate when the viscosity parameter crosses its critical value. As a result, the in falling matter inside the post-shock region exhibits quasi-periodic variations and causes periodic ejection of matter from the inner disc as outflows. In addition, the same hot and dense post-shock matter emits high energy r...
Two tandem flexible loops in a viscous flow
Ye, Huilin; Wei, Heng; Huang, Haibo; Lu, Xi-yun
2017-02-01
Interaction between two tandem flexible loops with tension and bending stiffness in a viscous flow is investigated by numerical simulations. In most cases, the heads of the loops facing the oncoming flow are fixed but flapping around the head is allowed. The effect of the gap distance between the two passive flapping loops (G) on the drag coefficient is investigated in detail. Here, for the first time, the sudden drag force reduction at a specific G, i.e., Gc for the downstream loop has been found in the two tandem flexible loops system. It is different from the drag "jump" behavior in the two tandem rigid cylinder system. Although the drag is partially associated with the flapping amplitude, the drag force reduction of the downstream loop may be mainly attributed to flow regimes transition or vortices merging mode transition. The vortices merging is also analysed from a Lagrangian viewpoint, which gives insight into the mechanism. The effects of Reynolds number (20 ≤ Re ≤100 ) , bending coefficient (10-4≤K ≤2 ×10-2 ) , and tension coefficient (10 ≤S ≤1000 ) are also investigated and the relevant mechanism is explored. If the head of the downstream loop is set free to move laterally, the critical distance (Gc) where the sudden drag reduction occurs would further decrease compared to the fixed case, which is due to the early shedding regime transition.
A calculation procedure for viscous flow in turbomachines, volume 3. [computer programs
Khalil, I.; Sheoran, Y.; Tabakoff, W.
1980-01-01
A method for analyzing the nonadiabatic viscous flow through turbomachine blade passages was developed. The field analysis is based upon the numerical integration of the full incompressible Navier-Stokes equations, together with the energy equation on the blade-to-blade surface. A FORTRAN IV computer program was written based on this method. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system. The flow may be axial, radial or mixed and there may be a change in stream channel thickness in the through-flow direction. The inputs required for two FORTRAN IV programs are presented. The first program considers laminar flows and the second can handle turbulent flows. Numerical examples are included to illustrate the use of the program, and to show the results that are obtained.
Wall laws for viscous fluids near rough surfaces
Directory of Open Access Journals (Sweden)
Dalibard Anne-Laure
2012-09-01
Full Text Available In this paper, we review recent results on wall laws for viscous fluids near rough surfaces, of small amplitude and wavelength ε. When the surface is “genuinely rough”, the wall law at first order is the Dirichlet wall law: the fluid satisfies a “no-slip” boundary condition on the homogenized surface. We compare the various mathematical characterizations of genuine roughness, and the corresponding homogenization results. At the next order, under ergodicity properties of the roughness distribution, a Navier wall law with a slip length of order ε can be derived, that leads to better error estimates. We also discuss the relationship beween the slip length and the position of the homogenized surface. In particular, we prove that for adherent rough walls, the Navier wall law associated to the roughness does not correspond to any tangible slip.
Flux change in viscous laminar flow under oscillating boundary condition
Ueda, R.; Mikada, H.; Goto, T.; Takekawa, J.
2012-12-01
The behavior of interstitial fluid is one of major interest in earth sciences in terms of the exploitation of water resources, the initiation of earthquakes, enhanced oil recovery (EOR), etc. Seismic waves are often known to increase the flux of interstitial fluid but the relationship between the flux and propagating seismic waves have not been well investigated in the past, although seismic stimulation has been applied in the oil industry for enhanced oil recovery (EOR). Many observations indicated that seismic waves could stimulate the oil production due to lowering of apparent viscosity coefficient, to the coalescence and/or the dispersion of droplets of a phase in multiphase fluids. However, the detailed mechanism of seismic stimulation has not been fully understood, either. In this study, We attempt to understand the mechanism of the flux change in viscous laminar flow under oscillating boundary condition for the simulation of interstitial flow. Here, we analyze a monophase flow in a pore throat. We first assume a Hagen-Poiseuille flow of incompressible fluid through a pore-throat in a porous medium. We adopt the Lattice Boltzmann method (LBM) in which the motion of fluid is simulated through the variation of velocity distribution function representing the distribution of discrete particle velocities. We use an improved incompressible LBKG model (d2q9i) proposed in Zou et. al. (1995) to accurately accommodate the boundary conditions of pressure and velocity in the Hagen-Poiseuille flow. We also use an half-way bounce back boundary condition as the velocity boundary condition. Also, we assume a uniform pressure (density) difference between inlet and outlet flow, and the density difference could initiate the flow in our simulation. The oscillating boundary condition is given by the body force acting on fluid particles. In this simulation, we found that the flux change is negligible under small amplitude of oscillation in both horizontal and vertical directions
RHEOLOGICAL PROPERTIES OF VISCOUS DEBRIS FLOWS IN THE JIANGJIA RAVINE, YUNNAN, CHINA
Institute of Scientific and Technical Information of China (English)
Yuyi WANG; Chyandeng JAN; Changzhi LI; Wenliang HAN
2001-01-01
The rheological properties of natural debris flow are studied using experimental data obtained from a rheometer built by the authors. The present study is aimed to address the rheological properties of viscous debris flow at low shear rate. It is found that overstress effect and shear-rate-thinning phenomenon characterize the viscous debris flow in the Jiangjia Ravine, China. Results obtained from this study are believed to lay the foundation for further study on the theory of debris flow rheology.
Modeling and control of flow-induced vibrations of a flexible hydrofoil in viscous flow
Caverly, Ryan James; Li, Chenyang; Chae, Eun Jung; Forbes, James Richard; Young, Yin Lu
2016-06-01
In this paper, a reduced-order model (ROM) of the flow-induced vibrations of a flexible cantilevered hydrofoil is developed and used to design an active feedback controller. The ROM is developed using data from high-fidelity viscous fluid-structure interaction (FSI) simulations and includes nonlinear terms to accurately capture the effect of lock-in. An active linear quadratic Gaussian (LQG) controller is designed based on a linearization of the ROM and is implemented in simulation with the ROM and the high-fidelity viscous FSI model. A controller saturation method is also presented that ensures that the control force applied to the system remains within a prescribed range. Simulation results demonstrate that the LQG controller successfully suppresses vibrations in both the ROM and viscous FSI simulations using a reasonable amount of control force.
Generalized primary/secondary flow analysis of viscous flow around bodies at incidence
Govindan, T. R.; Briley, W. R.; Chang, Ming-Shun
1991-01-01
Generalized primary/secondary flow equations, which are an approximation to the Navier-Stokes equations, have been utilized to compute the three-dimensional viscous flow around bodies at incidence. Two features central to the approximations in the primary/secondary flow equations are a locally specified primary flow direction and a decomposition of the secondary velocity field. For the flow around a body at incidence, the local primary flow direction is aligned with streamlines for the potential flow around the body at zero degrees incidence. A sequentially decoupled implicit algorithm exploits the form of the primary/secondary flow equations for fast run times. Computed solutions for flow around an ogive cylinder at incidence and an unappended submarine hull in drift have been presented. These solutions show the generation of strong lee-side vortices which are a source of propulsor inlet distortion and a side-force on the body. Computed solutions agree well with available experimental data. The combined efficiency and accuracy of the approximate equations and solution algorithm make this approach attractive for computing viscous flow around bodies at incidence.
Dynamics of Lipid Bilayer Vesicles in Viscous Flows
Schwalbe, Jonathan; Vlahovska, Petia; Miksis, Michael J.
2008-11-01
An analytical theory is developed to describe the dynamics of a closed lipid bilayer membrane (vesicle) in a general linear viscous flow. The dynamics of the membrane is governed by the Stokes equations in the fluid plus the normal and tangential stress condition along the bilayer interface. The effects of the membrane fluidity, incompressibility and resistance to bending are taken into account. The model is a generalization of the work on planar membranes by Seifert and Langer (Europhys. Lett. vol. 23, 71, 1993), which accounted for the variations in lipid density along both leaflets of the bilayer. Considering a nearly spherical vesicle, a perturbation solution is derived. The leading order analysis results in a nonlinear coupled system of equations for the dynamics of the shape and the mean lipid density difference between the inner and outer monolayer. Multiple solution states are found as a function of viscosity ratio and the monolayer slip coefficient. The dynamics and stability of these solutions is discussed. Comparisons are made to previous works based on the minimal curvature model which did not consider variable lipid density.
Mitchell, William H.; Spagnolie, Saverio E.
2017-03-01
A double-layer integral equation for the surface tractions on a body moving in a viscous fluid is derived which allows for the incorporation of a background flow and/or the presence of a plane wall. The Lorentz reciprocal theorem is used to link the surface tractions on the body to integrals involving the background velocity and stress fields on an imaginary bounding sphere (or hemisphere for wall-bounded flows). The derivation requires the velocity and stress fields associated with numerous fundamental singularity solutions which we provide for free-space and wall-bounded domains. Two sample applications of the method are discussed: we study the tractions on an ellipsoid moving near a plane wall, which provides a more detailed understanding of the well-studied glancing and reversing trajectories in the context of particle sedimentation, and the erosion of bodies by a viscous flow, in which the surface is ablated at a rate proportional to the local viscous shear stress. Simulations and analytical estimates suggest that a spherical body in a uniform flow first reduces nearly but not exactly to the drag minimizing profile and then vanishes in finite time. The shape dynamics of an eroding body in a shear flow and near a wall are also investigated. Stagnation points on the body surface lead generically to the formation of cusps, whose number depends on the flow configuration and/or the presence of nearby boundaries.
Drinking with a hairy tongue: viscous entrainment by dipping hairy surfaces
Nasto, Alice; Brun, Pierre-Thomas; Alvarado, José; Bush, John; Hosoi, Anette
2016-11-01
Nectar-drinking bats have tongues covered with hair-like papillae, enhancing their ability to take up viscous nectar by dipping. Using a combination of model experiments and theory reminiscent of Landau-Levich-Derjaguin dip coating, we rationalize this mechanism of viscous entrainment in a hairy texture. For the model experiments, hairy surfaces are fabricated using laser cut molds and casting samples with PDMS elastomer. Modeling the liquid trapped within the texture using a Darcy-Brinkman like approach, we derive the drainage flow solution. The amount of fluid that is entrained is dependent on the viscosity of the fluid, the density of the hairs, and the dipping speed. We find that there is an optimal hair density to maximize fluid uptake.
Rheological properties and the mechanism of a viscous flow of aqueous pectin solutions
Netesova, G. A.; Kotov, V. V.; Bodyakina, I. M.; Lukin, A. L.
2012-09-01
The rheological properties and mechanisms of a viscous flow of diluted apple pectin solutions are investigated. It is found that the rise in solution viscosity upon an increase in concentration and a drop in temperature is, along with the corresponding degree to which the interaction between pectin molecules and solvent is reduced, associated with the processes of structuring. The entropy of a viscous flow of pectin solutions is found to be positive: it grows with a rise in concentration is virtually temperature independent. It is established that the entropy factor makes the main contribution to the free energy value of a viscous flow.
Free surface flows: coalescence, spreading and dewetting
Hernandez Sanchez, Jose Federico
2015-01-01
Capillary and wetting phenomena are an essential part of nature. Its presence is noticed in many circumstances where solid and liquid surfaces come into contact. In this thesis different types of capillary free surface flows are studied. The topics discussed are mainly the coalescence of viscous ses
Surface deformations and wave generation by wind blowing over a viscous liquid
Paquier, Anna; Rabaud, Marc
2015-01-01
We investigate experimentally the early stage of the generation of waves by a turbulent wind at the surface of a viscous liquid. The spatio-temporal structure of the surface deformation is analyzed by the optical method Free Surface Synthetic Schlieren, which allows for time-resolved measurements with a micrometric accuracy. Because of the high viscosity of the liquid, the flow induced by the turbulent wind in the liquid remains laminar, with weak surface drift velocity. Two regimes of deformation of the liquid-air interface are identified. In the first regime, at low wind speed, the surface is dominated by rapidly propagating disorganized wrinkles, elongated in the streamwise direction, which can be interpreted as the surface response to the pressure fluctuations advected by the turbulent airflow. The amplitude of these deformations increases approximately linearly with wind velocity and are essentially independent of the fetch (distance along the channel). Above a threshold in wind speed, the perturbations ...
Modelling of fluid-structure interaction with multiphase viscous flows using an immersed-body method
Yang, P.; Xiang, J.; Fang, F.; Pavlidis, D.; Latham, J.-P.; Pain, C. C.
2016-09-01
An immersed-body method is developed here to model fluid-structure interaction for multiphase viscous flows. It does this by coupling a finite element multiphase fluid model and a combined finite-discrete element solid model. A coupling term containing the fluid stresses is introduced within a thin shell mesh surrounding the solid surface. The thin shell mesh acts as a numerical delta function in order to help apply the solid-fluid boundary conditions. When used with an advanced interface capturing method, the immersed-body method has the capability to solve problems with fluid-solid interfaces in the presence of multiphase fluid-fluid interfaces. Importantly, the solid-fluid coupling terms are treated implicitly to enable larger time steps to be used. This two-way coupling method has been validated by three numerical test cases: a free falling cylinder in a fluid at rest, elastic membrane and a collapsing column of water moving an initially stationary solid square. A fourth simulation example is of a water-air interface with a floating solid square being moved around by complex hydrodynamic flows including wave breaking. The results show that the immersed-body method is an effective approach for two-way solid-fluid coupling in multiphase viscous flows.
Tidal Modulation of Ice-shelf Flow: a Viscous Model of the Ross Ice Shelf
Brunt, Kelly M.; MacAyeal, Douglas R.
2014-01-01
Three stations near the calving front of the Ross Ice Shelf, Antarctica, recorded GPS data through a full spring-neap tidal cycle in November 2005. The data revealed a diurnal horizontal motion that varied both along and transverse to the long-term average velocity direction, similar to tidal signals observed in other ice shelves and ice streams. Based on its periodicity, it was hypothesized that the signal represents a flow response of the Ross Ice Shelf to the diurnal tides of the Ross Sea. To assess the influence of the tide on the ice-shelf motion, two hypotheses were developed. The first addressed the direct response of the ice shelf to tidal forcing, such as forces due to sea-surface slopes or forces due to sub-ice-shelf currents. The second involved the indirect response of ice-shelf flow to the tidal signals observed in the ice streams that source the ice shelf. A finite-element model, based on viscous creep flow, was developed to test these hypotheses, but succeeded only in falsifying both hypotheses, i.e. showing that direct tidal effects produce too small a response, and indirect tidal effects produce a response that is not smooth in time. This nullification suggests that a combination of viscous and elastic deformation is required to explain the observations.
Viscous Flow with Large Fluid-Fluid Interface Displacement
DEFF Research Database (Denmark)
Rasmussen, Henrik Koblitz; Hassager, Ole; Saasen, Arild
1998-01-01
The arbitrary Lagrange-Euler (ALE) kinematic description has been implemented in a 3D transient finite element program to simulate multiple fluid flows with fluid-fluid interface or surface displacements. The description of fluid interfaces includes variable interfacial tension, and the formulation...
Effect of viscous dissipation on mixed convection flow in a vertical ...
African Journals Online (AJOL)
Effect of viscous dissipation on mixed convection flow in a vertical double passage channel ... PROMOTING ACCESS TO AFRICAN RESEARCH ... The perturbation method which is valid for small values of perturbation parameter is used to ...
Viscous incompressible flow simulation using penalty finite element method
Directory of Open Access Journals (Sweden)
Sharma R.L.
2012-04-01
Full Text Available Numerical analysis of Navier–Stokes equations in velocity– pressure variables with traction boundary conditions for isothermal incompressible flow is presented. Specific to this study is formulation of boundary conditions on synthetic boundary characterized by traction due to friction and surface tension. The traction and open boundary conditions have been investigated in detail. Navier-Stokes equations are discretized in time using Crank-Nicolson scheme and in space using Galerkin finite element method. Pressure being unknown and is decoupled from the computations. It is determined as post processing of the velocity field. The justification to simulate this class of flow problems is presented through benchmark tests - classical lid-driven cavity flowwidely used by numerous authors due to its simple geometry and complicated flow behavior and squeezed flow between two parallel plates amenable to analytical solution. Results are presented for very low to high Reynolds numbers and compared with the benchmark results.
Institute of Scientific and Technical Information of China (English)
孟庆杰; 万德成
2016-01-01
By solving the unsteady Reynolds averaged Navier–Stokes (RANS) equations in combination with thek-ω SST turbulence model, the unsteady viscous flow around the obliquely towed tanker KVLCC2M model in both deep and shallow waters is simulated and the hydrodynamic forces, the surface pressure distribution, and the wake field are calculated. The overset grid technology is used to avoid the grid distortion in large drift angle cases. The effects of the free surface are taken into account. At the first stage, the deep water cases with five oblique angles are designed as the benchmark test cases. The predicted wake field, the surface pressure distribution and the hydrodynamic forces acting on the hull agree well with the corresponding experimental data, implying the capability of the present method in the prediction of the viscous flow around the tanker drifting in shallow water. A set of systematic computations with varying water depths and drift angles are then carried out to study the viscous flow around the model drifting in shallow water. The forces and moments, as well as the surface pressure distribution are predicted and analyzed. The most significant changes such as the increased stagnation pressure in the bow, the acceleration of the flow along the ship’s sides and in the gap between ship and seabed, the lower hull pressure and finally, the stronger vortices along the bilges and weaker vortices with larger diameters in the wake are noticed.
Viscous boundary lubrication of hydrophobic surfaces by mucin.
Yakubov, Gleb E; McColl, James; Bongaerts, Jeroen H H; Ramsden, Jeremy J
2009-02-17
The lubricating behavior of the weakly charged short-side-chain glycoprotein mucin "Orthana" (Mw=0.55 MDa) has been investigated between hydrophobic and hydrophilic PDMS substrates using soft-contact tribometry. It was found that mucin facilitates lubrication between hydrophobic PDMS surfaces, leading to a 10-fold reduction in boundary friction coefficient for rough surfaces. The presence of mucin also results in a shift of the mixed lubrication regime to lower entrainment speeds. The observed boundary lubrication behavior of mucin was found to depend on the bulk concentration, and we linked this to the structure and dynamics of the adsorbed mucin films, which are assessed using optical waveguide light spectroscopy. We observe a composite structure of the adsorbed mucin layer, with its internal structure governed by entanglement. The film thickness of this adsorbed layer increases with concentration, while the boundary friction coefficient for rough surfaces was found to be inversely proportional to the thickness of the adsorbed film. This link between lubrication and structure of the film is consistent with a viscous boundary lubrication mechanism, i.e., a thicker adsorbed film, at a given sliding speed, results in a lower local shear rate and, hence, in a lower local shear stress. The estimated local viscosities of the adsorbed layer, derived from the friction measurements and the polymer layer density, are in agreement with each other.
Schwab, J. R.; Povinelli, L. A.
1984-01-01
A comparison of the secondary flows computed by the viscous Kreskovsky-Briley-McDonald code and the inviscid Denton code with benchmark experimental data for turning duct is presented. The viscous code is a fully parabolized space-marching Navier-Stokes solver while the inviscid code is a time-marching Euler solver. The experimental data were collected by Taylor, Whitelaw, and Yianneskis with a laser Doppler velocimeter system in a 90 deg turning duct of square cross-section. The agreement between the viscous and inviscid computations was generally very good for the streamwise primary velocity and the radial secondary velocity, except at the walls, where slip conditions were specified for the inviscid code. The agreement between both the computations and the experimental data was not as close, especially at the 60.0 deg and 77.5 deg angular positions within the duct. This disagreement was attributed to incomplete modelling of the vortex development near the suction surface.
A fast integral equation method for solid particles in viscous flow using quadrature by expansion
Klinteberg, Ludvig af
2016-01-01
Boundary integral methods are advantageous when simulating viscous flow around rigid particles, due to the reduction in number of unknowns and straightforward handling of the geometry. In this work we present a fast and accurate framework for simulating spheroids in periodic Stokes flow, which is based on the completed double layer boundary integral formulation. The framework implements a new method known as quadrature by expansion (QBX), which uses surrogate local expansions of the layer potential to evaluate it to very high accuracy both on and off the particle surfaces. This quadrature method is accelerated through a newly developed precomputation scheme. The long range interactions are computed using the spectral Ewald (SE) fast summation method, which after integration with QBX allows the resulting system to be solved in M log M time, where M is the number of particles. This framework is suitable for simulations of large particle systems, and can be used for studying e.g. porous media models.
Nearly singular surfaces: origins of small-scale cutoff in 3D viscous entrainment
Zhang, Wendy
2004-11-01
Entrainment of a low-viscosity fluid against surface tension effects by a high-viscosity fluid often results in nearly singular steady-state interface shapes. Recent studies (Eggers PRL 01; Lorenceau et al. PRL 03) reveal that, in 2D, the viscous coupling between flows in the two fluids produces a small-scale cutoff which scales as (μ_0/μ)^4/3, where μ0 is the smaller viscosity. In contrast, results of a long-wavelength model of viscous entrainment from a nozzle show that the cutoff in 3D results from a different mechanism. The resultant cutoff lengthscale depends strongly on the boundary conditions imposed on the entrained spout shape at the nozzle opening but has no leading-order dependence on μ0 / μ. This is because viscous coupling has a far weaker effect in 3D than in 2D and only produces an exponentially small cutoff. Any mismatch between the entrainment dynamics on the largest lengthscale, as imposed by nozzle boundary conditions, and the dynamics on the smallest lengthscale necessary for the formation of a steady-state singularity produces a more appreciable cutoff. The lack of dependence on the viscosity contrast has been observed in 3D entrainment experiments (Cohen & Nagel, PRL 02).
Liska, Sebastian
2016-01-01
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...
FREE-SURFACE WAVES AND FAR WAKES GENERATED BY A FLOATING BODY IN A VISCOUS FLUID
Institute of Scientific and Technical Information of China (English)
Lu Dong-qiang
2003-01-01
The free-surface waves and the flow field due to a body moving on the surface of an incompressible viscous fluid of infinite depth were studied analytically. The floating body was modeled as a normal point pressure on the free surface. Based on the Oseen approximation for governing equations and the linearity assumption for boundary conditions, the exact solutions in integral form for the free-surface elevation, the velocities and the pressure were given. By employing Lighthill's two-stage scheme, the asymptotic representations in far field for large Reynolds numbers were derived explicitly. The effect of viscosity on the wave profiles was expressed by an exponential decay factor, which removes the singular behavior predicted by the potential theory.
Limiting flows of a viscous fluid with stationary separation zones with Re approaching infinity
Taganov, G. I.
1982-01-01
The limiting flows of a viscous noncondensable fluid, which are approached by flows with stationary separation zones behind planar symmetrical bodies, with an unlimited increase in the Reynolds number are studied. Quantitative results are obtained in the case of a circulation flow inside of a separation zone.
Bubbling at high flow rates in inviscid and viscous liquids (slags)
Engh, T. Abel; Nilmani, M.
1988-02-01
The behavior of gas discharging into melts at high velocities but still in the bubbling regime has been investigated in a laboratory modeling study for constant flow conditions. Air or helium was injected through a vertical tuyere into water, zinc-chloride, and aqueous glycerol solutions. High speed cinematography and pressure measurements in the tuyere have been carried out simultaneously. Pressure fluctuations at the injection point were monitored and correlated to the mode of bubble formation. The effects of high gas flow rates and high liquid viscosities have been examined in particular. Flow rates were employed up to 10-3 m3/s and viscosity to 0.5 Ns/m2. In order to attain a high gas momentum, the tuyere diameter was only 3 x 10-3 m. The experimental conditions and modeling liquids were chosen with special reference to the established practice of submerged gas injection to treat nonferrous slags. Such slags can be highly viscous. Bubble volume is smaller than that calculated from existing models such as those given by Davidson and Schüler10,11 due to the effect of gas momentum elongating the bubbles. On the other hand, viscosity tends to retard the bubble rise velocity, thus increasing volumes. To take elongation into account, a mathematical model is presented that assumes a prolate ellipsoidal shape of the bubbles. The unsteady potential flow equations for the liquid are solved for this case. Viscous effects are taken into account by noting that flow deviates from irrotational motion only in a thin boundary layer along the surface of the bubble. Thus, drag on the bubble can be obtained by calculating the viscous energy dissipation for potential flow past an ellipse. The time-dependent inertia coefficient for the ellipsoid is found by equating the vertical pressure increase inside and outside the bubble. This pressure change in the bubble is obtained by assuming that gas enters as a homogeneous jet and then calculating the stagnation pressure at the apex of
National Research Council Canada - National Science Library
Liushuai CAO; Jun ZHU; Guanghui ZENG
2016-01-01
.... In a collaborative exercise, the authors performed calculations on the bare hull DRAPA SUBOFF submarine to investigate the capability of viscous-flow solvers to predict the forces and moments as well...
Flow dynamical behavior and performance of a micro viscous pump with unequal inlet and outlet areas
Directory of Open Access Journals (Sweden)
Chenhui Hu
2016-01-01
Full Text Available The micro viscous pump is an important type of fluidic device. Optimizing the working performance of the pump is crucial for its wider application. A micro viscous pump design with unequal inlet and outlet areas is proposed in this paper. The flow field of the viscous pump is investigated using 2D laminar simulations. The mass flow rate and driving power are studied with different opening angles. The effects of the Reynolds number and the pressure load on the working performance are discussed in detail. Flow structures and vortex evolution are analyzed. With larger inlet and outlet areas, a higher mass flow rate is obtained and less driving power is achieved. A high pressure load results in a reduction in mass flow rate and an increase in driving power. Pumps with large opening angles are more susceptive to the Reynolds number and the pressure load. The adverse impact of the pressure load can be reduced by increasing the rotor speed. The vortex structure is affected by the geometric and operating parameters in the flow field. The flow dynamical behavior of the viscous pump exerts significant influence on its pumping ability. The present work gives rise to performance improvements for the micro viscous pump.
UNSTEADY WAVES DUE TO AN IMPULSIVE OSEENLET BENEATH THE CAPILLARY SURFACE OF A VISCOUS FLUID
Institute of Scientific and Technical Information of China (English)
LU Dong-qiang; CHEN Xiao-bo
2008-01-01
The two-dimensional free-surface waves due to a point force steadily moving beneath the capillary surface of an incompressible viscous fluid of infinite depth were analytically investigated. The unsteady Oseen equations were taken as the governing equations for the viscous flows. The kinematic and dynamic conditions including the combined effects of surface tension and viscosity were linearized for small-amplitude waves on the free-surface. The point force is modeled as an impulsive Oseenlet. The complex dispersion relation for the capillary-gravity waves shows that the wave patterns are characterized by the Weber number and the Reynolds number. The asymptotic expansions for the wave profiles were explicitly derived by means of Lighthill's theorem for the Fourier transform of a function with a finite number of singularities. Furthermore, it is found that the unsteady wave system consists of four families, that is, the steady-state gravity wave, the steady-state capillary wave, the transient gravity wave, and the transient capillary wave. The effect of viscosity on the capillary-gravity was analytically expressed.
Three vortex motion in the slightly viscous flow
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The dynamics of three vortices moving in an ideal fluid in a plane can be expressed in Hamiltonian form. However, when viscosity can not be ignored, the system of point vortices has not this delicious structure. This investigation focuses on the viscosity effect on the motion of three vortices. Since the viscous diffusion of vortices is simulated by Brownian motion, the equations of intervortical distances are obtained by Ito formula. These equations show that there exist two viscosity effects on intervortical distances: stable expansion and random impulse. Furthermore, via employing the asymptotic solution to these equations, these two viscous effects have been shown to destroy the self-similar process of collapse and make it into a new configuration, which is similar to the near collapse in the ideal case.
MOTION AND DEFORMATION OF VISCOUS DROP IN STOKES FLOW NEAR RIGID WALL
Institute of Scientific and Technical Information of China (English)
LU Hua-jian; ZHANG Hui-sheng
2005-01-01
A boundary integral method was developed for simulating the motion and deformation of a viscous drop in an axisymmetric ambient Stokes flow near a rigid wall and for direct calculating the stress on the wall. Numerical experiments by the method were performed for different initial stand-off distances of the drop to the wall, viscosity ratios, combined surface tension and buoyancy parameters and ambient flow parameters. Numerical results show that due to the action of ambient flow and buoyancy the drop is compressed and stretched respectively in axial and radial directions when time goes. When the ambient flow action is weaker than that of the buoyancy the drop raises and bends upward and the stress on the wall induced by drop motion decreases when time advances. When the ambient flow action is stronger than that of the buoyancy the drop descends and becomes flatter and flatter as time goes. In this case when the initial stand-off distance is large the stress on the wall increases as the drop evolutes but when the stand-off distance is small the stress on the wall decreases as a result of combined effects of ambient flow, buoyancy and the stronger wall action to the flow. The action of the stress on the wall induced by drop motion is restricted in an area near the symmetric axis, which increases when the initial stand-off distance increases.When the initial stand-off distance increases the stress induced by drop motion decreases substantially. The surface tension effects resist the deformation and smooth the profile of the drop surfaces. The drop viscosity will reduce the deformation and migration of the drop.
Optimum viscous flow in pressure-swirl atomizers
Amini, Ghobad; Pereira, Aaron; Yun, Sangsig; Li, Xianguo
2013-11-01
Due to their simple configuration and reliable operation, pressure-swirl atomizers are widely used in applications such as combustion, painting, humidification, and sprinkling. The liquid is swirled by entering into the atomizer tangentially and its surface area is increased as discharges in a large spray angle. Understanding the effects of nozzle geometry and inlet flow condition on the discharge coefficient and spray angle is very important in nozzle design. To this end, the flow field inside a pressure-swirl atomizer has been studied theoretically. The main body of the liquid is taken to be moving in circles round the axis. Within the boundary layer, containing transverse and longitudinal velocity components, the retarded liquid is slowed down by viscosity and driven towards the exit orifice by pressure gradient. The swirling motion of liquid creates a low pressure zone near the nozzle axis and leads to the formation of a helical air-core. Through studying the growth of the boundary layer from nozzle entry to the orifice exit, the portions of the outflow exits the orifice from boundary layer current and also from the main body of the swirling liquid are specified. For a given range of pressure drop values, the optimum nozzle geometry and liquid flowrate are predicted. Additionally, the reason of increasing the flow by increasing liquid viscosity or decreasing orifice diameter is explained. A series of experiments and numerical modeling have also been carried out to support the theoretical results.
Computation of Viscous Uniform and Shear Flow over A Circular Cylinder by A Finite Element Method
Institute of Scientific and Technical Information of China (English)
赵明; 滕斌
2004-01-01
The incompressible viscous uniform and shear flow past a circular cylinder is studied. The two-dimensional NavierStokes equations are solved by a finite element method. The governing equations are discretized by a weighted residual method in space. The stable three-step scheme is applied to the momentum equations in the time integration. The numerical model is firstly applied to the computation of the lid-driven cavity flow for its validation. The computed results agree well with the measured data and other numerical results. Then, it is used to simulate the viscous uniform and shear flow over a circular cylinder for Reynolds numbers from 100 to 1000. The transient time interval before the vortex shedding occurs is shortened considerably by introduction of artificial perturbation. The computed Strouhal number, drag and lift coefficients agree well with the experimental data. The computation shows that the finite element model can be successfully applied to the viscous flow problem.
INVESTIGATION OF VISCOUS FLOW FIELD AROUND AN APPENDED REVOLUTION BODY WITH GUIDE VANE PROPELLER
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A RANS solver is presented to numerically simulate the viscous wake of an appended revolution body with guide vane propeller at the Reynolds number 107. The k-ε turbulence model together with wall function is used. The resulting finite difference equations are solved by SIMPLEC and ADI. The technique of rising up the bottom surface is presented to overcome radial contraction problem in Cartesian coordinate system. The three-dimensional body forces are separately adopted to model the affection of the guide vane and propeller. The detailed flow characteristics,especially the counter-swirl component generated by the guide vane in the propeller inflow, are numerically seized successfully. Compared with the experimental data, The computational axial velocity on the propeller disk plane comes up to engineering requirement.
Simplex finite element analysis of viscous incompressible flow with penalty function formulation
Allaire, P. E.; Rosen, M. C.; Rice, J. G.
1985-01-01
Viscous flow calculations are important for the determination of separated flows, recirculating flows, secondary flows and so on. This paper presents a penalty function approach for the finite element analysis of steady incompressible viscous flow. A simplex element is used with linear velocity and constant pressure in contrast to other works which usually employ higher order elements. Simplex elements yield analytical expressions for the element matrices which in turn lead to efficient solutions. Earlier works have partially indicated how constraint and lock-up problems might be avoided for simplex elements. This paper extends the earlier works by indicating the approach in detail and verifying that it is successful for several applications not discussed in the literature so far. Solution times and accuracy considerations are discussed for Couette flow, plane Poiseuille flow, a driven cavity problem, and laminar and turbulent flow over a step.
Viscous flow in simple curved gaps. I - An asymptotic theory. II - Viscous stress and shape function
Fan, D.-N.; Tong, W.
1989-01-01
The present asymptotic theory for generalized incompressible two-dimensional steady flow in curved channels has been constructed in the limit when gas thickness approaches zero with its lateral dimensions fixed; successive asymptotic solution terms are analytically generated by quadratures. In the second part of this work, the curvature of the gap treated is arbitrary. It is established that each term in the series solution of velocity and pressure is the product of a scale factor and a universal shape functions. Various interaction modes between the volume rate-of-flow, curvature, and its variations, are identified and quantitatively characterized.
Buckling of thin viscous sheets with inhomogenous viscosity under extensional flows
Srinivasan, Siddarth; Wei, Zhiyan; Mahadevan, L.
2016-11-01
We investigate the dynamics, shape and stability of a thin viscous sheet subjected to an extensional flow under an imposed non-uniform temperature field. Using finite element simulations, we first solve for the stretching flow to determine the pre-buckling sheet thickness and in-plane flow velocities. Next, we use this solution as the base state and solve the linearized partial differential equation governing the out-of-plane deformation of the mid-surface as a function of two dimensionless operating parameters: the normalized stretching ratio α and a dimensionless width of the heating zone β. We show the sheet can become unstable via a buckling instability driven by the development of localized compressive stresses, and determine the global shape and growth rates of the most unstable mode. The growth rate is shown to exhibit a transition from stationary to oscillatory modes in region upstream of the heating zone. Finally, we investigate the effect of surface tension and present an operating diagram that indicates regions of the parameter space that minimizes or entirely suppresses the instability while achieving desired outlet sheet thickness. Therefore, our work is directly relevant to various industrial processes including the glass redraw & float-glass method.
Nanofluidic Transport over a Curved Surface with Viscous Dissipation and Convective Mass Flux
Mehmood, Zaffar; Iqbal, Z.; Azhar, Ehtsham; Maraj, E. N.
2017-03-01
This article is a numerical investigation of boundary layer flow of nanofluid over a bended stretching surface. The study is carried out by considering convective mass flux condition. Contribution of viscous dissipation is taken into the account along with thermal radiation. Suitable similarity transformations are employed to simplify the system of nonlinear partial differential equations into a system of nonlinear ordinary differential equations. Computational results are extracted by means of a shooting method embedded with a Runge-Kutta Fehlberg technique. Key findings include that velocity is a decreasing function of curvature parameter K. Moreover, Nusselt number decreases with increase in curvature of the stretching surface while skin friction and Sherwood number enhance with increase in K.
Nanofluidic transport over a curved surface with viscous dissipation and convective mass flux
Energy Technology Data Exchange (ETDEWEB)
Mehmood, Zaffar; Iqbal, Z.; Azhar, Ehtsham; Maraj, E.N. [HITEC Univ., Taxila (Pakistan). Dept. of Mathematics
2017-06-01
This article is a numerical investigation of boundary layer flow of nanofluid over a bended stretching surface. The study is carried out by considering convective mass flux condition. Contribution of viscous dissipation is taken into the account along with thermal radiation. Suitable similarity transformations are employed to simplify the system of nonlinear partial differential equations into a system of nonlinear ordinary differential equations. Computational results are extracted by means of a shooting method embedded with a Runge-Kutta Fehlberg technique. Key findings include that velocity is a decreasing function of curvature parameter K. Moreover, Nusselt number decreases with increase in curvature of the stretching surface while skin friction and Sherwood number enhance with increase in K.
Mass Transport in a Thin Layer of Bi-Viscous Mud Under Surface Waves
Institute of Scientific and Technical Information of China (English)
NG Chiu-on; FU Sau-chung; BAI Yu-chuan(白玉川)
2002-01-01
The mass transport in a thin layer of non-Newtonian bed mud under surface waves is examined with a two-fluidStokes boundary layer model. The mud is assumed to be a bi-viscous fluid, which tends to resist motion for small-appliedstresses, but flows readily when the yield stress is exceeded. Asymptotic expansions suitable for shallow fluid layers areapplied, and the second-order solutions for the mass transport induced by surface progressive waves are obtained numeri-cally. It is found that the stronger the non-Newtonian behavior of the mud, the more pronounced intermittency of theflow. Consequently, the mass transport velocity is diminished in magnitude, and can even become negative (i. e., oppo-site to wave propagation) for a certain range of yield stress.
Indian Academy of Sciences (India)
HARI MOHAN KUSHWAHA; SANTOSH K SAHU
2016-06-01
This paper presents an analytical investigation to study the heat transfer and fluid flow characteristics in the slip flow region for hydrodynamically and thermally fully developed flow between parallel plates.Both upper and lower plates are subjected to asymmetric heat flux boundary conditions. The effect of first ordervelocity slip, temperature jump, asymmetric heat flux ratio and viscous dissipation on the heat transfer performance is analyzed. Closed form expressions are obtained for the temperature distribution and Nusselt number. Present predictions are verified for the cases that neglect the viscous heating and microscale effects. The effect of asymmetric heat flux ratio with and without viscous dissipation on Nusselt number for both macroscale and microscale is highlighted. The heat transfer characteristics are found to depend on various modeling parameters, namely, modified Brinkman number, Knudsen number and heat flux ratio
Particle support mechanism in viscous debris flows at Jiangjia Ravine, Yunnan, China
Institute of Scientific and Technical Information of China (English)
王裕宜[1; 费祥俊[2
1999-01-01
Hyperconcentrated viscous debris flows can move rapidly on low-gradient ravine under shear, because they have highly excessive pore pressure. The relationship between excessive pore-pressure （Pe） and volume concentration (Cvt) in viscous debris flows, i.e. Pe=2 494.76Cvt0.94, is quantitatively shown; the correlation coefficient γ=0.9671, 95％ confidence interval is 0.9053<ρ<0.9937. About 92.29％ of all grains （by weight） is supported by excessive pore pressure.##属性不符
Lectures on Mathematical Foundation of Turbulent Viscous Flows
Miyakawa, Tetsuro
2006-01-01
Five leading specialists reflect on different and complementary approaches to fundamental questions in the study of the Fluid Mechanics and Gas Dynamics equations. Constantin presents the Euler equations of ideal incompressible fluids and discusses the blow-up problem for the Navier-Stokes equations of viscous fluids, describing some of the major mathematical questions of turbulence theory. These questions are connected to the Caffarelli-Kohn-Nirenberg theory of singularities for the incompressible Navier-Stokes equations that is explained in Gallavotti's lectures. Kazhikhov introduces the theory of strong approximation of weak limits via the method of averaging, applied to Navier-Stokes equations. Y. Meyer focuses on several nonlinear evolution equations - in particular Navier-Stokes - and some related unexpected cancellation properties, either imposed on the initial condition, or satisfied by the solution itself, whenever it is localized in space or in time variable. Ukai presents the asymptotic analysis th...
Viscous-shock-layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium
Anderson, E. C.; Moss, J. N.
1975-01-01
The viscous-shock-layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially-symmetric flow fields. Solutions were obtained using an implicit finite-difference scheme and results are presented for hypersonic flow over spherically-blunted cone configurations at freestream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.
Viscous shock layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium
Anderson, E. C.; Moss, J. N.
1975-01-01
The viscous shock layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially symmetric flow fields. Solutions are obtained using an implicit finite difference scheme and results are presented for hypersonic flow over spherically blunted cone configurations at free stream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.
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.
Entropy Generation In The Viscous Layer Of A Turbulent Channel Flow
Energy Technology Data Exchange (ETDEWEB)
D. M. McEligot; E. J. Walsh; E. Laurien; James R. Wolf
2006-09-01
The local (pointwise) entropy generation rate per unit volume S''' is a key to improving many energy processes and applications. Entropy generation due to friction occurs from viscous dissipation of mean-flow kinetic energy (called "direct dissipation") and dissipation of turbulent kinetic energy into thermal energy ("indirect" or turbulent dissipation). The objective of the present study is to compare two approaches for the prediction of S''' for the viscous layer in near asymptotic (high Reynolds number) turbulent flows. By employing available direct numerical simulations (DNS) it was found that about two-thirds of the entropy generation occurs in this layer. A popular approximate approach does not agree with the result from the more exact evaluation of S''' but its integral falls within about four per cent at the edge of the viscous layer.
An adaptive semi-implicit scheme for simulations of unsteady viscous compressible flows
Steinthorsson, Erlendur; Modiano, David; Crutchfield, William Y.; Bell, John B.; Colella, Phillip
1995-11-01
A numerical scheme for simulation of unsteady, viscous, compressible flows is considered. The scheme employs an explicit discretization of the inviscid terms of the Navier-Stokes equations and an implicit discretization of the viscous terms. The discretization is second order accurate in both space and time. Under appropriate assumptions, the implicit system of equations can be decoupled into two linear systems of reduced rank. These are solved efficiently using a Gauss-Seidel method with multigrid convergence acceleration. When coupled with a solution-adaptive mesh refinement technique, the hybrid explicit-implicit scheme provides an effective methodology for accurate simulations of unsteady viscous flows. The methodology is demonstrated for both body-fitted structured grids and for rectangular (Cartesian) grids.
Directory of Open Access Journals (Sweden)
S. Srinivas
2016-01-01
Full Text Available The present work investigates the effects of thermal-diffusion and diffusion-thermo on MHD flow of viscous fluid between expanding or contracting rotating porous disks with viscous dissipation. The partial differential equations governing the flow problem under consideration have been transformed by a similarity transformation into a system of coupled nonlinear ordinary differential equations. An analytical approach, namely the homotopy analysis method is employed in order to obtain the solutions of the ordinary differential equations. The effects of various emerging parameters on flow variables have been discussed numerically and explained graphically. Comparison of the HAM solutions with the numerical solutions is performed.
Jamaludin, Anuar; Nazar, Roslinda; Shafie, Sharidan
2017-08-01
This study presents the numerical solutions of boundary layer flow and heat transfer over a stretching sheet with viscous dissipation and internal heat generation. Thermal boundary condition on the surface, namely prescribed heat flux (PHF) is used. The governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations by applying the similarity transformations before reduced to the system of first order ordinary differential equations. Then the system of first order ordinary differential equations is solved numerically using an implicit finite difference scheme, known as the Keller-box method. The numerical solutions are generated using MATLAB. Temperature profiles and the temperature gradient for some values of the Prandtl number, Eckert number and heat/source sink parameter are presented in figures and discussed in details.
Bounds on the Phase Velocity in the Linear Instability of Viscous Shear Flow Problem in the -Plane
Indian Academy of Sciences (India)
R G Shandil; Jagjit Singh
2003-05-01
Results obtained by Joseph (J. Fluid Mech. 33 (1968) 617) for the viscous parallel shear flow problem are extended to the problem of viscous parallel, shear flow problem in the beta plane and a sufficient condition for stability has also been derived.
Linear stability of the Couette flow of a vibrationally excited gas. 2. viscous problem
Grigor'ev, Yu. N.; Ershov, I. V.
2016-03-01
Based on the linear theory, stability of viscous disturbances in a supersonic plane Couette flow of a vibrationally excited gas described by a system of linearized equations of two-temperature gas dynamics including shear and bulk viscosity is studied. It is demonstrated that two sets are identified in the spectrum of the problem of stability of plane waves, similar to the case of a perfect gas. One set consists of viscous acoustic modes, which asymptotically converge to even and odd inviscid acoustic modes at high Reynolds numbers. The eigenvalues from the other set have no asymptotic relationship with the inviscid problem and are characterized by large damping decrements. Two most unstable viscous acoustic modes (I and II) are identified; the limits of these modes were considered previously in the inviscid approximation. It is shown that there are domains in the space of parameters for both modes, where the presence of viscosity induces appreciable destabilization of the flow. Moreover, the growth rates of disturbances are appreciably greater than the corresponding values for the inviscid flow, while thermal excitation in the entire considered range of parameters increases the stability of the viscous flow. For a vibrationally excited gas, the critical Reynolds number as a function of the thermal nonequilibrium degree is found to be greater by 12% than for a perfect gas.
Streng, Martin; Streng, M.; ten Cate, Eric; ten Cate, Eric (H.H.); Geurts, Bernardus J.; Kuerten, Johannes G.M.
1998-01-01
We consider several aspects of efficient numerical simulation of viscous compressible flow on both homogeneous and heterogeneous workstation-clusters. We consider dedicated systems, as well as clusters operating in a multi-user environment. For dedicated homogeneous clusters, we show that with
Two Experiments to Approach the Boltzmann Factor: Chemical Reaction and Viscous Flow
Fazio, Claudio; Battaglia, Onofrio R.; Guastella, Ivan
2012-01-01
In this paper we discuss a pedagogical approach aimed at pointing out the role played by the Boltzmann factor in describing phenomena usually perceived as regulated by different mechanisms of functioning. Experimental results regarding some aspects of a chemical reaction and of the viscous flow of some liquids are analysed and described in terms…
Institute of Scientific and Technical Information of China (English)
DONG BoQing; JIANG Wei
2008-01-01
This article concerns large time behavior of Ladyzhenskaya model for incompressible viscous flows in R3. Based on linear Lp-Lq estimates, the auxiliary decay properties of the solutions and generalized Gronwall type arguments, some optimal upper and lower bounds for the decay of higher order derivatives of solutions are derived without assuming any decay properties of solutions and using Fourier splitting technology.
Two Experiments to Approach the Boltzmann Factor: Chemical Reaction and Viscous Flow
Fazio, Claudio; Battaglia, Onofrio R.; Guastella, Ivan
2012-01-01
In this paper we discuss a pedagogical approach aimed at pointing out the role played by the Boltzmann factor in describing phenomena usually perceived as regulated by different mechanisms of functioning. Experimental results regarding some aspects of a chemical reaction and of the viscous flow of some liquids are analysed and described in terms…
Olson, L. E.; Dvorak, F. A.
1976-01-01
The viscous subsonic flow past two-dimensional and infinite-span swept multi-component airfoils is studied theoretically and experimentally. The computerized analysis is based on iteratively coupled boundary-layer and potential-flow analysis. The method, which is restricted to flows with only slight separation, gives surface pressure distribution, chordwise and spanwise boundary-layer characteristics, lift, drag, and pitching moment for airfoil configurations with up to four elements. Merging confluent boundary layers are treated. Theoretical predictions are compared with an exact theoretical potential flow solution and with experimental measures made in the Ames 40- by 80-Foot Wind Tunnel for both two-dimensional and infinite-span swept wing configurations. Section lift characteristics are accurately predicted for zero and moderate sweep angles where flow separation effects are negligible.
Olson, L. E.; Dvorak, F. A.
1975-01-01
The viscous subsonic flow past two-dimensional and infinite-span swept multi-component airfoils is studied theoretically and experimentally. The computerized analysis is based on iteratively coupled boundary layer and potential flow analysis. The method, which is restricted to flows with only slight separation, gives surface pressure distribution, chordwise and spanwise boundary layer characteristics, lift, drag, and pitching moment for airfoil configurations with up to four elements. Merging confluent boundary layers are treated. Theoretical predictions are compared with an exact theoretical potential flow solution and with experimental measures made in the Ames 40- by 80-Foot Wind Tunnel for both two-dimensional and infinite-span swept wing configurations. Section lift characteristics are accurately predicted for zero and moderate sweep angles where flow separation effects are negligible.
Surface deformations and wave generation by wind blowing over a viscous liquid
Paquier, A.; Moisy, F.; Rabaud, M.
2015-12-01
We investigate experimentally the early stage of the generation of waves by a turbulent wind at the surface of a viscous liquid. The spatio-temporal structure of the surface deformation is analyzed by the optical method Free Surface Synthetic Schlieren, which allows for time-resolved measurements with a micrometric accuracy. Because of the high viscosity of the liquid, the flow induced by the turbulent wind in the liquid remains laminar, with weak surface drift velocity. Two regimes of deformation of the liquid-air interface are identified. In the first regime, at low wind speed, the surface is dominated by rapidly propagating disorganized wrinkles, elongated in the streamwise direction, which correspond to the surface response to the pressure fluctuations advected by the turbulent airflow. The amplitude of these deformations increases approximately linearly with wind velocity and are essentially independent of the fetch (distance along the channel). Above a threshold in wind speed, we observe the growth of well defined gravity-capillary waves with crests nearly perpendicular to the wind direction. In this second regime, the wave amplitude increases with wind speed but far more quickly than in the first regime.
Directory of Open Access Journals (Sweden)
Mukesh Kumar Awasthi
2013-01-01
Full Text Available The instability of a thin sheet of viscous and dielectric liquid moving in the same direction as an air stream in the presence of a uniform horizontal electric field has been carried out using viscous potential flow theory. It is observed that aerodynamic-enhanced instability occurs if the Weber number is much less than a critical value related to the ratio of the air and liquid stream velocities, viscosity ratio of two fluids, the electric field, and the dielectric constant values. Liquid viscosity has stabilizing effect in the stability analysis, while air viscosity has destabilizing effect.
Deformation of a flexible fiber in a viscous flow past an obstacle
Lopez, H M; Auradou, H; D'Angelo, M V
2015-01-01
We study the deformation and transport of elastic fibers in a viscous Hele-Shaw flow with curved streamlines. The variations of the global velocity and orientation of the fiber follow closely those of the local flow velocity. The ratios of the curvatures of the fibers by the corresponding curvatures of the streamlines reflect a balance between elastic and viscous forces: this ratio is shown experimentally to be determined by a dimensionless {\\it Sperm number} $Sp$ combining the characteristic parameters of the flow (transverse velocity gradient, viscosity, fiber diameter/cell gap ratio) and those of the fiber (diameter, effective length, Young's modulus). For short fibers, the effective length is that of the fiber; for long ones, it is equal to the transverse characteristic length of the flow. For $S\\_p \\lesssim 250$, the ratio of the curvatures increases linearly with $Sp$; For $S\\_p \\gtrsim 250$, the fiber reaches the same curvature as the streamlines.
The semi-discrete Galerkin finite element modelling of compressible viscous flow past an airfoil
Meade, Andrew J., Jr.
1992-01-01
A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid which provides high resolution near the wall and automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes, through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past NACA 0012 and RAE 2822 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack. All results show good agreement with experiment, and the coupled code proved to be a computationally-efficient and accurate airfoil analysis tool.
Inkjet Printing of Viscous Monodisperse Microdroplets by Laser-Induced Flow Focusing
Delrot, Paul; Modestino, Miguel A.; Gallaire, François; Psaltis, Demetri; Moser, Christophe
2016-08-01
The on-demand generation of viscous microdroplets to print functional or biological materials remains challenging using conventional inkjet-printing methods, mainly due to aggregation and clogging issues. In an effort to overcome these limitations, we implement a jetting method to print viscous microdroplets by laser-induced shockwaves. We experimentally investigate the dependence of the jetting regimes and the droplet size on the laser-pulse energy and on the inks' physical properties. The range of printable liquids with our device is significantly extended compared to conventional inkjet printers's performances. In addition, the laser-induced flow-focusing phenomenon allows us to controllably generate viscous microdroplets up to 210 mPa s with a diameter smaller than the nozzle from which they originated (200 μ m ). Inks containing proteins are printed without altering their functional properties, thus demonstrating that this jetting technique is potentially suitable for bioprinting.
Simulations of Viscous Accretion Flow around Black Holes in Two-Dimensional Cylindrical Geometry
Lee, Seong-Jae; Kumar, Rajiv; Hyung, Siek; Ryu, Dongsu
2016-01-01
We simulate shock-free and shocked viscous accretion flow onto a black hole in a two dimensional cylindrical geometry, where initial conditions were chosen from analytical solutions. The simulation code used the Lagrangian Total Variation Diminishing (LTVD) and remap routine, which enabled us to attain high accuracy in capturing shocks and to handle the angular momentum distribution correctly. Inviscid shock-free accretion disk solution produced a thick disk structure, while the viscous shock-free solution attained a Bondi-like structure, but in either case, no jet activity nor any QPO-like activity developed. The steady state shocked solution in the inviscid, as well as, in the viscous regime, matched theoretical predictions well. However, increasing viscosity renders the accretion shock unstable. Large amplitude shock oscillation is accompanied by intermittent, transient inner multiple shocks. Such oscillation of the inner part of disk is interpreted as the source of QPO in hard X-rays observed in micro-qua...
The discontinuous Galerkin method for the numerical simulation of compressible viscous flow
Directory of Open Access Journals (Sweden)
Česenek Jan
2014-03-01
Full Text Available In this paper we deal with numerical simulation of the compressible viscous flow. The mathematical model of flow is represented by the system of non-stationary compressible Navier-Stokes equations. This system of equations is discretized by the discontinuous Galerkin finite element method in space and in time using piecewise polynomial discontinuous approximations. We present some numerical experiments to demonstrate the applicability of the method using own-developed code.
Pressure development due to viscous fluid flow through a converging gap
Imhamed, Ahmed
2004-01-01
The behaviour of fluid flow in industrial processes is essential for numerous applications and there have been vast amount of work on the hydrodynamic pressure generated due to the flow of viscous fluid. One major manifestation of hydrodynamic pressure application is the wire coating/drawing process, where the wire is pulled through a unit either conical or cylindrical bore filled with a polymer melt that gives rise to the hydrodynamic pressure inside the unit. The hydrodynamic pressure distr...
Viscous effect at an orthotropic micropolar boundary surface
Indian Academy of Sciences (India)
Rajneesh Kumar; Praveen Ailawalia
2005-08-01
Steady state responses at viscous ﬂuid/ orthotropic micropolar solid interfaces to moving point loads have been studied. An eigenvalue approach using the Fourier transform has been employed to solve the problem. The displacement, microrotation and stress components for the orthotropic micropolar solids so obtained in the physical domain are computed numerically by applying numerical inversion technique. Viscosity and anisotropy effects on normal displacement, normal force stress and tangential couple stress have been shown graphically for a particular model. Some special cases of interest have been presented.
Renaud, Earl W.; Tan, Choon S.
1991-01-01
The three dimensional viscous flow through a planar turbine cascade is numerically simulated by direct solution of the incompressible Navier-Stokes equations. Flow dependence in the spanwise direction is represented by direct expansion in Chebyshev polynomials, while the discretization on planes parallel to the endwalls is accomplished using the spectral element method. Elemental mapping from the physical to the computational space uses an algebraic mapping technique. A fractional time stepping method that consists of an explicit nonlinear convective step, an implicit pressure correction step, and an implicit viscous step is used to advance the Navier-Stokes equations forward in time. Results computed at moderate Reynolds numbers show a three dimensional endwall flow separation, a midspan separation of the blade suction surface boundary layer, and other three-dimensional features such as the presence of a saddle point flow in the endwall region. In addition, the computed skin friction lines are shown to be orthogonal to the surface vorticity lines, demonstrating the accuracy achievable in the present method.
Collective dynamics of particles from viscous to turbulent flows
2017-01-01
The book surveys the state-of-the-art methods that are currently available to model and simulate the presence of rigid particles in a fluid flow. For particles that are very small relative to the characteristic flow scales and move without interaction with other particles, effective equations of motion for particle tracking are formulated and applied (e.g. in gas-solid flows). For larger particles, for particles in liquid-solid flows and for particles that interact with each other or possibly modify the overall flow detailed model are presented. Special attention is given to the description of the approximate force coupling method (FCM) as a more general treatment for small particles, and derivations in the context of low Reynolds numbers for the particle motion as well as application at finite Reynolds numbers are provided. Other topics discussed in the book are the relation to higher resolution immersed boundary methods, possible extensions to non-spherical particles and examples of applications of such met...
Improved numerical methods for turbulent viscous recirculating flows
Turan, A.; Vandoormaal, J. P.
1988-01-01
The performance of discrete methods for the prediction of fluid flows can be enhanced by improving the convergence rate of solvers and by increasing the accuracy of the discrete representation of the equations of motion. This report evaluates the gains in solver performance that are available when various acceleration methods are applied. Various discretizations are also examined and two are recommended because of their accuracy and robustness. Insertion of the improved discretization and solver accelerator into a TEACH mode, that has been widely applied to combustor flows, illustrates the substantial gains to be achieved.
Flow Induced Coalescence of Drops in a Viscous Liquid
Leal, L. Gary
2002-11-01
The problem of flow-induced coalescence has been the subject of many experimental and theoretical studies. In recent years, this work has been motivated by the role that this process plays in the formation of polymer blends, which is currently the major route to new polymeric materials with desired macroscopic properties. In order to control this process, we need to understand the conditions for coalescence and their dependence on fluid and flow properties, including the effects of surfactants (known as "compatibilizers" in the polymer blend literature). With a few exceptions, experimental studies have been based upon measurements of the mean drop size (or size distribution) in an emulsion or blend following flow in either blending devices or simple rheometry flows. The four-roll mill, on the other hand, provides an opportunity to study the coalescence process at the scale of individual drops. When such experiments are carried out, we find some surprises vis a vis expectations from simple models of the drop collision/film drainage and rupture process that leads to coalescence. In this talk, we review recent experimental work in this field, and discuss the relationship to present theory
Moortgat, J.; Amooie, M. A.; Soltanian, M. R.
2016-12-01
Problems in hydrogeology and hydrocarbon reservoirs generally involve the transport of solutes in a single solvent phase (e.g., contaminants or dissolved injection gas), or the flow of multiple phases that may or may not exchange mass (e.g., brine, NAPL, oil, gas). Often, flow is viscously and gravitationally unstable due to mobility and density contrasts within a phase or between phases. Such instabilities have been studied in detail for single-phase incompressible fluids and for two-phase immiscible flow, but to a lesser extent for multiphase multicomponent compressible flow. The latter is the subject of this presentation. Robust phase stability analyses and phase split calculations, based on equations of state, determine the mass exchange between phases and the resulting phase behavior, i.e., phase densities, viscosities, and volumes. Higher-order finite element methods and fine grids are used to capture the small-scale onset of flow instabilities. A full matrix of composition dependent coefficients is considered for each Fickian diffusive phase flux. Formation heterogeneity can have a profound impact and is represented by realistic geostatistical models. Qualitatively, fingering in multiphase compositional flow is different from single-phase problems because 1) phase mobilities depend on rock wettability through relative permeabilities, and 2) the initial density and viscosity ratios between phases may change due to species transfer. To quantify mixing rates in different flow regimes and for varying degrees of miscibility and medium heterogeneities, we define the spatial variance, scalar dissipation rate, dilution index, skewness, and kurtosis of the molar density of introduced species. Molar densities, unlike compositions, include compressibility effects. The temporal evolution of these measures shows that, while transport at the small-scale (cm) is described by the classical advection-diffusion-dispersion relations, scaling at the macro-scale (> 10 m) shows
Slip Magnetohydrodynamic Viscous Flow over a Permeable Shrinking Sheet
Institute of Scientific and Technical Information of China (English)
FANG Tie-Gang; ZHANG Ji; YAO Shan-shan
2010-01-01
@@ The magnetohydrodynamic(MHD)flow under slip conditions over a shrinMng sheet js solved analytically.The solution is given in a closed form equation and is an exact solution of the full governing Navier-Stokes equations.Interesting solution behavior is observed with muiriple solution branches for certain parameter domain.The effects of the mass transfer,slip,andmagnetic parameters are discussed.
On a finite-difference method for solving transient viscous flow problems
Li, C. P.
1983-01-01
A method has been developed to solve the unsteady, compressible Navier-Stokes equation with the property of consistency and the ability of minimizing the equation stiffness. It relies on innovative extensions of the state-of-the-art finite-difference techniques and is composed of: (1) the upwind scheme for split-flux and the central scheme for conventional flux terms in the inviscid and viscous regions, respectively; (2) the characteristic treatment of both inviscid and viscous boundaries; (3) an ADI procedure compatible with interior and boundary points; and (4) a scalar matrix coefficient including viscous terms. The performance of this method is assessed with four sample problems; namely, a standing shock in the Laval duct, a shock reflected from the wall, the shock-induced boundary-layer separation, and a transient internal nozzle flow. The results from the present method, an existing hybrid block method, and a well-known two-step explicit method are compared and discussed. It is concluded that this method has an optimal trade-off between the solution accuracy and computational economy, and other desirable properties for analyzing transient viscous flow problems.
Finite-amplitude steady waves in plane viscous shear flows
Milinazzo, F. A.; Saffman, P. G.
1985-01-01
Computations of two-dimensional solutions of the Navier-Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.
Finite-volume WENO scheme for viscous compressible multicomponent flows
Coralic, Vedran; Colonius, Tim
2014-01-01
We develop a shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible Navier-Stokes equations. The numerical method is high-order accurate in smooth regions of the flow, discretely conserves the mass of each component, as well as the total momentum and energy, and is oscillation-free, i.e. it does not introduce spurious oscillations at the locations of shockwaves and/or material interfaces. The method is of Godunov-type and utilizes a fifth-order, finite-volume, weighted essentially non-oscillatory (WENO) scheme for the spatial reconstruction and a Harten-Lax-van Leer contact (HLLC) approximate Riemann solver to upwind the fluxes. A third-order total variation diminishing (TVD) Runge-Kutta (RK) algorithm is employed to march the solution in time. The derivation is generalized to three dimensions and nonuniform Cartesian grids. A two-point, fourth-order, Gaussian quadrature rule is utilized to build the spatial averages of the reconstructed variables inside the cells, as well as at cell boundaries. The algorithm is therefore fourth-order accurate in space and third-order accurate in time in smooth regions of the flow. We corroborate the properties of our numerical method by considering several challenging one-, two- and three-dimensional test cases, the most complex of which is the asymmetric collapse of an air bubble submerged in a cylindrical water cavity that is embedded in 10% gelatin. PMID:25110358
Institute of Scientific and Technical Information of China (English)
Hongde Qin; Jing Shen; Xiaobo Chen
2011-01-01
The free-surface Green function method is widely used in solving the radiation or diffraction problems caused by a ship or ocean structure oscillating on the waves.In the context of inviscid potential flow,hydrodynamic problems such as multi-body interaction and tank side wall effect cannot be properly dealt with based on the traditional free-surface frequency domain Green function method,in which the water viscosity is omitted and the energy dissipation effect is absent.In this paper,an open-sea Green function with viscous dissipation was presented within the theory of visco-potential flow.Then the tank Green function with a partial reflection from the side walls in wave tanks was formulated as a formal sum of open-sea Green functions representing the infinite images between two parallel side walls of the source in the tank.The new far-field characteristics of the tank Green function is vitally important for improving the validity of side-wall effects evaluation,which can be used in supervising the tank model tests.
Qin, Hongde; Shen, Jing; Chen, Xiaobo
2011-09-01
The free-surface Green function method is widely used in solving the radiation or diffraction problems caused by a ship or ocean structure oscillating on the waves. In the context of inviscid potential flow, hydrodynamic problems such as multi-body interaction and tank side wall effect cannot be properly dealt with based on the traditional free-surface frequency domain Green function method, in which the water viscosity is omitted and the energy dissipation effect is absent. In this paper, an open-sea Green function with viscous dissipation was presented within the theory of visco-potential flow. Then the tank Green function with a partial reflection from the side walls in wave tanks was formulated as a formal sum of open-sea Green functions representing the infinite images between two parallel side walls of the source in the tank. The new far-field characteristics of the tank Green function is vitally important for improving the validity of side-wall effects evaluation, which can be used in supervising the tank model tests.
Goal-oriented model adaptivity for viscous incompressible flows
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.
Pipe Poiseuille flow of viscously anisotropic, partially molten rock
Allwright, Jane
2014-01-01
Laboratory experiments in which synthetic, partially molten rock is subjected to forced deformation provide a context for testing hypotheses about the dynamics and rheology of the mantle. Here our hypothesis is that the aggregate viscosity of partially molten mantle is anisotropic, and that this anisotropy arises from deviatoric stresses in the rock matrix. We formulate a model of pipe Poiseuille flow based on theory by Takei and Holtzman [2009a] and Takei and Katz [2013]. Pipe Poiseuille is a configuration that is accessible to laboratory experimentation but for which there are no published results. We analyse the model system through linearised analysis and numerical simulations. This analysis predicts two modes of melt segregation: migration of melt from the centre of the pipe toward the wall and localisation of melt into high-porosity bands that emerge near the wall, at a low angle to the shear plane. We compare our results to those of Takei and Katz [2013] for plane Poiseuille flow; we also describe a ne...
Circulation-preserving plane flows of incompressible viscous fluids
Yin, W.-L.
1983-06-01
The present investigation is concerned with a systematic use of the method of complex variables in a study of (generally unsteady) plane solutions of the Navier-Stokes equation. Circulation-preserving flows are considered in the investigation. However, the employed method can also be applied to more general cases. A circulation-preserving plane solution of the Navier-Stokes equation possesses a biharmonic stream function. The stream function may, therefore, be expressed in terms of two complex analytic functions, taking into account Goursat's representation. Attention is given to differential equations in the complex form, the case of steady vorticity, the case of unsteady vorticity with a spatially constant vorticity gradient, solutions with logarithmic vorticity fields, and a proof of completeness.
Gpu Implementation of a Viscous Flow Solver on Unstructured Grids
Xu, Tianhao; Chen, Long
2016-06-01
Graphics processing units have gained popularities in scientific computing over past several years due to their outstanding parallel computing capability. Computational fluid dynamics applications involve large amounts of calculations, therefore a latest GPU card is preferable of which the peak computing performance and memory bandwidth are much better than a contemporary high-end CPU. We herein focus on the detailed implementation of our GPU targeting Reynolds-averaged Navier-Stokes equations solver based on finite-volume method. The solver employs a vertex-centered scheme on unstructured grids for the sake of being capable of handling complex topologies. Multiple optimizations are carried out to improve the memory accessing performance and kernel utilization. Both steady and unsteady flow simulation cases are carried out using explicit Runge-Kutta scheme. The solver with GPU acceleration in this paper is demonstrated to have competitive advantages over the CPU targeting one.
Viscous flow lobes in central Taylor Valley, Antarctica: Origin as remnant buried glacial ice
Swanger, Kate M.; Marchant, David R.; Kowalewski, Douglas E.; Head, James W., III
2010-08-01
Viscous flow lobes are common throughout the McMurdo Dry Valleys (MDV) of Antarctica. These features have been described as rock glaciers, gelifluction lobes, solifluction lobes, talus mobilized by pore ice and/or segregation ice, and debris-covered glaciers. We investigate the origin, modification, and flow of a 2-km-long lobe (East Stocking Lobe or ESL) along the north wall of central Taylor Valley using field mapping techniques, shallow seismic surveys, time-dependent displacement surveys, and isotopic analyses of buried-ice samples. On the basis of these integrated analyses, we show that the ESL is cored with remnant glacier ice, most probably derived from an advance of nearby Stocking Glacier ˜ 130 kyr BP. Seismic data, coupled with results from ice-flow modeling assuming plastic flow of clean ice, suggest that the buried core of glacier ice is ˜ 14- to 30-m thick. Near its terminus, the ESL flows at a rate of ˜ 2.4 to 6.7 mm a - 1 . The loose drift that caps the buried ice (typically analyses of samples from the upper 30 cm of the ice lie on a slope of ˜ 5.8 (when plotted on a δD vs. δ18O graph), well below the local meteoric water line of 7.75, suggesting modification by freeze/thaw processes and evaporation/sublimation. Measured air and soil temperatures show that intermittent melting is most likely possible during summer months where buried ice is ≤ 35 cm below the ground surface. Morphological comparisons with ice-cored deposits in upland regions of the Dry Valleys, e.g., Mullins and Beacon Valleys (30 km inland and ˜ 500 m higher in elevation), and near the coast (40 km distant and ˜ 500 m lower) reveal marked contrasts in the style of near-surface ice degradation and cryoturbation. From these morphological comparisons, we infer that buried-ice deposits in the stable upland zone have not experienced the relatively warm climate conditions now found at the ESL and at lower elevations in the Dry Valleys region (e.g. sustained summertime
Topology Method for Analyses of 3—D Viscous Flow Structure in Transonic Turbomachinery
Institute of Scientific and Technical Information of China (English)
YanhuGuo; BaoguoWang; 等
1997-01-01
A topology method is presented in this paper to reveal flow tructure occurring insie turbomachinery,in which near wall flow structure is revealed by using wall limiting streamilines and space flow feature is revealed by using space streamilines and cross-section streamlines,As an example ,a computational three-dimensional viscous flow field inside a transonic turbine cascade is studied.Through the analysis,the form and evolution of vortex system and the whole process of separation occurring within this cascade are revealed.The application of topology method for analyze flow structure inside turbomachinmery is very important for understanding flow features and mechanism of flow loss even for improving the design of turbomachinery and increasing its efficiency.
Physical hydrodynamic propulsion model study on creeping viscous flow through a ciliated porous tube
Indian Academy of Sciences (India)
NOREEN SHER AKBAR; ADIL WAHID BUTT; DHARMENDRA TRIPATHI; O ANWAR BÉG
2017-03-01
The present investigation focusses on a mathematical study of creeping viscous flow induced by metachronal wave propagation in a horizontal ciliated tube containing porous media. Creeping flow limitations are imposed, i.e. inertial forces are small compared to viscous forces and therefore a very low Reynolds number (Re $\\ll$ 1) is taken into account. The wavelength of metachronal wave is also considered to be very large for cilia movement. The physical problem is linearized and exact solutions are developed for the differential equation problem. Mathematica software is used to compute and illustrate numerical results. The influence of slip parameter and Darcy number on velocity profile, pressure gradient and trapping of bolus are discussed with the aid of graphs. It is found that with increasing magnitude of the slip parameter, the trapped bolus inside the streamlines increases in size. The study is relevant to biological propulsion of medical micromachines in drug delivery.
Flow of the Viscous-Elastic Liquid in the Non- Homogeneous Tube
Babanly, V Yu
2009-01-01
A problem on propagation of waves in deformable shells with flowing liquid is very urgent in connection with wide use of liquid transportation systems in living organisms and technology. It is necessary to consider shell motion equations for influence of moving liquid in cavity on the dynamics of a shell by solving such kind problems. Nowadays a totality of such problems is a widely developed field of hydrodynamics. However, a number of peculiarities connected with taking into account viscous-elastic properties of the liquid and inhomogeneity of the shell material generates considerable mathematical difficulties connected with integration of boundary value problems with variable coefficients. In the paper we consider wave flow of the liquid enclosed in deformable tube. The used mathematical model is described by the equation of motion of incompressible viscous elastic liquid combined with equation of continuity and dynamics equation for a tube inhomogeneous in length. It is accepted that the tube is cylindric...
Physical hydrodynamic propulsion model study on creeping viscous flow through a ciliated porous tube
Akbar, Noreen Sher; Butt, Adil Wahid; Tripathi, Dharmendra; Bég, O. Anwar
2017-03-01
The present investigation focusses on a mathematical study of creeping viscous flow induced by metachronal wave propagation in a horizontal ciliated tube containing porous media. Creeping flow limitations are imposed, i.e. inertial forces are small compared to viscous forces and therefore a very low Reynolds number (Re ≪ 1) is taken into account. The wavelength of metachronal wave is also considered to be very large for cilia movement. The physical problem is linearized and exact solutions are developed for the differential equation problem. Mathematica software is used to compute and illustrate numerical results. The influence of slip parameter and Darcy number on velocity profile, pressure gradient and trapping of bolus are discussed with the aid of graphs. It is found that with increasing magnitude of the slip parameter, the trapped bolus inside the streamlines increases in size. The study is relevant to biological propulsion of medical micromachines in drug delivery.
Peace, Andrew J.; May, Nicholas E.; Pocock, Mark F.; Shaw, Jonathon A.
1994-04-01
This paper is concerned with the flow modelling capabilities of an advanced CFD simulation system known by the acronym SAUNA. This system is aimed primarily at complex aircraft configurations and possesses a unique grid generation strategy in its use of block-structured, unstructured or hybrid grids, depending on the geometric complexity of the addressed configuration. The main focus of the paper is in demonstrating the recently developed multi-grid, block-structured grid, viscous flow capability of SAUNA, through its evaluation on a number of configurations. Inviscid predictions are also presented, both as a means of interpreting the viscous results and with a view to showing more completely the capabilities of SAUNA. It is shown that accuracy and flexibility are combined in an efficient manner, thus demonstrating the value of SAUNA in aerodynamic design.
The design/analysis of flows through turbomachinery: A viscous/inviscid approach
Miller, D. P.; Reddy, D. R.
1991-01-01
The development of a design/analysis flow solver at NASA Lewis Research Center is discussed. The solver is axisymmetric and can be run inviscidly with assumed or calculated blockages, or with the viscous terms computed. The blade forces for each blade row are computed from blade-to-blade solutions, correlated data or force model, or from a full three dimensional solution. Codes currently under development can be separated into three distinct elements: the turbomachinery interactive grid generator energy distribution restart code (TIGGERC), the interactive blade element geometry generator (IBEGG), and the viscous/inviscid multi-blade-row average passage flow solver (VIADAC). Several experimental test cases were run to validate the VIADAC code. The tests, representative of typical axial turbomachinery duct axisymmetric wind tunnel body problems, were conducted on an SR7 Spinner axisymmetric body, a NASA Rotor 67 Fan test bed, and a transonic boatail body. The results show the computations to be in good agreement with test data.
Cavitation structures formed during the collision of a sphere with an ultra-viscous wetted surface
Mansoor, Mohammad M.
2016-05-05
We investigate the inception of cavitation and resulting structures when a sphere collides with a solid surface covered with a layer of non-Newtonian liquid having a kinematic viscosity of up to (Formula presented.) cSt. We show the existence of shear-stress-induced cavitation during sphere approach towards the base wall (i.e. the pressurization stage) in ultra-viscous films using a synchronized dual-view high-speed imaging system. For the experimental parameters employed, liquids having viscoelastic properties of (Formula presented.) are shown to enable sphere rebound without any prior contact with the solid wall. Cavitation by depressurization (i.e. during rebound) in such non-contact cases is observed to onset after a noticeable delay from when the minimum gap distance is reached. Also, the cavities created originate from remnant bubbles, being the remains of the primary bubble entrapment formed by the lubrication pressure of the air during film entry. Cases where physical contact occurs (contact cases) in 10 000 cSt (Formula presented.) cSt films produce cavities attached to the base wall, which extend into an hourglass shape. In contrast, strikingly different structures occur in the most viscous liquids due to the disproportionality in radial expansion and longitudinal extension along the cavity length. Horizontal shear rates calculated using particle image velocimetry (PIV) measurements show the apparent fluid viscosity to vary substantially as the sphere approaches and rebounds away from the base wall. A theoretical model based on the lubrication assumption is solved for the squeeze flow in the regime identified for shear-induced cavity events, to investigate the criterion for cavity inception in further detail. © 2016 Cambridge University Press
Sevick, E M; Jain, R K
1991-05-15
Elevated glucose level and low pH have been shown to increase red blood cell (RBC) rigidity. This increased rigidity has been proposed as one factor which mediates the tumor blood flow (TBF) reduction during hyperglycemia by (a) causing RBC entrapment and hence increasing geometric resistance and (b) increasing viscous resistance to blood flow. However, due to the inability to measure these resistances in vivo in tumors directly, the relative contribution of RBC rigidity in TBF reduction has not been quantified. In the present study, blood flow resistance was measured in "tissue-isolated" mammary adenocarcinoma R3230AC perfused ex vivo with (a) normally deformable, (b) glutaraldehyde-hardened, and (c) glucose-incubated RBC suspensions. Flow resistance measured during tumor perfusion with Krebs-Henseleit buffer prior to and following perfusion with the glutaraldehyde-hardened RBC suspensions showed no significant change, suggesting constant geometric resistance and lack of RBC entrapment. Instead, our measurements indicated increased viscous resistance with loss of deformability due to glutaraldehyde and glucose incubation even though glucose incubation did not significantly alter the apparent blood viscosity measured in vitro. Thus, the TBF reduction during hyperglycemia may be due to subtle changes in RBC deformability. These results suggest the development of strategies to increase the delivery of drugs or oxygen must take into account any changes in intratumor viscous resistance. For example, the increase in the oxygen-carrying capacity of blood using RBC transfusion or fluorocarbon emulsions may be offset by the increase in viscous resistance and the corresponding reduction in TBF.
Velocity-vorticity formulation of three-dimensional, steady, viscous, incompressible flows
Energy Technology Data Exchange (ETDEWEB)
Meir, A.J. [Auburn Univ., AL (United States)
1994-12-31
In this work we discuss some aspects of the velocity-vorticity formulation of three-dimensional, steady, viscous, incompressible flows. We describe reasonable boundary conditions that should be imposed on the vorticity and a compatibility condition that the vorticity must satisfy. This formulation may give rise to efficient numerical algorithms for approximating solutions of the Stokes problem, which in turn yields an iterative method for approximating solutions of the Navier-Stokes equations.
Analysis of boundary conditions for SSME subsonic internal viscous flow analysis
Baker, A. J.
1986-01-01
A study was completed of mathematically proper boundary conditions for unique numerical solution of internal, viscous, subsonic flows in the space shuttle main engine. The study has concentrated on well posed considerations, with emphasis on computational efficiency and numerically stable boundary condition statements. The method of implementing the established boundary conditions is applicable to a wide variety of finite difference and finite element codes, as demonstrated.
Heat Transfer for Elastico-Viscous Flow Between Two Rotating Porous Discs
Directory of Open Access Journals (Sweden)
P. R. Sharma
1983-04-01
Full Text Available The problem of temperature distribution and heat transfer for elastico-viscous fluid flow between two rotating porous discs is studied. The equations of motion and energy are solved by a regular Perturbation method for small Reynolds number. The effects of the elasticity of the fluid, suction/injection parameter, rotation parameter, Prandt1 number and Eckert number on Nusselt numbers at the two discs have been discussed numerically and compared with Newtonian fluid case.
Institute of Scientific and Technical Information of China (English)
2008-01-01
This article concerns large time behavior of Ladyzhenskaya model for incompressible viscous flows in R~3.Based on linear L~P-L~q estimates,the auxiliary decay properties of the solutions and generalized Gronwall type arguments,some optimal upper and lower bounds for the decay of higher order derivatives of solutions are derived without assuming any decay properties of solutions and using Fourier splitting technology.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
An efficient analytical decomposition technique was presented for solving the singular nonlinear boundary value problem arising in viscous flow when the Crocco variable was introduced. The approximate analytical solution may be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solutions were verified by numerical ones in the literature. The approximate analytical solutions can be successfully applied to give the values of skin friction coefficient.
On the research of flow around obstacle using the viscous Cartesian grid technique
Directory of Open Access Journals (Sweden)
Liu Yan-Hua
2012-01-01
Full Text Available A new 2-D viscous Cartesian grid is proposed in current research. It is a combination of the existent body-fitted grid and Cartesian grid technology. On the interface of the two different type of grid, a fined triangular mesh is used to connect the two grids. Tests with flow around the cylinder and aerofoil NACA0012 show that the proposed scheme is easy for implement with high accuracy.
Amooie, Mohammad Amin; Soltanian, Mohammad Reza; Moortgat, Joachim
2016-11-01
Fluid mixing and its interplay with viscous fingering as well as flow channeling through heterogeneous media have been traditionally studied for fully (im)miscible conditions in which a (two-) single-phase system is represented by two components, e.g. a solvent and a solute, with (zero) infinite mutual solubility. However, many subsurface problems, e.g. gas injection/migration in hydrocarbon reservoirs, involve multiple species transfer. Multicomponent fluid properties behave non-linearly, through an equation of state, as a function of temperature, pressure, and compositions. Depending on the minimum miscibility pressure, a two-phase region with finite, non-zero mutual solubility may develop, e.g. in a partially-miscible system. Here we study mixing of fluids with partial mutual solubility, induced by viscous flow fingering, channeling, and species transport within and between phases. We uncover non-linear mixing dynamics of a finite-size slug of a less viscous fluid attenuated by a carrier fluid during rectilinear displacement. We perform accurate numerical simulations that are thermodynamically-consistent to capture fingering patterns and complex phase behavior of mixtures. The results provide a broad perspective into how multiphase flow can alter fluid mixing in porous media.
Viscous-flow properties and viscosity-average molecular mass of orange peel pectin
Institute of Scientific and Technical Information of China (English)
周尽花; 吴宇雄; 沈志强
2008-01-01
The viscous-flow properties of pectin from the residue of orange peel after extraction of essential oil and flavonoid were studied and the viscosity-average molecular mass(Mv,ave) of this kind of pectin was determined.Experimental results show that Arrhenius viscous-flow equation can be applied to describing the effect of temperature on viscosity of this kind of orange peel pectin solutions with the average viscous-flow activation energy being 17.91 kJ/mol(depending on the concentration).Neither power equation,η =K1 cA1,nor exponential equation,η=K2exp(A2c) can describe the effect of concentration on viscosity of this kind of orange peel pectin solutions well.However,it seems that exponential equation model is more suitable to describe their relation due to its higher linear correlation coefficient.Schulz-Blaschke equation can be used to calculate the intrinsic viscosity of this kind of orange peel pectin.The Mv,ave of the orange peel pectin is 1.65×105 g/mol.
3-D Viscous Flow Analysis of a Mixed Flow Pump Impeller
Directory of Open Access Journals (Sweden)
Steven M. Miner
2001-01-01
Full Text Available This paper presents the results of a study using a coarse grid to analyze the flow in the impeller of a mixed flow pump. A commercial computational fluid dynamics code (FLOTRAN is used to solve the 3-D Reynolds Averaged Navier Stokes equations in a rotating cylindrical coordinate system. The standard k-ε turbulence model is used. The mesh for this study uses 26,000 nodes and the model is run on a SPARCstation 20. This is in contrast to typical analyses using in excess of 100,000 nodes that are run on a super computer platform. The smaller mesh size has advantages in the design environment. Stage design parameters are, rotational speed 1185 rpm, flow coefficient φ=0.116, head coefficient ψ=0.094, and specific speed 2.01 (5475 US. Results for the model include circumferentially averaged results at the leading and trailing edges of the impeller, and analysis of the flow field within the impeller passage. Circumferentially averaged results include axial and tangential velocities, static pressure, and total pressure. Within the impeller passage the static pressure and velocity results are presented on surfaces from the leading edge to the trailing edge, the hub to the shroud, and the pressure surface to the suction surface. Results of this study are consistent with the expected flow characteristics of mixed flow impellers, indicating that small CFD models can be used to evaluate impeller performance in the design environment.
Comparing two methods of simulating mirco-scale viscous flows in a porous channel
Gao, Hui; Han, Jie; Jin, Yan; Wang, Lian-Ping
2007-11-01
Water flows in natural soil porous media are important to colloid-facilitated transport of contaminants and other phenomena with groundwater as the carrier. The 3D micro-scale flow is complicated due to the complex geometry. The transport and deposition of colloids in such flows are affected by several physical and chemical forces involved. In this talk, we first compare two methods of simulating viscous flows in both 2D and 3D channels filled with glass-bead particles. The first method is Physalis developed by Prosperetti's group, at Johns Hopkins, based on solving the Navier-Stokes equation using a combination of numerical solution and local analytical Stokes flow representation. The second method is a meso-scale approach by solving a lattice Boltzmann equation. Specific implementation issues will be discussed. The two methods yield almost identical flows. Preliminary simulation results as well as parallel experimental results on colloid deposition in the porous channel will also be presented.
Directory of Open Access Journals (Sweden)
K.V.S. Raju
2014-06-01
Full Text Available This paper deals with a steady MHD forced convective flow of a viscous fluid of finite depth in a saturated porous medium over a fixed horizontal channel with thermally insulated and impermeable bottom wall in the presence of viscous dissipation and joule heating. The governing equations are solved in the closed form and the exact solutions are obtained for velocity and temperature distributions when the temperatures on the fixed bottom and on the free surface are prescribed. The expressions for flow rate, mean velocity, temperature, mean temperature, mean mixed temperature in the flow region and the Nusselt number on the free surface have been obtained. The cases of large and small values of porosity coefficients have been obtained as limiting cases. Further, the cases of small depth (shallow fluid and large depth (deep fluid are also discussed. The results are presented and discussed with the help of graphs.
Paul, Tanaji; Harimkar, Sandip P.
2017-07-01
The viscous flow behavior of Fe-based amorphous alloy powder during isochronal spark plasma sintering was analyzed under the integrated theoretical background of the Arrhenius and directional structural relaxation models. A relationship between viscous flow activation energy and heating rate was derived. An extension of the pertinent analysis to Ti-based amorphous alloys confirmed the broad applicability of such a relationship for predicting the activation energy for sintering below the glass transition temperature (T g) of the amorphous alloy powders.
Solution of 3-dimensional time-dependent viscous flows. Part 2: Development of the computer code
Weinberg, B. C.; Mcdonald, H.
1980-01-01
There is considerable interest in developing a numerical scheme for solving the time dependent viscous compressible three dimensional flow equations to aid in the design of helicopter rotors. The development of a computer code to solve a three dimensional unsteady approximate form of the Navier-Stokes equations employing a linearized block emplicit technique in conjunction with a QR operator scheme is described. Results of calculations of several Cartesian test cases are presented. The computer code can be applied to more complex flow fields such as these encountered on rotating airfoils.
HIGH-ORDER I-STABLE CENTERED DIFFERENCE SCHEMES FOR VISCOUS COMPRESSIBLE FLOWS
Institute of Scientific and Technical Information of China (English)
Weizhu Bao; Shi Jin
2003-01-01
In this paper we present high-order I-stable centered difference schemes for the numer-ical simulation of viscous compressible flows. Here I-stability refers to time discretizationswhose linear stability regions contain part of the imaginary axis. This class of schemeshas a numerical stability independent of the cell-Reynolds number Rc, thus allows one tosimulate high Reynolds number flows with relatively larger Rc, or coarser grids for a fixedRc. On the other hand, Rc cannot be arbitrarily large if one tries to obtain adequatenumerical resolution of the viscous behavior. We investigate the behavior of high-orderI-stable schemes for Burgers' equation and the compressible Navier-Stokes equations. Wedemonstrate that, for the second order scheme, Rc ≤ 3 is an appropriate constraint for nu-merical resolution of the viscous profile, while for the fourth-order schemes the constraintcan be relaxed to Rc ≤ 6. Our study indicates that the fourth order scheme is preferable:better accuracy, higher resolution, and larger cell-Reynolds numbers.
Flow harmonics from self-consistent particlization of a viscous fluid
Wolff, Zack
2016-01-01
The quantitative extraction of quark-gluon plasma (QGP) properties from heavy-ion data, such as its specific shear viscosity $\\eta /s$, typically requires comparison to viscous hydrodynamic or "hybrid" hydrodynamics+transport simulations. In either case, one has to convert the fluid to hadrons, yet without additional theory input the conversion is ambiguous for dissipative fluids. Here, shear viscous phase-space corrections calculated using linearized transport theory are applied in Cooper-Frye freezeout to quantify the effects on anisotropic flow coefficients $v_n(p_T)$ at both RHIC and LHC energies. Expanding upon our previous flow harmonics studies [1,2], we calculate pion and proton $v_2(p_T)$, $v_4(p_T)$, and $v_6(p_T)$. Unlike in Ref. [1], we incorporate a hadron gas that is chemically frozen below a temperature of 175 MeV, and use hypersurfaces from realistic viscous hydrodynamic simulations. With additive quark model cross sections and relative phase-space corrections with $p^{3/2}$ momentum dependenc...
Monodisperse granular flows in viscous dispersions in a centrifugal acceleration field
Cabrera, Miguel Angel; Wu, Wei
2016-04-01
Granular flows are encountered in geophysical flows and innumerable industrial applications with particulate materials. When mixed with a fluid, a complex network of interactions between the particle- and fluid-phase develops, resulting in a compound material with a yet unclear physical behaviour. In the study of granular suspensions mixed with a viscous dispersion, the scaling of the stress-strain characteristics of the fluid phase needs to account for the level of inertia developed in experiments. However, the required model dimensions and amount of material becomes a main limitation for their study. In recent years, centrifuge modelling has been presented as an alternative for the study of particle-fluid flows in a reduced scaled model in an augmented acceleration field. By formulating simple scaling principles proportional to the equivalent acceleration Ng in the model, the resultant flows share many similarities with field events. In this work we study the scaling principles of the fluid phase and its effects on the flow of granular suspensions. We focus on the dense flow of a monodisperse granular suspension mixed with a viscous fluid phase, flowing down an inclined plane and being driven by a centrifugal acceleration field. The scaled model allows the continuous monitoring of the flow heights, velocity fields, basal pressure and mass flow rates at different Ng levels. The experiments successfully identify the effects of scaling the plastic viscosity of the fluid phase, its relation with the deposition of particles over the inclined plane, and allows formulating a discussion on the suitability of simulating particle-fluid flows in a centrifugal acceleration field.
Numerical simulation of orbitally shaken viscous fluids with free surface
Discacciati, Marco; Hacker, David; Quarteroni, A.; Quinodoz, Samuel; Tissot, Stéphanie; Wurm, M. Florian
2013-01-01
Orbitally shaken bioreactors are an emerging alternative to stirred-tank bioreactors for large-scale mam- malian cell culture, but their fluid dynamics is still not well defined. Among the theoretical and practical issues that remain to be resolved, the characterization of the liquid free surface during orbital shaking remains a major challenge because it is an essential aspect of gas transfer and mixing in these reactors. To simulate the fluid behavior and the free surface shape, we develope...
Chen, Yong; Huang, Yiyong; Chen, Xiaoqian
2013-02-01
Ultrasonic flow meter with non-invasive no-moving-parts construction has good prospective application for space on-orbit fluid gauging. In traditional pulse transit time flow meter, inconsistency of ultrasonic transducers leads to measurement error and plane wave theory, bases of transit time flow meter, is valuable only for low-frequency wave propagation in inviscid fluid and will lose feasibility when fluid viscosity is considered. In this paper, based on the hydrodynamics of viscous fluid, wave propagation with uniform flow profile is mathematically formulated and a novel solution for viscous fluid using potential theory is firstly presented. Then a novel design methodology of continuous ultrasonic flow meter is proposed, where high measurement rangeability and accuracy are guaranteed individually by solving the integral ambiguity using multi-tone wide laning strategy and the fractional phase shift using phase lock loop tracking method. A comparison with transit time ultrasonic flow meter shows the advantage of proposed methodology. In the end, parametric analysis of viscosity on wave propagation and ultrasonic flow meter is compressively investigated.
Nelson, Daniel A.; Jacobs, Gustaaf B.; Kopriva, David A.
2016-08-01
The effect of curved-boundary representation on the physics of the separated flow over a NACA 65(1)-412 airfoil is thoroughly investigated. A method is presented to approximate curved boundaries with a high-order discontinuous-Galerkin spectral element method for the solution of the Navier-Stokes equations. Multiblock quadrilateral element meshes are constructed with the grid generation software GridPro. The boundary of a NACA 65(1)-412 airfoil, defined by a cubic natural spline, is piecewise-approximated by isoparametric polynomial interpolants that represent the edges of boundary-fitted elements. Direct numerical simulation of the airfoil is performed on a coarse mesh and fine mesh with polynomial orders ranging from four to twelve. The accuracy of the curve fitting is investigated by comparing the flows computed on curved-sided meshes with those given by straight-sided meshes. Straight-sided meshes yield irregular wakes, whereas curved-sided meshes produce a regular Karman street wake. Straight-sided meshes also produce lower lift and higher viscous drag as compared with curved-sided meshes. When the mesh is refined by reducing the sizes of the elements, the lift decrease and viscous drag increase are less pronounced. The differences in the aerodynamic performance between the straight-sided meshes and the curved-sided meshes are concluded to be the result of artificial surface roughness introduced by the piecewise-linear boundary approximation provided by the straight-sided meshes.
The new high resolution method of Godunov`s type for 3D viscous flow calculations
Energy Technology Data Exchange (ETDEWEB)
Yershov, S.V.; Rusanov, A.V. [Ukranian National Academy of Sciences, Kahrkov (Ukraine)
1996-12-31
The numerical method is suggested for the calculations of the 3D viscous compressible flows described by the thin-layer Reynolds-averaged Navier-Stokes equations. The method is based on the Godunov`s finite-difference scheme and it uses the ENO reconstruction suggested by Harten to achieve the uniformly high-order accuracy. The computational efficiency is provided with the simplified multi grid approach and the implicit step written in {delta} -form. The turbulent effects are simulated with the Baldwin - Lomax turbulence model. The application package FlowER is developed to calculate the 3D turbulent flows within complex-shape channels. The numerical results for the 3D flow around a cylinder and through the complex-shaped channels show the accuracy and the reliability of the suggested method. (author)
Viscous flow features in scaled-up physical models of normal and pathological vocal phonation
Energy Technology Data Exchange (ETDEWEB)
Erath, Byron D., E-mail: berath@purdue.ed [School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907 (United States); Plesniak, Michael W., E-mail: plesniak@gwu.ed [Department of Mechanical and Aerospace Engineering, George Washington University, 801 22nd Street NW, Suite 739, Washington, DC 20052 (United States)
2010-06-15
Unilateral vocal fold paralysis results when the recurrent laryngeal nerve, which innervates the muscles of the vocal folds becomes damaged. The loss of muscle and tension control to the damaged vocal fold renders it ineffectual. The mucosal wave disappears during phonation, and the vocal fold becomes largely immobile. The influence of unilateral vocal fold paralysis on the viscous flow development, which impacts speech quality within the glottis during phonation was investigated. Driven, scaled-up vocal fold models were employed to replicate both normal and pathological patterns of vocal fold motion. Spatial and temporal velocity fields were captured using particle image velocimetry, and laser Doppler velocimetry. Flow parameters were scaled to match the physiological values associated with human speech. Loss of motion in one vocal fold resulted in a suppression of typical glottal flow fields, including decreased spatial variability in the location of the flow separation point throughout the phonatory cycle, as well as a decrease in the vorticity magnitude.
Analysis of Viscous Heating in a Micro-Rocket Flow and Performance
Institute of Scientific and Technical Information of China (English)
José A. Morí(n)igo; José Hermida Quesada
2008-01-01
Micro-rockets for propulsion of small spacecrafts exhibit significant differences with regard to their macroscale counterparts, mainly caused by the role of the viscous dissipation and heat transfer processes in the micron-sized scale. The goal of this work is to simulate the transient operation of a micro-rocket to investigate the effects of viscous heating on the flow and performance for four configurations of the expanding gas and wafer material. The modelling follows a multiphysics approach that solves the fluid and solid regions fully coupled. A continuum-based description that incorporates the effects of gas rarefaction through the micro-nozzle, viscous dissipation and heat transfer at the solid-gas interface is presented. Non-equilibrium is addressed with the implementation of a 2nd-order slip-model for the velocity and temperature at the walls. The results stress that solid-fluid coupling exerts a strong influence on the flowfield and performance as well as the effect of the wafer during the first instants of the transient in micro-rockets made of low and high thermal conductivity materials.
Simulations of Viscous Accretion Flow around Black Holes in a Two-dimensional Cylindrical Geometry
Lee, Seong-Jae; Chattopadhyay, Indranil; Kumar, Rajiv; Hyung, Siek; Ryu, Dongsu
2016-11-01
We simulate shock-free and shocked viscous accretion flows onto a black hole in a two-dimensional cylindrical geometry, where initial conditions were chosen from analytical solutions. The simulation code used the Lagrangian total variation diminishing plus remap routine, which enabled us to attain high accuracy in capturing shocks and to handle the angular momentum distribution correctly. The inviscid shock-free accretion disk solution produced a thick disk structure, while the viscous shock-free solution attained a Bondi-like structure, but in either case, no jet activity nor any quasi-periodic oscillation (QPO)-like activity developed. The steady-state shocked solution in the inviscid as well as in the viscous regime matched theoretical predictions well. However, increasing viscosity renders the accretion shock unstable. Large-amplitude shock oscillation is accompanied by intermittent, transient inner multiple shocks. This oscillation of the inner part of the disk is interpreted as the source of QPO in hard X-rays observed in micro-quasars. Strong shock oscillation induces strong episodic jet emission. The jets also show the existence of shocks, which are produced as one shell hits the preceding one. The periodicities of the jets and shock oscillation are similar; the jets for the higher viscosity parameter appear to be stronger and faster.
Archibong Eso, A.; Zhao, Yabin; Yeung, Hoi
2014-04-01
Multiphase flow is a common occurrence in industries such as nuclear, process, oil & gas, food and chemical. A prior knowledge of its features and characteristics is essential in the design, control and management of such processes due to its complex nature. Electrical Capacitance Tomography (ECT) and Gamma Densitometer (Gamma) are two promising approaches for multiphase visualization and characterization in process industries. In two phase oil & gas flow, ECT and Gamma are used in multiphase flow monitoring techniques due to their inherent simplicity, robustness, and an ability to withstand wide range of operational temperatures and pressures. High viscous oil (viscosity > 100 cP) is of interest because of its huge reserves, technological advances in its production and unlike conventional oil (oil viscosity oil and gas flows comes with certain associated concerns which include; increased entrainment of gas bubbles dispersed in oil, shorter and more frequent slugs as well as oil film coatings on the walls of flowing conduits. This study aims to determine the suitability of both devices in the visualization and characterization of high-viscous oil and gas flow. Static tests are performed with both devices and liquid holdup measurements are obtained. Dynamic experiments were also conducted in a 1 & 3 inch facility at Cranfield University with a range of nominal viscosities (1000, 3000 & 7500 cP). Plug, slug and wavy annular flow patterns were identified by means of Probability Mass Function and time series analysis of the data acquired from Gamma and ECT devices with high speed camera used to validate the results. Measured Liquid holdups for both devices were also compared.
THREE-DIMENSIONAL INSTABILITY OF AN OSCILLATING VISCOUS FLOW PAST A CIRCULAR CYLINDER
Institute of Scientific and Technical Information of China (English)
陆夕云; 凌国灿
2003-01-01
A systematically numerical study of the sinusoidally oscillating viscous flowaround a circular cylinder was performed to investigate vortical instability by solving thethree-dimensional incompressible Navier-Stokes equations. The transition from two- to three-dimensional flow structures along the axial direction due to the vortical instability appears,and the three-dimensional structures lie alternatively on the two sides of the cylinder.Numerical study has been taken for the Keulegan-Carpenter(KC) numbers from 1 to 3.2and frequency parameters from 1O0 to 600. The force behaviors are also studied by solvingthe Morison equation. Calculated results agree well with experimental data and theoreticalprediction.
Simulation of viscous flows using a multigrid-control volume finite element method
Energy Technology Data Exchange (ETDEWEB)
Hookey, N.A. [Memorial Univ., Newfoundland (Canada)
1994-12-31
This paper discusses a multigrid control volume finite element method (MG CVFEM) for the simulation of viscous fluid flows. The CVFEM is an equal-order primitive variables formulation that avoids spurious solution fields by incorporating an appropriate pressure gradient in the velocity interpolation functions. The resulting set of discretized equations is solved using a coupled equation line solver (CELS) that solves the discretized momentum and continuity equations simultaneously along lines in the calculation domain. The CVFEM has been implemented in the context of both FMV- and V-cycle multigrid algorithms, and preliminary results indicate a five to ten fold reduction in execution times.
MHD flow of a viscous fluid on a nonlinear porous shrinking sheet with homotopy analysis method
Institute of Scientific and Technical Information of China (English)
S. Nadeem; Anwar Hussain
2009-01-01
The present paper investigates the magnetohydrodynamic (MHD) flow of a viscous fluid towards a nonlinear porous shrinking sheet. The governing equations are simplified by similarity transformations. The reduced problem is then solved by the homotopy analysis method. The pertinent parameters appearing in the problem are discussed graphically and presented in tables. It is found that the shrinking solutions exist in the presence of MHD. It is also observed from the tables that the solutions for f"(0) with different values of parameters are convergent.
On the mechanism of low-pressure imprint lithography: capillarity vs viscous flow.
Khang, Dahl-Young; Lee, Hong H
2008-05-20
Dominant mechanisms in low-pressure imprint lithography processes have been identified for the regimes that are definable in terms of applied pressure, temperature, and mold material characteristics. Capillarity is found to be the dominant mechanism at high temperature and low pressure when stiff, hard molds are used. In the case of flexible thin-film ( approximately 20 microm) molds, both the capillarity and the viscous flow are involved. Both mechanisms are operative in the initial stage of the imprinting, but the capillarity takes over as time progresses.
Drop Impact of Viscous Suspensions on Solid Surfaces
Bolleddula, Daniel; Aliseda, Alberto
2009-11-01
Droplet impact is a well studied subject with over a century of progress. Most studies are motivated by applications such as inkjet printing, agriculture spraying, or printed circuit boards. Pharmaceutically relevant fluids provide an experimental set that has received little attention. Medicinal tablets are coated by the impaction of micron sized droplets of aqueous suspensions and subsequently dried for various purposes such as brand recognition, mask unpleasant taste, or functionality. We will present a systematic study of micron sized drop impact of Newtonian and Non-Newtonian fluids used in pharmaceutical coating processes. In our experiments we extend the range of Ohnesorge numbers, O(1), of previous studies on surfaces of varying wettability and roughness.
Taylor, Arthur C., III; Hou, Gene W.; Korivi, Vamshi M.
1991-01-01
A gradient-based design optimization strategy for practical aerodynamic design applications is presented, which uses the 2D thin-layer Navier-Stokes equations. The strategy is based on the classic idea of constructing different modules for performing the major tasks such as function evaluation, function approximation and sensitivity analysis, mesh regeneration, and grid sensitivity analysis, all driven and controlled by a general-purpose design optimization program. The accuracy of aerodynamic shape sensitivity derivatives is validated on two viscous test problems: internal flow through a double-throat nozzle and external flow over a NACA 4-digit airfoil. A significant improvement in aerodynamic performance has been achieved in both cases. Particular attention is given to a consistent treatment of the boundary conditions in the calculation of the aerodynamic sensitivity derivatives for the classic problems of external flow over an isolated lifting airfoil on 'C' or 'O' meshes.
Walitt, L.
1982-01-01
The VANS successive approximation numerical method was extended to the computation of three dimensional, viscous, transonic flows in turbomachines. A cross-sectional computer code, which conserves mass flux at each point of the cross-sectional surface of computation was developed. In the VANS numerical method, the cross-sectional computation follows a blade-to-blade calculation. Numerical calculations were made for an axial annular turbine cascade and a transonic, centrifugal impeller with splitter vanes. The subsonic turbine cascade computation was generated in blade-to-blade surface to evaluate the accuracy of the blade-to-blade mode of marching. Calculated blade pressures at the hub, mid, and tip radii of the cascade agreed with corresponding measurements. The transonic impeller computation was conducted to test the newly developed locally mass flux conservative cross-sectional computer code. Both blade-to-blade and cross sectional modes of calculation were implemented for this problem. A triplet point shock structure was computed in the inducer region of the impeller. In addition, time-averaged shroud static pressures generally agreed with measured shroud pressures. It is concluded that the blade-to-blade computation produces a useful engineering flow field in regions of subsonic relative flow; and cross-sectional computation, with a locally mass flux conservative continuity equation, is required to compute the shock waves in regions of supersonic relative flow.
Lakshminarayana, B.; Ho, Y.; Basson, A.
1993-01-01
The objective of this research is to simulate steady and unsteady viscous flows, including rotor/stator interaction and tip clearance effects in turbomachinery. The numerical formulation for steady flow developed here includes an efficient grid generation scheme, particularly suited to computational grids for the analysis of turbulent turbomachinery flows and tip clearance flows, and a semi-implicit, pressure-based computational fluid dynamics scheme that directly includes artificial dissipation, and is applicable to both viscous and inviscid flows. The values of these artificial dissipation is optimized to achieve accuracy and convergency in the solution. The numerical model is used to investigate the structure of tip clearance flows in a turbine nozzle. The structure of leakage flow is captured accurately, including blade-to-blade variation of all three velocity components, pitch and yaw angles, losses and blade static pressures in the tip clearance region. The simulation also includes evaluation of such quantities of leakage mass flow, vortex strength, losses, dominant leakage flow regions and the spanwise extent affected by the leakage flow. It is demonstrated, through optimization of grid size and artificial dissipation, that the tip clearance flow field can be captured accurately. The above numerical formulation was modified to incorporate time accurate solutions. An inner loop iteration scheme is used at each time step to account for the non-linear effects. The computation of unsteady flow through a flat plate cascade subjected to a transverse gust reveals that the choice of grid spacing and the amount of artificial dissipation is critical for accurate prediction of unsteady phenomena. The rotor-stator interaction problem is simulated by starting the computation upstream of the stator, and the upstream rotor wake is specified from the experimental data. The results show that the stator potential effects have appreciable influence on the upstream rotor wake
Chang, Chau-Lyan; Venkatachari, Balaji
2016-11-01
Flow physics near the viscous wall is intrinsically anisotropic in nature, namely, the gradient along the wall normal direction is much larger than that along the other two orthogonal directions parallel to the surface. Accordingly, high aspect ratio meshes are employed near the viscous wall to capture the physics and maintain low grid count. While such arrangement works fine for structured-grid based methods with dimensional splitting that handles derivatives in each direction separately, similar treatments often lead to numerical instability for unstructured-mesh based methods when triangular or tetrahedral meshes are used. The non-splitting treatment of near-wall gradients for high-aspect ratio triangular or tetrahedral elements results in an ill-conditioned linear system of equations that is closely related to the numerical instability. Altering the side lengths of the near wall tetrahedrons in the gradient calculations would make the system less unstable but more dissipative. This research presents recent progress in applying numerical dissipation control in the space-time conservation element solution element (CESE) method to reduce or alleviate the above-mentioned instability while maintaining reasonable solution accuracy.
Numerical analysis of acoustically driven viscous flow through a circular hole
Notomi, Tetsuo; Namba, Masanobu
1990-12-01
Periodic viscous flows through a circular hole driven by fluctuating far field pressure are numerically studied. The time-dependent incompressible Navier-Stokes equations formulated with orthogonal curvilinear coordinates are solved by using a finite difference method. The flow patterns are classified into three regimes by fluctuating pressure amplitude and frequency: flows with no laminar separation (high frequency-low pressure range), flows with attached separation bubble (intermediate frequency and pressure range) and flows with detached vortex ring (low frequency-high pressure range). The flow resistance of the circular hole is proportional to the acoustic particle velocity but independent of the viscosity of the fluid and almost invariant with the frequency for the low frequency-high pressure range. On the other hand, for the high frequency-low pressure range, the flow resistance is independent of the periodic pressure amplitude and varies directly with 2/3 powers of frequency. Finally, the predicted circular hole impedance is in good agreement with Ingard and Ising's (1967) experimental data for the orifice impedance.
Progress Towards a Cartesian Cut-Cell Method for Viscous Compressible Flow
Berger, Marsha; Aftosmis, Michael J.
2011-01-01
The proposed paper reports advances in developing a method for high Reynolds number compressible viscous flow simulations using a Cartesian cut-cell method with embedded boundaries. This preliminary work focuses on accuracy of the discretization near solid wall boundaries. A model problem is used to investigate the accuracy of various difference stencils for second derivatives and to guide development of the discretization of the viscous terms in the Navier-Stokes equations. Near walls, quadratic reconstruction in the wall-normal direction is used to mitigate mesh irregularity and yields smooth skin friction distributions along the body. Multigrid performance is demonstrated using second-order coarse grid operators combined with second-order restriction and prolongation operators. Preliminary verification and validation for the method is demonstrated using flat-plate and airfoil examples at compressible Mach numbers. Simulations of flow on laminar and turbulent flat plates show skin friction and velocity profiles compared with those from boundary-layer theory. Airfoil simulations are performed at laminar and turbulent Reynolds numbers with results compared to both other simulations and experimental data
On the viscous dissipation modeling of thermal fluid flow in a porous medium
Salama, Amgad
2011-02-24
The problem of viscous dissipation and thermal dispersion in saturated porous medium is numerically investigated for the case of non-Darcy flow regime. The fluid is induced to flow upward by natural convection as a result of a semi-infinite vertical wall that is immersed in the porous medium and is kept at constant higher temperature. The boundary layer approximations were used to simplify the set of the governing, nonlinear partial differential equations, which were then non-dimensionalized and solved using the finite elements method. The results for the details of the governing parameters are presented and investigated. It is found that the irreversible process of transforming the kinetic energy of the moving fluid to heat energy via the viscosity of the moving fluid (i.e.; viscous dissipation) resulted in insignificant generation of heat for the range of parameters considered in this study. On the other hand, thermal dispersion has shown to disperse heat energy normal to the wall more effectively compared with the normal diffusion mechanism. © 2011 Springer-Verlag.
Fluid flow of incompressible viscous fluid through a non-linear elastic tube
Energy Technology Data Exchange (ETDEWEB)
Lazopoulos, A.; Tsangaris, S. [National Technical University of Athens, Fluids Section, School of Mechanical Engineering, Zografou, Athens (Greece)
2008-11-15
The study of viscous flow in tubes with deformable walls is of specific interest in industry and biomedical technology and in understanding various phenomena in medicine and biology (atherosclerosis, artery replacement by a graft, etc) as well. The present work describes numerically the behavior of a viscous incompressible fluid through a tube with a non-linear elastic membrane insertion. The membrane insertion in the solid tube is composed by non-linear elastic material, following Fung's (Biomechanics: mechanical properties of living tissue, 2nd edn. Springer, New York, 1993) type strain-energy density function. The fluid is described through a Navier-Stokes code coupled with a system of non linear equations, governing the interaction with the membrane deformation. The objective of this work is the study of the deformation of a non-linear elastic membrane insertion interacting with the fluid flow. The case of the linear elastic material of the membrane is also considered. These two cases are compared and the results are evaluated. The advantages of considering membrane nonlinear elastic material are well established. Finally, the case of an axisymmetric elastic tube with variable stiffness along the tube and membrane sections is studied, trying to substitute the solid tube with a membrane of high stiffness, exhibiting more realistic response. (orig.)
Ultrafast viscous water flow through nanostrand-channelled graphene oxide membranes.
Huang, Hubiao; Song, Zhigong; Wei, Ning; Shi, Li; Mao, Yiyin; Ying, Yulong; Sun, Luwei; Xu, Zhiping; Peng, Xinsheng
2013-01-01
Pressure-driven ultrafiltration membranes are important in separation applications. Advanced filtration membranes with high permeance and enhanced rejection must be developed to meet rising worldwide demand. Here we report nanostrand-channelled graphene oxide ultrafiltration membranes with a network of nanochannels with a narrow size distribution (3-5 nm) and superior separation performance. This permeance offers a 10-fold enhancement without sacrificing the rejection rate compared with that of graphene oxide membranes, and is more than 100 times higher than that of commercial ultrafiltration membranes with similar rejection. The flow enhancement is attributed to the porous structure and significantly reduced channel length. An abnormal pressure-dependent separation behaviour is also reported, where the elastic deformation of nanochannels offers tunable permeation and rejection. The water flow through these hydrophilic graphene oxide nanochannels is identified as viscous. This nanostrand-channelling approach is also extendable to other laminate membranes, providing potential for accelerating separation and water-purification processes.
Deformation of an Elastic Beam due to Viscous Flow in an Embedded Parallel Channel Network
Matia, Yoav
2015-01-01
Elastic deformation due to embedded fluidic networks is currently studied in the context of soft-actuators and soft-robotic applications. In this work, we analyze interaction between the elastic deflection of a slender beam and viscous flow within a long serpentine channel, embedded in the elastic beam. The channel is positioned asymmetrically with regard to the midplane of the beam, and thus pressure within the channel creates a local moment deforming the beam. We focus on creeping flows and small deflections of the elastic beam and obtain, in leading order, a fourth-order partial integro-differential equation governing the time-dependent deflection field. This relation enables the design of complex time-dependent deformation patterns of beams with embedded channel networks, including inertia-like standing and moving wave solutions in configurations with negligible inertia.
Hydromagnetic flow of third grade nanofluid with viscous dissipation and flux conditions
Energy Technology Data Exchange (ETDEWEB)
Hussain, T. [Faculty of Computing, Mohammad Ali Jinnah University, Islamabad 44000 (Pakistan); Shehzad, S. A., E-mail: ali-qau70@yahoo.com [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Hayat, T. [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia); Alsaedi, A. [Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia)
2015-08-15
This article investigates the magnetohydrodynamic flow of third grade nanofluid with thermophoresis and Brownian motion effects. Energy equation is considered in the presence of thermal radiation and viscous dissipation. Rosseland’s approximation is employed for thermal radiation. The heat and concentration flux conditions are taken into account. The governing nonlinear mathematical expressions of velocity, temperature and concentration are converted into dimensionless expressions via transformations. Series solutions of the dimensionless velocity, temperature and concentration are developed. Convergence of the constructed solutions is checked out both graphically and numerically. Effects of interesting physical parameters on the temperature and concentration are plotted and discussed in detail. Numerical values of skin-friction coefficient are computed for the hydrodynamic and hydromagnetic flow cases.
Directory of Open Access Journals (Sweden)
S. Das
2015-06-01
Full Text Available The combined effects of viscous dissipation and Joule heating on the momentum and thermal transport for the magnetohydrodynamic flow past an inclined plate in both aiding and opposing buoyancy situations have been carried out. The governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Runge–Kutta fourth order method with shooting technique. Numerical results are obtained for the fluid velocity, temperature as well as the shear stress and the rate of heat transfer at the plate. The results show that there are significant effects of pertinent parameters on the flow fields.
Entropy resistance analyses of a two-stream parallel flow heat exchanger with viscous heating
Institute of Scientific and Technical Information of China (English)
Cheng Xue-Tao; Liang Xin-Gang
2013-01-01
Heat exchangers are widely used in industry,and analyses and optimizations of the performance of heat exchangers are important topics.In this paper,we define the concept of entropy resistance based on the entropy generation analyses of a one-dimensional heat transfer process.With this concept,a two-stream parallel flow heat exchanger with viscous heating is analyzed and discussed.It is found that the minimization of entropy resistance always leads to the maximum heat transfer rate for the discussed two-stream parallel flow heat exchanger,while the minimizations of entropy generation rate,entropy generation numbers,and revised entropy generation number do not always.
Numerical study of roll motion of a 2-D floating structure in viscous flow
Institute of Scientific and Technical Information of China (English)
Lifen CHEN; Liang SUN; Jun ZANG; A J HILLIS; A R PLUMMER
2016-01-01
In the present study, an open source CFD tool, OpenFOAM has been extended and applied to investigate roll motion of a 2-D rectangular barge induced by nonlinear regular waves in viscous flow. Comparisons of the present OpenFOAM results with published potential-flow solutions and experimental data have indicated that the newly extended OpenFOAM model is very capable of accurate modelling of wave interaction with freely rolling structures. The wave-induced roll motions, hydrodynamic forces on the barge, velocities and vorticity fields in the vicinity of the structure in the presence of waves have been investigated to reveal the real physics involved in the wave induced roll motion of a 2-D floating structure. Parametric analysis has been carried out to examine the effect of structure dimension and body draft on the roll motion.
Computational Modelling of Couette Flow of Nanofluids with Viscous Heating and Convective Cooling
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Oluwole Daniel Makinde
2014-01-01
Full Text Available The combined effect of viscous heating and convective cooling on Couette flow and heat transfer characteristics of water base nanofluids containing Copper Oxide (CuO and Alumina (Al2O3 as nanoparticles is investigated. It is assumed that the nanofluid flows in a channel between two parallel plates with the channel’s upper plate accelerating and exchange heat with the ambient surrounding following the Newton’s law of cooling, while the lower plate is stationary and maintained at a constant temperature. Using appropriate similarity transformation, the governing Navier-Stokes and the energy equations are reduced to a set of nonlinear ordinary differential equations. These equations are solved analytically by regular perturbation method with series improvement technique and numerically by an efficient Runge-Kutta-Fehlberg integration technique coupled with shooting method. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, pressure drop and Nusselt number are presented graphically, and discussed quantitatively.
Brown-Dymkoski, Eric; Kasimov, Nurlybek; Vasilyev, Oleg V.
2014-04-01
In order to introduce solid obstacles into flows, several different methods are used, including volume penalization methods which prescribe appropriate boundary conditions by applying local forcing to the constitutive equations. One well known method is Brinkman penalization, which models solid obstacles as porous media. While it has been adapted for compressible, incompressible, viscous and inviscid flows, it is limited in the types of boundary conditions that it imposes, as are most volume penalization methods. Typically, approaches are limited to Dirichlet boundary conditions. In this paper, Brinkman penalization is extended for generalized Neumann and Robin boundary conditions by introducing hyperbolic penalization terms with characteristics pointing inward on solid obstacles. This Characteristic-Based Volume Penalization (CBVP) method is a comprehensive approach to conditions on immersed boundaries, providing for homogeneous and inhomogeneous Dirichlet, Neumann, and Robin boundary conditions on hyperbolic and parabolic equations. This CBVP method can be used to impose boundary conditions for both integrated and non-integrated variables in a systematic manner that parallels the prescription of exact boundary conditions. Furthermore, the method does not depend upon a physical model, as with porous media approach for Brinkman penalization, and is therefore flexible for various physical regimes and general evolutionary equations. Here, the method is applied to scalar diffusion and to direct numerical simulation of compressible, viscous flows. With the Navier-Stokes equations, both homogeneous and inhomogeneous Neumann boundary conditions are demonstrated through external flow around an adiabatic and heated cylinder. Theoretical and numerical examination shows that the error from penalized Neumann and Robin boundary conditions can be rigorously controlled through an a priori penalization parameter η. The error on a transient boundary is found to converge as O
Vortex Matter in Highly Strained Nb_{75}Zr_{25}: Analogy with Viscous Flow of Disordered Solids
Chandra, Jagdish; Manekar, Meghmalhar; Sharma, V. K.; Mondal, Puspen; Tiwari, Pragya; Roy, S. B.
2017-01-01
We present the results of magnetization and magneto-transport measurements in the superconducting state of an as-cast Nb_{75}Zr_{25} alloy. We also report the microstructure of our sample at various length scales by using optical, scanning electron and transmission electron microscopies. The information of microstructure is used to understand the flux pinning properties in the superconducting state within the framework of collective pinning. The magneto-transport measurements show a non-Arrhenius behaviour of the temperature- and field-dependent resistivity across the resistive transition and is understood in terms of a model for viscous flow of disordered solids which is popularly known as the `shoving model'. The activation energy for flux flow is assumed to be mainly the elastic energy stored in the flux-line lattice. The scaling of pinning force density indicates the presence of two pinning mechanisms of different origins. The elastic constants of the flux-line lattice are used to estimate the length scale of vortex lattice movement, or the volume displaced by the flux-line lattice. It appears that the vortex lattice displacement estimated from elastic energy considerations is of the same order of magnitude as that of the flux bundle hopping length during flux flow. Our results could provide possible directions for establishing a framework where vortex matter and glass-forming liquids or amorphous solids can be treated in a similar manner for understanding the phenomenon of viscous flow in disordered solids or more generally the pinning and depinning properties of elastic manifolds in random media. It is likely that the vortex molasses scenario is more suited to explain the vortex dynamics in conventional low-T_C superconductors.
Hydrodynamics of Highly Viscous Flow past a Compound Particle: Analytical Solution
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Longhua Zhao
2016-11-01
Full Text Available To investigate the translation of a compound particle in a highly viscous, incompressible fluid, we carry out an analytic study on flow past a fixed spherical compound particle. The spherical object is considered to have a rigid kernel covered with a fluid coating. The fluid within the coating has a different viscosity from that of the surrounding fluid and is immiscible with the surrounding fluid. The inertia effect is negligible for flows both inside the coating and outside the object. Thus, flows are in the Stokes regime. Taking advantage of the symmetry properties, we reduce the problem in two dimensions and derive the explicit formulae of the stream function in the polar coordinates. The no-slip boundary condition for the rigid kernel and the no interfacial mass transfer and force equilibrium conditions at fluid interfaces are considered. Two extreme cases: the uniform flow past a sphere and the uniform flow past a fluid drop, are reviewed. Then, for the fluid coating the spherical object, we derive the stream functions and investigate the flow field by the contour plots of stream functions. Contours of stream functions show circulation within the fluid coating. Additionally, we compare the drag and the terminal velocity of the object with a rigid sphere or a fluid droplet. Moreover, the extended results regarding the analytical solution for a compound particle with a rigid kernel and multiple layers of fluid coating are reported.
Weinberg, B. C.; Mcdonald, H.
1982-01-01
A numerical scheme is developed for solving the time dependent, three dimensional compressible viscous flow equations to be used as an aid in the design of helicopter rotors. In order to further investigate the numerical procedure, the computer code developed to solve an approximate form of the three dimensional unsteady Navier-Stokes equations employing a linearized block implicit technique in conjunction with a QR operator scheme is tested. Results of calculations are presented for several two dimensional boundary layer flows including steady turbulent and unsteady laminar cases. A comparison of fourth order and second order solutions indicate that increased accuracy can be obtained without any significant increases in cost (run time). The results of the computations also indicate that the computer code can be applied to more complex flows such as those encountered on rotating airfoils. The geometry of a symmetric NACA four digit airfoil is considered and the appropriate geometrical properties are computed.
CALCULATION OF VISCOUS FLOW AROUND CIRCULAR CYLINDER WITH THREE-DIMENSIONAL NUMERICAL SIMULATION
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Three-dimensional numerical simulation of a uniform incompressible viscous flow around a stationary circular cylinder was conducted. The CFX-4 software was used to calculate the hydrodynamic characteristics of the flow and the finite volume method for incompressible Navier-Stokes equations was employed in the program. The simulation of the flow was performed for Re=103 and Re=104 respectively within the sub-critical region. In order to overcome numerical instability for the high Reynolds number flows, a quadratic upwind scheme was incorporated for the Navier-Stokes equations. The periodicity boundary condition was used at the ends of the cylinder. It was found that the evolution of the lift and drag coefficients in each plane along the cylinder span is different. Comparison between the predicted results based on the three-dimensional and the two-dimensional analysis was also given. It is concluded that at the high Reynolds number the effect of three-dimensionality of the flow around the circular cylinder is remarkable, and in addition hydrodynamic coefficients with of 3-D simulation are less than those given by 2-D simulation.
Lift and drag in three-dimensional steady viscous and compressible flow
Liu, Luoqin; Kang, Linlin; Wu, Jiezhi
2016-01-01
In a recent paper, Liu, Zhu & Wu (2015, J. Fluid Mech. 784: 304; LZW for short) present a far-field theory for the aerodynamic force experienced by a body in a two-dimensional, viscous, compressible and steady flow. In this companion theoretical paper we do the same for three-dimensional flow. By a rigorous fundamental solution method of the linearized Navier-Stokes equations, we not only improve the far-field force formula for incompressible flow originally derived by Goldstein in 1931 and summarized by Milne-Thomson in 1968, both being far from complete, to its perfect final form, but also prove that this final form holds universally true in a wide range of compressible flow, from subsonic to supersonic flows. We call this result the unified force theorem (UF theorem for short) and state it as a theorem, which is exactly the counterpart of the two-dimensional compressible Joukowski-Filon theorem obtained by LZW. Thus, the steady lift and drag are always exactly determined by the values of vector circula...
Particle-laden viscous channel flows - model regularization and parameter study
O'Naraigh, Lennon
2016-01-01
We characterize the flow of a viscous suspension in an inclined channel where the flow is maintained in a steady state under the competing influences of gravity and an applied pressure drop. The basic model relies on a diffusive-flux formalism. Such models are common in the literature, yet many of them possess an unphysical singularity at the channel centreline where the shear rate vanishes. We therefore present a regularization of the basic diffusive-flux model that removes this singularity. This introduces an explicit (physical) dependence on the particle size into the model equations. This approach enables us to carry out a detailed parameter study showing in particular the opposing effects of the pressure drop and gravity. Conditions for counter-current flow and complete flow reversal are obtained from numerical solutions of the model equations. These are supplemented by an analytic lower bound on the ratio of the gravitational force to the applied pressure drop necessary to bring about complete flow reve...
On the pressure and stress singularities induced by steady flows of incompressible viscous fluids
Institute of Scientific and Technical Information of China (English)
G.B.Sinclair; X.Chi; T.I-P.Shih
2009-01-01
Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, to date there has been relatively little explicit identification of stress singularities caused by fluid flows. In this study, stress and pressure singularities induced by steady flows of viscous incompressible fluids are asymptotically identified. This is done by taking advantage of an earlier result that the Navier-Stokes equations are locally governed by Stokes flow in angular corners. Findings for power singularities are confirmed by developing and using an analogy with solid mechanics. This analogy also facilitates the identification of flow-induced log singularities. Both types of singularity are further confirmed for two global configurations by applying convergence-divergence checks to numerical results. Even though these flow-induced stress singularities are analogous to singularities in solid mechanics, they nonetheless render a number of structural configurations singular that were not previously appreciated as such from identifications within solid mechanics alone.
The viscous surface-internal wave problem: nonlinear Rayleigh-Taylor instability
Wang, Yanjin
2011-01-01
We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom in a three-dimensional horizontally periodic setting. The effect of surface tension is either taken into account at both free boundaries or neglected at both. We are concerned with the Rayleigh-Taylor instability, so we assume that the upper fluid is heavier than the lower fluid. When the surface tension at the free internal interface is below a critical value, which we identify, we establish that the problem under consideration is nonlinearly unstable.
Minimum divergence viscous flow simulation through finite difference and regularization techniques
Victor, Rodolfo A.; Mirabolghasemi, Maryam; Bryant, Steven L.; Prodanović, Maša
2016-09-01
We develop a new algorithm to simulate single- and two-phase viscous flow through a three-dimensional Cartesian representation of the porous space, such as those available through X-ray microtomography. We use the finite difference method to discretize the governing equations and also propose a new method to enforce the incompressible flow constraint under zero Neumann boundary conditions for the velocity components. Finite difference formulation leads to fast parallel implementation through linear solvers for sparse matrices, allowing relatively fast simulations, while regularization techniques used on solving inverse problems lead to the desired incompressible fluid flow. Tests performed using benchmark samples show good agreement with experimental/theoretical values. Additional tests are run on Bentheimer and Buff Berea sandstone samples with available laboratory measurements. We compare the results from our new method, based on finite differences, with an open source finite volume implementation as well as experimental results, specifically to evaluate the benefits and drawbacks of each method. Finally, we calculate relative permeability by using this modified finite difference technique together with a level set based algorithm for multi-phase fluid distribution in the pore space. To our knowledge this is the first time regularization techniques are used in combination with finite difference fluid flow simulations.
Deciphering viscous flow of frictional melts with the mini-AMS method
Ferré, Eric C.; Chou, Yu-Min; Kuo, Ruo Lin; Yeh, En-Chao; Leibovitz, Natalie R.; Meado, Andrea L.; Campbell, Lucy; Geissman, John W.
2016-09-01
The anisotropy of magnetic susceptibility (AMS) is widely used to analyze magmatic flow in intrusive igneous bodies including plutons, sills and dikes. This method, owing its success to the rapid nature of measurements, provides a proxy for the orientation of markers with shape anisotropy that flow and align in a viscous medium. AMS specimens typically are 25 mm diameter right cylinders or 20 mm on-a-side cubes, representing a volume deemed statistically representative. Here, we present new AMS results, based on significantly smaller cubic specimens, which are 3.5 mm on a side, hence∼250 times volumetrically smaller than conventional specimens. We show that, in the case of frictional melts, which inherently have an extremely small grain size, this small volume is in most cases sufficient to characterize the pseudotachylyte fabric, particularly when magnetite is present. Further, we demonstrate that the mini-AMS method provides new opportunities to investigate the details of frictional melt flow in these coseismic miniature melt bodies. This new method offers significant potential to investigate frictional melt flow in pseudotachylyte veins including contributions to the lubrication of faults at shallow to moderate depths.
The boundary element method applied to viscous and vortex shedding flows around cylinders
Farrant, Tim
Studies are presented to further extend the use of the boundary element method (BEM) for the solution of viscous flows around bluff bodies, governed by the incompressible Navier-Stokes equations. Two distinct formulations are applied to various flows around cylindrical geometries for Reynolds numbers Tan (1994) and known herein as the global BEM, was coded to execute in parallel on multi-processor computers. Reductions in execution time were achieved and the method was employed to solve an oscillating cylinder problem. In this study, the displacement undergone by the body was very large but the Reynolds number was always Tan et al (1998). A validation for isolated and double circular cylinders in a uniform stream was performed against experimental evidence to demonstrate the method's stability and accuracy for laminar vortex shedding with geometries involving multiply connected domains. Finally, computational results for flows around four equispaced circular cylinders of equal diameter and two cylinders, one circular the other elliptical, are reported. Many of the concepts established for the flow around two cylinders of equal diameter were found to be useful in interpretation of these more complicated arrangements.
The viscous surface-internal wave problem: global well-posedness and decay
Wang, Yanjin; Kim, Chanwoo
2011-01-01
We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a general rigid bottom in a three-dimensional horizontally periodic setting. We establish the global well-posedness of the problem both with and without surface tension. We prove that without surface tension the solution decays to the equilibrium state at an almost exponential rate; with surface tension, we show that the solution decays at an exponential rate. Our results include the case in which a heavier fluid lies above a lighter one, provided that the surface tension at the free internal interface is above a critical value, which we identify. This means that sufficiently large surface tension stabilizes the Rayleigh-Taylor instability in the nonlinear setting. As a part of our analysis, we establish elliptic estimates for the two-phase stationary Stokes problem.
A Parallel Multigrid Solver for Viscous Flows on Anisotropic Structured Grids
Prieto, Manuel; Montero, Ruben S.; Llorente, Ignacio M.; Bushnell, Dennis M. (Technical Monitor)
2001-01-01
This paper presents an efficient parallel multigrid solver for speeding up the computation of a 3-D model that treats the flow of a viscous fluid over a flat plate. The main interest of this simulation lies in exhibiting some basic difficulties that prevent optimal multigrid efficiencies from being achieved. As the computing platform, we have used Coral, a Beowulf-class system based on Intel Pentium processors and equipped with GigaNet cLAN and switched Fast Ethernet networks. Our study not only examines the scalability of the solver but also includes a performance evaluation of Coral where the investigated solver has been used to compare several of its design choices, namely, the interconnection network (GigaNet versus switched Fast-Ethernet) and the node configuration (dual nodes versus single nodes). As a reference, the performance results have been compared with those obtained with the NAS-MG benchmark.
Shear banding analysis of plastic models formulated for incompressible viscous flows
Lemiale, V.; Mühlhaus, H.-B.; Moresi, L.; Stafford, J.
2008-12-01
We investigate shear band orientations for a simple plastic formulation in the context of incompressible viscous flow. This type of material modelling has been introduced in literature to enable the numerical simulation of the deformation and failure of the lithosphere coupled with the mantle convection. In the present article, we develop a linear stability analysis to determine the admissible shear band orientations at the onset of bifurcation. We find that the so-called Roscoe angle and Coulomb angle are both admissible solutions. We present numerical simulations under plane strain conditions using the hybrid particle-in-cell finite element code Underworld. The results both in compressional and extensional stress conditions show that the variation of the numerical shear bands angle with respect to the internal friction angle follows closely the evolution of the Coulomb angle.
Numerical Investigation of Viscous Flow Velocity Field around a Marine Cavitating Propeller
Directory of Open Access Journals (Sweden)
Zhifeng Zhu
2014-11-01
Full Text Available Velocity field around a ship cavitating propeller is investigated based on the viscous multiphase flow theory. Using a hybrid grid, the unsteady Navier-stokes (N-S and the bubble dynamics equations are solved in this paper to predict the velocity in a propeller wake and the vapor volume fraction on the back side of propeller blade for a uniform inflow. Compared with experimental results, the numerical predictions of cavitation and axial velocity coincide with the measured data. The evolution of tip vortex is shown, and the interaction between the tip vortex of the current blade and the wake of the next one occurs in the far propeller wake. The frequency of velocity signals changes from shaft rate to blade rate. The phenomena reflect the instability of propeller wake.
Flow of an Elastico-viscous Fluid Past an Infinite Platewith Variable Suction
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Ch. V. Ramana Murthy
2007-07-01
Full Text Available Unsteady state flow of an incompressible elastico-viscous fluid of second-order type pastan infinite vertical porous flat plate by considering uniform and variable suction normal to theplate has been studied and an exact solution is obtained for the velocity field. In the presentsituation, only two prescribed boundary conditions are available while the governing equationof motion is of third-order due to the presence of elastico-viscosity parameter. The conceptfollowing Walters has been used for a much more meaningful solution. The results for thevelocity distribution and skin friction have been analysed and discussed for different values ofthe parameters encountered in the governing equation of motion and skin friction on the plate.It is found that the effect of elastico-viscosity and suction has significant contribution on thebackflow at the wall
Directory of Open Access Journals (Sweden)
Alok Kumar Pandey
2016-12-01
Full Text Available The purpose of present study is to identify the effects of viscous dissipation and suction/injection on MHD flow of a nanofluid past a wedge with convective surface in the appearance of slip flow and porous medium. The basic non-linear PDEs of flow and energy are altered into a set of non-linear ODEs using auxiliary similarity transformations. The system of equations together with coupled boundary conditions have been solved numerically by applying Runge-Kutta-Fehlberg procedure via shooting scheme. The influence of relevant parameters on non-dimensional velocity and temperature profiles are depicted graphically and investigated in detail. The results elucidate that as enhance in the Eckert number, the skin friction coefficient increases, while heat transfer rate decreases. The outcomes also specify that thermal boundary layer thickness declines with an increase in suction parameter. Moreover, it is accelerated with augment in injection parameter. The results are analogized with the study published earlier and it creates a fine concord.
Derivation of a viscous KP including surface tension, and related equations
Meur, Hervé Le
2015-01-01
The aim of this article is to derive surface wave models in the presence of surface tension and viscosity. Using the Navier-Stokes equations with a free surface, flat bottom and surface tension, we derive the viscous 2D Boussinesq system with a weak transverse variation. The assumed transverse variation is on a larger scale than along the main propagation direction. This Boussinesq system is only an intermediate result that enables us to derive the Kadomtsev-Petviashvili (KP) equation which is a 2D generalization of the KdV equation. In addition, we get the 1D KdV equation, and lastly the Boussinesq equation. All these equations are derived for non-vanishing initial conditions.
Transverse and lateral confinement effects on the oscillations of a free cylinder in a viscous flow
Gianorio, Luciano; Cachile, Mario; Hulin, Jean-Pierre; Auradou, Harold
2013-01-01
The different types of instabilities of free cylinders (diameter $D$, length $L$) have been studied in a viscous flow (velocity $U$) between parallel vertical walls of horizontal width $W$ at a distance $H$: the influence of the confinement parameters $D/H$ and $L/W$ has been investigated. As $D/H$ increases, there is a transition from stable flow to oscillations transverse to the walls and then to a fluttering motion with oscillations of the angle of the axis with respect to the horizontal. The two types of oscillations may be superimposed in the transition domain. The frequency $f$ of the transverse oscillations is independent of the lateral confinement $L/W$ in the range: 0.055 \\le L/W \\le 0.94$ for a given cylinder velocity $V_{cx}$ and increases only weakly with $V_{cx}$. These results are accounted for by assuming a 2D local flow over the cylinder with a characteristic velocity independent of $L/W$ for a given $V_{cx}$ value. The experimental values of $f$ are also independent of the transverse confinem...
Schneiders, Lennart; Günther, Claudia; Meinke, Matthias; Schröder, Wolfgang
2016-04-01
A Cartesian cut-cell method for viscous flows interacting with freely moving boundaries is presented. The method enables a sharp resolution of the embedded boundaries and strictly conserves mass, momentum, and energy. A new explicit Runge-Kutta scheme (PC-RK) is introduced by which the overall computational time is reduced by a factor of up to 2.5. The new scheme is a predictor-corrector type reformulation of a popular class of Runge-Kutta methods which substantially reduces the computational effort for tracking the moving boundaries and subsequently reinitializing the solver impairing neither stability nor accuracy. The structural motion is computed by an implicit scheme with good stability properties due to a strong-coupling strategy and the conservative discretization of the flow solver at the material interfaces. A new formulation for the treatment of small cut cells is proposed with high accuracy and robustness for arbitrary geometries based on a weighted Taylor-series approach solved via singular-value decomposition. The efficiency and the accuracy of the new method are demonstrated for several three-dimensional cases of laminar and turbulent particulate flow. It is shown that the new method remains fully conservative even for large displacements of the boundaries leading to a fast convergence of the fluid-solid coupling while spurious force oscillations inherent to this class of methods are effectively suppressed. The results substantiate the good stability and accuracy properties of the scheme even on relatively coarse meshes.
Institute of Scientific and Technical Information of China (English)
M. Turkyilmazoglu
2012-01-01
The present paper is concerned with a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow due to a porous disk rotating with a constant angular speed.The three-dimensional hydromagnetic equations of motion are treated analytically to obtained exact solutions with the inclusion of suction and injection.The well-known thinning/thickening flow field effect of the suction/injection is better understood from the constructed closed form velocity equations.Making use of this solution,analytical formulas for the angular velocity components as well as for the permeable wall shear stresses are derived.Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation.The temperature field is shown to accord with the dissipation and the Joule heating.As a result,exact formulas are obtained for the temperature field which take different forms corresponding to the condition of suction or injection imposed on the wall.
Palassini, M; Remuzzi, A
1998-01-01
Viscous flow through fibrous media is characterized macroscopically by the Darcy permeability (KD). The relationship between KD and the microscopic structure of the medium has been the subject of experimental and theoretical investigations. Calculations of KD based on the solution of the hydrodynamic flow at fiber scale exist in literature only for two-dimensional arrays of parallel fibers. We considered a fiber matrix consisting of a three-dimensional periodic array of cylindrical fibers with uniform radius (r) and length connected in a tetrahedral structure. According to recent ultrastructural studies, this array of fibers can represent a model for the glomerular basement membrane (GBM). The Stokes flow through the periodic array was simulated using a Galerkin finite element method. The dimensionless ratio K* = KD/r2 was determined for values of the fractional solid volume (phi) in the range 0.005 equation only for phi > 0.4. Among the other theoretical analysis considered, only that of Spielman and Goren (Environ. Sci. Technol. 2: 279-287, 1968) gives satisfactory agreement in the whole range of phi considered. These results can be useful to model combined transport of water and macromolecules through the GBM for the estimation of the radius and length of extracellular protein fibrils.
Tiwari, S. N.; Szema, K. Y.
1979-01-01
The influence of change in the precursor region flow properties on the entire shock layer flow phenomena around a Jovian entry body was investigated. The flow in the shock layer was assumed to be steady, axisymmetric, and viscous. Both the chemical equilibrium and the nonequilibrium composition of the shock layer gas were considered. The effects of transitional range behavior were included in the analysis of high altitude entry conditions. Realistic thermophysical and radiation models were used, and results were obtained by employing the implicit finite difference technique in the shock layer and an iterative procedure for the entire shock layer precursor zone. Results obtained for a 45 degree angle hyperboloid blunt body entering Jupiter's atmosphere at zero angle of attack indicates that preheating the gas significantly increases the static pressure and temperature ahead of the shock for entry velocities exceeding 36 km/sec. The nonequilibrium radiative heating rate to the body is found to be significantly higher than the corresponding equilibrium heating. The precursor heating generally increases the radiative and convective heating of a body. That increase is slightly higher for the nonequilibrium conditions.
Institute of Scientific and Technical Information of China (English)
VAJRAVELU Kuppalapalle; PRASAD Kerehalli Vinayaka; NG Chiu-On
2013-01-01
A numerical study is carried out to study the effects of the temperature dependent viscosity on the flow and heat transfer of a nanofluid over a flat surface in the presence of viscous dissipation.The governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations,and are solved numerically by the Keller-box method.The numerical results indicate that the effect of nanoparticle volume fraction is to increase the heat transfer and hence enhance the thermal boundary layer thickness.This is true even in the presence of variable viscosity and the viscous dissipation.Furthermore,the results obtained for heat transfer characteristics with nanoparticles reveal many interesting behaviors that warrant further study on the effects of the "nano-solid-particles".
Three-Dimensional Viscous Numerical Simulation of Tip Clearance Flow in Axial-Flow Pump
Institute of Scientific and Technical Information of China (English)
Changming Yang; Cichang Chen; Jinnuo Wang; Quankai Ji
2003-01-01
The blade tip clearance flow in axial-flow pump is simulated based on three-dimensional N-S equations, RNG k-ε turbulence model, and SIMPLEC algorithm. It shows that numerical results agree well with experiment data measured by 5-hole probe through validation. Flow fields at the blade tip and velocity distribution at the exit of rotor are analyzed in detail. The numerical results show that the increase in tip clearance reduces hydro-head, especially at small flow rate. Experiment equipment is also introduced.
Directory of Open Access Journals (Sweden)
Sushila
2013-09-01
Full Text Available In this paper, we present an efficient analytical approach based on new homotopy perturbation sumudu transform method (HPSTM to investigate the magnetohydrodynamics (MHD viscous flow due to a stretching sheet. The viscous fluid is electrically conducting in the presence of magnetic field and the induced magnetic field is neglected for small magnetic Reynolds number. Finally, some numerical comparisons among the new HPSTM, the homotopy perturbation method and the exact solution have been made. The numerical solutions obtained by the proposed method show that the approach is easy to implement and computationally very attractive.
Bhuiyan, A. S.; Biswas, M. R.
2011-11-01
The effects of pressure stress work and viscous dissipation in mixed convection flow along a vertical flat plate have been investigated. The results are obtained numerically by transforming the governing system of boundary layer equations into a system of non-dimensional equations. Numerical results for different values of pressure stress work parameter, viscous dissipation parameter, and Prandtl number have been obtained. The velocity profiles, temperature distributions, skin friction coefficient, and the rate of heat transfer have been presented graphically for the effects of the aforementioned parameters. Results are compared with previous investigation.
Institute of Scientific and Technical Information of China (English)
FU Xudong; WANG Guangqian; KANG Zhicheng; FEI Xiangjun
2007-01-01
Characteristics of planar velocity distribution of viscous debris flow were analyzed using the measured data at Jiangjia Ravine, Yunnan, China. The velocity data were measured through using two radar velocimeters. The cross-sectional mean velocities were calculated and used to examine Kang et al's (2004) relationship, which was established for converting the flow velocity at river centerline measured by a radar velocimeter into the mean velocity based on the stop-watch method. The velocity coefficient, K, defined by the ratio of the mean velocity to the maximum velocity, ranges from 0.2 to 0.6. Kang et al's (2004) relationship was found being inapplicable to flows with K smaller than 0.43. This paper contributes to show the complexity of the planar velocity distribution of viscous debris flows and the applicability of Kang et al's relationship.
Two-Dimensional Wave Motion on the Charged Surface of a Viscous Liquid
Institute of Scientific and Technical Information of China (English)
LI Fang; YIN Xie-Yuan; YIN Xie-Zhen
2008-01-01
The wave motion on the charged surface of a viscous Newtonian liquid is solved as an initial-value problem. Both the leaky dielectric and perfect dielectric cases are considered. The amplitude of wave is assumed to be small. The electric field induced by surface charge is shown to have a generally destabilizing effect on surface wave. The neutral stability curve is drawn in the (G, N,e) plane (G: the gravitational bond number; Ne: the electrical Bond number). The Ohnesorge number, Taylor-Melcher number and permittivity ratio have little influence on the neutral stability curve. It is testified that the classical normal mode method cannot predict wave behaviour at small times.
水坝绕流的数值研究%Numerical Study of Two-Dimensional Viscous Flow over Dams
Institute of Scientific and Technical Information of China (English)
王利兵; 刘宇陆; 涂敏杰
2003-01-01
In this paper, the characteristics of two-dimensional viscous flow over two dams were numerically investigated. The results show that the behavior of the vortices is closely related to the space between two dams, water depth, Fr number and Reynolds number. In addition, the flow properties behind each dam are different, and the changes over two dams are more complex than over one dam. Finally, the relevant turbulent characteristics were analyzed.
Directory of Open Access Journals (Sweden)
Liushuai CAO
2016-01-01
Full Text Available To estimate the maneuverability of a submarine at the early design stage, an accurate evaluation of the hydrodynamic coefficients is important. In a collaborative exercise, the authors performed calculations on the bare hull DRAPA SUBOFF submarine to investigate the capability of viscous-flow solvers to predict the forces and moments as well as flow field around the body. A typical simulation program was performed for both the steady drift tests and rotating arm tests. The same grid topology based on multi-block mesh strategy was used to discretize the computational domain. A procedure designated drift sweep was implemented to automatically increment the drift angle during the simulation of steady drift tests. The rotating coordinate system was adopted to perform the simulation of rotating arm tests. The Coriolis force and centrifugal force due to the computation in a rotating frame of reference were treated explicitly and added to momentum equations as source terms. Lastly, the computed forces and moment as a function of angles of drift in both conditions are compared with experimental results and literature values. They always show the correct trend. Flow field quantities including pressure coefficients and vorticity and axial velocity contours are also visualized to vividly describe the evolution of flow motions along the hull.
Ice Shelves as Floating Channel Flows of Viscous Power-Law Fluids
Banik, Indranil
2013-01-01
We attempt to better understand the flow of marine ice sheets. Treating ice as a viscous shear-thinning power law fluid, we develop an asymptotic (late-time) theory in two cases - the presence or absence of contact with sidewalls. Most real-world situations fall somewhere between the two extreme cases considered. When sidewalls are absent, we obtain the equilibrium grounding line thickness using a simple computer model and have an analytic approximation. For shelves in contact with sidewalls, we obtain an asymptotic theory, valid for long shelves. Our theory is based on the velocity profile across the channel being a generalised version of Poiseuille flow, which works when lateral shear dominates the force balance. We determine when this is. We conducted experiments using a laboratory model for ice. This was a suspension of xanthan in water, at a concentration of 0.5% by mass. The lab model has $n \\approx 3.8$ (similar to that of ice). The experiments agreed extremely well with our theories for all relevant p...
Large-scale computation of incompressible viscous flow by least-squares finite element method
Jiang, Bo-Nan; Lin, T. L.; Povinelli, Louis A.
1993-01-01
The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The simple substitution of the Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. The Taylor-Goertler-like vortices are observed for Re = 1,000.
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I. J. Uwanta
2014-01-01
Full Text Available This study investigates the unsteady natural convection and mass transfer flow of viscous reactive, heat generating/absorbing fluid in a vertical channel formed by two infinite parallel porous plates having temperature dependent thermal conductivity. The motion of the fluid is induced due to natural convection caused by the reactive property as well as the heat generating/absorbing nature of the fluid. The solutions for unsteady state temperature, concentration, and velocity fields are obtained using semi-implicit finite difference schemes. Perturbation techniques are used to get steady state expressions of velocity, concentration, temperature, skin friction, Nusselt number, and Sherwood number. The effects of various flow parameters such as suction/injection (γ, heat source/sinks (S, Soret number (Sr, variable thermal conductivity δ, Frank-Kamenetskii parameter λ, Prandtl number (Pr, and nondimensional time t on the dynamics are analyzed. The skin friction, heat transfer coefficients, and Sherwood number are graphically presented for a range of values of the said parameters.
Efficiency of Slit Dam Prevention against Non-Viscous Debris Flow
Institute of Scientific and Technical Information of China (English)
HAN Wenbing; OU Guoqiang
2006-01-01
This paper describes an experimental work in order to assess the efficiency of slit dam on non-viscous debris flow. Some results have been acquired as follows: ① there are three kinds of blocking type: Total-blocking, opening and part-blocking. The blocking conditions of slit dam are closely link to b/dmax (the ratio of slit width to maximum diameter of solid matter), as b/dmax is less than 0.739, the slit dam is total- blocking; and b/dmax is more than 1.478, the slit dam will be opening; whereas b/dmax ranges from 0.739 to 1.478, the slit dam is part-blocking. ② Variation of the mean density passing through slit dam is the most obvious as b/dmax ranges from 0.739 to 1.232. ③ According to experimental results, slit dams have been shown to be effective in reducing debris flow density while slit density ∑b/B (B is slit dam width) ranges from 0.2 to 0.5.
Multi-Dimensional, Compressible Viscous Flow on a Moving Voronoi Mesh
Muñoz, Diego; Marcus, Robert; Vogelsberger, Mark; Hernquist, Lars
2012-01-01
Numerous formulations of finite volume schemes for the Euler and Navier-Stokes equations exist, but in the majority of cases they have been developed for structured and stationary meshes. In many applications, more flexible mesh geometries that can dynamically adjust to the problem at hand and move with the flow in a (quasi) Lagrangian fashion would, however, be highly desirable, as this can allow a significant reduction of advection errors and an accurate realization of curved and moving boundary conditions. Here we describe a novel formulation of viscous continuum hydrodynamics that solves the equations of motion on a Voronoi mesh created by a set of mesh-generating points. The points can move in an arbitrary manner, but the most natural motion is that given by the fluid velocity itself, such that the mesh dynamically adjusts to the flow. Owing to the mathematical properties of the Voronoi tessellation, pathological mesh-twisting effects are avoided. Our implementation considers the full Navier-Stokes equat...
Energy Technology Data Exchange (ETDEWEB)
Aydin, Orhan; Avci, Mete [Karadeniz Technical University, Trabzon (Turkey). Department of Mechanical Engineering
2006-08-15
In this study, analytical solutions are obtained to predict laminar heat-convection in a Couette-Poiseuille flow between two plane parallel plates with a simultaneous pressure gradient and an axial movement of the upper plate. A Newtonian fluid with constant properties is considered with an emphasis on the viscous-dissipation effect. Both hydrodynamically and thermally fully-developed flow cases are investigated. The axial heat-conduction in the fluid is neglected. Two different orientations of the thermal boundary-conditions are considered: the constant heat-flux at the upper plate with an adiabatic lower plate (Case A) and the constant heat-flux at the lower plate with an adiabatic upper plate (Case B). For different values of the relative velocity of the upper plate, the effect of the modified Brinkman number on the temperature distribution and the Nusselt number are discussed. Comparison of the present analytical results for a special case with those available in the literature indicates an excellent agreement. (author)
Energy Technology Data Exchange (ETDEWEB)
Duckworth, Robert C.; Baylor, Larry R.; Meitner, Steven J.; Combs, Stephen K.; Ha, Tam; Morrow, Michael; Biewer, T. [Fusion and Materials for Nuclear System Division, Oak Ridge National Laboratory, Oak Ridge (United States); Rasmussen, David A.; Hechler, Michael P. [U.S. ITER Project Office, Oak Ridge National Laboratory, Oak Ridge (United States); Pearce, Robert J. H.; Dremel, Mattias [ITER Organization, 13115 St. Paul-lez-Durance (France); Boissin, J.-C. [Consultant, Grenoble (France)
2014-01-29
As part of the U.S. ITER contribution to the vacuum systems for the ITER fusion project, a cryogenic viscous compressor (CVC) is being designed and fabricated to cryopump hydrogenic gases in the torus and neutral beam exhaust streams and to regenerate the collected gases to controlled pressures such that they can be mechanically pumped with controlled flows to the tritium reprocessing facility. One critical element of the CVC design that required additional investigation was the determination of flow rates of the low pressure (up to 1000 Pa) exhaust stream that would allow for complete pumping of hydrogenic gases while permitting trace levels of helium to pass through the CVC to be pumped by conventional vacuum pumps. A sub-scale prototype test facility was utilized to determine the effectiveness of a static mixer pump tube concept, which consisted of a series of rotated twisted elements brazed into a 2-mm thick, 5-cm diameter stainless steel tube. Cold helium gas flow provided by a dewar and helium transfer line was used to cool the exterior of the static mixer pump tube. Deuterium gas was mixed with helium gas through flow controllers at different concentrations while the composition of the exhaust gas was monitored with a Penning gauge and optical spectrometer to determine the effectiveness of the static mixer. It was found that with tube wall temperatures between 6 K and 9 K, the deuterium gas was completely cryopumped and only helium passed through the tube. These results have been used to design the cooling geometry and the static mixer pump tubes in the full-scale CVC prototype.
Energy Technology Data Exchange (ETDEWEB)
Duckworth, Robert C [ORNL; Baylor, Larry R [ORNL; Meitner, Steven J [ORNL; Combs, Stephen Kirk [ORNL; Ha, Tam T [ORNL; Morrow, Michael [ORNL; Biewer, Theodore M [ORNL; Rasmussen, David A [ORNL; Hechler, Michael P [ORNL; Pearce, R.J.H. [ITER Organization, Cadarache, France; Dremel, M. [ITER Organization, Cadarache, France; Boissin, Jean Claude [Consultant
2014-01-01
As part of the U.S. ITER contribution to the vacuum systems for the ITER fusion project, a cryogenic viscous compressor (CVC) is being designed and fabricated to cryopump hydrogenic gases in the torus and neutral beam exhaust streams and to regenerate the collected gases to controlled pressures such that they can be mechanically pumped with controlled flows to the tritium reprocessing facility. One critical element of the CVC design that required additional investigation was the determination of flow rates of the low pressure (50 to 1000 Pa) exhaust stream that would allow for complete pumping of hydrogenic gases while permitting trace levels of helium to pass through the CVC to be pumped by conventional vacuum pumps. A sub-scale prototype test facility was utilized to determine the effectiveness of a static mixer pump tube concept, which consisted of a series of rotated twisted elements brazed into a 2-mm thick, 5-cm diameter stainless steel tube. Cold helium gas flow provided by a dewar and helium transfer line was used to cool the exterior of the static mixer pump tube. Deuterium gas was mixed with helium gas through flow controllers at different concentrations while the composition of the exhaust gas was monitored with a Penning gauge and optical spectrometer to determine the effectiveness of the static mixer. It was found that with tube wall temperatures between 6 K and 9 K, the deuterium gas was completely cryopumped and only helium passed through the tube. These results have been used to design the cooling geometry and the static mixer pump tubes in the full-scale CVC prototype
Barnett, Mark
This investigation is concerned with calculating strong viscous-inviscid interactions in two-dimensional laminar supersonic flows with and without separation. The equations solved are the so-called parabolized Navier-Stokes equations. The streamwise pressure gradient term is written as a combination of a forward and a backward difference to provide a path for upstream propogation of information. Global iteration is employed to repeatedly update the solution from an initial guess until convergence is achieved. Interacting boundary layer theory is discussed in order to provide some essential background information for the development of the present calculation technique. The numerical scheme used is an alternating direction explicit (ADE) procedure which is adapted from the Saul'yev method. This technique is chosen as an alternative to the more difficult to program multigrid strategy used by other investigators and the slower converging Gauss-Seidel method. Separated flows are computed using the ADE method. Only small or moderate separation bubbles are considered. This restriction permits simple approximations to the convective terms in reversed flow regions without introducing severe error since the reversed flow velocities are small. Results are presented for a number of geometries including compression ramps and humps on flat plates with separation. The present results are compared with those obtained by other investigators using the full Navier-Stokes equations and interacting boundary layer theory. Comparisons were found to be qualitatively good. The quantitative comparisons varied, however mesh refinement studies indicated that the parabolized Navier-Stokes solutions tended towards second-order accurate full Navier-Stokes solutions as well as interacting boundary layer solutions for which mesh refinement studies were also executed.
Technology and Development Trends of China's Viscous Crude Surface Production Facilities
Institute of Scientific and Technical Information of China (English)
Miao Chengwu
1996-01-01
@@ Main Technical Characteristics Technique of viscous crude gathering, transportation and treatment approaches the international level (1) Diluent oil-blended gathering and transportation process, an original creation of China, plays an important and guarantee role in increasing viscous crude output,especially in the viscous crude fields with dilute crude resources nearby.
Directory of Open Access Journals (Sweden)
K. V. Litvinov
2016-01-01
Full Text Available In this paper, we analyzed the flat non-isothermal stationary flow of abnormally viscous fluid in the channels with asymmetric boundary conditions and an unknown output boundary. The geometry of the channels in which the problem is considered, is such regions, that at the transition to bipolar a system of coordinates map into rectangles. This greatly simplifies the boundary conditions, since it is possible to use an orthogonal grid and boundary conditions are given in its nodes. Fields of this type are often found in applications. The boundary conditions are set as follows: the liquid sticks to the boundaries of the channels, which rotate at different speeds and have different radius and temperature; moreover, temperature at the entrance to deformation is known, while on the boundary with the surface the material has the surface temperature; the pressure on the enter and exit of the region becomes zero. The rheological model only takes into account the anomaly of viscosity. The material is not compressible. This process can be described by a system consisting of continuity equations, the equations of conservation of momentum and an energy equation: ∇
Highly stable superhydrophobic surfaces under flow conditions
Lee, Moonchan; Yim, Changyong; Jeon, Sangmin
2015-01-01
We synthesized hydrophobic anodic aluminum oxide nanostructures with pore diameters of 35, 50, 65, and 80 nm directly on quartz crystal microresonators, and the stability of the resulting superhydrophobicity was investigated under flow conditions by measuring changes in the resonance frequency and dissipation factor. When the quartz substrates were immersed in water, their hydrophobic surfaces did not wet due to the presence of an air interlayer. The air interlayer was gradually replaced by water over time, which caused decreases in the resonance frequency (i.e., increases in mass) and increases in the dissipation factor (i.e., increases in viscous damping). Although the water contact angles of the nanostructures increased with increasing pore size, the stability of their superhydrophobicity increased with decreasing pore size under both static conditions (without flow) and dynamic conditions (with flow); this increase can be attributed to an increase in the solid surface area that interacts with the air layer above the nanopores as the pore size decreases. Further, the effects of increasing the flow rate on the stability of the superhydrophobicity were quantitatively determined.
Chen, Yong; Huang, Yiyong; Chen, Xiaoqian
2013-11-01
This paper deals with the problem of wave propagation in a compressible viscous fluid confined by a rigid-walled circular pipeline in the presence of a shear mean flow. On the assumption of isentropic and axisymmetric wave propagation, the convected acoustic equations are mathematically deduced from the conservations of continuity and momentum, leading to a set of coupled second-order differential equations with respect of the acoustic pressure and velocity components in radial and axial directions. A solution based on the Fourier-Bessel theory, which is complete and orthogonal in Lebesgue space, is introduced to transform the differential equations to an infinite set of homogeneous algebraic equations, thus the wave number can be calculated due to the existence condition of a non-trivial solution. After the discussion of the method's convergence, the cut-off frequency of the wave mode is theoretically analyzed. Furthermore, wave attenuation of the first four wave modes due to fluid viscosity is numerically studied in the presence of the laminar and turbulent flow profiles. Meanwhile, the measurement performance of an ultrasonic flow meter based on the difference of downstream and upstream wave propagations is parametrically addressed.
Akaydin, H. Dogus; Moini-Yekta, Shayan; Housman, Jeffrey A.; Nguyen, Nhan
2015-01-01
In this paper, we present a static aeroelastic analysis of a wind tunnel test model of a wing in high-lift configuration using a viscous flow simulation code. The model wing was tailored to deform during the tests by amounts similar to a composite airliner wing in highlift conditions. This required use of a viscous flow analysis to predict the lift coefficient of the deformed wing accurately. We thus utilized an existing static aeroelastic analysis framework that involves an inviscid flow code (Cart3d) to predict the deformed shape of the wing, then utilized a viscous flow code (Overflow) to compute the aerodynamic loads on the deformed wing. This way, we reduced the cost of flow simulations needed for this analysis while still being able to predict the aerodynamic forces with reasonable accuracy. Our results suggest that the lift of the deformed wing may be higher or lower than that of the non-deformed wing, and the washout deformation of the wing is the key factor that changes the lift of the deformed wing in two distinct ways: while it decreases the lift at low to moderate angles of attack simply by lowering local angles of attack along the span, it increases the lift at high angles of attack by alleviating separation.
Temporal Entropy Generation in the Viscous Layers of Laterally-converging Duct Flows
Energy Technology Data Exchange (ETDEWEB)
Donald M. McEligot; Robert S. Brodkey; Helmut Eckelmann
2008-12-01
Since insight into entropy generation is a key to increasing efficiency and thereby reducing fuel consumption and/or waste and -- for wall-bounded flows -- most entropy is generated in the viscous layer, we examine the transient behavior of its dominant contributor there for a non-canonical flow. New measurements in oil flow are presented for the effects of favorable streamwise mean pressure gradients on temporal entropy generation rates and, in the process, on key Reynolds-stress-producing events such as sweep front passage and on the deceleration/outflow phase of the overall bursting process. Two extremes have been considered: (1) a high pressure gradient, nearing "laminarization," and (2), for comparison, a low pressure gradient corresponding to many earlier experiments. In both cases, the peak temporal entropy generation rate occurs shortly after passage of the ejection/sweep interface. Whether sweep and ejection rates appear to decrease or increase with the pressure gradient depends on the feature examined and the manner of sampling. When compared using wall coordinates for velocities, distances and time, the trends and magnitudes of the transient behaviors are mostly the same. The main effects of the higher pressure gradient are (1) changes in the time lag between detections -- representing modification of the shape of the sweep front and the sweep angle with the wall, (2) modification of the magnitude of an instantaneous Reynolds shear stress with wall distance and (3) enlarging the sweeps and ejections. Results new for both low and high pressure gradients are the temporal behaviors of the dominant contribution to entropy generation; it is found to be much more sensitive to distance from the wall than to streamwise pressure gradient.
Film Flow Dominated Simultaneous Flow of Two Viscous Incompressible Fluids Through a Porous Medium
Directory of Open Access Journals (Sweden)
Olav eAursjø
2014-11-01
Full Text Available We present an experimental study of two-phase flow in a quasi-two-dimensional porous medium. The two phases, a water-glycerol solution and a commercial food grade rapeseed/canola oil, having an oil to water-glycerol viscosity ratio of 1.3, are injected simultaneously into a Hele-Shaw cell with a mono-layer of randomly distributed glass beads. The two liquids are injected into the model from alternating point inlets. Initially, the porous model is filled with the water-glycerol solution. We observe that after an initial transient state, an overall static cluster configuration is obtained. While the oil is found to create a connected system spanning cluster, a large part of the water-glycerol clusters left behind the initial invasion front is observed to remain immobile throughout the rest of the experiment. This could suggest that the water-glycerol flow-dynamics is largely dominated by film flow. The flow pathways are thus given through the dynamics of the initial invasion. This behavior is quite different from that observed in systems with large viscosity differences between the two fluids, and where compressibility plays an important part of the process.
Stability of viscous film flow coating the interior of a vertical tube with a porous wall
Liu, Rong; Ding, Zijing
2017-05-01
The stability of the gravity-driven flow of a viscous film coating the inside of a tube with a porous wall is studied theoretically. We used Darcy's law to describe the motion of fluids in a porous medium. The Beaver-Joseph condition is used to describe the discontinuity of velocity at the porous-fluid interface. We derived an evolution equation for the film thickness using a long-wave approximation. The effect of velocity slip at the porous wall is identified by a parameter β . We examine the effect of β on the temporal stability, the absolute-convective instability (AI-CI), and the nonlinear evolution of the interface deformation. The results of the temporal stability reveal that the effect of velocity slip at the porous wall is destabilizing. The parameter β plays an important role in determining the AI-CI behavior and the nonlinear evolution of the interface. The presence of the porous wall promotes the absolute instability and the formation of the plug in the tube.
Peters, I.R.
2012-01-01
Reducing the area through which a fluid is allowed to flow often leads to an increase of flow velocity. A familiar example of this is a garden hose, where one can change the rather weak stream that usually flows out into a strong jet by narrowing the orifice at the end of the hose. In this example,
Peters, I.R.
2012-01-01
Reducing the area through which a fluid is allowed to flow often leads to an increase of flow velocity. A familiar example of this is a garden hose, where one can change the rather weak stream that usually flows out into a strong jet by narrowing the orifice at the end of the hose. In this example,
Institute of Scientific and Technical Information of China (English)
T HAYAT; S ASAD; A ALSAEDI
2014-01-01
The aim of the present study is to investigate the flow of the Casson fluid by an inclined stretching cylinder. A heat transfer analysis is carried out in the presence of thermal radiation and viscous dissipation effects. The temperature dependent thermal conductivity of the Casson fluid is considered. The relevant equations are first simplified under usual boundary layer assumptions, and then transformed into ordinary differential equations by suitable transformations. The transformed ordinary differential equations are computed for the series solutions of velocity and temperature. A convergence analysis is shown explicitly. Velocity and temperature fields are discussed for different physical parameters by graphs and numerical values. It is found that the velocity decreases with the increase in the angle of inclination while increases with the increase in the mixed convection parameter. The enhancement in the thermal conductivity and radiation effects corresponds to a higher fluid temperature. It is also found that heat transfer is more pronounced in a cylinder when it is compared with a flat plate. The thermal boundary layer thickness increases with the increase in the Eckert number. The radiation and variable thermal conductivity decreases the heat transfer rate at the surface.
Dorney, Suzanne; Dorney, Daniel J.; Huber, Frank; Sheffler, David A.; Turner, James E. (Technical Monitor)
2001-01-01
The advent of advanced computer architectures and parallel computing have led to a revolutionary change in the design process for turbomachinery components. Two- and three-dimensional steady-state computational flow procedures are now routinely used in the early stages of design. Unsteady flow analyses, however, are just beginning to be incorporated into design systems. This paper outlines the transition of a three-dimensional unsteady viscous flow analysis from the research environment into the design environment. The test case used to demonstrate the analysis is the full turbine system (high-pressure turbine, inter-turbine duct and low-pressure turbine) from an advanced turboprop engine.
Talygin, E A; Zazybo, N A; Zhorzholiany, S T; Krestinich, I M; Mironov, A A; Kiknadze, G I; Bokerya, L A; Gorodkov, A Y; Makarenko, V N; Alexandrova, S A
2016-01-01
New approach to intracardiac blood flow condition analysis based on geometric parameters of left ventricle flow channel has been suggested. Parameters, that used in this method, follow from exact solutions of nonstationary Navier-Stocks equations for selforganized tornado-like flows of viscous incompressible fluid. The main advantage of this method is considering dynamic anatomy of intracardiac cavity and trabeculae relief of left ventricle streamlined surface, both registered in a common mri-process, as flow condition indicator. Calculated quantity options that characterizes blood flow condition can be use as diagnostic criterias for estimation of violation in blood circulation function which entails heart ejection reduction. Developed approach allows to clarify heart jet organization mechanism and estimate the share of the tornado-like flow self-organization in heart ejection structure.
Energy Technology Data Exchange (ETDEWEB)
Boualit, A.; Boualit, S. [Unite de recherche appliquee en energies renouvelables, Ghardaia (Algeria); Zeraibi, N. [Universite de Boumerdes, Faculte des hydrocarbures dept. Transport et equipement, Boumerdes (Algeria); Amoura, M. [Universite des Sciences et de la Technologie Houari Boumedienne, Faculte de Physique, Dept. Energetique, Alger (Algeria)
2011-01-15
The thermal development of the hydrodynamically developing laminar flow of a viscoplastic fluid (fluid of Bingham) between two plane plates maintained at a constant temperature has been studied numerically. This analysis has shown the effect caused by inertia and the rheological behaviour of the fluid on the velocity, pressure and temperature fields. The effects of Bingham and Peclet numbers on the Nusselt values with the inclusion of viscous dissipation are also discussed. (authors)
Georgievskii, D. V.
2007-06-01
Material functions are necessary element of the constitutive relations determining any model of continuum. These functions can be defined as a collection of objects from which the operator of constitutive relations can be reconstructed completely. The material functions are found in test experiments and show the differences between a given medium and other media in the framework of the same model [1]. The "test experiment theory" is an important part of modern experimental mechanics. Just as in any experiment, from determining the viscosity coefficient by using the rotational viscosimeters to constructing the yield surface by using machines combined loading, the material functions are determined with an unavoidable error. For example, experimenters know that, in experiments with arbitrary accuracy, the moduli of elasticity can only be measured with an unimprovable tolerance of about 7%. Starting already from [2], the investigators' attention has been repeatedly drawn to the fact that it is necessary to take into account this tolerance in determining the material constants, functions, and functionals in problems of mechanics and especially in analyzing the stability of deformation processes. Mathematically, this means that problems of stability under perturbations of the initial data, external constantly acting forces, domain boundaries, etc. should be supplemented with the assumption that the material functions have unknown perturbations of a certain class [3]. The variations of material functions in the framework of the linearized stability theory were considered in [2, 4, 5]. In what follows, we study isotropic tensor functions in the most general case of scalar and tensor nonlinearity. These functions are assigned the meaning of constitutive relations between the stress and strain rate tensors in continuum. These constitutive relations contain scalar material functions of invariants on which, as follows from the above, some variations proportional to a small
Viscous dissipation effects on heat transfer in flow past a continuous moving plate
Digital Repository Service at National Institute of Oceanography (India)
Soundalgekar, V.M.; Murty, T.V.R.
The study of thermal boundary layer on taking into account the viscous dissipative heat, on a continuously moving semi-infinite flat plate is presented here.Similarity solutions are derived and the resulting equations are integrated numerically...
MHD Flow and Heat Transfer Analysis in the Wire Coating Process Using Elastic-Viscous
Zeeshan Khan; Rehan Ali Shah; Saeed Islam; Hamid Jan; Bilal Jan; Haroon-Ur Rasheed; Aurangzeeb Khan
2017-01-01
The most important plastic resins used for wire coating are polyvinyl chloride (PVC), nylon, polysulfone, and low-/high-density polyethylene (LDPE/HDPE). In this article, the coating process is performed using elastic-viscous fluid as a coating material for wire coating in a pressure type coating die. The elastic-viscous fluid is electrically conducted in the presence of an applied magnetic field. The governing non-linear equations are modeled and then solved analytically by utilizing an Adom...
Yang, Jing; Ren, Yan-Yu
2016-01-01
We examine the evolution of quark-gluon plasma (QGP) droplets with viscous hydrodynamics and analyze pion transverse-momentum spectrum, elliptic flow, and Hanbury-Brown-Twiss (HBT) interferometry in a granular source model consisting of the viscous QGP droplets. The shear viscosity of the QGP droplet speeds up the droplet evolution and the effect of the bulk viscosity on the evolution is negligible. Although there are viscous effects on the droplet evolution, the pion momentum spectrum and elliptic flow change little for the granular sources with and without viscosity. On the other hand, the influence of viscosity on HBT radius $R_{\\rm out}$ is significant. It makes $R_{\\rm out}$ decrease in the granular source model. We determine the model parameters of granular sources by the experimental data of pion transverse-momentum spectrum, elliptic flow, and HBT radii together, and investigate the effects of viscosity on the model parameters. The results indicate that the granular source model may reproduce the expe...
Ha, Hojin; Lantz, Jonas; Haraldsson, Henrik; Casas, Belen; Ziegler, Magnus; Karlsson, Matts; Saloner, David; Dyverfeldt, Petter; Ebbers, Tino
2016-12-01
Flow-induced blood damage plays an important role in determining the hemodynamic impact of abnormal blood flow, but quantifying of these effects, which are dominated by shear stresses in highly fluctuating turbulent flow, has not been feasible. This study evaluated the novel application of turbulence tensor measurements using simulated 4D Flow MRI data with six-directional velocity encoding for assessing hemodynamic stresses and corresponding blood damage index (BDI) in stenotic turbulent blood flow. The results showed that 4D Flow MRI underestimates the maximum principal shear stress of laminar viscous stress (PLVS), and overestimates the maximum principal shear stress of Reynolds stress (PRSS) with increasing voxel size. PLVS and PRSS were also overestimated by about 1.2 and 4.6 times at medium signal to noise ratio (SNR) = 20. In contrast, the square sum of the turbulent viscous shear stress (TVSS), which is used for blood damage index (BDI) estimation, was not severely affected by SNR and voxel size. The square sum of TVSS and the BDI at SNR >20 were underestimated by less than 1% and 10%, respectively. In conclusion, this study demonstrated the feasibility of 4D Flow MRI based quantification of TVSS and BDI which are closely linked to blood damage.
Efficient numerical solution of steady free-surface Navier-Stokes flow
Brummelen, E.H. van; Raven, H.C.; Koren, B.
2001-01-01
Numerical solution of flows that are partially bounded by a freely moving boundary is of great importance in practical applications such as ship hydrodynamics. The usual method for solving steady viscous free-surface flow subject to gravitation is alternating time integration of the kinematic cond
Thermocapillary Flow on Superhydrophobic Surfaces
Baier, Tobias; Hardt, Steffen
2010-01-01
A liquid in Cassie-Baxter state above a structured superhydrophobic surface is ideally suited for surface driven transport due to its large free surface fraction in close contact to a solid. We investigate thermal Marangoni flow over a superhydrophobic array of fins oriented parallel or perpendicular to an applied temperature gradient. In the Stokes limit we derive an analytical expression for the bulk flow velocity above the surface and compare it with numerical solutions of the Navier-Stokes equation. Even for moderate temperature gradients comparatively large flow velocities are induced, suggesting to utilize this principle for microfluidic pumping.
Directory of Open Access Journals (Sweden)
Prasad K.V.
2017-02-01
Full Text Available The effect of thermal radiation and viscous dissipation on a combined free and forced convective flow in a vertical channel is investigated for a fully developed flow regime. Boussinesq and Roseseland approximations are considered in the modeling of the conduction radiation heat transfer with thermal boundary conditions (isothermal-thermal, isoflux-thermal, and isothermal-flux. The coupled nonlinear governing equations are also solved analytically using the Differential Transform Method (DTM and regular perturbation method (PM. The results are analyzed graphically for various governing parameters such as the mixed convection parameter, radiation parameter, Brinkman number and perturbation parameter for equal and different wall temperatures. It is found that the viscous dissipation enhances the flow reversal in the case of a downward flow while it counters the flow in the case of an upward flow. A comparison of the Differential Transform Method (DTM and regular perturbation method (PM methods shows the versatility of the Differential Transform Method (DTM. The skin friction and the wall temperature gradient are presented for different values of the physical parameters and the salient features are analyzed.
Energy Technology Data Exchange (ETDEWEB)
Rusanov, A.V.; Yershov, S.V. [Institute of Mechanical Engineering Problems of National Academy of Sciences of Ukraine Kharkov (Ukraine)
1997-12-31
The numerical method is suggested for the calculation of the 3D periodically unsteady viscous cascade flow evoked by the aerodynamics interaction of blade rows. Such flow is described by the thin-layer Reynolds-averaged unsteady Navier-Stokes equations. The turbulent effects are simulated with the modified Baldwin-Lomax turbulence model. The problem statement allows to consider an unsteady flow through either a single turbo-machine stage or a multi stage turbomachine. The sliding mesh techniques and the time-space non-oscillatory square interpolation are used in axial spacings to calculate the flow in a computational domain that contains the reciprocally moving elements. The gasdynamical equations are integrated numerically with the implicit quasi-monotonous Godunov`s type ENO scheme of the second or third order of accuracy. The suggested numerical method is incorporated in the FlowER code developed by authors for calculations of the 3D viscous compressible flows through multi stage turbomachines. The numerical results are presented for unsteady turbine stage throughflows. The method suggested is shown to simulate qualitatively properly the main unsteady cascade effects in particular the periodically blade loadings, the propagation of stator wakes through rotor blade passage and the unsteady temperature flowfields for stages with cooled stator blades. (author) 21 refs.
Dynamics of viscous liquid bridges inside microchannels subject to external oscillatory flow
Ahmadlouydarab, Majid; Azaiez, Jalel; Chen, Zhangxin
2015-02-01
We report on two-dimensional simulations of liquid bridges' dynamics inside microchannels of uniform wettability and subject to an external oscillatory flow rate. The oscillatory flow results in a zero net flow rate and its effects are compared to those of a stationary system. To handle the three phase contact lines motion, Cahn-Hilliard diffuse-interface formulation was used and the flow equations were solved using the finite element method with adaptively refined unstructured grids. The results indicate that the liquid bridge responds in three different ways depending on the substrate wettability properties and the frequency of the oscillatory flow. In particular below a critical frequency, the liquid bridge will rupture when the channel walls are philic or detach from the surface when they are phobic. However, at high frequencies, the liquid bridge shows a perpetual periodic oscillatory motion for both philic and phobic surfaces. Furthermore, an increase in the frequency of the flow velocity results in stabilization effects and a behavior approaching that of the stationary system where no rupture or detachment can be observed. This stable behavior is the direct result of less deformation of the liquid bridge due to the fast flow direction change and motion of contact lines on the solid substrate. Moreover, it was found that the flow velocity is out of phase with the footprint and throat lengths and that the latter two also show a phase difference. These differences were explained in terms of the motion of the two contact lines on the solid substrates and the deformation of the two fluid-fluid interfaces.
Guha, Abhijit; Sengupta, Sayantan
2014-03-01
In this article, the fluid dynamics of work transfer within the narrow spacing (usually of the order of 100 μm) of multiple concentric discs of a Tesla disc turbomachine (turbine or compressor) has been analysed theoretically and computationally. Both the overall work transfer and its spatial development have been considered. It has been established that the work transfer mechanism in a Tesla disc turbomachine is very different from that in a conventional turbomachine, and the formulation of the Euler's work equation for the disc turbomachine contains several conceptual subtleties because of the existence of complex, three dimensional, non-uniform, viscous flow features. A work equivalence principle has been enunciated, which establishes the equality between the magnitudes of work transfer determined rigorously from two different approaches—one based on the shear stress acting on the disc surfaces and the other based on the change in angular momentum of the fluid. Care is needed in identifying the shear stress components that are responsible for the generation or absorption of useful power. It is shown from the Reynolds transport theorem that mass-flow-averaged tangential velocities (as opposed to the normally used area-averaged values) must be used in determining the change in angular momentum; the calculation has to be carefully formulated since both radial velocity (that determines throughput) and tangential velocity (that generates torque) depend strongly on the coordinate perpendicular to the disc surfaces. The principle of work transfer has been examined both in the absolute and relative frames of reference, revealing the subtle role played by Coriolis force. The concept of a new non-dimensional quantity called the torque potential fraction (Δ tilde H) is introduced. The value of Δ tilde H at any radial position increases with a decrease in inter-disc spacing. The computational fluid dynamic analysis shows that, for small value of inter-disc spacing and
Heat Transfer in Bubble Columns with High Viscous and Low Surface Tension Media
Energy Technology Data Exchange (ETDEWEB)
Kim, Wan Tae; Lim, Dae Ho; Kang, Yong [Chungnam National University, Daejeon (Korea, Republic of)
2014-08-15
Axial and overall heat transfer coefficients were investigated in a bubble column with relatively high viscous and low surface tension media. Effects of superficial gas velocity (0.02-0.1 m/s), liquid viscosity (0.1-3 Pa·s) and surface tension (66.1-72.9x10{sup -3} N/m) on the local and overall heat transfer coefficients were examined. The heat transfer field was composed of the immersed heater and the bubble column; a vertical heater was installed at the center of the column coaxially. The heat transfer coefficient was determined by measuring the temperature differences continuously between the heater surface and the column which was bubbling in a given operating condition, with the knowledge of heat supply to the heater. The local heat transfer coefficient increased with increasing superficial gas velocity but decreased with increasing axial distance from the gas distributor and liquid surface tension. The overall heat transfer coefficient increased with increasing superficial gas velocity but decreased with increasing liquid viscosity or surface tension. The overall heat transfer coefficient was well correlated in terms of operating variables such as superficial gas velocity, liquid surface tension and liquid viscosity with a correlation coefficient of 0.91, and in terms of dimensionless groups such as Nusselt, Reynolds, Prandtl and Weber numbers with a correlation of 0.92; h=2502U{sub G}{sup 0.236}{sub L}{sup -0.250}{sub L}{sup -}0{sup .028} Nu=3.25Re{sup 0.180}Pr{sup -0.067}We{sup 0.028}.
The self–vibrations of cylindrical shell, filled by the flowing non viscous Gas-Liquid mixture
Directory of Open Access Journals (Sweden)
Ohanyan G.G.
2014-03-01
Full Text Available The problem of non-symmetrical self–vibrations of the infinite long shell, filled by the flowing non viscous Liquid with large or small sizes of bubbles is considered. The subsonic regime of the shell–mixture system with small bubbles which vibration frequencies exceed the frequencies values of those with the large bubbles is considered. The frequency values of the system is increased, when shell thickness and flow speed are increased as when vibration modes are decreased analogous to the case of shell with the pure liquids.
Buoy Relay Method for Instantaneous Fluid Flow with Free Surface
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Several methods have been used to approximate free surface boundaries in finite-difference numerical simulations. Each of these methods has its advantages and disadvantages. This paper presents a new technique for the numerical solution of transient incompressible free surface fluid flows. This powerful method, which is based on the concepts of "Buoy positioning" and "Buoy relaying", successfully represents the free surface using a Lagrangian method on a Eulerian grid by directly solving the free surface evolution equation. The Eulerian finite-difference forms of the full Navier-Stokes equations are solved by the Successive over Relaxation (SOR) method with a set of buoys to keep track of the free surface. The capabilities of the analysis procedure are demonstrated through viscous free surface fluid flow examples. The method is simpler and more efficient than other methods especially in treating complicated free boundary configurations.
Institute of Scientific and Technical Information of China (English)
Yu.V. STARODUBTSEV; I.G. GOGOLEV; V.G. SOLODOV
2005-01-01
@@ The paper describes 3D numerical Reynolds Averaged Navier-Stokes (RANS) model and approximate sector approach for viscous turbulent flow through flow path of one stage axial supercharge gas turbine of marine diesel engine. Computational data are tested by comparison with experimental data. The back step flow path opening and tip clearance jet are taken into account.This approach could be applied for variety of turbine theory and design tasks: for offer optimal design in order to minimize kinetic energy stage losses; for solution of partial supply problem; for analysis of flow pattern in near extraction stages; for estimation of rotational frequency variable forces on blades; for sector vane adjustment (with thin leading edges mainly), for direct flow modeling in the turbine etc. The development of this work could be seen in the direction of unsteady stage model application.
Mechanics of fluid flow over compliant wrinkled polymeric surfaces
Raayai, Shabnam; McKinley, Gareth; Boyce, Mary
2014-03-01
Skin friction coefficients (based on frontal area) of sharks and dolphins are lower than birds, fish and swimming beetles. By either exploiting flow-induced changes in their flexible skin or microscale textures, dolphins and sharks can change the structure of the fluid flow around them and thus reduce viscous drag forces on their bodies. Inspired by this ability, investigators have tried using compliant walls and riblet-like textures as drag reduction methods in aircraft and marine industries and have been able to achieve reductions up to 19%. Here we investigate flow-structure interaction and wrinkling of soft polymer surfaces that can emulate shark riblets and dolphin's flexible skin. Wrinkling arises spontaneously as the result of mismatched deformation of a thin stiff coating bound to a thick soft elastic substrate. Wrinkles can be fabricated by controlling the ratio of the stiffness of the coating and substrate, the applied displacement and the thickness of the coating. In this work we will examine the evolution in the kinematic structures associated with steady viscous flow over the polymer wrinkled surfaces and in particular compare the skin friction with corresponding results for flow over non-textured and rigid surfaces.
Directory of Open Access Journals (Sweden)
Sharma Pushkar Raj
2009-01-01
Full Text Available Aim of the paper is to investigate effects of ohmic heating and viscous dissipation on steady flow of a viscous incompressible electrically conducting fluid in the presence of uniform transverse magnetic field and variable free stream near a stagnation point on a stretching non-conducting isothermal sheet. The governing equations of continuity, momentum, and energy are transformed into ordinary differential equations and solved numerically using Runge-Kutta fourth order with shooting technique. The velocity and temperature distributions are discussed numerically and presented through graphs. Skin-friction coefficient and the Nusselt number at the sheet are derived, discussed numerically, and their numerical values for various values of physical parameters are compared with earlier results and presented through tables.
Wake flow and heat transfer due to a spherical viscous droplet
DEFF Research Database (Denmark)
Bhattacharyya, S.; Singh, Ashok
2010-01-01
to the viscous droplet and its influence on heat transfer and drag coefficient are analyzed for a wide range of physical parameters. It is found that by increasing the Reynolds number, the predicted rate of heat transfer is significantly increased for a liquid droplet compared to a solid sphere. The increment...... of viscosity of the droplet increases the drag experienced by the droplet but reduces the rate of heat transfer. An increase in Richardson number produces an increment in drag coefficient as well as in heat transfer. In order to establish a simplified model for heat transfer due to a viscous droplet, we...
Multi-dimensional upwind fluctuation splitting scheme with mesh adaption for hypersonic viscous flow
Wood, William Alfred, III
production is shown relative to DMFDSFV. Remarkably the fluctuation splitting scheme shows grid converged skin friction coefficients with only five points in the boundary layer for this case. A viscous Mach 17.6 (perfect gas) cylinder case demonstrates solution monotonicity and heat transfer capability with the fluctuation splitting scheme. While fluctuation splitting is recommended over DMFDSFV, the difference in performance between the schemes is not so great as to obsolete DMFDSFV. The second half of the dissertation develops a local, compact, anisotropic unstructured mesh adaption scheme in conjunction with the multi-dimensional upwind solver, exhibiting a characteristic alignment behavior for scalar problems. This alignment behavior stands in contrast to the curvature clustering nature of the local, anisotropic unstructured adaption strategy based upon a posteriori error estimation that is used for comparison. The characteristic alignment is most pronounced for linear advection, with reduced improvement seen for the more complex non-linear advection and advection-diffusion cases. The adaption strategy is extended to the two-dimensional and axisymmetric Navier-Stokes equations of motion through the concept of fluctuation minimization. The system test case for the adaption strategy is a sting mounted capsule at Mach-10 wind tunnel conditions, considered in both two-dimensional and axisymmetric configurations. For this complex flowfield the adaption results are disappointing since feature alignment does not emerge from the local operations. Aggressive adaption is shown to result in a loss of robustness for the solver, particularly in the bow shock/stagnation point interaction region. Reducing the adaption strength maintains solution robustness but fails to produce significant improvement in the surface heat transfer predictions.
Flow over riblet curved surfaces
Energy Technology Data Exchange (ETDEWEB)
Loureiro, J B R; Freire, A P Silva, E-mail: atila@mecanica.ufrj.br [Mechanical Engineering Program, Federal University of Rio de Janeiro (COPPE/UFRJ), C.P. 68503, 21.941-972, Rio de Janeiro, RJ (Brazil)
2011-12-22
The present work studies the mechanics of turbulent drag reduction over curved surfaces by riblets. The effects of surface modification on flow separation over steep and smooth curved surfaces are investigated. Four types of two-dimensional surfaces are studied based on the morphometric parameters that describe the body of a blue whale. Local measurements of mean velocity and turbulence profiles are obtained through laser Doppler anemometry (LDA) and particle image velocimetry (PIV).
Surface obstacles in pulsatile flow
Carr, Ian A.; Plesniak, Michael W.
2016-11-01
Flows past obstacles mounted on flat surfaces have been widely studied due to their ubiquity in nature and engineering. For nearly all of these studies, the freestream flow over the obstacle was steady, i.e. constant velocity unidirectional flow. Unsteady, pulsatile flows occur frequently in biology, geophysics, biomedical engineering, etc. Our study is aimed at extending the comprehensive knowledge base that exists for steady flows to considerably more complex pulsatile flows. Beyond the important practical applications, characterizing the vortex and wake dynamics of flows around surface obstacles embedded in pulsatile flows can provide insights into the underlying physics in all wake and junction flows. In this study, we experimentally investigated the wake of four canonical surface obstacles: hemisphere, cube, and circular cylinders with aspect ratio of 1:1 and 2:1. Phase-averaged PIV and hot-wire anemometry are used to characterize the dynamics of coherent structures in the wake and at the windward junction of the obstacles. Complex physics occur during the deceleration phase of the pulsatile inflow. We propose a framework for understanding these physics based on self-induced vortex propagation, similar to the phenomena exhibited by vortex rings. This material is based in part upon work supported by the National Science Foundation under Grant Number CBET-1236351, and GW Centeor Biomimetics and Bioinspired Engineering (COBRE).
Anderson, O. L.; Briley, W. R.; Mcdonald, H.
1978-01-01
An approximate analysis is presented for calculating three-dimensional, low Mach number, laminar viscous flows in curved passages with large secondary flows and corner boundary layers. The analysis is based on the decomposition of the overall velocity field into inviscid and viscous components with the overall velocity being determined from superposition. An incompressible vorticity transport equation is used to estimate inviscid secondary flow velocities to be used as corrections to the potential flow velocity field. A parabolized streamwise momentum equation coupled to an adiabatic energy equation and global continuity equation is used to obtain an approximate viscous correction to the pressure and longitudinal velocity fields. A collateral flow assumption is invoked to estimate the viscous correction to the transverse velocity fields. The approximate analysis is solved numerically using an implicit ADI solution for the viscous pressure and velocity fields. An iterative ADI procedure is used to solve for the inviscid secondary vorticity and velocity fields. This method was applied to computing the flow within a turbine vane passage with inlet flow conditions of M = 0.1 and M = 0.25, Re = 1000 and adiabatic walls, and for a constant radius curved rectangular duct with R/D = 12 and 14 and with inlet flow conditions of M = 0.1, Re = 1000, and adiabatic walls.
Institute of Scientific and Technical Information of China (English)
SHEN Fang; WU WangYi
2009-01-01
Basic function method is developed to treat the incompressible viscous flow. Artificial compressibility coefficient, the technique of flux splitting method and the combination of central and upwind schemes are applied to construct the basic function scheme of trigonometric function type for solving three-dimensional incompressible Navier-Stokes equations numerically. To prove the method, flows in finite-length-pipe are calculated, the velocity and pressure distribution of which solved by our method quite coincide with the exact solutions of Poiseuille flow except in the areas of entrance and exit. After the method is proved elementary, the hemodynamics in two- and three-dimensional aneurysms is researched numerically by using the basic function method of trigonometric function type and unstructured grids generation technique. The distributions of velocity, pressure and shear force in steady flow of aneurysms are calculated, and the influence of the shape of the aneurysms on the hemodynamics is studied.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Basic function method is developed to treat the incompressible viscous flow. Artificial compressibility coefficient, the technique of flux splitting method and the combination of central and upwind schemes are applied to construct the basic function scheme of trigonometric function type for solving three-dimensional incompressible Navier-Stokes equations numerically. To prove the method, flows in finite-length-pipe are calculated, the velocity and pressure distribution of which solved by our method quite coincide with the exact solutions of Poiseuille flow except in the areas of entrance and exit. After the method is proved elementary, the hemodynamics in two-and three-dimensional aneurysms is researched numerically by using the basic function method of trigonometric function type and unstructured grids generation technique. The distributions of velocity, pressure and shear force in steady flow of aneurysms are calculated, and the influence of the shape of the aneurysms on the hemodynamics is studied.
Directory of Open Access Journals (Sweden)
A. Boulahia
2014-01-01
Full Text Available Work performed in this study concerns mainly the analysis and the wisely use of TVD type schemes (total variation diminishing for numerical simulation of reactive flows, these schemes are first presented in scalar equation. Their extension to Euler equations for a reactive gas mixture is conducted through the approximate extended solver of Riemann problem. A comparative study of specific variants of TVD schemes has been made in the case of one-dimensional unsteady flow for an inert and reactive gas mixture, which represents the classical instance of a shock tube. The purpose of this investigation is to highlight the general behaviour (order of accuracy and performance of TVD schemes with various flux limiters for the simulation of reactive flows and in particular, to make possible the capture of the shock wave together with waves expansion for choosing the appropriate scheme to apply eventually in simulation of hypersonic viscous flow in chemical non equilibrium.
Computational Methods for Inviscid and Viscous Two-and-Three-Dimensional Flow Fields.
1975-01-01
speeds. J. Comput. Phys.. vol. 3. No. 2. 1971, p. 197-213. 111. HANIN. M.. WOLFSHTEIN. M.. and LANDAU . U.E. - Numerical solution of NavierStokes...viscous in lungul unei placi plane la numere Reynolds mici) D. Dumitrescu and C.I. Craciun Studii si Cercetari de Mecanica Aplicata, vol. 28, no. 3
Effect of viscous dissipation on mixed convection flow in a vertical ...
African Journals Online (AJOL)
convection in a vertical channel saturated with porous medium was studied by ... However temperature boundary condition of third kind (the local wall heat flux is a ... Hajmohammadi and Nourazar (2014) studied the effect of a thin gas layer in ...... with viscous dissipation in a vertical channel, Int. J. Heat and Mass Transfer ,.
Institute of Scientific and Technical Information of China (English)
Sun Di-Hua; Peng Guang-Han
2009-01-01
In this paper,the viscous continuum traffic flow model for a single lane is extended to the traffic flow for two-lane freeways. The proposed model is a higher-order continuum model considering the coupling and lane changing effects of the vehicles on two adjacent lanes. It results from integrating the Taylor series expansion of the viscous continuum traffic flow model proposed by Ge (2006 Physics A 371 667) into the multi-lane model presented by Daganzo (1997Transpn. Res. B 31 83). Our proposed model may be used to describe non-anisotropic behaviour because of lane changing in multi-lane traffic. A linear stability analysis is given and the neutral stability condition is obtained. Also,issues related to lane changing,shock waves and rarefaction waves,local clustering and phase transition are investigated through a simulation experiment. The simulation results show that the proposed model is capable of explaining some particular traffic phenomena commonly observable in real world traffic flow.
Kelly; Humphrey
1998-03-01
Considerable debate has occurred over the use of hydrofoil impellers in large-scale fermentors to improve mixing and mass transfer in highly viscous non-Newtonian systems. Using a computational fluid dynamics software package (Fluent, version 4.30) extensive calculations were performed to study the effect of impeller speed (70-130 rpm), broth rheology (value of power law flow behavior index from 0.2 to 0.6), and distance between the cooling coil bank and the fermentor wall (6-18 in.) on flow near the perimeter of a large (75-m3) fermentor equipped with A315 impellers. A quadratic model utilizing the data was developed in an attempt to correlate the effect of A315 impeller speed, power law flow behavior index, and distance between the cooling coil bank and the fermentor wall on the average axial velocity in the coil bank-wall region. The results suggest that there is a potential for slow or stagnant flow in the coil bank-wall region which could result in poor oxygen and heat transfer for highly viscous fermentations. The results also indicate that there is the potential for slow or stagnant flow in the region between the top impeller and the gas headspace when flow through the coil bank-wall region is slow. Finally, a simple guideline was developed to allow fermentor design engineers to predict the degree of flow behind a bank of helical cooling coils in a large fermentor with hydrofoil flow impellers.
Surface flow measurements from drones
Tauro, Flavia; Porfiri, Maurizio; Grimaldi, Salvatore
2016-09-01
Drones are transforming the way we sense and interact with the environment. However, despite their increased capabilities, the use of drones in geophysical sciences usually focuses on image acquisition for generating high-resolution maps. Motivated by the increasing demand for innovative and high performance geophysical observational methodologies, we posit the integration of drone technology and optical sensing toward a quantitative characterization of surface flow phenomena. We demonstrate that a recreational drone can be used to yield accurate surface flow maps of sub-meter water bodies. Specifically, drone's vibrations do not hinder surface flow observations, and velocity measurements are in agreement with traditional techniques. This first instance of quantitative water flow sensing from a flying drone paves the way to novel observations of the environment.
Drag reduction in turbulent flows over superhydrophobic surfaces
Daniello, Robert J.; Waterhouse, Nicholas E.; Rothstein, Jonathan P.
2009-08-01
In this paper, we demonstrate that periodic, micropatterned superhydrophobic surfaces, previously noted for their ability to provide laminar flow drag reduction, are capable of reducing drag in the turbulent flow regime. Superhydrophobic surfaces contain micro- or nanoscale hydrophobic features which can support a shear-free air-water interface between peaks in the surface topology. Particle image velocimetry and pressure drop measurements were used to observe significant slip velocities, shear stress, and pressure drop reductions corresponding to drag reductions approaching 50%. At a given Reynolds number, drag reduction is found to increase with increasing feature size and spacing, as in laminar flows. No observable drag reduction was noted in the laminar regime, consistent with previous experimental results for the channel geometry considered. The onset of drag reduction occurs at a critical Reynolds number where the viscous sublayer thickness approaches the scale of the superhydrophobic microfeatures and performance is seen to increase with further reduction in viscous sublayer height. These results indicate superhydrophobic surfaces may provide a significant drag reducing mechanism for marine vessels.
Feng, Rui; Xenos, Michalis; Girdhar, Gaurav; Kang, Wei; Davenport, James W; Deng, Yuefan; Bluestein, Danny
2012-01-01
Flow and stresses induced by blood flow acting on the blood cellular constituents can be represented to a certain extent by a continuum mechanics approach down to the order of the μm level. However, the molecular effects of, e.g., adhesion/aggregation bonds of blood clotting can be on the order of nm. The coupling of the disparate length and timescales between such molecular levels and macroscopic transport represents a major computational challenge. To address this challenge, a multiscale numerical approach based on discrete particle dynamics (DPD) methodology derived from molecular dynamics (MD) principles is proposed. The feasibility of the approach was firstly tested for its ability to simulate viscous flow conditions. Simulations were conducted in low Reynolds numbers flows (Re = 25-33) through constricted tubes representing blood vessels with various degrees of stenosis. Multiple discrete particles interacting with each other were simulated, with 1.24-1.36 million particles representing the flow domain and 0.4 million particles representing the vessel wall. The computation was carried out on the massive parallel supercomputer NY BlueGene/L employing NAMD-a parallel MD package for high performance computing (HPC). Typical recirculation zones were formed distal to the stenoses. The velocity profiles and recirculation zones were in excellent agreement with computational fluid dynamics (CFD) 3D Navier-Stokes viscous fluid flow simulations and with classic numerical and experimental results by YC Fung in constricted tubes. This feasibility analysis demonstrates the potential of a methodology that widely departs from a continuum approach to simulate multiscale phenomena such as flow induced blood clotting.
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Dr. G. Prabhakara Rao,
2015-04-01
Full Text Available We consider a two-dimensional MHD natural convection flow of an incompressible viscous and electrically conducting fluid through porous medium past a vertical impermeable flat plate is considered in presence of a uniform transverse magnetic field. The governing equations of velocity and temperature fields with appropriate boundary conditions are solved by the ordinary differential equations by introducing appropriate coordinate transformations. We solve that ordinary differential equations and find the velocity profiles, temperature profile, the skin friction and nusselt number. The effects of Grashof number (Gr, Hartmann number (M and Prandtl number (Pr, Darcy parameter (D-1 on velocity profiles and temperature profiles are shown graphically.
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A.S. Idowu
2015-03-01
Full Text Available Radiation on magnetohydrodynamic (MHD boundary layer flow of a viscous fluid over an exponentially stretching sheet was considered together with it’s effects. The new technique of homotopy analysis method (nHAM was used to obtain the convergent series expressions for velocity and temperature, where the governig system of partial differential equations has been transformed into ordinary differential equations. The interpretation to these expressions is shown physically through graphs. We observed that the effects of Prandtl and Magnetic number acts in opposite to each other on the temperature.
Kweon, Jae Ryong
2016-09-01
In this paper, when the initial density has a jump across an interior curve in a bounded domain, we show unique existence, piecewise regularity and jump discontinuity dynamics for the density and the velocity vector governed by the Navier-Stokes equations of compressible viscous barotropic flows. A critical difficulty is in controlling the gradient of the pressure across the jump curve. This is resolved by constructing a vector function associated with the pressure jump value on the convecting curve and extending it to the whole domain.
Rohindra, D. R.; Lata, R. A.; Coll, R. K.
2012-09-01
A simple viscometry experiment undertaken by an undergraduate polymer class as a research project is described. Viscosity is a measure of a fluid's resistance to flow and is affected by several factors, such as concentration and temperature. In this experiment, the viscosities of polyvinylpyrrolidone solutions (a polymeric material) of different concentrations were prepared in water and measured at various temperatures. The solution viscosity was found to increase gradually with increasing concentration up to ∼5 mass%, with a dramatic increase after this. The calculated viscosity of water at different temperatures was comparable to reported values. The activation energy of viscous flow (Ea) of the different solutions was calculated and followed a similar trend as that for the viscosities of solutions of various concentrations. This experiment allowed students to better understand and explain the behaviour of macromolecules with respect to changing concentration and temperature. Furthermore, students correlated the viscosity and Ea results to understand how an increase in the concentration of a polymer solution resulted in increased entanglement of the polymer chains, consequently leading to an increase in viscosity and an increase in the activation energy of viscous flow. This experiment is safe, low cost, simple and requires only readily available apparatus.
Trajectory control of PbSe-γ-Fe2O3 nanoplatforms under viscous flow and an external magnetic field
Etgar, Lioz; Nakhmani, Arie; Tannenbaum, Allen; Lifshitz, Efrat; Tannenbaum, Rina
2010-04-01
The flow behavior of nanostructure clusters, consisting of chemically bonded PbSe quantum dots and magnetic γ-Fe2O3 nanoparticles, has been investigated. The clusters are regarded as model nanoplatforms with multiple functionalities, where the γ-Fe2O3 magnets serve as transport vehicles, manipulated by an external magnetic field gradient, and the quantum dots act as fluorescence tags within an optical window in the near-infrared regime. The clusters' flow was characterized by visualizing their trajectories within a viscous fluid (mimicking a blood stream), using an optical imaging method, while the trajectory pictures were analyzed by a specially developed processing package. The trajectories were examined under various flow rates, viscosities and applied magnetic field strengths. The results revealed a control of the trajectories even at low magnetic fields (<1 T), validating the use of similar nanoplatforms as active targeting constituents in personalized medicine.
Etgar, Lioz; Nakhmani, Arie; Tannenbaum, Allen; Lifshitz, Efrat; Tannenbaum, Rina
2010-04-30
The flow behavior of nanostructure clusters, consisting of chemically bonded PbSe quantum dots and magnetic gamma-Fe(2)O(3) nanoparticles, has been investigated. The clusters are regarded as model nanoplatforms with multiple functionalities, where the gamma-Fe(2)O(3) magnets serve as transport vehicles, manipulated by an external magnetic field gradient, and the quantum dots act as fluorescence tags within an optical window in the near-infrared regime. The clusters' flow was characterized by visualizing their trajectories within a viscous fluid (mimicking a blood stream), using an optical imaging method, while the trajectory pictures were analyzed by a specially developed processing package. The trajectories were examined under various flow rates, viscosities and applied magnetic field strengths. The results revealed a control of the trajectories even at low magnetic fields (<1 T), validating the use of similar nanoplatforms as active targeting constituents in personalized medicine.
Verification of a three-dimensional viscous flow analysis for a single stage compressor
Matsuoka, Akinori; Hashimoto, Keisuke; Nozaki, Osamu; Kikuchi, Kazuo; Fukuda, Masahiro; Tamura, Atsuhiro
1992-12-01
A transonic flowfield around rotor blades of a highly loaded single stage axial compressor was numerically analyzed by a three dimensional compressible Navier-Stokes equation code using Chakravarthy and Osher type total variation diminishing (TVD) scheme. A stage analysis which calculates both flowfields around inlet guide vane (IGV) and rotor blades simultaneously was carried out. Comparing with design values and experimental data, computed results show slight difference quantitatively. But the numerical calculation simulates well the pressure rise characteristics of the compressor and its flow pattern including strong shock surface.
A convergent mixed method for the Stokes approximation of viscous compressible flow
Karlsen, Kenneth
2009-01-01
We propose a mixed finite element method for the motion of a strongly viscous, ideal, and isentropic gas. At the boundary we impose a Navier-slip condition such that the velocity equation can be posed in mixed form with the vorticity as an auxiliary variable. In this formulation we design a finite element method, where the velocity and vorticity is approximated with the div- and curl- conforming Nedelec elements, respectively, of the first order and first kind. The mixed scheme is coupled to a standard piecewise constant upwind discontinuous Galerkin discretization of the continuity equation. For the time discretization, implicit Euler time stepping is used. Our main result is that the numerical solution converges to a weak solution as the discretization parameters go to zero. The convergence analysis is inspired by the continuous analysis of Feireisl and Lions for the compressible Navier-Stokes equations. Tools used in the analysis include an equation for the effective viscous flux and various renormalizatio...
MHD Flow and Heat Transfer Analysis in the Wire Coating Process Using Elastic-Viscous
Directory of Open Access Journals (Sweden)
Zeeshan Khan
2017-01-01
Full Text Available The most important plastic resins used for wire coating are polyvinyl chloride (PVC, nylon, polysulfone, and low-/high-density polyethylene (LDPE/HDPE. In this article, the coating process is performed using elastic-viscous fluid as a coating material for wire coating in a pressure type coating die. The elastic-viscous fluid is electrically conducted in the presence of an applied magnetic field. The governing non-linear equations are modeled and then solved analytically by utilizing an Adomian decomposition method (ADM. The convergence of the series solution is established. The results are also verified by Optimal Homotopy Asymptotic Method (OHAM. The effect of different emerging parameters such as non-Newtonian parameters α and β, magnetic parameter Mand the Brinkman number Br on solutions (velocity and temperature profiles are discussed through several graphs. Additionally, the current results are compared with published work already available.
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.
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 variab...
Two-Phase Flow in Wire Coating with Heat Transfer Analysis of an Elastic-Viscous Fluid
Directory of Open Access Journals (Sweden)
Zeeshan Khan
2016-01-01
Full Text Available This work considers two-phase flow of an elastic-viscous fluid for double-layer coating of wire. The wet-on-wet (WOW coating process is used in this study. The analytical solution of the theoretical model is obtained by Optimal Homotopy Asymptotic Method (OHAM. The expression for the velocity field and temperature distribution for both layers is obtained. The convergence of the obtained series solution is established. The analytical results are verified by Adomian Decomposition Method (ADM. The obtained velocity field is compared with the existing exact solution of the same flow problem of second-grade fluid and with analytical solution of a third-grade fluid. Also, emerging parameters on the solutions are discussed and appropriate conclusions are drawn.
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Reza Hosseini
2012-01-01
Full Text Available The flow of an incompressible electrically conducting viscous fluid in convergent or divergent channels under the influence of an externally applied homogeneous magnetic field is studied both analytically and numerically. Navier-Stokes equations of fluid mechanics and Maxwell’s electromagnetism equations are reduced into highly non-linear ordinary differential equation. The resulting non-linear equation has been solved analytically using a very efficient technique, namely, differential transform method (DTM. The DTM solution is compared with the results obtained by a numerical method (shooting method, coupled with fourth-order Runge-Kutta scheme. The plots have revealed the physical characteristics of flow by changing angles of the channel, Hartmann and Reynolds numbers.
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N. Khan
2015-05-01
Full Text Available The investigation of heat transfer analysis on steady MHD axi-symmetric flow between two infinite stretching disks in the presence of viscous dissipation and Joule heating is basic objective of this paper. Attention has been focused to acquire the similarity solutions of the equations governing the flow and thermal fields. The transformed boundary value problem is solved analytically using homotopy analysis method. The series solutions are developed and the convergence of these solutions is explicitly discussed. The analytical expressions for fluid velocity, pressure and temperature are constructed and analyzed for various set of parameter values. The numerical values for skin friction coefficient and the Nusselt number are presented in tabular form. Particular attention is given to the variations of Prandtl and Eckert numbers. We examined that the dimensionless temperature field is enhanced when we increase the values of Eckert number and Prandtl number.
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V. Srinivasa Rao
2013-01-01
Full Text Available The objectives of the present study are to investigate the radiation effects on unsteady heat and mass transfer flow of a chemically reacting fluid past a semi-infinite vertical plate with viscous dissipation. The method of solution is applied using Finite element technique. Numerical results for the velocity, the temperature and the concentration are shown graphically for various flow parameters. The expressions for the skin-frication, Nusselt number and Sherwood number are obtained. The result shows that increased cooling (Gr>0 of the plate and the Eckert number leads to a rise in the velocity. Also, an increase in the Eckert number leads to an increase in the temperature, whereas increase in radiation lead to a decrease in the temperature distribution when the plate is being cooled.
An Explicit,Totally Analytic Solution of Laminar Viscous FLow over a Semi—Infinite Flat Plate
Institute of Scientific and Technical Information of China (English)
Shi－JunLIAO
1998-01-01
In this paper,a new kind of analytic technique for nonlinear problems,namely the Homotopy Analysis Method,is applied to give an explicit,totally analytic solution of the Blasius' flow.i.e.,the two dimensional (2D) laminar viscous flow over a semi-infinite flat plate.This analytic solution is valid in the whole region having physical meanings.To our knowledge,it is the first time in history that such a kind of explicit,totally analytic solution is given.This fact well verifies the great potential and validity of the Honmotopy Analysis Method as a kind of powerful analytic tool for nonlinear problems in science and engineering.
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Man Singh
2011-05-01
Full Text Available
Viscosity and surface tension of upper critical solutions (UCS of water + phenol with ΔG > 0 are reported. The phenol upper critical solutions within before (B and after (A UCS temperatures range are depicted as BUCS and AUCS respectively and were used for study. Viscous flow times (t, sec and pendant drop numbers (n were measured together with Survismeter for h/N m s^{-2} and g/mN m^{-1 }respectively. The t and n were repeated for UCS with 0.5 millimol/L proteins (casein, pepsin, EA-Egg, albumin, vitamins [thiamine (B_{1}, riboflavin (B_{2}, pyridoxine (B_{6}], amino acids (glycine, b-alanine, L-leucine, surfactants dodecyltrimethylammoniumbromide (DTAB, trimethylsulphoxoniumiodide (TMSOI, methyltrioctylammoniumchloride (MTOAC, orcinol and melamineformaldehyde-polyvinylpyrrolidone (MFP. Additives formed UCS at lower temperature with about 60% thermal energy saving. The t and n were used to calculate tn sec^{-1} for density calculation with Mansingh equation. The BUCS, UCS and AUCS as pre UCS and post UCS were obtained at 60^{0}C, 70^{0}C and 61^{0}C respectively. The tn with water were obtained for 25 to 70^{0}C and plotted with corresponding densities (± 0.05 kg m^{-3} for calibration curve used for density calculations. The densities were noted as TMSOI > orcinol > MFP > DTAB > MTOAC, with lower values at 66.5 and higher at 66^{0}C.
Hafez, M.; Soliman, M.; White, S.
1992-01-01
A new formulation (including the choice of variables, their non-dimensionalization, and the form of the artificial viscosity) is proposed for the numerical solution of the full Navier-Stokes equations for compressible and incompressible flows with heat transfer. With the present approach, the same code can be used for constant as well as variable density flows. The changes of the density due to pressure and temperature variations are identified and it is shown that the low Mach number approximation is a special case. At zero Mach number, the density changes due to the temperature variation are accounted for, mainly through a body force term in the momentum equation. It is also shown that the Boussinesq approximation of the buoyancy effects in an incompressible flow is a special case. To demonstrate the new capability, three examples are tested. Flows in driven cavities with adiabatic and isothermal walls are simulated with the same code as well as incompressible and supersonic flows over a wall with and without a groove. Finally, viscous flow simulations of an oblique shock reflection from a flat plate are shown to be in good agreement with the solutions available in literature.
Muralidharan, Balaji; Menon, Suresh
2016-09-01
A new adaptive finite volume conservative cut-cell method that is third-order accurate for simulation of compressible viscous flows is presented. A high-order reconstruction approach using cell centered piecewise polynomial approximation of flow quantities, developed in the past for body-fitted grids, is now extended to the Cartesian based cut-cell method. It is shown that the presence of cut-cells of very low volume results in numerical oscillations in the flow solution near the embedded boundaries when standard small cell treatment techniques are employed. A novel cell clustering approach for polynomial reconstruction in the vicinity of the small cells is proposed and is shown to achieve smooth representation of flow field quantities and their derivatives on immersed interfaces. It is further shown through numerical examples that the proposed clustering method achieves the design order of accuracy and is fairly insensitive to the cluster size. Results are presented for canonical flow past a single cylinder and a sphere at different flow Reynolds numbers to verify the accuracy of the scheme. Investigations are then performed for flow over two staggered cylinders and the results are compared with prior data for the same configuration. All the simulations are carried out with both quadratic and cubic reconstruction, and the results indicate a clear improvement with the cubic reconstruction. The new cut-cell approach with cell clustering is able to predict accurate results even at relatively low resolutions. The ability of the high-order cut-cell method in handling sharp geometrical corners and narrow gaps is also demonstrated using various examples. Finally, three-dimensional flow interactions between a pair of spheres in cross flow is investigated using the proposed cut-cell scheme. The results are shown to be in excellent agreement with past studies, which employed body-fitted grids for studying this complex case.
Comparison of predicting drag methods using computational fluid dynamics in 2d/3d viscous flow
Institute of Scientific and Technical Information of China (English)
ZHU; ZiQiang; WANG; XiaoLu; LIU; Jie; LIU; Zhou
2007-01-01
As a result of the necessity of aircraft engineering design and the progress of computational fluid dynamics (CFD), techniques of accurately predicting aerodynamic drag are being increasingly explored. According to the momentum balance, the drag can be represented by an integral over a cross-flow plane (called wake integration method) at an arbitrary distance behind the configuration. A formulation to reduce the size of the wake cross plane region required for calculating the drag is developed by using cutoff parameters of vorticity and entropy. This increases the calculation accuracy and decreases the computation time required. Numerical experiments are made to obtain the threshold values of these cutoff parameters. The wake integration method is applied to predict drags of some examples including airfoil, a variety of wings and wing-body combination. Numerical results are compared with those of traditional surface integration method, showing that the predicting drag values with the wake integration method are closer to the experimental data. The results also show that drag prediction within engineering accuracy is possible by using CFD and the numerical drag optimization of complex aircraft configurations is possible, too.
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Samir Kumar Nandy
2014-01-01
Full Text Available An analysis is carried out to study the steady two-dimensional flow of an incompressible viscous fluid past a porous deformable sheet, which is stretched in its own plane with a velocity proportional to the distance from the fixed point subject to uniform suction or blowing. A uniform shear flow of strain rate β is considered over the stretching sheet. The analysis of the result obtained shows that the magnitude of the wall shear stress increases with the increase of suction velocity and decreases with the increase of blowing velocity and this effect is more pronounced for suction than blowing. It is seen that the horizontal velocity component (at a fixed streamwise position along the plate increases with the increase in the ratio of shear rate β and stretching rate (c (i.e., β/c and there is an indication of flow reversal. It is also observed that this flow reversal region increases with the increase in β/c.
Putnam, L. E.; Hodges, J.
1983-01-01
The Langley Research Center of the National Aeronautics and Space Administration and the Royal Aircraft Establishment have undertaken a cooperative program to conduct an assessment of their patched viscous-inviscid interaction methods for predicting the transonic flow over nozzle afterbodies. The assessment was made by comparing the predictions of the two methods with experimental pressure distributions and boattail pressure drag for several convergent circular-arc nozzle configurations. Comparisons of the predictions of the two methods with the experimental data showed that both methods provided good predictions of the flow characteristics of nozzles with attached boundary layer flow. The RAE method also provided reasonable predictions of the pressure distributions and drag for the nozzles investigated that had separated boundary layers. The NASA method provided good predictions of the pressure distribution on separated flow nozzles that had relatively thin boundary layers. However, the NASA method was in poor agreement with experiment for separated nozzles with thick boundary layers due primarily to deficiencies in the method used to predict the separation location.
McDonald, James G.; Groth, Clinton P. T.
2013-09-01
The ability to predict continuum and transition-regime flows by hyperbolic moment methods offers the promise of several advantages over traditional techniques. These methods offer an extended range of physical validity as compared with the Navier-Stokes equations and can be used for the prediction of many non-equilibrium flows with a lower expense than particle-based methods. Also, the hyperbolic first-order nature of the resulting partial differential equations leads to mathematical and numerical advantages. Moment equations generated through an entropy-maximization principle are particularly attractive due to their apparent robustness; however, their application to practical situations involving viscous, heat-conducting gases has been hampered by several issues. Firstly, the lack of closed-form expressions for closing fluxes leads to numerical expense as many integrals of distribution functions must be computed numerically during the course of a flow computation. Secondly, it has been shown that there exist physically realizable moment states for which the entropy-maximizing problem on which the method is based cannot be solved. Following a review of the theory surrounding maximum-entropy moment closures, this paper shows that both of these problems can be addressed in practice, at least for a simplified one-dimensional gas, and that the resulting flow predictions can be surprisingly good. The numerical results described provide significant motivations for the extension of these ideas to the fully three-dimensional case.
Yuan, Ruifeng
2016-01-01
An immersed-boundary (IB) method is proposed and applied in the gas-kinetic BGK scheme to simulate incompressible/compressible viscous flow with stationary/moving boundary. In present method the ghost-cell technique is adopted to fulfill the boundary condition on the immersed boundary. A novel idea "local boundary determination" is put forward to identify the ghost cells, each of which may have several different ghost-cell constructions corresponding to different boundary segments, thus eliminating the singularity of the ghost cell. Furthermore, the so-called "fresh-cell" problem when implementing the IB method in moving-boundary simulation is resolved by a simple extrapolation in time. The method is firstly applied in the gas-kinetic BGK scheme to simulate the Taylor-Couette flow, where the second-order spatial accuracy of the method is validated and the "super-convergence" of the BGK scheme is observed. Then the test cases of supersonic flow around a stationary cylinder, incompressible flow around an oscill...
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O. D. Makinde
2014-01-01
Full Text Available Heat transfer characteristics of a Berman flow of water based nanofluids containing copper (Cu and alumina (Al2O3 as nanoparticles in a porous channel with Navier slip, viscous dissipation, and convective cooling are investigated. It is assumed that the exchange of heat with the ambient surrounding takes place at the channel walls following Newton’s law of cooling. The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using appropriate similarity transformations. These equations are solved analytically by regular perturbation methods with series improvement technique and numerically using an efficient Runge-Kutta Fehlberg integration technique coupled with shooting scheme. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, pressure drop, and Nusselt numbers are presented graphically and discussed quantitatively.
Yasin, Mohd Hafizi Mat; Ishak, Anuar; Pop, Ioan
2015-12-09
The steady two-dimensional stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet with effects of viscous dissipation, Joule heating and partial velocity slip in the presence of a magnetic field is investigated. The partial differential equations are reduced to nonlinear ordinary differential equations by using a similarity transformation, before being solved numerically by shooting technique. Results indicate that the skin friction coefficient and the local Nusselt number increase as magnetic parameter increases. It is found that for the stretching sheet the solution is unique while for the shrinking sheet there exist nonunique solutions (dual solutions) in certain range of parameters. The stability analysis shows that the upper branch solution is stable while the lower branch solution is unstable.
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Alok Kumar Pandey
2017-03-01
Full Text Available The purpose of the present work is to examine the collective influence of thermal radiation and convection flow of Cu-water nanofluid due to a stretching cylinder in a porous medium along with viscous dissipation and slip boundary conditions. The governing non-linear ODEs and auxiliary boundary conditions those obtained by applying assisting similarity transformations have been handled numerically with shooting scheme through Runge-Kutta-integration procedure of fourth-fifth order. The non-dimensional velocity and temperature distribution are designed and also skin friction coefficient as well as heat transfer rate are tabulated for various values of relatable parameters. The results explain that Nusselt number depreciates with boost in radiation parameter, thermal slip parameter and Eckert number. Moreover, it is accelerated with increase in velocity slip parameter and natural convection parameter. The results are distinguished via published ones and excellent accord has been detected.
Mat Yasin, Mohd Hafizi; Ishak, Anuar; Pop, Ioan
2015-12-01
The steady two-dimensional stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet with effects of viscous dissipation, Joule heating and partial velocity slip in the presence of a magnetic field is investigated. The partial differential equations are reduced to nonlinear ordinary differential equations by using a similarity transformation, before being solved numerically by shooting technique. Results indicate that the skin friction coefficient and the local Nusselt number increase as magnetic parameter increases. It is found that for the stretching sheet the solution is unique while for the shrinking sheet there exist nonunique solutions (dual solutions) in certain range of parameters. The stability analysis shows that the upper branch solution is stable while the lower branch solution is unstable.
Viscous Damping of Anisotropic Flow in 7.7 ‑ 200 GeV Au+Au Collisions
Magdy, Niseem; STAR Collaboration
2017-01-01
Recent STAR measurements of the anisotropic flow coefficients v n (2 ≤ n ≤ 5) in Au+Au collisions at RHIC, are presented for the full span of energies (7.7 ‑ 200 GeV) employed in beam energy scan I (BES-I). The measurements which can provide strong constraints for the baryon chemical potential (µ B ) and temperature (T ) dependence of the specific shear viscosity η/s, indicate sizable dependencies on harmonic number n, p T and centrality, with similar patterns [but different magnitudes] across the beam energies studied. An excitation function for the viscous coefficient, extracted via specific ratios of v n for a fixed centrality, indicates a non-monotonic pattern which could be related to the onset of critical reaction dynamics in the BES-I energy range.
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M.R. Krishnamurthy
2015-12-01
Full Text Available This paper considers the problem of steady, boundary layer flow and heat transfer of a nanofluid with fluid-particle suspension over an exponentially stretching surface in the presence of transverse magnetic field and viscous dissipation. The stretching velocity and wall temperature are assumed to vary according to specific exponential form. The governing equations in partial forms are reduced to a system of coupled non-linear ordinary differential equations using suitable similarity transformations. An effective Runge–Kutta–Fehlberg (RKF-45 is used to solve the obtained differential equations with the help of a symbolic software MAPLE. The effects of flow parameters—such as nanofluid interaction parameter, magnetic parameter, solid volume fraction of nanoparticle parameter, Prandtl number and Eckert number—on the flow field and heat-transfer characteristics were obtained and are tabulated. Useful discussions were carried out with the help of plotted graphs and tables. Under the limiting cases, comparison with the existing results was made and found to be in good agreement. The results demonstrate that the skin friction coefficient increases for both magnetic and solid volume fraction nanoparticle parameters. However, dusty fluid with copper (Cu nanoparticles has the appreciable cooling performance than other fluids.
Kodama, Yukinobu; Horishita, Miyuki; Fumoto, Shintaro; Mine, Toyoharu; Miyamoto, Hirotaka; Yoshikawa, Naoki; Hirata, Haruna; Sasaki, Hitoshi; Nakamura, Junzo; Nishida, Koyo
2012-10-01
Objectives The aim was to study the effect of viscous additives on the absorption and hepatic disposition of 5-fluorouracil (5-FU) after application to the liver surface in rats. Methods 5-FU solution with or without viscous additives was applied to the rat liver surface with a cylindrical diffusion cell. Then, blood and the remaining solution in the diffusion cell were collected at selected times, followed by excision of the liver. The excised liver was divided into three sites and assayed for 5-FU content. Key findings The absorption rate of 5-FU from the liver surface was decreased in the presence of carboxymethylcellulose sodium (CMC-Na) and polyvinyl alcohol (PVA) as compared with the control. The k(a) values of PVA 15% and CMC-Na 1% were reduced to about 80 and 67% of the control. The maximum plasma concentration of 5-FU was decreased by incorporation of viscous additives. The 5-FU concentration at the diffusion cell attachment site of the liver (site 1) plateaued at 180 min in the absence of viscous additives. On the other hand, the concentration of 5-FU at site 1 increased in a time-dependent manner until 360 min in the presence of viscous additives. Conclusion Viscous additives might be useful for retaining drugs at their application site and controlling the rate of absorption from the liver surface.
Magnetohydrodynamic Stagnation Point Flow with a Convective Surface Boundary Condition
Jafar, Khamisah; Ishak, Anuar; Nazar, Roslinda
2011-09-01
This study analyzes the steady laminar two-dimensional stagnation point flow and heat transfer of an incompressible viscous fluid impinging normal to a horizontal plate, with the bottom surface of the plate heated by convection from a hot fluid. A uniform magnetic field is applied in a direction normal to the flat plate, with a free stream velocity varying linearly with the distance from the stagnation point. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically. The analysis includes the effects of the magnetic parameter, the Prandtl number, and the convective parameter on the heat transfer rate at the surface. Results showed that the heat transfer rate at the surface increases with increasing values of these quantities.
Magnetohydrodynamic stagnation point flow with a convective surface boundary condition
Energy Technology Data Exchange (ETDEWEB)
Jafar, Khamisah [Universiti Kebangsaan Malaysia, Bangi, Selangor (Malaysia). Faculty of Engineering and Built Environment; Ishak, Anuar; Nazar, Roslinda [Universiti Kebangsaan, Bangi, Selangor (Malaysia). School of Mathematical Sciences
2011-08-15
This study analyzes the steady laminar two-dimensional stagnation point flow and heat transfer of an incompressible viscous fluid impinging normal to a horizontal plate, with the bottom surface of the plate heated by convection from a hot fluid. A uniform magnetic field is applied in a direction normal to the flat plate, with a free stream velocity varying linearly with the distance from the stagnation point. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically. The analysis includes the effects of the magnetic parameter, the Prandtl number, and the convective parameter on the heat transfer rate at the surface. Results showed that the heat transfer rate at the surface increases with increasing values of these quantities. (orig.)
Effect of Viscosity on Free-Surface Waves in Oseen Flows
Institute of Scientific and Technical Information of China (English)
卢东强
2004-01-01
Based on the complex dispersion relation for the two-dimensional free-surface waves generated by a moving body in the steady Oseen flows, the effect of viscosity on wavelength and wave amplitude was investigated by means of an asymptotic method and a numerical analysis. A comparison between the asymptotic and numerical analysis for the viscous decay factor demonstrates the validity of the perturbation expansions for the wave profile. The numerical result shows that the wavelength of viscous wave is slightly elongated in comparison with that of inviscid wave.
Improved numerical methods for turbulent viscous flows aerothermal modeling program, phase 2
Karki, K. C.; Patankar, S. V.; Runchal, A. K.; Mongia, H. C.
1988-01-01
The details of a study to develop accurate and efficient numerical schemes to predict complex flows are described. In this program, several discretization schemes were evaluated using simple test cases. This assessment led to the selection of three schemes for an in-depth evaluation based on two-dimensional flows. The scheme with the superior overall performance was incorporated in a computer program for three-dimensional flows. To improve the computational efficiency, the selected discretization scheme was combined with a direct solution approach in which the fluid flow equations are solved simultaneously rather than sequentially.
A General Approach to Time Periodic Incompressible Viscous Fluid Flow Problems
Geissert, Matthias; Hieber, Matthias; Nguyen, Thieu Huy
2016-06-01
This article develops a general approach to time periodic incompressible fluid flow problems and semilinear evolution equations. It yields, on the one hand, a unified approach to various classical problems in incompressible fluid flow and, on the other hand, gives new results for periodic solutions to the Navier-Stokes-Oseen flow, the Navier-Stokes flow past rotating obstacles, and, in the geophysical setting, for Ornstein-Uhlenbeck and various diffusion equations with rough coefficients. The method is based on a combination of interpolation and topological arguments, as well as on the smoothing properties of the linearized equation.
Directory of Open Access Journals (Sweden)
S. N. Maitra
1986-01-01
Full Text Available A magnetohydrodynamic flow of a viscous, incompressible and slightly conducting fluid is developed between a parallel flat wall and a wavy wall whereas at the same time fluid is continuously sucked through the flat wall with a constant suction velocity. The velocity and temperature distribution are determined alongwith the pressure gradient and co-efficient of skin friction.
M. Cibiş (Merih); K. Jarvis (Kelly); M. Markl (Michael); M. Rose (Michael); C. Rigsby (Cynthia); A.J. Barker (Alex J.); J.J. Wentzel (Jolanda)
2015-01-01
textabstractViscous dissipation inside Fontan circulation, a parameter associated with the exercise intolerance of Fontan patients, can be derived from computational fluid dynamics (CFD) or 4D flow MRI velocities. However, the impact of spatial resolution and measurement noise on the estimation of
Viscous-flow calculations for KVLCC2 in deep and shallow water
Toxopeus, S.L.
2011-01-01
In the SIMMAN 2008 workshop, the capability of CFD tools to predict the flow around manoeuvring ships has been investigated. It was decided to continue this effort but to extend the work to the flow around ships in shallow water. In this paper, CFD calculations for the KLVCC2 are presented. The aim
Viscous-flow calculations for KVLCC2 in deep and shallow water
Toxopeus, S.L.
2011-01-01
In the SIMMAN 2008 workshop, the capability of CFD tools to predict the flow around manoeuvring ships has been investigated. It was decided to continue this effort but to extend the work to the flow around ships in shallow water. In this paper, CFD calculations for the KLVCC2 are presented. The aim
Directory of Open Access Journals (Sweden)
Muhammad Ramzan
Full Text Available The present exploration discusses the influence of Newtonian heating on the magnetohydrodynamic (MHD three dimensional couple stress nanofluid past a stretching surface. Viscous dissipation and Joule heating effects are also considered. Moreover, the nanofluid model includes the combined effects of thermophoresis and Brownian motion. Using an appropriate transformation, the governing non linear partial differential equations are converted into nonlinear ordinary differential equations. Series solutions using Homotopy Analysis method (HAM are computed. Plots are presented to portrait the arising parameters in the problem. It is seen that an increase in conjugate heating parameter results in considerable increase in the temperature profile of the stretching wall. Skin friction coefficient, local Nusselt and local Sherwood numbers tabulated and analyzed. Higher values of conjugate parameter, Thermophoresis parameter and Brownian motion parameter result in enhancement of temperature distribution.
Ledesma-Aguilar, R; Hernández-Machado, A
2007-01-01
We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional Lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Secondly, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.
Incompressible viscous flow computations for the pump components and the artificial heart
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.
Simulation of three-dimensional viscous flow within a multistage turbine
Adamczyk, John J.; Celestina, Mark L.; Beach, Tim A.; Barnett, Mark
1989-01-01
This work outlines a procedure for simulating the flow field within multistage turbomachinery which includes the effects of unsteadiness, compressibility, and viscosity. The associated modeling equations are the average passage equation system which governs the time-averaged flow field within a typical passage of a blade row embedded within a multistage configuration. The results from a simulation of a low aspect ratio stage and a one-half turbine will be presented and compared with experimental measurements. It will be shown that the secondary flow field generated by the rotor causes the aerodynamic performance of the downstream vane to be significantly different from that of an isolated blade row.
Simulation of 3-D viscous flow within a multi-stage turbine
Adamczyk, John J.; Celestina, Mark L.; Beach, Tim A.; Barnett, Mark
1989-01-01
This work outlines a procedure for simulating the flow field within multistage turbomachinery which includes the effects of unsteadiness, compressibility, and viscosity. The associated modeling equations are the average passage equation system which governs the time-averaged flow field within a typical passage of a blade row embedded within a multistage configuration. The results from a simulation of a low aspect ratio stage and a one-half turbine will be presented and compared with experimental measurements. It will be shown that the secondary flow field generated by the rotor causes the aerodynamic performance of the downstream vane to be significantly different from that of an isolated blade row.
High-Reynolds Number Viscous Flow Simulations on Embedded-Boundary CartesianGrids
2016-05-05
term goal of this research is to develop algorithms to simulate high Reynolds number turbulent flow in complicated geometries using embedded boundary...Spalding’s formula of matching the pro- files actually computed in the flow field by the Spalart-Allmaras turbulence model. In particular the profiles ...turbu- lent viscosity to be computed, see e.g. the profiles in the bottom row of Fig. 4. The streamwise velocity and especially the turbulent viscosity
The evolution of viscous flow structures in the esophagus during tracheoesophageal speech
Erath, Byron; Hemsing, Frank
2015-11-01
A laryngectomy is an invasive surgical procedure whereby the entire larynx is removed, usually as a result of cancer. Removal of the larynx renders conventional voiced speech impossible, with the most common remediation following surgery being tracheoeosphageal (TE) speech. TE speech is produced by inserting a one-way valve to connect the posterior wall of the trachea with the anterior wall of the esophagus. As air is forced up from the lungs it passes through the prosthesis and into the esophagus. The resulting esophageal pressure field incites self-sustained oscillations of the pharyngoesophageal segment (PES), which ultimately produces sound. Unfortunately, the physics of TE speech are not well understood, with up to 50% of individuals unable to produce intelligible sound. This failure can be related to a lack of understanding regarding the esophageal flow field, where all previous scientific investigations have assumed the flow is one-dimensional and steady. An experimental TE speech flow facility was constructed and particle image velocimetry measurements were acquired at the exit of the model prosthesis (entrance of the esophagus). The flow is observed to be highly unsteady, and the formation and propagation of vortical flow structures through the esophageal tract are identified. Observations regarding the influence of the flow dynamics on the esophageal pressure field and its relation to the successful production of TE speech are discussed.
Self-Similar Solutions for Viscous and Resistive Advection Dominated Accretion Flows
Indian Academy of Sciences (India)
Kazem Faghei
2012-03-01
In this paper, self-similar solutions of resistive advection dominated accretion flows (ADAF) in the presence of a pure azimuthal magnetic field are investigated. The mechanism of energy dissipation is assumed to be the viscosity and the magnetic diffusivity due to turbulence in the accretion flow. It is assumed that the magnetic diffusivity and the kinematic viscosity are not constant and vary by position and -prescription is used for them. In order to solve the integrated equations that govern the behavior of the accretion flow, a self-similar method is used. The solutions show that the structure of accretion flow depends on the magnetic field and the magnetic diffusivity. As the radial infall velocity and the temperature of the flow increase by magnetic diffusivity, the rotational velocity decreases. Also, the rotational velocity for all selected values of magnetic diffusivity and magnetic field is sub-Keplerian. The solutions show that there is a certain amount of magnetic field for which rotational velocity of the flow becomes zero. This amount of the magnetic field depends upon the gas properties of the disc, such as adiabatic index and viscosity, magnetic diffusivity, and advection parameters. The mass accretion rate increases by adding the magnetic diffusivity and the solutions show that in high magnetic pressure, the ratio of the mass accretion rate to the Bondi accretion rate is reduced with an increase in magnetic pressure. Also, the study of Lundquist and magnetic Reynolds numbers based on resistivity indicates that the linear growth of magnetorotational instability (MRI) of the flow reduces by resistivity. This property is qualitatively consistent with resistive magnetohydrodynamics (MHD) simulations.
Radial and elliptic flow in Pb+Pb collisions at the Large Hadron Collider from viscous hydrodynamic
Shen, Chun; Huovinen, Pasi; Song, Huichao
2011-01-01
A comprehensive viscous hydrodynamic fit of spectra and elliptic flow for charged hadrons and identified pions and protons from Au+Au collisions of all centralities measured at the Relativistic Heavy Ion Collider is performed and used as the basis for predicting the analogous observables for Pb+Pb collisions at the Large Hadron Collider at sqrt(s)=2.76 and 5.5 A TeV. Comparison with recent measurements of the elliptic flow of charged hadrons by the ALICE experiment shows that the model slightly over-predicts the data if the same (constant) specific shear viscosity eta/s is assumed at both collision energies. In spite of differences in our assumptions for the equation of state, the freeze-out temperature, the chemical composition at freeze-out, and the starting time for the hydrodynamic evolution, our results agree remarkably well with those of Luzum [M. Luzum, Phys. Rev. C 83, 044911 (2011)], indicating robustness of the hydrodynamic model extrapolations. Future measurements of the centrality and transverse m...
Computation of incompressible viscous flows through artificial heart devices with moving boundaries
Kiris, Cetin; Rogers, Stuart; Kwak, Dochan; Chang, I.-DEE
1991-01-01
The extension of computational fluid dynamics techniques to artificial heart flow simulations is illustrated. Unsteady incompressible Navier-Stokes equations written in 3-D generalized curvilinear coordinates are solved iteratively at each physical time step until the incompressibility condition is satisfied. 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. The efficiency and robustness of the time accurate formulation of the algorithm are tested by computing the flow through model geometries. A channel flow with a moving indentation is computed and validated with experimental measurements and other numerical solutions. In order to handle the geometric complexity and the moving boundary problems, a zonal method and an overlapping grid embedding scheme are used, respectively. Steady state solutions for the flow through a tilting disk heart valve was compared against experimental measurements. Good agreement was obtained. The flow computation during the valve opening and closing is carried out to illustrate the moving boundary capability.
Institute of Scientific and Technical Information of China (English)
余永亮; 童秉纲; 马晖扬
2003-01-01
Numerous studies on the aerodynamics of insect wing flapping were carried out on different approaches of flight investigations, model experiments, and numerical simulations, but the theoretical modeling remains to be explored. In the present paper, an analytic approach is presented to model the flow interactions of wing flapping in air for small insects with the surrounding flow fields being highly unsteady and highly viscous. The model of wing flapping is a 2-D flat plate, which makes plunging and pitching oscillations as well as quick rotations reversing its positions of leading and trailing edges, respectively, during stroke reversals. It contains three simplified aerodynamic assumptions:(i) unsteady potential flow; (ii) discrete vortices shed from both leading and trailing edges of the wing; (iii) Kutta conditions applied at both edges. Then the problem is reduced to the solution of the unsteady Laplace equation, by using distributed singularities, i.e., sources/sinks, and vortices in the field. To validate the present physical model and analytic method proposed via benchmark examples, two elemental motions in wing flapping and a case of whole flapping cycles are analyzed,and the predicted results agree well with available experimental and numerical data. This verifies that the present analytical approach may give qualitatively correct and quantitatively reasonable results.Furthermore, the total fluid-dynamic force in the present method can be decomposed into three parts:one due to the added inertial (or mass) effect, the other and the third due to the induction of vortices shed from the leading- and the trailing-edge and their images respectively, and this helps to reveal the flow control mechanisms in insect wing flapping.
Indian Academy of Sciences (India)
A K De
2014-10-01
A discrete forcing based Cartesian grid method is presented. The nonstaggered arrangement of velocity and pressure is considered. The pressure gradient in localized discrete form is added separately with the velocity making them explicitly coupled. The governing equation is time-integrated implicitly with both linearized and non-linear forms are investigated. Both linear and bi-linear reconstruction techniques are tested for extrapolation of velocity near a complex boundary. The present method is tested for vortical flow in an inclined cavity, flow past circular and inclined square cylinder. Both homogeneous and non-homogeneous Dirichlet forcing problems are tested. The parallelized version of the method is applied to 2D-to-3D transitional flow behind a single and multiple circular cylinders. The present numerical results compare well with the previously documented results.
Solution of Two-Dimensional Viscous Flow Driven by Motion of Flexible Walls
Directory of Open Access Journals (Sweden)
Mohamed Gad-el-Hak
2010-03-01
Full Text Available An exact solution of the Navier–Stokes equations for a flow driven by motion of flexible wall is developed. A simple two-dimensional channel with deforming walls is considered as domain. The governing equations are linearized for low Reynolds number and large Womersley number Newtonian flows. Appropriate boundary conditions for general deformation are decomposed into harmonic excitations in space by Fourier series decomposition. A model of harmonic boundary deformation is considered and results are compared with computational fluid dynamics predictions. The results of velocity profiles across the channel and the centerline velocities of the channel are in good agreement with CFD solution. The analytical model developed provides quantitative descriptions of the flow field for a wide spectrum of actuating frequnecy and boundary conditions. The presented model can be used as an effective framework for preliminary design and optimization of displacement micropumps and other miniature applications.
Directory of Open Access Journals (Sweden)
T. M. Ajayi
2017-01-01
Full Text Available The problem of a non-Newtonian fluid flow past an upper surface of an object that is neither a perfect horizontal/vertical nor inclined/cone in which dissipation of energy is associated with temperature-dependent plastic dynamic viscosity is considered. An attempt has been made to focus on the case of two-dimensional Casson fluid flow over a horizontal melting surface embedded in a thermally stratified medium. Since the viscosity of the non-Newtonian fluid tends to take energy from the motion (kinetic energy and transform it into internal energy, the viscous dissipation term is accommodated in the energy equation. Due to the existence of internal space-dependent heat source; plastic dynamic viscosity and thermal conductivity of the non-Newtonian fluid are assumed to vary linearly with temperature. Based on the boundary layer assumptions, suitable similarity variables are applied to nondimensionalized, parameterized and reduce the governing partial differential equations into a coupled ordinary differential equations. These equations along with the boundary conditions are solved numerically using the shooting method together with the Runge-Kutta technique. The effects of pertinent parameters are established. A significant increases in Rex1/2Cfx is guaranteed with St when magnitude of β is large. Rex1/2Cfx decreases with Ec and m.
Recent development of vortex method in incompressible viscous bluff body flows
Institute of Scientific and Technical Information of China (English)
LIU Lan; JI Feng; FAN Jian-ren; CEN Ke-fa
2005-01-01
Vortex methods have been alternative tools of finite element and finite difference methods for several decades. This paper presents a brief review of vortex method development in the last decades and introduces efficient vortex methods developed for high Reynolds number bluffbody flows and suitable for running on parallel computer architectures. Included in this study are particle strength exchange methods, core-spreading method, deterministic particle method and hybrid vortex methods. Combined with conservative methods, vortex methods can comprise the most available tools for simulations of three-dimensional complex bluff body flows at high Reynolds numbers.
Karki, K. C.; Mongia, H. C.; Patankar, Suhas V.; Runchal, A. K.
1987-01-01
The objective of this effort is to develop improved numerical schemes for predicting combustor flow fields. Various candidate numerical schemes were evaluated, and promising schemes were selected for detailed assessment. The criteria for evaluation included accuracy, computational efficiency, stability, and ease of extension to multidimensions. The candidate schemes were assessed against a variety of simple one- and two-dimensional problems. These results led to the selection of the following schemes for further evaluation: flux spline schemes (linear and cubic) and controlled numerical diffusion with internal feedback (CONDIF). The incorporation of the flux spline scheme and direct solution strategy in a computer program for three-dimensional flows is in progress.
Derived Metric Tensors for Flow Surface Visualization.
Obermaier, H; Joy, K I
2012-12-01
Integral flow surfaces constitute a widely used flow visualization tool due to their capability to convey important flow information such as fluid transport, mixing, and domain segmentation. Current flow surface rendering techniques limit their expressiveness, however, by focusing virtually exclusively on displacement visualization, visually neglecting the more complex notion of deformation such as shearing and stretching that is central to the field of continuum mechanics. To incorporate this information into the flow surface visualization and analysis process, we derive a metric tensor field that encodes local surface deformations as induced by the velocity gradient of the underlying flow field. We demonstrate how properties of the resulting metric tensor field are capable of enhancing present surface visualization and generation methods and develop novel surface querying, sampling, and visualization techniques. The provided results show how this step towards unifying classic flow visualization and more advanced concepts from continuum mechanics enables more detailed and improved flow analysis.
Towards a segregated time spectral solution method for incompressible viscous flows
Sabine, Baumbach
2016-06-01
Considering the growth of interest in understanding flow phenomena in rotational machines, computational fluid dynamics (CFD) is a powerful tool to reach this goal. Especially unsteady simulations are becoming a focus of interest. Nevertheless, unsteady simulations require huge computational times and ressources, thus it is necessary to investigate other methods to find more appropriate approaches to model time-periodic cases. For time-periodic flows the time spectral method (TSM) presents an interesting alternative to the regular time marching solvers. The TSM is well-known for computation of compressible time-periodic flows, but applications to incompressible cases are limited. This paper presents an extension of the TSM to incompressible flows. While there have been previous implementations using pressure correction method with an explicit treatment of time coupling, here an implicit treatment is chosen. To increase efficiency and employ a more robust coupling of the individual time instances the momentum equations are solved in block-coupled fashion. The pressure correction term is solved segregatedly. To consider cases with dynamic mesh motion an arbitrary lagrange Euler (ALE) formulation is also used in the solver. The efficiency of the method is demonstrated using a basic 2D aerodynamic test case and the results are compared to traditional time-stepping approaches.
Survey on Discrete Surface Ricci Flow
Institute of Scientific and Technical Information of China (English)
Min Zhang; Wei Zeng; Ren Guo; Feng Luo; Xianfeng David Gu
2015-01-01
Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a nonlinear heat diffusion process, and becomes constant eventually. Ricci flow is a powerful computational tool to design Riemannian metrics by prescribed curvatures. Surface Ricci flow has been generalized to the discrete setting. This work surveys the theory of discrete surface Ricci flow, its computational algorithms, and the applications for surface registration and shape analysis.
Goradia, S. H.; Mehta, J. M.; Shrewsbury, G. S.
1977-01-01
The viscous flow phenomena associated with sharp and blunt trailing edge airfoils were investigated. Experimental measurements were obtained for a 17 percent thick, high performance GAW-1 airfoil. Experimental measurements consist of velocity and static pressure profiles which were obtained by the use of forward and reverse total pressure probes and disc type static pressure probes over the surface and in the wake of sharp and blunt trailing edge airfoils. Measurements of the upper surface boundary layer were obtained in both the attached and separated flow regions. In addition, static pressure data were acquired, and skin friction on the airfoil upper surface was measured with a specially constructed device. Comparison of the viscous flow data with data previously obtained elsewhere indicates reasonable agreement in the attached flow region. In the separated flow region, considerable differences exist between these two sets of measurements.
FINITE ELEMENT ANALYSIS OF THE FLOW INDUCED BY ROTATING BLADES IN AN INCOMPRESSIBLE VISCOUS FLUID
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Aerodynamic loads on a multi-bladed helicopter rotor in hovering flight were calculated by solving the three-dimensional incompressible Navier-Stokes equations. The rotor wake effects were accounted by the correction of local geometric angle of attack according to a free-wake modeling in addition to an empirical modification for the tip flow effect. The validity and efficiency of the present method were verified by the comparisons between numerical results and experimental data.
Numerical investigations on cavitation intensity for 3D homogeneous unsteady viscous flows
Leclercq, C.; Archer, A.; Fortes-Patella, R.
2016-11-01
The cavitation erosion remains an industrial issue. In this paper, we deal with the cavitation intensity which can be described as the aggressiveness - or erosive capacity - of a cavitating flow. The estimation of this intensity is a challenging problem both in terms of modelling the cavitating flow and predicting the erosion due to cavitation. For this purpose, a model was proposed to estimate cavitation intensity from 3D unsteady cavitating flow simulations. An intensity model based on pressure and void fraction derivatives was developped and applied to a NACA 65012 hydrofoil tested at LMH-EPFL (École Polytechnique Fédérale de Lausanne) [1]. 2D and 3D unsteady cavitating simulations were performed using a homogeneous model with void fraction transport equation included in Code_Saturne with cavitating module [2]. The article presents a description of the numerical code and the physical approach considered. Comparisons between 2D and 3D simulations, as well as between numerical and experimental results obtained by pitting tests, are analyzed in the paper.
Directory of Open Access Journals (Sweden)
K. Majidi
2000-01-01
Full Text Available The flow field in volute and circular casings interacting with a centrifugal impeller is obtained by numerical analysis. In the present study, effects of the volute and circular casings on the flow pattern have been investigated by successively combining a volute casing and a circular casing with a single centrifugal impeller. The numerical calculations are carried out with a multiple frame of reference to predict the flow field inside the entire impeller and casings. The impeller flow field is solved in a rotating frame and the flow field in the casings in a stationary frame. The static pressure and velocity in the casing and impeller, and the static pressures and secondary velocity vectors at several cross-sectional planes of the casings are calculated. The calculations show that the curvature of the casings creates pressure gradients that cause vortices at cross-sectional planes of the casings.
Decay estimates of heat transfer to melton polymer flow in pipes with viscous dissipation
Directory of Open Access Journals (Sweden)
Dongmin Wei
2001-05-01
Full Text Available In this work, we compare a parabolic equation with an elliptic equation both of which are used in modeling temperature profile of a power-law polymer flow in a semi-infinite straight pipe with circular cross section. We show that both models are well-posed and we derive exponential rates of convergence of the two solutions to the same steady state solution away from the entrance. We also show estimates for difference between the two solutions in terms of physical data.
Ilin, K
2010-01-01
We study the steady streaming between two infinitely long circular cylinders produced by small amplitude transverse vibrations of the inner cylinder about the axis of the outer cylinder. The Vishik-Lyusternik method is employed to construct an asymptotic expansion of the solution of the Navier-Stokes equations in the limit of high-frequency vibrations for Reynolds numbers of order of unity. The effect of the Stokes drift of fluid particles is also studied. It is shown that it is nonzero not only within the boundary layers but also in higher order terms of the expansion of the averaged outer flow.
Viscous flow past a collapsible channel as a model for self-excited oscillation of blood vessels.
Tang, Chao; Zhu, Luoding; Akingba, George; Lu, Xi-Yun
2015-07-16
Motivated by collapse of blood vessels for both healthy and diseased situations under various circumstances in human body, we have performed computational studies on an incompressible viscous fluid past a rigid channel with part of its upper wall being replaced by a deformable beam. The Navier-Stokes equations governing the fluid flow are solved by a multi-block lattice Boltzmann method and the structural equation governing the elastic beam motion by a finite difference method. The mutual coupling of the fluid and solid is realized by the momentum exchange scheme. The present study focuses on the influences of the dimensionless parameters controlling the fluid-structure system on the collapse and self-excited oscillation of the beam and fluid dynamics downstream. The major conclusions obtained in this study are described as follows. The self-excited oscillation can be intrigued by application of an external pressure on the elastic portion of the channel and the part of the beam having the largest deformation tends to occur always towards the end portion of the deformable wall. The blood pressure and wall shear stress undergo significant variations near the portion of the greatest oscillation. The stretching motion has the most contribution to the total potential elastic energy of the oscillating beam.
Directory of Open Access Journals (Sweden)
Rasool Alizadeh
2016-03-01
Full Text Available The steady-state viscous flow and heat transfer in the vicinity of an unaxisymmetric stagnation-point of an infinite stationary cylinder with non-uniform normal transpiration U0φ and uniform transverse magnetic field and constant wall temperature are investigated. The impinging free-stream is steady and with a constant strain rate k¯. A reduction of Navier–Stokes and energy equations is obtained by use of appropriate similarity transformations. The semi-similar solution of the Navier–Stokes equations and energy equation has been obtained numerically using an implicit finite-difference scheme. All the solutions aforesaid are presented for Reynolds numbers, Re=k¯a2/2υ, ranging from 0.01 to 100 for different values of Prandtl number and magnetic parameter and for selected values of transpiration rate function, S(φ=U0(φ/k¯a, where a is cylinder radius and υ is kinematic viscosity of the fluid. Dimensionless shear-stresses corresponding to all the cases increase with the increase in Reynolds number and transpiration rate function while dimensionless shear-stresses decrease with the increase in magnetic parameter. The local coefficient of heat transfer (Nusselt number increases with the increasing transpiration rate function and Prandtl number.
Berkenbusch, M K; Berkenbusch, Marko Kleine; Zhang, Wendy W.
2005-01-01
In selective withdrawal, the interface between two liquid layers is deformed by an imposed withdrawal flow. A shape transition occurs at a threshold flow rate that changes the topology of the interface from a steady-state hump to an entrained spout. Near the transition a very sharp hump tip occurs, with the minimum tip radius far smaller than the characteristic lateral length-scale. Previous measurements [Cohen and Nagel, Phys. Rev. Lett. 88, 2002] suggest the sharp hump is created via an approach towards a singular steady-state shape which is cut off at a small lengthscale. To help unfold the mechanism underlying the shape transition and to determine the origin of the cutoff lengthscale, we construct a numerical model and compare its results against experimental measurements. The increased resolution in the simulation enables us to identify the shape transition both in the experiment and the numerics as a saddle-node bifurcation. The transition does not involve an approach towards a singular shape as the hum...
Leclercq, Colin; Kerswell, Rich R
2016-01-01
The `Rayleigh line' mu=eta^2, where mu=Omega_o/Omega_i and eta=r_i/r_o are respectively the rotation and radius ratios between inner (subscript `i') and outer (subscript `o') cylinders, is regarded as marking the limit of centrifugal instability (CI) in unstratified inviscid Taylor--Couette flow, for both axisymmetric [1] and non-axisymmetric [2] modes. Non-axisymmetric stratorotational instability (SRI) is known to set in for anticyclonic rotation ratios beyond that line, i.e. eta^2<\\mu<1 for axially stably-stratified Taylor--Couette flow [3,4], but the competition between CI and SRI in the range mu
Directory of Open Access Journals (Sweden)
Moradi Amir
2015-01-01
Full Text Available This article considers the influence of heat transfer on the nonlinear Jeffery-Hamel flow problem in a nanofluid. Analysis is performed for three types of nanoparticles namely copper Cu, alumina Al2O3 and titania TiO2 by considering water as a base fluid. The resulting nonlinear mathematical problems are solved for both analytic and numerical solutions. Analytic solution is developed by using differential transformation method (DTM whereas the numerical solution is presented by Runge-Kutta scheme. A comparative study between the analytical and numerical solutions is made. Dimensionless velocity and temperature, skin friction coefficient and Nusselt number are addressed for the involved pertinent parameters. It is observed that the influence of solid volume fraction of nanoparticles on the heat transfer and fluid flow parameters is more pronounced when compared with the type of nanoparticles. It is also found that skin friction coefficient and Nusselt number for Al2O3 nanofluid is highest in comparison to the other two nanoparticles.
Formation of Fiber Materials by Pneumatic Spraying of Polymers in Viscous-Flow States
Lysak, I. A.; Malinovskaya, T. D.; Lysak, G. V.; Potekaev, A. I.; Kulagina, V. V.; Tazin, D. I.
2017-02-01
Using a novel ejection spraying unit and relying on new approaches, fibers are formed by the method of pneumatic melt blowing of polycarbonate, polypropylene, and polyethylene terephthalate. The proposed approach is based on the concepts of atomization of the polymer melt flow as a preferential regime for fibermaterial formation. From the analysis of the values of numerical characteristics in the zone of atomization and the physical background of the criteria under study a conclusion is drawn that the essential role in destruction of the jet belongs to the formation of a boundary layer in the melt under the action of friction forces, followed by its separation. An assumption is made on the prevailing action of the separating destruction of the melt jet via the mechanism of `skinning' of the boundary layer of the melt due to a shorter time of its persistence compared to the development of the Kelvin-Helmholtz instability.
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
It was proved numerically that the Domain Decomposition Method (DDM) with one layer overlapping grids is identical to the block iterative method of linear algebra equations. The results obtained using DDM could be in reasonable aggeement with the results of full-domain simulation. With the three dimensional solver developed by the authors, the flow field in a pipe was simulated using the full-domain DDM with one layer overlapping grids and with patched grids respectively. Both of the two cases led to the convergent solution. Further research shows the superiority of the DDM with one layer overlapping grids to the DDM with patched grids. A comparison between the numerical results obtained by the authors and the experimental results given by Enayet[3] shows that the numerical results are reasonable.
Surfing wavy surfaces: Bacteria-surface interactions in flow
Miño, Gastón L.; Kantsler, Vasily; Stocker, Roman
2014-11-01
Complex processes occur when microbes interact with surfaces, from mixture enhancement and motion rectification to biofilm formation. Microbe-surface interactions frequently occur in flowing fluids, and flow has recently been shown to have itself unexpected consequences on the dynamics of motile microbes. Here we report on microfluidic experiments in which the interactions of Escherichia coli bacteria with wavy surfaces was quantified in the presence of fluid flow, a model system for naturally occurring topography of many real surfaces. We quantify surface interactions in terms of incident and scattering angles over a range of flow conditions, and compare results to the observations for a microchannel with straight walls.
Uwanta, I. J.; Hamza, M. M.
2014-01-01
An investigation is performed to study the effect of suction/injection on unsteady hydromagnetic natural convection flow of viscous reactive fluid between two vertical porous plates in the presence of thermal diffusion. The partial differential equations governing the flow have been solved numerically using semi-implicit finite-difference scheme. For steady case, analytical solutions have been derived using perturbation series method. Suction/injection is used to control the fluid flow in the channel, and an exothermic chemical reaction of Arrhenius kinetic is considered. Numerical results are presented graphically and discussed quantitatively with respect to various parameters embedded in the problem. PMID:27382632
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 ÃŽÂ» (injection/suction is investigated by the graphs and tables.
A time accurate prediction of the viscous flow in a turbine stage including a rotor in motion
Shavalikul, Akamol
In this current study, the flow field in the Pennsylvania State University Axial Flow Turbine Research Facility (AFTRF) was simulated. This study examined four sets of simulations. The first two sets are for an individual NGV and for an individual rotor. The last two sets use a multiple reference frames approach for a complete turbine stage with two different interface models: a steady circumferential average approach called a mixing plane model, and a time accurate flow simulation approach called a sliding mesh model. The NGV passage flow field was simulated using a three-dimensional Reynolds Averaged Navier-Stokes finite volume solver (RANS) with a standard kappa -- epsilon turbulence model. The mean flow distributions on the NGV surfaces and endwall surfaces were computed. The numerical solutions indicate that two passage vortices begin to be observed approximately at the mid axial chord of the NGV suction surface. The first vortex is a casing passage vortex which occurs at the corner formed by the NGV suction surface and the casing. This vortex is created by the interaction of the passage flow and the radially inward flow, while the second vortex, the hub passage vortex, is observed near the hub. These two vortices become stronger towards the NGV trailing edge. By comparing the results from the X/Cx = 1.025 plane and the X/Cx = 1.09 plane, it can be concluded that the NGV wake decays rapidly within a short axial distance downstream of the NGV. For the rotor, a set of simulations was carried out to examine the flow fields associated with different pressure side tip extension configurations, which are designed to reduce the tip leakage flow. The simulation results show that significant reductions in tip leakage mass flow rate and aerodynamic loss reduction are possible by using suitable tip platform extensions located near the pressure side corner of the blade tip. The computations used realistic turbine rotor inlet flow conditions in a linear cascade arrangement
Ganesh Kumar, K.; Rudraswamy, N. G.; Gireesha, B. J.; Krishnamurthy, M. R.
2017-09-01
Present exploration discusses the combined effect of viscous dissipation and Joule heating on three dimensional flow and heat transfer of a Jeffrey nanofluid in the presence of nonlinear thermal radiation. Here the flow is generated over bidirectional stretching sheet in the presence of applied magnetic field by accounting thermophoresis and Brownian motion of nanoparticles. Suitable similarity transformations are employed to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. These nonlinear ordinary differential equations are solved numerically by using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. Graphically results are presented and discussed for various parameters. Validation of the current method is proved by comparing our results with the existing results under limiting situations. It can be concluded that combined effect of Joule and viscous heating increases the temperature profile and thermal boundary layer thickness.
Scovazzi, G.; Huang, H.; Collis, S. S.; Yin, J.
2013-11-01
We present a new approach to the simulation of viscous fingering instabilities in incompressible, miscible displacement flows in porous media. In the past, high resolution computational simulations of viscous fingering instabilities have always been performed using high-order finite difference or Fourier-spectral methods which do not posses the flexibility to compute very complex subsurface geometries. Our approach, instead, by means of a fully-coupled nonlinear implementation of the discontinuous Galerkin method, possesses a fundamental differentiating feature, in that it maintains high-order accuracy on fully unstructured meshes. In addition, the proposed method shows very low sensitivity to mesh orientation, in contrast with classical finite volume approximation used in porous media flow simulations. The robustness and accuracy of the method are demonstrated in a number of challenging computational problems.
Zhang, Wendy; Cohen, Itai
2005-11-01
In selective withdrawal, the interface between two liquid layers is pulled apart by an imposed withdrawal flow. The shape transition creates a sharp hump on the interface, with the minimum hump radius of curvature far smaller than the characteristic lateral length-scale. Previous measurements [Cohen & Nagel Phys. Rev. Lett. 2002] on equal-viscosity layers suggest the sharp hump is created via an approach towards a steady-state singular shape which is cut off at a small length-scale. In contrast, an analogous shape transition in drop emulsification has been shown to occur via a saddle-node bifurcation, without an approach towards a singular shape. Here we present a numerical model of the selective withdrawal experiment and examine the dynamics near the transition with higher resolution. Our numerical results are consistent with previous measurements, but the increased resolution enables us to identify the shape transition as a saddle-node bifurcation. The transition does not involve approach towards a singular shape. (We thank Sidney R. Nagel for helpful discussions.)
Institute of Scientific and Technical Information of China (English)
毛在砂
2002-01-01
The cell model developed since 1950s is a useful tool for exploring the behavior of particle assemblages,but it demands further careful development of the outer cell boundary conditions so that interaction in a particleswarm is better represented. In this paper, the cell model and its development were reviewed, and the modificationsof outer cell boundary conditions were suggested. At the cell outer boundary, the restriction of uniform liquid flowwas removed in our simulation conducted in the reference frame fixed with the particle. Zero shear stress conditionwas used to evaluate the outer boundary value of the stream function. Boundary vorticity was allowed to evolve tovalues compatible to existing stream function at the free shear outer boundary. The fore-aft symmetry of vorticitydistribution at the outer boundary is thought critical to ensure the continuity of inflow and outflow between touchingneighbor cells, and is also tested in the modified cell model. Numerical simulation in terms of stream function andvorticity based on the modified cell models was carried out to shed light on the interaction between liquid andparticles. Lower predicted drag coefficient by the modified cell models was interpreted with the feature of flowstructure. The drag coefficient from the simulation was also compared with correlations of drag coefficient reportedin literature. It is found that the modified cell model with the uniformity of external flow relaxed and the fore-aftsymmetry of boundary vorticity enforced was the most satisfactory on the overall performance of prediction.
Directory of Open Access Journals (Sweden)
Ahmed M. Elsayed
2013-01-01
Full Text Available Film cooling is vital to gas turbine blades to protect them from high temperatures and hence high thermal stresses. In the current work, optimization of film cooling parameters on a flat plate is investigated numerically. The effect of film cooling parameters such as inlet velocity direction, lateral and forward diffusion angles, blowing ratio, and streamwise angle on the cooling effectiveness is studied, and optimum cooling parameters are selected. The numerical simulation of the coolant flow through flat plate hole system is carried out using the “CFDRC package” coupled with the optimization algorithm “simplex” to maximize overall film cooling effectiveness. Unstructured finite volume technique is used to solve the steady, three-dimensional and compressible Navier-Stokes equations. The results are compared with the published numerical and experimental data of a cylindrically round-simple hole, and the results show good agreement. In addition, the results indicate that the average overall film cooling effectiveness is enhanced by decreasing the streamwise angle for high blowing ratio and by increasing the lateral and forward diffusion angles. Optimum geometry of the cooling hole on a flat plate is determined. In addition, numerical simulations of film cooling on actual turbine blade are performed using the flat plate optimal hole geometry.
Investigation of the Viscous Flow Around Two Model Propellers in Uniform Inflow
DEFF Research Database (Denmark)
Olsen, Anders Smærup
2001-01-01
The performance of two model ship propellers in open water condition is predicted with the FINFLO RANSE-solver. Chien´s low Reynolds number k-e turbulence model is applied and the method of artificial compressibility is used. For propeller P21 the predicted torque coefficient for advance number 0.......324 and 0.519 differ by less than 1,6% from experimentally obtained values. The difference for the thrust coefficient and the open water efficiency is a little higher, but still less than 7% for both advance numbers. For propeller P89 the open water efficiency differs by less than 1,0% for advance number 0.......331 and 0.514. The thrust and torque coefficients are predicted within 3,3% for both advance numbers. The averaged velocities in the flow around the propellers correspond very well to measurements. The largest difference is for the tangential velocities behind the propeller. The best agreement is achieved...
Lowengrub, John; Allard, Jun; Aland, Sebastian
2016-03-01
The formation of membrane vesicles from a larger membrane that occurs during endocytosis and other cell processes is typically orchestrated by curvature-inducing molecules attached to the membrane. Recent reports demonstrate that vesicles can form de novo in a few milliseconds. Membrane dynamics at these scales are strongly influenced by hydrodynamic interactions. To study this problem, we develop new diffuse interface models for the dynamics of inextensible vesicles in a viscous fluid with stiff, curvature-inducing molecules. The model couples the Navier-Stokes equations with membrane-induced bending forces that incorporate concentration-dependent bending stiffness coefficients and spontaneous curvatures, with equations for molecule transport and for a Lagrange multiplier to enforce local inextensibility. Two forms of surface transport equations are considered: Fickian surface diffusion and Cahn-Hilliard surface dynamics, with the former being more appropriate for small molecules and the latter being better for large molecules. The system is solved using adaptive finite element methods in 3D axisymmetric geometries. The results demonstrate that hydrodynamics can indeed enable the rapid formation of a small vesicle attached to the membrane by a narrow neck. When the Fickian model is used, this is a transient state with the steady state being a flat membrane with a uniformly distributed molecule concentration due to diffusion. When the Cahn-Hilliard model is used, molecule concentration gradients are sustained, the neck stabilizes and the system evolves to a steady-state with a small, compact vesicle attached to the membrane. By varying the membrane coverage of molecules in the Cahn-Hilliard model, we find that there is a critical (smallest) neck radius and a critical (fastest) budding time. These critical points are associated with changes in the vesicle morphology from spherical to mushroom-like as the molecule coverage on the membrane is increased.
Shateyi, Stanford
2017-07-01
The spectral relaxation method is employed to examine natural convective heat and mass transfer, MHD flow over a permeable moving vertical plate with convective boundary condition in the presence of viscous dissipation, thermal radiation and chemical reaction. The governing partial differential equations were transformed into a system of nonlinear ordinary differential equations by using a similarity approach. The pertinent results are then displayed in tabular form and graphically.
Unsteady Free-surface Waves Due to a Submerged Body in Two-dimensional Oseen Flows
Institute of Scientific and Technical Information of China (English)
LUDong-qiang; AllenT.CHWANG
2004-01-01
The two-dimensional unsteady free-surface waves due to a submerged body moving in an incompressible viscous fluid of infinite depth is considered.The disturbed flow is governed by the unsteadyOseen equations with the kinematic and dynamic boundary conditions linearized for the free-surface waves.Accordingly, the body is mathematically simulated by an Oseenlet with a periodically oscillating strength.By means of Fourier transforms,the exact solution for the free-surface waves is expressed by an integral with a complex dispersion function, which explicitly shows that the wave dynamics is characterized by a Reynolds number and a Strouhal number.By applying Lighthill's theorem, asymptotic representations are derived for the far-field waves with a sub-critical and a super-critical Strouhal number. It is found that the generated waves due to the oscillating Oseenlet consist of the steady-state and transient responses. For the viscous flow with a sub-critical Strouhal number, there exist four waves: three propagate downstream while one propagates upstream.However, for the viscous flow with a super-critical Strouhal number, there exist two waves only,which propagate downstream.
Numerical simulation of fluid/structure interaction phenomena in viscous dominated flows
Tran, Hai Duong
2001-12-01
The accurate prediction of buffet boundaries is essential in modern military aircraft and suspension bridge design in order to avoid the potentially disastrous consequences of unsteady loads. The design of lightweight structures and thermal protection systems for supersonic and hypersonic vehicles depends on the accurate prediction of the aerothermal loads, the structural temperatures and their gradients, and the structural deformations and stresses. Despite their bounded nature, limit-cycle oscillations can exhibit important amplitudes which affect the fatigue life of aircraft structures. Therefore, the main objective of this thesis is to develop and design an integrated multidisciplinary computational methodology for the analyses of the coupled responses exhibited by these phenomena. To simulate fluid/structure interaction problems in turbulent flows, we formulate the k--epsilon turbulence model and Reichardt's wall law in ALE form for dynamic meshes. This law is used with the generalized boundary conditions on k and epsilon of Jaeger and Dhatt and allows a closer integration to the wall compared to standard logarithmic laws and boundary conditions on k and epsilon. In order to apply the methodology to buffeting problems dominated by vortex shedding, we validate our solution approach on the square cylinder benchmark problem. There, we stress the minimization of numerical dissipation induced by an upwinding scheme, and apply our methodology to the aeroelastic stability analysis of a sectional dynamic model of the Tacoma Narrows Bridge. Then, we extend the three field formulation of aeroelasticity to a four-field formulation of aerothermoelasticity for the analysis of aerodynamic heating on structures. With a k--epsilon model, the time-averaged Navier-Stokes equations are integrated up to a distance delta from the real wall. This gap creates a problem for the transmission of the structural temperature to the fluid system. To resolve this problem, we exchange the
Flow visualization of Taylor-mode breakup of a viscous liquid jet
Tsai, Shirley C.; Luu, Patrick; Tam, Patrick; Roski, Gerald; Tsai, Chen S.
1999-06-01
We recently reported a new spray technique called ultrasound-modulated two-fluid (UMTF) atomization and the pertinent "resonant liquid capillary wave (RLCW) theory" based on linear models of Taylor-mode breakup of capillary waves. In this article, flow visualizations of liquid jets near the nozzle tip are presented to verify the central assumption of the RLCW theory that the resonant liquid capillary wave in UMTF atomization is initiated by the ultrasound at the nozzle tip. Specifically, a bright band beneath the nozzle tip was seen in ultrasonic and UMTF atomization separately, but not in two-fluid atomization. The bright band can be attributed to scattering of laser light sheet by the capillary waves generated by the ultrasound on the intact liquid jet. As the capillary wave travels downstream in the direction of airflow, it is amplified by the air blowing around it and eventually collapsed into drops. Therefore, the jet breakup time can be determined by dividing the measured band length with the capillary wave velocity. The breakup times thus determined for water and glycerol/water jets are twice the values predicted by the modified Taylor's model with a sheltering parameter, and are one order of magnitude shorter than those in conventional two-fluid atomization. Furthermore, the images of the spray in the proximity of the nozzle tip obtained by 30 ns laser pulses are consistent with the drop sizes obtained 2.3-6 cm downstream from the nozzle tip by 13 s time average of continuous laser light. Also reported in this article is the good agreement between the measured viscosity effects on the drop-size and size distribution in UMTF atomization and those on the relative amplitude growth rates of capillary waves at different wavelengths predicted by Taylor's model as a result of its inclusion of higher order terms other than the first in viscosity. These new findings have led to the conclusion that UMTF atomization occurs via Taylor-mode breakup of capillary waves
Fereidoon, A.; Andalib, E.; Mirafzal, A.
2016-07-01
This article studies the nonlinear vibration of viscoelastic embedded nano-sandwich structures containing of a double walled carbon nanotube (DWCNT) integrated with two piezoelectric Zinc oxide (ZnO) layers. DWCNT and ZnO layers are subjected to magnetic and electric fields, respectively. This system is conveying viscous fluid and the related force is calculated by modified Navier-Stokes relation considering slip boundary condition and Knudsen number. Visco-Pasternak model with three parameters of the Winkler modulus, shear modulus, and damp coefficient is used for simulation of viscoelastic medium. The nano-structure is simulated as an orthotropic Timoshenko beam (TB) and the effects of small scale, structural damping and surface stress are considered based on Eringen's, Kelvin-voigt and Gurtin-Murdoch theories. Energy method and Hamilton's principle are employed to derive motion equations which are then solved using differential quadrature method (DQM). The detailed parametric study is conducted, focusing on the combined effects of small scale effect, fluid velocity, thickness of piezoelectric layer, boundary condition, surface effects, van der Waals (vdW) force on the frequency and critical velocity of nano-structure. Results indicate that the frequency and critical velocity increases with assume of surface effects.
An adaptive numerical method for free surface flows passing rigidly mounted obstacles
Nikitin, Kirill D; Terekhov, Kirill M; Vassilevski, Yuri V; Yanbarisov, Ruslan
2016-01-01
The paper develops a method for the numerical simulation of a free-surface flow of incompressible viscous fluid around a streamlined body. The body is a rigid stationary construction partially submerged in the fluid. The application we are interested in the paper is a flow around a surface mounted offshore oil platform. The numerical method builds on a hybrid finite volume / finite difference discretization using adaptive octree cubic meshes. The mesh is dynamically refined towards the free surface and the construction. Special care is taken to devise a discretization for the case of curvilinear boundaries and interfaces immersed in the octree Cartesian background computational mesh. To demonstrate the accuracy of the method, we show the results for two benchmark problems: the sloshing 3D container and the channel laminar flow passing the 3D cylinder of circular cross-section. Further, we simulate numerically a flow with surface waves around an offshore oil platform for the realistic set of geophysical data.
Numerical study on cavitating flow due to a hydrofoil near a free surface
Directory of Open Access Journals (Sweden)
Ping-Chen Wu
2016-09-01
Full Text Available A numerical strategy is proposed for a viscous uniform flow past a 2-D partially cavitating hydrofoil placed at a finite depth from the free surface. The flow was modeled by the Reynolds-averaged Navier–Stokes (RANS equations. A finite-volume method with the SIMPLE scheme and k-ε turbulence model were employed for computations. The “full cavitation model,” which included the effects of vaporization, noncondensible gases and compressibility, was incorporated in the computation of cavitating flow. The cavity shape and free surface were updated iteratively till a reasonable convergence was reached. As for the determination of the free surface, the VOF approach was adopted. The test cases show the accuracy and stability of our procedure to capture the cavitating flow near the free surface.
Application of photogrammetry to surface flow visualization
Energy Technology Data Exchange (ETDEWEB)
Karthikeyan, N.; Venkatakrishnan, L. [Council of Scientific and Industrial Research, Experimental Aerodynamics Division, National Aerospace Laboratories, Delhi (India)
2011-03-15
The construction of three-dimensional surface flow fields is an extremely difficult task owing largely to the fragmented information available in the form of 2D images. Here, the method of photogrammetric resection based on a comprehensive camera model has been used to map oil flow visualization images on to the surface grid of the model. The data exported in the VRML format allow for user interaction in a manner not possible with 2D images. The technique is demonstrated here using the surface oil flow visualization images of a simplified landing gear model at low speed in a conventional wind tunnel without any specialized rigs for photogrammetry. The results are not limited to low-speed regimes and show that this technique can have significant impact on understanding the flow physics associated with the surface flow topology of highly three-dimensional separated flows on complex models. (orig.)
Directory of Open Access Journals (Sweden)
Prabhakar Reddy B.
2016-02-01
Full Text Available In this paper, a numerical solution of mass transfer effects on an unsteady free convection flow of an incompressible electrically conducting viscous dissipative fluid past an infinite vertical porous plate under the influence of a uniform magnetic field considered normal to the plate has been obtained. The non-dimensional governing equations for this investigation are solved numerically by using the Ritz finite element method. The effects of flow parameters on the velocity, temperature and concentration fields are presented through the graphs and numerical data for the skin-friction, Nusselt and Sherwood numbers are presented in tables and then discussed.
Khosravian, N; Rafii-Tabar, H
2008-07-09
In the design of nanotube-based fluidic devices, a critical issue is the effect of the induced vibrations in the nanotube arising from the fluid flow, since these vibrations can promote structural instabilities, such as buckling transitions. It is known that the induced resonant frequencies depend on the fluid flow velocity in a significant manner. We have studied, for the first time, the flow of a non-viscous fluid in stubby multi-walled carbon nanotubes, using the Timoshenko classical beam theory to model the nanotubes as a continuum structure. We have obtained the variations of the resonant frequencies with the fluid flow velocity under several experimentally interesting boundary conditions and aspect ratios of the nanotube. The main finding from our work is that, compared to an Euler-Bernoulli classical beam model of a nanotube, the Timoshenko beam predicts the loss of stability at lower fluid flow velocities.
El-Amin, Mohamed
2012-01-01
In this paper, the effects of viscous dissipation on unsteady free convection from an isothermal vertical flat plate in a fluidsaturated porous medium are investigated. The Darcy-Brinkman model is employed to describe the flow field. A new model of viscous dissipation is used for the Darcy-Brinkman model of porous media. The simultaneous development of the momentum and thermal boundary layers is obtained by using a finite-difference method. Boundary layer and Boussinesq approximation have been incorporated. Numerical calculations are carried out for various parameters entering into the problem. Velocity and temperature profiles as well as the local friction factor and local Nusselt number are displayed graphically. It is found that as time approaches infinity, the values of the friction factor and heat transfer coefficient approach steady state. © 2012 by Begell House, Inc.
Uwanta, Ime Jimmy; Usman, Halima
2014-01-01
The present paper investigates the combined effects of Soret and Dufour on free convective heat and mass transfer on the unsteady one-dimensional boundary layer flow over a vertical channel in the presence of viscous dissipation and constant suction. The governing partial differential equations are solved numerically using the implicit Crank-Nicolson method. The velocity, temperature, and concentration distributions are discussed numerically and presented through graphs. Numerical values of the skin-friction coefficient, Nusselt number, and Sherwood number at the plate are discussed numerically for various values of physical parameters and are presented through tables. It has been observed that the velocity and temperature increase with the increase in the viscous dissipation parameter and Dufour number, while an increase in Soret number causes a reduction in temperature and a rise in the velocity and concentration.
Surface oscillations in channeled snow flows
Rastello, Marie
2007-01-01
An experimental device has been built to measure velocity profiles and friction laws in channeled snow flows. The measurements show that the velocity depends linearly on the vertical position in the flow and that the friction coefficient is a first-order polynomial in velocity (u) and thickness (h) of the flow. In all flows, oscillations on the surface of the flow were observed throughout the channel and measured at the location of the probes. The experimental results are confronted with a shallow water approach. Using a Saint-Venant modeling, we show that the flow is effectively uniform in the streamwise direction at the measurement location. We show that the surface oscillations produced by the Archimedes's screw at the top of the channel persist throughout the whole length of the channel and are the source of the measured oscillations. This last result provides good validation of the description of such channeled snow flows by a Saint-Venant modeling.
A Model for the Propagation of Nonlinear Surface Waves over Viscous Muds
2007-07-05
grained, cohesive sedimentary 1993; Foda et al., 1993). With the exception of fluidization environments is well known. Extreme dissipation rates have...processes ( Foda et al., 1993; DeWit, 1995), these models focus on a single, well-defined mud phase. Although the models Corresponding author. Tel.: +1...However, surface-interface wave interactions ( Foda , 1989; Hill and Foda , our focus at the present is on a wave model which can be 1998; Jamali et al
Matsushima, M.
2016-12-01
Diffusive processes of large scales in the Earth's core are dominated not by the molecular diffusion but by the eddy diffusion. To carry out numerical simulations of realistic geodynamo models, it is important to adopt appropriate parameters. However, the eddy viscous diffusion, or the eddy viscosity, is not a property of the core fluid but of the core flow. Hence it is significant to estimate the eddy viscosity from core flow models. In fact, fluid motion near the Earth's core surface provides useful information on core dynamics, features of the core-mantle boundary (CMB), and core-mantle coupling, for example. Such core fluid motion can be estimated from spatial and temporal distributions of the geomagnetic field. Most of core surface flow models rely on the frozen-flux approximation (Roberts and Scott, 1965), in which the magnetic diffusion is neglected. It should be noted, however, that there exists a viscous boundary layer at the CMB, where the magnetic diffusion may play an important role in secular variations of geomagnetic field. Therefore, a new approach to estimation of core surface flow has been devised by Matsushima (2015). That is, the magnetic diffusion is explicitly incorporated within the viscous boundary layer, while it is neglected below the boundary layer at the CMB which is assumed to be a spherical surface. A core surface flow model between 1840 and 2015 has been derived from a geomagnetic field model, COV-OBS.x1 (Gillet et al., 2015). Temporal variations of core flows contain information on phenomena in relation with core-mantle coupling, such as the LOD (length-of-day), and spin-up/spin-down of core flows. In particular, core surface flows inside the viscous boundary layer at the CMB may reveal an interesting feature in relation with Earth's rotation. We have examined time series of the LOD and vorticity derived from the core surface flow model. We have found a possible correlation between the LOD and the axial component of global vorticity
Viscous-elastic interaction as a mechanism to create adhesion in frogs' toe pads
Gat, Amir; Tulchinsky, Arie
2013-11-01
The toe pads of frogs consist of soft hexagonal structures and a network of channels between and within the soft structures, containing a viscous liquid. It has been hypothesized that this configuration creates adhesion by allowing for long range capillary forces, or alternatively, that the channel network allows for exit of the viscous liquid and thus improve contact of the toe pad. In this work we suggest interaction between viscous flow and elastic forces as a mechanism to create temporary adhesion, even in the absence of capillary or van der Waals forces. We study the dynamics of a solid body covered with an array of protruding elastic cylinders, immersed within a viscous liquid, and pressed against a flat surface. Inertia is neglected and the elastic-viscous dynamics yield the governing differential equation describing the relative motion between the body and the surface. The compressed elastic cylinders apply a force acting to separate the solid body from the surface. The relative motion between the body and the surface creates a viscous flow and pressure field resisting the elastic force and significantly reducing the speed of separation. We show that the viscous-elastic interaction can prevent motion tangential and normal to the surface and can create temporary adhesion.
Ashyralyev, Allaberen; Gambo, Yusuf Ya'u.
2016-08-01
The nonlocal boundary value problem for viscous Burgers' equation is considered. Solutions to the 1-D equation are presented numerically by Rothe, Crank-Nicholson and r-modified Crank-Nicholson difference schemes. Matlab codes for all the three schemes are designed based on the idea of fixed-point iteration procedure and modified Gauss elimination method. The numerical results are compared.
Free Surface Thin Film Flow of a Sisko’s Fluid over a Surface Topography
Directory of Open Access Journals (Sweden)
R. A. Shah
2017-01-01
Full Text Available The flow of a thin film down an inclined surface over topography is considered for the case of liquids with Sisko’s model viscosity. For the first time lubrication theory is used to reduce the governing equations to a non-linear evolution equation for a current of a Sisko’s model non-Newtonian fluid on an inclined plane under the action of gravity and the viscous stresses. This model is solved numerically using an efficient Full Approximation Storage (FAS multigrid algorithm. Free surface results are plotted and carefully examined near the topography for different values of power-law index np, viscosity parameter m, the aspect ratio A and for different inclination angle of the plane with the horizontal. Number of complications and additional physical effects are discussed that enrich real situations. It is observed that the flows into narrow trenches develop a capillary ridge just in front of the upstream edge of a trench followed by a small trough. For relatively small width trenches, the free surface is almost everywhere flat as the dimensional width of the trench is much smaller than the capillary length scale. In this region, surface tension dominates the solution and acts so as to stretch a membrane across the trench leading to smaller height deviations. The ridge originates from the topographic forcing which works to force fluid upstream immediately prior to the trench before helping to accelerate it over. The upstream forcing slows down the fluid locally and increases the layer thickness.
Directory of Open Access Journals (Sweden)
K.C. Saha
2015-04-01
Full Text Available The effects of MHD free convection heat and mass transfer of power-law Non-Newtonian fluids along a stretching sheet with viscous dissipation has been analyzed. This has been done under the simultaneous action of suction, thermal radiation and uniform transverse magnetic field. The stretching sheet is assumed to continuously moving with a power-law velocity and maintaining a uniform surface heat-flux. The governing non-linear partial differential equations are transformed into non-linear ordinary differential equations, using appropriate similarity transformations and the resulting problem is solved numerically using Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. A parametric study of the parameters arising in the problem such as the Eckert number due to viscous dissipation, radiation number, buoyancy parameter, Schmidt number, Prandtl number etc are studied and the obtained results are shown graphically and the physical aspects of the problem are discussed.
Huang, Brendan K.; Khokha, Mustafa K.; Loewenberg, Michael; Choma, Michael A.
2016-03-01
In cilia-driven fluid flow physiology, quantification of flow velocity, shearing force, and power dissipation is important in defining abnormal ciliary function. The capacity to generate flow can be robustly described in terms of shearing force. Dissipated power can be related to net ATP consumption by ciliary molecular motors. To date, however, only flow velocity can be routinely quantified in a non-invasive, non-contact manner. Additionally, traditional power-based metrics rely on metabolic consumption that reflects energy consumption not just from cilia but also from all active cellular processes. Here, we demonstrate the estimation of all three of these quantities (flow velocity, shear force, and power dissipation) using only optical coherence tomography (OCT). Specifically, we develop a framework that can extract force and power information from vectorial flow velocity fields obtained using OCT-based methods. We do so by (a) estimating the viscous stress tensor from flow velocity fields to estimate shearing force and (b) using the viscous stress tensor to estimate the power dissipation function to infer total mechanical power. These estimates have the advantage of (a) requiring only a single modality, (b) being non-invasive in nature, and (c) being reflective of only the net power work generated by a ciliated surface. We demonstrate our all-optical approach to the estimation of these parameters in the Xenopus animal model system under normal and increased viscous loading. Our preliminary data support the hypothesis that the Xenopus ciliated surface can increase force output under loading conditions.
The curved shape of the bacterium Caulobacter crescentus enhances colonization of surfaces in flow
Persat, Alexandre; Gitai, Zemer; Stone, Howard
2014-11-01
Bacteria thrive in all types of fluid environments; flow is thus a ubiquitous aspect of their lives. Bacteria have evolved a variety of cellular components contributing to their growth in specific environments. However, cellular features that help them survive and develop in flow have been rarely characterized. Here, we show that Caulobacter crescentus may have evolved its curved shape to enhance the colonization of surfaces in flow. C. crescentus curvature is preserved in the wild but straight mutants have no known growth disadvantage in standard laboratory conditions. Leveraging microfluidics and single-cell imaging, we demonstrate that curvature enhances surface colonization in flow, promoting the formation of larger microcolonies. Cells attach to a surface from a single pole, so that flow affects their orientation. In flow, viscous forces generate a torque on the curved cell body, which reorients the cell in the direction of the flow. The curved cell appears to arc above the surface, optimally orienting its unattached pole towards the surface. This reduces the distance between the surface and the pole, thereby enhancing attachment of its progeny. Additionally, we show that curved shape enhances colony spreading across the direction of the flow, generating more robust biofilm compared to straight mutants.
Modification of Turbulent Boundary Layer Flows by Superhydrophobic Surfaces
Gose, James W.; Golovin, Kevin; Barros, Julio; Schultz, Michael P.; Tuteja, Anish; Perlin, Marc; Ceccio, Steven L.
2016-11-01
Measurements of near zero pressure gradient turbulent boundary layer (TBL) flow over several superhydrophobic surfaces (SHSs) are presented and compared to those for a hydraulically smooth baseline. The surfaces were developed at the University of Michigan as part of an ongoing research thrust to investigate the feasibility of SHSs for skin-friction drag reduction in turbulent flow. The SHSs were previously evaluated in fully-developed turbulent channel flow and have been shown to provide meaningful drag reduction. The TBL experiments were conducted at the USNA in a water tunnel with a test section 2.0 m (L) x 0.2 m (W) x 0.2 m (H). The free-stream speed was set to 1.26 m/s which corresponded to a friction Reynolds number of 1,500. The TBL was tripped at the test section inlet with a 0.8 mm diameter wire. The upper and side walls provided optical access, while the lower wall was either the smooth baseline or a spray coated SHS. The velocity measurements were obtained with a TSI FSA3500 two-component Laser-Doppler Velocimeter (LDV) and custom-designed beam displacer operated in coincidence mode. The LDV probe volume diameter was 45 μm (approx. one wall-unit). The measurements were recorded 1.5 m downstream of the trip. When the measured quantities were normalized using the inner variables, the results indicated a significant reduction in the near wall viscous and total stresses with little effect on the flow outside the inner layer.
Coherent flow structures at earth's surface
National Research Council Canada - National Science Library
Venditti, J.G; Best, J.L; Church, M; Hardy, R.J
2013-01-01
This book reviews the recent progress in the study of the turbulent flows that sculpt the Earth's surface, focusing in particular on the organized structures that have been identified in recent years...
Petit, Benjamin,; Letouzey, Antoine; Boyer, Edmond; Franco, Jean-Sébastien
2011-01-01
International audience; In this paper we study the estimation of dense, instantaneous 3D motion ﬁelds over a non-rigidly moving surface observed by multi-camera systems. The motivation arises from multi-camera applications that require motion information, for arbitrary subjects, in order to perform tasks such as surface tracking or segmentation. To this aim, we present a novel framework that allows to efﬁciently compute dense 3D displacement ﬁelds using low level visual cues and geometric con...
Yirga, Y.; Shankar, B.
2015-09-01
This article investigates the convective heat and mass transfer in nanofluid flow through a porous media due to a stretching sheet subjected to magnetic field, viscous dissipation, chemical reaction, and Soret effects. The governing equations are reduced to ordinary differential equations using similarity transformations and then solved numerically by the Keller box method. Numerical results are obtained for the skin friction coefficient, Nusselt number, Sherwood number, as well as for the velocity, temperature, and concentration profiles for selected values of the governing parameters. Excellent validation of the present numerical results has been achieved with the earlier studies in the literature.
Energy Technology Data Exchange (ETDEWEB)
Etgar, Lioz; Lifshitz, Efrat; Tannenbaum, Rina [Russell Berrie Nanotechnology Institute (RBNI), Technion-Israel Institute of Technology, Haifa 32000 (Israel); Nakhmani, Arie; Tannenbaum, Allen, E-mail: ssefrat@tx.technion.ac.il, E-mail: rinatan@tx.technion.ac.il [Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000 (Israel)
2010-04-30
The flow behavior of nanostructure clusters, consisting of chemically bonded PbSe quantum dots and magnetic {gamma}-Fe{sub 2}O{sub 3} nanoparticles, has been investigated. The clusters are regarded as model nanoplatforms with multiple functionalities, where the {gamma}-Fe{sub 2}O{sub 3} magnets serve as transport vehicles, manipulated by an external magnetic field gradient, and the quantum dots act as fluorescence tags within an optical window in the near-infrared regime. The clusters' flow was characterized by visualizing their trajectories within a viscous fluid (mimicking a blood stream), using an optical imaging method, while the trajectory pictures were analyzed by a specially developed processing package. The trajectories were examined under various flow rates, viscosities and applied magnetic field strengths. The results revealed a control of the trajectories even at low magnetic fields (<1 T), validating the use of similar nanoplatforms as active targeting constituents in personalized medicine.
Lifespan theorem for constrained surface diffusion flows
McCoy, James; Williams, Graham; 10.1007/s00209-010-0720-7
2012-01-01
We consider closed immersed hypersurfaces in $\\R^{3}$ and $\\R^4$ evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for which a smooth solution exists, and a small upper bound on a power of the total curvature during this time. By phrasing the theorem in terms of the concentration of curvature in the initial surface, our result holds for very general initial data and has applications to further development in asymptotic analysis for these flows.
Directory of Open Access Journals (Sweden)
Sin Wei Wong
2013-01-01
Full Text Available An analysis is carried out to study the steady two-dimensional stagnation-point flow of an incompressible viscous fluid towards a stretching vertical sheet. It is assumed that the sheet is stretched nonlinearly, with prescribed surface heat flux. This problem is governed by three parameters: buoyancy, velocity exponent, and velocity ratio. Both assisting and opposing buoyant flows are considered. The governing partial differential equations are transformed into a system of ordinary differential equations and solved numerically by finite difference Keller-box method. The flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Dual solutions are found in the opposing buoyant flows, while the solution is unique for the assisting buoyant flows.
CISM Course on Free Surface Flows
Rath, Hans-Josef
1998-01-01
The book covers selected problems in free surface flows. The topics range from linear and nonlinear gravity and capillary waves, thin film dynamics, equilibrium shape, stability, and dynamics of capillary surfaces to thermal Marangoni effects in several geometries. The fluid dynamical problems are supplemented by a review Eulerian based computational methods.
Liquid infused surfaces in turbulent channel flow
Fu, Matthew; Stone, Howard; Smits, Alexander; Jacobi, Ian; Samaha, Mohamed; Wexler, Jason; Shang, Jessica; Rosenberg, Brian; Hellström, Leo; Fan, Yuyang; Wang, Karen; Lee, Kevin; Hultmark, Marcus
2014-11-01
A turbulent channel flow facility is used to measure the drag reduction capabilities and dynamic behavior of liquid-infused micro-patterned surfaces. Liquid infused surfaces have been proposed as a robust alternative to traditional air-cushion-based superhydrophobic surfaces. The mobile liquid lubricant creates a surface slip with the outer turbulent shear flow as well as an energetic sink to dampen turbulent fluctuations. Micro-manufactured surfaces can be mounted flush in the channel and exposed to turbulent flows. Two configurations are possible, both capable of producing laminar and turbulent flows. The first configuration allows detailed investigation of the infused liquid layer and the other allows well resolved pressure gradient measurements. Both of the configurations have high aspect ratios 15-45:1. Drag reduction for a variety of liquid-infused surface architectures is quantified by measuring pressure drop in the channel. Flow in the oil film is simultaneously visualized using fluorescent dye. Supported under ONR Grants N00014-12-1-0875 and N00014-12-1-0962 (program manager Ki-Han Kim).
Viscous erosion at low Reynolds number
Mitchell, William; Sagnolie, Saverio
2016-11-01
We study the shape evolution of immersed particles in a viscous fluid under several flow configurations, including uniform background flows and shear flows in wall-bounded or free domains. The surface recedes proportionally to local shear stress, which we compute using a new traction integral formulation of Newtonian Stokes flow. This opens the door to efficient numerical simulation of the evolving particle geometry. Analytical predictions from reduced-order models are then compared against the numerical simulations. For the case of particles held fixed against an oncoming background flow, the theory predicts the finite time required for complete particle dissolution as well as the emergence and locations of sharp corners on the eroding bodies. Simulations involving force- and torque-free particles and multibody systems are also presented.
Solidity of viscous liquids. II
DEFF Research Database (Denmark)
Dyre, Jeppe
1999-01-01
Recent findings on displacements in the surroundings of isotropic flow events in viscous liquids [Phys. Rev. E 59, 2458 (1999)] are generalized to the anisotropic case. Also, it is shown that a flow event is characterized by a dimensionless number reflecting the degree of anisotropy....
An improved parallel SPH approach to solve 3D transient generalized Newtonian free surface flows
Ren, Jinlian; Jiang, Tao; Lu, Weigang; Li, Gang
2016-08-01
In this paper, a corrected parallel smoothed particle hydrodynamics (C-SPH) method is proposed to simulate the 3D generalized Newtonian free surface flows with low Reynolds number, especially the 3D viscous jets buckling problems are investigated. The proposed C-SPH method is achieved by coupling an improved SPH method based on the incompressible condition with the traditional SPH (TSPH), that is, the improved SPH with diffusive term and first-order Kernel gradient correction scheme is used in the interior of the fluid domain, and the TSPH is used near the free surface. Thus the C-SPH method possesses the advantages of two methods. Meanwhile, an effective and convenient boundary treatment is presented to deal with 3D multiple-boundary problem, and the MPI parallelization technique with a dynamic cells neighbor particle searching method is considered to improve the computational efficiency. The validity and the merits of the C-SPH are first verified by solving several benchmarks and compared with other results. Then the viscous jet folding/coiling based on the Cross model is simulated by the C-SPH method and compared with other experimental or numerical results. Specially, the influences of macroscopic parameters on the flow are discussed. All the numerical results agree well with available data, and show that the C-SPH method has higher accuracy and better stability for solving 3D moving free surface flows over other particle methods.
Surface Structure Enhanced Microchannel Flow Boiling
Zhu, Yangying; Antao, Dion Savio; Chu, Kuang-Han; Chen, Siyu; Hendricks, Terry J.; Zhang, Tiejun; Wang, Evelyn N.
2016-01-01
We investigated the role of surface microstructures in two-phase microchannels on suppressing flow instabilities and enhancing heat transfer. We designed and fabricated microchannels with well-defined silicon micropillar arrays on the bottom heated microchannel wall to promote capillary flow for thin film evaporation while facilitating nucleation only from the sidewalls. Our experimental results show significantly reduced temperature and pressure drop fluctuation especially at high heat fluxe...
Superhydrophobic surfaces in turbulent channel flow
Li, Yixuan; Alame, Karim; Mahesh, Krishnan
2016-11-01
The drag reduction effect of superhydrophobic surfaces in turbulent channel flow is studied using direct numerical simulation. The volume of fluid (VOF) methodology is used to resolve the dynamics of the interface. Laminar flow simulations show good agreement with experiment, and illustrate the relative importance of geometry and interface boundary condition. An analytical solution for the multi-phase problem is obtained that shows good agreement with simulation. Turbulent simulations over a longitudinally grooved surface show drag reduction even in the fully wetted regime. The statistics show that geometry alone can cause an apparent slip to the external flow. Instantaneous plots indicate that the grooves prevent the penetration of near wall vorticity, yielding overall drag reduction. Results for spectra, wall pressure fluctuations and correlations will be presented. Unsteady effects on the air-vapor interface will be discussed. Results for random roughness surfaces will be presented. Supported by Office of Naval Research.
Directory of Open Access Journals (Sweden)
Q Joyce Han
Full Text Available Right ventricular (RV function has increasingly being recognized as an important predictor for morbidity and mortality in patients with pulmonary arterial hypertension (PAH. The increased RV after-load increase RV work in PAH. We used time-resolved 3D phase contrast MRI (4D flow MRI to derive RV kinetic energy (KE work density and energy loss in the pulmonary artery (PA to better characterize RV work in PAH patients.4D flow and standard cardiac cine images were obtained in ten functional class I/II patients with PAH and nine healthy subjects. For each individual, we calculated the RV KE work density and the amount of viscous dissipation in the PA.PAH patients had alterations in flow patterns in both the RV and the PA compared to healthy subjects. PAH subjects had significantly higher RV KE work density than healthy subjects (94.7±33.7 mJ/mL vs. 61.7±14.8 mJ/mL, p = 0.007 as well as a much greater percent PA energy loss (21.1±6.4% vs. 2.2±1.3%, p = 0.0001 throughout the cardiac cycle. RV KE work density and percent PA energy loss had mild and moderate correlations with RV ejection fraction.This study has quantified two kinetic energy metrics to assess RV function using 4D flow. RV KE work density and PA viscous energy loss not only distinguished healthy subjects from patients, but also provided distinction amongst PAH patients. These metrics hold promise as imaging markers for RV function.
Directory of Open Access Journals (Sweden)
M.S Uddin
2011-01-01
Full Text Available The paper is concerned to find the distribution of the chemically reactant solute in the MHD flow of an electrically conducting viscous incompressible fluid over a stretching surface. The first order chemical reaction and the variable solute distribution along the surface are taken into consideration. The governing partial differential equations along with appropriate boundary conditions for flow field and reactive solute are transformed into a set of non-linear self-similar ordinary differential equations by using scaling group of transformations. An exact analytic solution is obtained for the velocity field. Using this velocity field, we obtain numerical solution for the reactant concentration field. It reveals from the study that the values of concentration profile enhances with the increase of the magnetic field and decreases with increase of Schmidt number as well as the reaction rate parameter. Most importantly, when the solute distribution along the surface increases then the concentration profile decreases.
Liquid Infused Surfaces in Turbulent Channel Flow
Fu, Matthew; Liu, Ying; Stone, Howard; Hultmark, Marcus
2016-11-01
Liquid infused surfaces have been proposed as a robust method for turbulent drag reduction. These surfaces consist of functionalized roughness elements wetted with a liquid lubricant that is immiscible with external fluids. The presence of the lubricant creates mobile, fluid-fluid interfaces, each of which can support a localized slip. Collectively, these interfaces yield a finite slip velocity at the effective surface, which has been demonstrated to reduce skin friction drag in turbulent flows. Retention of the lubricant layer is critical to maintaining the drag reduction effect. A turbulent channel-flow facility is used to characterize the drag reduction and robustness of various liquid infused surfaces. Micro-manufactured surfaces are mounted flush in the channel and exposed to turbulent flows. The retention of fluorescent lubricants and pressure drop are monitored to characterize the effects of surface geometry and lubricant properties. Supported under ONR Grants N00014-12-1-0875 and N00014-12-1-0962 (program manager Ki-Han Kim) and by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.
Gravity-capillary free-surface flows
Vanden-Broeck, Jean-Marc
2010-01-01
Free surface problems occur in many aspects of science and of everyday life such as the waves on a beach, bubbles rising in a glass of champagne, melting ice, pouring flows from a container and sails billowing in the wind. Consequently, the effect of surface tension on gravity-capillary flows continues to be a fertile field of research in applied mathematics and engineering. Concentrating on applications arising from fluid dynamics, Vanden-Broeck draws upon his years of experience in the field to address the many challenges involved in attempting to describe such flows mathematically. Whilst careful numerical techniques are implemented to solve the basic equations, an emphasis is placed upon the reader developing a deep understanding of the structure of the resulting solutions. The author also reviews relevant concepts in fluid mechanics to help readers from other scientific fields who are interested in free boundary problems.
Polygon formation and surface flow on a rotating fluid surface
DEFF Research Database (Denmark)
Bergmann, Raymond; Tophøj, Laust Emil Hjerrild; Homan, T. A. M.;
2011-01-01
We present a study of polygons forming on the free surface of a water flow confined to a stationary cylinder and driven by a rotating bottom plate as described by Jansson et al. (Phys. Rev. Lett., vol. 96, 2006, 174502). In particular, we study the case of a triangular structure, either completel...
Surface-acoustic-wave (SAW) flow sensor
Joshi, Shrinivas G.
1991-03-01
The use of a surface-acoustic-wave (SAW) device to measure the rate of gas flow is described. A SAW oscillator heated to a suitable temperature above ambient is placed in the path of a flowing gas. Convective cooling caused by the gas flow results in a change in the oscillator frequency. A 73-MHz oscillator fabricated on 128 deg rotated Y-cut lithium niobate substrate and heated to 55 C above ambient shows a frequency variation greater than 142 kHz for flow-rate variation from 0 to 1000 cu cm/min. The output of the sensor can be calibrated to provide a measurement of volume flow rate, pressure differential across channel ports, or mass flow rate. High sensitivity, wide dynamic range, and direct digital output are among the attractive features of this sensor. Theoretical expressions for the sensitivity and response time of the sensor are derived. It is shown that by using ultrasonic Lamb waves propagating in thin membranes, a flow sensor with faster response than a SAW sensor can be realized.
Peng, Naifu; Yang, Yue
2016-11-01
We investigate the evolution of vortex-surface fields (VSFs) in viscous compressible Taylor-Green flows. The VSF is applied to the direct numerical simulation of the Taylor-Green flows at a range of Mach numbers from Ma = 0 . 6 to Ma = 2 . 2 for characterizing the Mach-number effects on evolving vortical structures. We find that the dilatation and baroclinic force strongly influence the geometry of vortex surfaces and the energy dissipation rate in the transitional stage. The vortex tubes in compressible flows are less curved than those in incompressible flows, and the maximum dissipation rate occurs earlier in high-Mach-number flows perhaps owing to the conversion of kinetic energy into heat. Moreover, the relations between the evolutionary geometry of vortical structures and flow statistics are discussed. This work has been supported in part by the National Natural Science Foundation of China (Grant Nos. 11522215 and 11521091), and the Thousand Young Talents Program of China.
Three dimensional boundary layers in internal flows
Bodonyi, R. J.
1987-01-01
A numerical study of the effects of viscous-inviscid interactions in three-dimensional duct flows is presented. In particular interacting flows for which the oncoming flow is not fully-developed were considered. In this case there is a thin boundary layer still present upstream of the surface distortion, as opposed to the fully-developed pipe flow situation wherein the flow is viscous across the cross section.
Efficient Computation of N-S Equation with Free Surface Flow Around an ACV on ShirazUCFD Grid
Sheikhalishahi, Seyyed Mehdi; Alizadehrad, Davood; Dastghaibyfard, Gholamhossein; Alishahi, Mohammad Mehdi; Nikseresht, Amir Hossein
This paper presents the application of a parallel high accuracy simulation code for Incompressible Navier-Stokes solution with free surface flow around an ACV (Air Cushion Vehicle) on ShirazUCFD Grid environment. The parallel finite volume code is developed for incompressible Navier-Stokes solver on general curvilinear coordinates system for modeling free surface flows. A single set of dimensionless equations is derived to handle both liquid and air phases in viscous incompressible free surface flow in general curvilinear coordinates. The volume of fluid (VOF) method with lagrangian propagation in computational domain for modeling the free surface flow is implemented. The parallelization approach uses a domain decomposition method for the subdivision of the numerical grid, the SPMD program model and MPICH-G2 as the message passing environment is used to obtain a portable application.
Directory of Open Access Journals (Sweden)
KHEM CHAND
2011-07-01
Full Text Available The heat transfer and hydromagnetic boundary layer flow of an electrically conducting viscous ,incompressible fluid over a continuous flat surface moving in a parallel free stream is investigated. The porous infinite surface is subjected to a slightly sinusoidal transverse suction velocity distribution. The flow becomes three dimensional due to this type of suction velocity without taking into account the induced magnetic field; the mathematical analysis is presented for the hydromagnetic laminar boundary layer flow. For the asymptotic flow condition, the components of the surface skin friction and the rate of heat transfer are obtained. During discussion it is found that with the increase of Hartmann number M, the skin friction factor F1 increase sharply for lower values of theReynolds number, but for the large value it increases steadily. But if the surface velocity is more than that of free stream velocity then the reverse trend is observed.
Hussain, Arif; Malik, M. Y.; Bilal, S.; Awais, M.; Salahuddin, T.
Present communication presents numerical investigation of magnetohydrodynamic Sisko fluid flow over linearly stretching cylinder along with combined effects of temperature depending thermal conductivity and viscous dissipation. The arising set of flow govern equations are simplified under usual boundary layer assumptions. A set of variable similarity transforms are employed to shift the governing partial differential equations into ordinary differential equations. The solution of attained highly nonlinear simultaneous equations is computed by an efficient technique (shooting method). Numerical computations are accomplished and interesting aspects of flow velocity and temperature are visualized via graphs for different parametric conditions. A comprehensive discussion is presented to reveal the influence of flow parameters on wall shear stress and local Nusselt number via figures and tables.Furthermore, it is observed that magnetic field provides noticeable resistance to the fluid motion while both material parameter and curvature accelerates it. The progressing values of both Eckert number and thermal conductivity parameter have qualitively same effects i.e. they rise the temperature. Additionally, material parameter and curvature parameter increase the coefficient of skin friction absolutely and qualitively similar effects are noticed for Nusselt number against variations in Prandtl number and curvature parameter. On the other hand local Nusselt diminishes for larger values of Eckert number and power law index. The present results are compared with existing literature via tables, they have good covenant with previous results.
Directory of Open Access Journals (Sweden)
Prasad Ramachandra V.
2007-01-01
Full Text Available An unsteady, two-dimensional, hydromagnetic, laminar free convective boundary-layer flow of an incompressible, Newtonian, electrically-conducting and radiating fluid past an infinite heated vertical porous plate with heat and mass transfer is analyzed, by taking into account the effect of viscous dissipation. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. Numerical evaluation of the analytical results is performed and graphical results for velocity, temperature and concentration profiles within the boundary layer and tabulated results for the skin-friction coefficient, Nusselt number and Sherwood number are presented and discussed. It is observed that, when the radiation parameter increases, the velocity and temperature decrease in the boundary layer, whereas when thermal and solutal Grashof increases the velocity increases.
Blais, Bruno; Lassaigne, Manon; Goniva, Christoph; Fradette, Louis; Bertrand, François
2016-08-01
Although viscous solid-liquid mixing plays a key role in the industry, the vast majority of the literature on the mixing of suspensions is centered around the turbulent regime of operation. However, the laminar and transitional regimes face considerable challenges. In particular, it is important to know the minimum impeller speed (Njs) that guarantees the suspension of all particles. In addition, local information on the flow patterns is necessary to evaluate the quality of mixing and identify the presence of dead zones. Multiphase computational fluid dynamics (CFD) is a powerful tool that can be used to gain insight into local and macroscopic properties of mixing processes. Among the variety of numerical models available in the literature, which are reviewed in this work, unresolved CFD-DEM, which combines CFD for the fluid phase with the discrete element method (DEM) for the solid particles, is an interesting approach due to its accurate prediction of the granular dynamics and its capability to simulate large amounts of particles. In this work, the unresolved CFD-DEM method is extended to viscous solid-liquid flows. Different solid-liquid momentum coupling strategies, along with their stability criteria, are investigated and their accuracies are compared. Furthermore, it is shown that an additional sub-grid viscosity model is necessary to ensure the correct rheology of the suspensions. The proposed model is used to study solid-liquid mixing in a stirred tank equipped with a pitched blade turbine. It is validated qualitatively by comparing the particle distribution against experimental observations, and quantitatively by compairing the fraction of suspended solids with results obtained via the pressure gauge technique.
Thermocouple Rakes for Measuring Boundary Layer Flows Extremely Close to Surface
Hwang, Danny P.; Fralick, Gustave C.; Martin, Lisa C.; Blaha, Charles A.
2001-01-01
Of vital interest to aerodynamic researchers is precise knowledge of the flow velocity profile next to the surface. This information is needed for turbulence model development and the calculation of viscous shear force. Though many instruments can determine the flow velocity profile near the surface, none of them can make measurements closer than approximately 0.01 in. from the surface. The thermocouple boundary-layer rake can measure much closer to the surface than conventional instruments can, such as a total pressure boundary layer rake, hot wire, or hot film. By embedding the sensors (thermocouples) in the region where the velocity is equivalent to the velocity ahead of a constant thickness strut, the boundary-layer flow profile can be obtained. The present device fabricated at the NASA Glenn Research Center microsystem clean room has a heater made of platinum and thermocouples made of platinum and gold. Equal numbers of thermocouples are placed both upstream and downstream of the heater, so that the voltage generated by each pair at the same distance from the surface is indicative of the difference in temperature between the upstream and downstream thermocouple locations. This voltage differential is a function of the flow velocity, and like the conventional total pressure rake, it can provide the velocity profile. In order to measure flow extremely close to the surface, the strut is made of fused quartz with extremely low heat conductivity. A large size thermocouple boundary layer rake is shown in the following photo. The latest medium size sensors already provide smooth velocity profiles well into the boundary layer, as close as 0.0025 in. from the surface. This is about 4 times closer to the surface than the previously used total pressure rakes. This device also has the advantage of providing the flow profile of separated flow and also it is possible to measure simultaneous turbulence levels within the boundary layer.
Insect contamination protection for laminar flow surfaces
Croom, Cynthia C.; Holmes, Bruce J.
1986-01-01
The ability of modern aircraft surfaces to achieve laminar flow was well-accepted in recent years. Obtaining the maximum benefit of laminar flow for aircraft drag reduction requires maintaining minimum leading-edge contamination. Previously proposed insect contamination prevention methods have proved impractical due to cost, weight, or inconvenience. Past work has shown that insects will not adhere to water-wetted surfaces, but the large volumes of water required for protection rendered such a system impractical. The results of a flight experiment conducted by NASA to evaluate the performance of a porous leading-edge fluid discharge ice protection system operated as an insect contamination protections system are presented. In addition, these flights explored the environmental and atmospheric conditions most suitable for insect accumulation.
Viscous Glass Sealants for SOFC Applications
Energy Technology Data Exchange (ETDEWEB)
Scott Misture
2012-09-30
Two series of silicate glasses that contain gallium as the primary critical component have been identified and optimized for viscous sealing of solid oxide fuel cells operating from 650 to 850Â°C. Both series of glass sealants crystallize partially upon heat treatment and yield multiphase microstructures that allow viscous flow at temperatures as low as 650Â°C. A fully amorphous sealant was also developed by isolating, synthesizing and testing a silicate glass of the same composition as the remnant glassy phase in one of the two glass series. Of ~40 glasses tested for longer than 500 hours, a set of 5 glasses has been further tested for up to 1000h in air, wet hydrogen, and against both yttria-stabilized zirconia and aluminized stainless steel. In some cases the testing times reached 2000h. The reactivity testing has provided new insight into the effects of Y, Zr, and Al on bulk and surface crystallization in boro-gallio-silicate glasses, and demonstrated that at least 5 of the newly-developed glasses are viable viscous sealants.
Parallel Simulation of Three-Dimensional Free Surface Fluid Flow Problems
Energy Technology Data Exchange (ETDEWEB)
BAER,THOMAS A.; SACKINGER,PHILIP A.; SUBIA,SAMUEL R.
1999-10-14
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.
Energy Technology Data Exchange (ETDEWEB)
Wuensch, O.; Boehme, G. [Universitaet der Bundeswehr, Hamburg (Germany). Inst. fuer Stroemungslehre und Stroemungsmaschinen
2001-05-01
Peoples running screw machines are strongly interested in a detailed theoretical analysis of the transport processes for real highly viscous liquids which are non-Newtonian in general. The paper deals with an unconventional strategy which enables to simulate the three-dimensional unsteady flow in the kneading zone of intermeshing twin-screw extruders numerically. The concept is pointed at a finite element approximation of the flow field at particular times well chosen after the computation domain has been minimized with the aid of periodicities and symmetries existing in space and time. The method has been realized numerically and proved by means of a typical kneading geometry. Selected results show that the flow and deformation processes in the kneading element differ substantially from those in a screwed segment. (orig.) [German] Es besteht ein erhebliches Interesse daran, die Transportprozesse in Schneckenmaschinen fuer reale hochviskose, nichtnewtonsche Fluessigkeiten im Detail theoretisch zu analysieren und berechenbar zu machen. In der Arbeit wird eine unkonventionelle Strategie beschrieben, nach der die dreidimensionale instationaere Stroemung im Knetbereich kaemmender Doppelschnecken numerisch simuliert werden kann. Das theoretisch fundierte Konzept zielt auf eine Finite-Elemente-Approximation des Stroemungsfelds zu gewissen Zeitpunkten, wobei das Berechnungsgebiet mit Hilfe raeumlicher und zeitlicher Periodizitaeten und Symmetrien minimiert wird. Das Konzept wurde numerisch realisiert und an einer typischen Knetgeometrie erprobt. Ausgewaehlte Ergebnisse machen deutlich, da paragraph sich die Stroemungs- und Deformationsprozesse in einem Knetelement wesentlich von denen in einem Schraubenelement gleicher Geometrie unterscheiden. (orig.)
Fluorescent beeswax for surface flow velocity observations
Grimaldi, S.; Tauro, F.; Petroselli, A.; Mocio, G.; Capocci, I.; Rapiti, E.; Rapiti, R.; Cipollari, G.; Porfiri, M.
2012-12-01
Watershed surface processes control downstream runoff phenomena, waste and pollutant diffusion, erosion mechanics, and sediment transport. A quantitative understanding of the flow physics is currently limited by the lack of effective tracing techniques suitable for basin-scale observations. More specifically, field experiments require environmentally resilient, non-invasive, and low cost measurement systems that can potentially operate in remotely-controlled or unmanned conditions. Traditional tracing methodologies are largely not capable to cope with extreme in-situ conditions, including practical logistic challenges as well as inherent flow complexity. Specifically, most of available technologies need physical sampling to estimate the tracer concentration and do not allow for continuous-time measurements. In addition, commonly used tracers, such as isotopes, dyes, and chemicals, are not directly applicable to monitor surface hillslope processes and large-scale microchannel networks due to elaborate detection processes and dispersion issues. In this context, the feasibility of using buoyant fluorescent microspheres as particle tracers in natural water flows is investigated. Specifically, a novel fabrication methodology is designed to manufacture particles from natural beeswax and a highly diluted solution of a nontoxic fluorescent red dye. The fabrication procedure allows for adjusting the size of the particles from tens of microns up to a few millimeters and their density from positively to negatively-buoyant with respect to water. An array of experimental techniques is employed to conduct a thorough characterization of the fluorescence and morphology of the tracers. In addition, ad-hoc experiments are designed to assess the fluorescence response due to Ultra Violet (UV) exposure and thermal processes. Proof-of-concept laboratory analysis are conducted to illustrate the integration of the novel particle tracers in existing tracing methods for surface flow
Free surface flows under compensated gravity conditions
Dreyer, Miachel E
2007-01-01
This book considers the behavior of fluids in a low-gravity environment with special emphasis on application in PMD (propellant management device) systems . In the compensated gravity environment of a spacecraft, the hydrostatic pressure decreases to very low values depending on the residual acceleration, and surface tension forces become dominant. Consequently, surface tension can be used to transport and position liquids if the residual acceleration and the resulting hydrostatic pressure are small compared to the capillary pressure. One prominent application is the use of PMDs in surface-tension satellite tanks. PMDs must ensure that the tank outlet is covered with liquid whenever outflow is demanded. Furthermore, PMDs are used to ensure expulsion and refilling of tanks for liquids and gases for life support, reactants, and experiment supplies. Since most of the PMD designs are not testable on ground and thus rely on analytical or numerical concepts, this book treats three different flow problems with analy...
Chakrabarti, Brato
2015-01-01
This work explores a simple model of a slender, flexible structure in a uniform flow, providing analytical solutions for the translating, axially flowing equilibria of strings subjected to a uniform body force and drag forces linear in the velocities. The classical catenaries are extended to a five-parameter family of curves. A sixth parameter affects the tension in the curves. Generic configurations are planar, represented by a single first order equation for the tangential angle. The effects of varying parameters on representative shapes, orbits in angle-curvature space, and stress distributions are shown. As limiting cases, the solutions include configurations corresponding to "lariat chains" and the towing, reeling, and sedimentation of flexible cables in a highly viscous fluid. Regions of parameter space corresponding to infinitely long, semi-infinite, and finite length curves are delineated. Almost all curves subtend an angle less than $\\pi$ radians, but curious special cases with doubled or infinite ra...
Dissipation on Steady MHD Marangoni Convection Flow over a Flat Surface with Suction and Injection
Directory of Open Access Journals (Sweden)
S. Mohammed Ibrahim
2013-01-01
Full Text Available The combined effects of radiation and mass transfer on a steady MHD two-dimensional Marangoni convection flow over a flat surface in presence of Joule heating and viscous dissipation under influence of suction and injection is studied numerically. The general governing partial differential equations are transformed into a set of nonlinear ordinary differential equations by using unique similarity transformation. Numerical solutions of the similarity equations are obtained using the Runge-Kutta method along with shooting technique. The effects of governing parameters on velocity, temperature, and concentration as well as interface velocity, the surface temperature gradient, and the surface concentration gradient were presented in graphical and tabular forms. Comparisons with previously published work are performed and the results are found to be in excellent agreement.
Oseen流动中粘性对自由表面波的影响%Effect of Viscosity on Free-Surface Waves in Oseen Flows
Institute of Scientific and Technical Information of China (English)
卢东强
2004-01-01
Based on the complex dispersion relation for the two-dimensional free-surface waves generated by a moving body in the steady Oseen flows, the effect of viscosity on wavelength and wave amplitude was investigated by means of an asymptotic method and a numerical analysis.A comparison between the asymptotic and numerical analysis for the viscous decay factor demonstrates the validity of the perturbation expansions for the wave profile.The numerical result shows that the wavelength of viscous wave is slightly elongated in comparison with that of inviscid wave.
Surface Effects on Nanoscale Gas Flows
Beskok, Ali; Barisik, Murat
2010-11-01
3D MD simulations of linear Couette flow of argon gas confined within nano-scale channels are performed in the slip, transition and free molecular flow regimes. The velocity and density profiles show deviations from the kinetic theory based predictions in the near wall region that typically extends three molecular diameters (s) from each surface. Utilizing the Irwin-Kirkwood theorem, stress tensor components for argon gas confined in nano-channels are investigated. Outside the 3s region, three normal stress components are identical, and equal to pressure predicted using the ideal gas law, while the shear stress is a constant. Within the 3s region, the normal stresses become anisotropic and the shear stress shows deviations from its bulk value due to the surface virial effects. Utilizing the kinetic theory and MD predicted shear stress values, the tangential momentum accommodation coefficient for argon gas interacting with FCC structured walls (100) plane facing the fluid is calculated to be 0.75; this value is independent of the Knudsen number. Results show emergence of the 3s region as an additional characteristic length scale in nano-confined gas flows.
Directory of Open Access Journals (Sweden)
Penem Mohan KRISNA
2014-03-01
Full Text Available In this study, we analyze the effects of thermal radiation and chemical reaction on the steady 2 dimensional stagnation point flow of a viscous incompressible electrically conducting fluid over a stretching surface, with suction and heat generation. The partial differential equations governing the flow are solved numerically by using the shooting technique. The effects of various parameters on velocity, temperature, and concentration profiles, as well as Nusselt number, Skin friction coefficient, and Sherwood number, are examined, and presented graphically and through tables. It is found that velocity, temperature, and rate of heat transfer of the fluid are influenced more by radiation and chemical reaction parameters, along with applied magnetic field.
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Prabhakar Reddy B.
2014-05-01
Full Text Available The thermal diffusion and viscous dissipation effects on an unsteady MHD free convection heat and mass transfer flow of an incompressible, electrically conducting, fluid past an infinite vertical porous plate embedded in a porous medium of time dependent permeability under oscillatory suction velocity in the presence of a heat absorbing sink have been studied. It is considered that the influence of a uniform magnetic field acts normal to the flow and the permeability of the porous medium fluctuates with time. The dimensionless governing equations for this investigation have been solved numerically by using the efficient Galerkin finite element method. The numerical results obtained have been presented through graphs and tables for the thermal Grashof number (Gr > 0 corresponding to the cooling of the porous plate and (Gr < 0 corresponding to heating of the porous plate to observe the effects of various material parameters encountered in the problem under investigation. Numerical data for skin-friction, Nusselt and Sherwood numbers are tabulated and then discussed.
Viscous erosion with a generalized traction integral equation
Mitchell, William H
2016-01-01
A double-layer integral equation for the surface tractions on a body moving in a viscous fluid is derived, allowing for the incorporation of a background flow and/or the presence of a plane wall. The Lorentz reciprocal theorem is used to link the surface tractions on the body to integrals involving the background velocity and stress fields on an imaginary bounding sphere (or hemisphere for wall-bounded flows). The derivation requires the velocity and stress fields associated with numerous fundamental singularity solutions which we provide for free-space and wall-bounded domains. Two sample applications of the method are discussed: we study the tractions on an ellipsoid moving near a plane wall, which provides a more detailed understanding of the well-studied glancing and reversing trajectories, and we explore a new problem, erosion of bodies by a viscous flow, in which the surface is ablated at a rate proportional to the local viscous shear stress. Simulations and analytical estimates suggest that a spherical...
Directory of Open Access Journals (Sweden)
B. Mahanthesh
2017-06-01
Full Text Available The purpose of this study is to investigate the unsteady magnetohydrodynamic three-dimensional flow induced by a stretching surface. An incompressible electrically conducting Eyring-Powell fluid fills the convectively heated stretching surface in the presence of nanoparticles. The effects of thermal radiation, viscous dissipation and Joule heating are accounted in heat transfer equation. The model used for the nanofluid includes the effects of Brownian motion and thermophoresis. The highly nonlinear partial differential equations are reduced to ordinary differential equations with the help of similarity method. The reduced complicated two-point boundary value problem is treated numerically using Runge–Kutta–Fehlberg 45 method with shooting technique. A comparison of the obtained numerical results with existing results in a limiting sense is also presented. At the end, the effects of influential parameters on velocity, temperature and nanoparticles concentration fields are also discussed comprehensively. Further, the physical quantities of engineering interest such as the Nusselt number and Sherwood number are also calculated.
1996-12-01
conditions with friction, gap two surface triangulations. Other types of surface opening, spotwelds. etc. For civil engineering alplica- elements call be...Internacional de M6todos Numericos en Ingenieria (CIMNE) at the Universidad Polit6cnica de Catalunya. Barcelona, Spain. The support for this visit is
Hathaway, M. D.; Wood, J. R.; Wasserbauer, C. A.
1991-01-01
A low speed centrifugal compressor facility recently built by the NASA Lewis Research Center is described. The purpose of this facility is to obtain detailed flow field measurements for computational fluid dynamic code assessment and flow physics modeling in support of Army and NASA efforts to advance small gas turbine engine technology. The facility is heavily instrumented with pressure and temperature probes, both in the stationary and rotating frames of reference, and has provisions for flow visualization and laser velocimetry. The facility will accommodate rotational speeds to 2400 rpm and is rated at pressures to 1.25 atm. The initial compressor stage being tested is geometrically and dynamically representative of modern high-performance centrifugal compressor stages with the exception of Mach number levels. Preliminary experimental investigations of inlet and exit flow uniformly and measurement repeatability are presented. These results demonstrate the high quality of the data which may be expected from this facility. The significance of synergism between computational fluid dynamic analysis and experimentation throughout the development of the low speed centrifugal compressor facility is demonstrated.
Directory of Open Access Journals (Sweden)
Ohanyan G.G.
2014-12-01
Full Text Available The problem of non-symmetrical free vibrations of infinite cylindrical tube corresponding to model of Timoshenko’s theory is investigated. The tube filled by the flowing Gas–Liquid mixture, containing big and small bubbles. The frequencies of tube free vibrations, computed using the models of Kirchhoff-Love and Timoshenko are compared.
Axisymmetric Stagnation-Point Flow with a General Slip Boundary Condition over a Lubricated Surface
Institute of Scientific and Technical Information of China (English)
M. Sajid; K. Mahmood; Z. Abbas
2012-01-01
We investigate the axisymmetric stagnation-point flow of a viscous fluid over a lubricated surface by imposing a generalized slip condition at the fluid-fluid interface.The power law non-Newtonian fluid is considered as a lubricant.The lubrication layer is thin and assumed to have a variable thickness.The transformed nonlinear ordinary differential equation governing the flow is linearized using quasilinearization.The method of superposition is adopted to convert the boundary value problem into an initial value problem and the solution is obtained numerically by using the fourth-order RungeKutta method.The results are discussed to see the influence of pertinent parameters.The limiting cases of Navier and no-slip boundary conditions are obtained as the special cases and found to be in excellent agreement with the existing results in the literature.%We investigate the axisymmetric stagnation-point flow of a viscous fluid over a lubricated surface by imposing a generalized slip condition at the fluid-fluid interface. The power law non-Newtonian fluid is considered as a lubricant. The lubrication layer is thin and assumed to have a variable thickness. The transformed nonlinear ordinary differential equation governing the flow is linearized using quasilinearization. The method of superposition is adopted to convert the boundary value problem into an initial value problem and the solution is obtained numerically by using the fourth-order Runge Kutta method. The results arc discussed to see the influence of pertinent parameters. The limiting cases of Navier and no-slip boundary conditions are obtained as the special cases and found to be in excellent agreement with the existing results in the literature.
Turbulent Flow past High Temperature Surfaces
Mehmedagic, Igbal; Thangam, Siva; Carlucci, Pasquale; Buckley, Liam; Carlucci, Donald
2014-11-01
Flow over high-temperature surfaces subject to wall heating is analyzed with applications to projectile design. In this study, computations are performed using an anisotropic Reynolds-stress model to study flow past surfaces that are subject to radiative flux. The model utilizes a phenomenological treatment of the energy spectrum and diffusivities of momentum and heat to include the effects of wall heat transfer and radiative exchange. The radiative transport is modeled using Eddington approximation including the weighted effect of nongrayness of the fluid. The time-averaged equations of motion and energy are solved using the modeled form of transport equations for the turbulence kinetic energy and the scalar form of turbulence dissipation with an efficient finite-volume algorithm. The model is applied for available test cases to validate its predictive capabilities for capturing the effects of wall heat transfer. Computational results are compared with experimental data available in the literature. Applications involving the design of projectiles are summarized. Funded in part by U.S. Army, ARDEC.
Directory of Open Access Journals (Sweden)
V. Ashok
2014-01-01
Full Text Available A hybrid solution methodology has been developed to solve chemically reacting laminar hypersonic flow in chemical Non-equilibrium and thermal equilibrium, by a Cartesian mesh based hybrid solution methodology, which uses an unstructured prism layer solution near the wall and a Cartesian mesh solution away from the wall. The unstructured prism layer for near wall solution is obtained from the normal projection of wall panels of the Cartesian mesh and are stitched with the outer Cartesian mesh. The solver, developed based on this approach when compared with other chemically reacting CFD codes and limited experimental results show good comparison. This procedure has a good potential to handle near-wall resolution for chemically reacting flows with a Cartesian mesh for complex geometries as well.
A.A. Boroujerdi; M. Esmaeili
2015-01-01
In this paper, new relations for calculating heat transfer and pressure drop characteristics of oscillatory flow through wire-mesh screen regenerator such as Darcy permeability, Forchheimer’s inertial coefficient, and heat transfer area per unit volume, as a function of the wire diameter are presented. According to the derived relations, thinner wires have higher pressure drop and higher heat transfer rate. The relations are applicable for all regenerative cryocoolers. Embedding the new relat...
Directory of Open Access Journals (Sweden)
Zhentao Wang
2014-07-01
Full Text Available A model based on the volume of fluid (VOF method and leaky dielectric theory is established to predict the deformation and internal flow of the droplet suspended in another vicious fluid under the influence of the electric field. Through coupling with hydrodynamics and electrostatics, the rate of deformation and internal flow of the single droplet are simulated and obtained under the different operating parameters. The calculated results show that the direction of deformation and internal flow depends on the physical properties of fluids. The numerical results are compared with Taylor's theory and experimental results by Torza et al. When the rate of deformation is small, the numerical results are consistent with theory and experimental results, and when the rate is large the numerical results are consistent with experimental results but are different from Taylor's theory. In addition, fluid viscosity hardly affects the deformation rate and mainly dominates the deformation velocity. For high viscosity droplet spends more time to attain the steady state. The conductivity ratio and permittivity ratio of two different liquids affect the direction of deformation. When fluid electric properties change, the charge distribution at the interface is various, which leads to the droplet different deformation shapes.
Institute of Scientific and Technical Information of China (English)
Wei Gao; Ru-Xun Liu; Hong Li
2012-01-01
This paper proposes a hybrid vertex-centered finite volume/finite element method for sol ution of the two dimensional (2D) incompressible Navier-Stokes equations on unstructured grids.An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling.The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by joining the centroid of cells sharing the common vertex.For the temporal integration of the momentum equations,an implicit second-order scheme is utilized to enhance the computational stability and eliminate the time step limit due to the diffusion term.The momentum equations are discretized by the vertex-centered finite volume method (FVM) and the pressure Poisson equation is solved by the Galerkin finite element method (FEM).The momentum interpolation is used to damp out the spurious pressure wiggles.The test case with analytical solutions demonstrates second-order accuracy of the current hybrid scheme in time and space for both velocity and pressure.The classic test cases,the lid-driven cavity flow,the skew cavity flow and the backward-facing step flow,show that numerical results are in good agreement with the published benchmark solutions.
Influence of the enclosed fluid on the flow over a microstructured surface in the Cassie state
Schönecker, Clarissa; Hardt, Steffen
2013-01-01
Analytical expressions for the flow field as well as for the effective slip length of a shear flow over a surface with periodic rectangular grooves are derived. The primary fluid is in the Cassie state with the grooves being filled with a secondary immiscible fluid. The coupling of both fluids is reflected in a locally varying slip distribution along the fluid-fluid interface, which models the effect of the secondary fluid on the outer flow. The obtained closed-form analytical expressions for the flow field and effective slip length of the primary fluid explicitly contain the influence of the viscosities of the two fluids as well as the magnitude of the local slip, which is a function of the surface geometry. They agree well with results from numerical computations of the full geometry. The analytical expressions allow investigating the influence of the viscous stresses inside the secondary fluid for arbitrary geometries of the rectangular grooves. For classic superhydrophobic surfaces, the deviations in the ...
Biomechanics of cell rolling: shear flow, cell-surface adhesion, and cell deformability.
Dong, C; Lei, X X
2000-01-01
The mechanics of leukocyte (white blood cell; WBC) deformation and adhesion to endothelial cells (EC) has been investigated using a novel in vitro side-view flow assay. HL-60 cell rolling adhesion to surface-immobilized P-selectin was used to model the WBC-EC adhesion process. Changes in flow shear stress, cell deformability, or substrate ligand strength resulted in significant changes in the characteristic adhesion binding time, cell-surface contact and cell rolling velocity. A 2-D model indicated that cell-substrate contact area under a high wall shear stress (20 dyn/cm2) could be nearly twice of that under a low stress (0.5 dyn/cm2) due to shear flow-induced cell deformation. An increase in contact area resulted in more energy dissipation to both adhesion bonds and viscous cytoplasm, whereas the fluid energy that inputs to a cell decreased due to a flattened cell shape. The model also predicted a plateau of WBC rolling velocity as flow shear stresses further increased. Both experimental and computational studies have described how WBC deformation influences the WBC-EC adhesion process in shear flow.
Slippery liquid-infused porous surfaces in fully developed pipe flow
Sulaimon, Hafeez; Lee, Marcus; Hellström, Leo; Rosenberg, Brian; Smits, Alexander; Hultmark, Marcus
2013-11-01
Slippery liquid-infused porous surfaces (SLIPS) are created by locking a thin layer of viscous lubricating oil into a porous surface that is textured at the micro/nano scale, with resulting omniphobicity. The oil layer lies between the solid boundary and the surrounding flow, with the potential to create a partial-slip condition at the boundary. SLIPS therefore offers a new approach to achieve drag reduction. Here, SLIPS is applied to fully developed pipe flow for Reynolds numbers ranging from 600 to 1 . 8 ×105 . The pipe flow facility consists of two test sections, an untreated and a SLIPS treated section, both 32 diameters long. The two test sections are mounted in series, the first preceded by a 120 diameter long untreated developing section and the second preceded by a 60 diameter long SLIPS treated developing section, to ensure fully developed pipe flow. The effects of SLIPS using oils of different viscosity on the flow resistance is quantified by simultaneously measuring and comparing the pressure drop along the untreated and the SLIPS treated test sections. Supported under ONR Grants N00014-12-1-0875 and N00014-12-1-0962 (program manager Ki-Han Kim). M.L. was supported by the Lewis fund for innovation in Energy and the Environment through Princeton Andlinger Center for Energy and the Environment.
Energy Technology Data Exchange (ETDEWEB)
Mahanthesh, B., E-mail: bmanths@gmail.com [Department of Mathematics, AIMS Institutes, Peenya, 560058 Bangalore (India); Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577451 Shimoga, Karnataka (India); Gireesha, B.J., E-mail: bjgireesu@rediffmail.com [Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577451 Shimoga, Karnataka (India); Department of Mechanical Engineering, Cleveland State University, Cleveland, OH (United States); Gorla, R.S. Reddy, E-mail: r.gorla@csuohio.edu [Department of Mechanical Engineering, Cleveland State University, Cleveland, OH (United States); Abbasi, F.M., E-mail: abbasisarkar@gmail.com [Department of Mathematics, Comsats Institute of Information Technology, Islamabad 44000 (Pakistan); Shehzad, S.A., E-mail: ali_qau70@yahoo.com [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan)
2016-11-01
Numerical solutions of three-dimensional flow over a non-linear stretching surface are developed in this article. An electrically conducting flow of viscous nanoliquid is considered. Heat transfer phenomenon is accounted under thermal radiation, Joule heating and viscous dissipation effects. We considered the variable heat flux condition at the surface of sheet. The governing mathematical equations are reduced to nonlinear ordinary differential systems through suitable dimensionless variables. A well-known shooting technique is implemented to obtain the results of dimensionless velocities and temperature. The obtained results are plotted for multiple values of pertinent parameters to discuss the salient features of these parameters on fluid velocity and temperature. The expressions of skin-friction coefficient and Nusselt number are computed and analyzed comprehensively through numerical values. A comparison of present results with the previous results in absence of nanoparticle volume fraction, mixed convection and magnetic field is computed and an excellent agreement noticed. We also computed the results for both linear and non-linear stretching sheet cases. - Highlights: • Hydromagnetic flow of nanofluid over a bidirectional non-linear stretching surface is examined. • Cu, Al{sub 2}O3 and TiO{sub 2} types nanoparticles are taken into account. • Numerical solutions have been computed and addressed. • The values of skin-friction and Nusselt number are presented.
von Tscharner, M.; Schmalholz, S. M.; Epard, J.-L.
2016-05-01
The Helvetic nappe system exhibits three-dimensional (3-D) features such as the lateral variation in geometry between the Morcles and Doldenhorn fold nappes or the Rawil depression. We perform 3-D finite element simulations of linear and power-law viscous flow to investigate fold nappe formation during shortening of a half graben with laterally varying thickness. 3-D ellipsoids and corresponding 2-D intersection ellipses are used to quantify finite strain. Fold nappes which formed above a thicker graben have (i) larger amplitudes, (ii) a less sheared and thinned overturned limb, and (iii) a larger thickness than fold nappes formed above a thinner graben. These results agree with observations for the Morcles and Doldenhorn nappes. We also perform 3-D simulations for a tectonic scenario suggested for the evolution of the Rawil depression. The basement is shortened and extended laterally and includes a graben which is oblique to the shortening direction and acts as mechanical weak zone. The graben causes laterally varying basement uplift generating a depression whose amplitude depends on the graben orientation and the stress exponent of basement and sediments. The axial plunge of the depression is smaller (approximately 10°) than the observed plunge (approximately 30°) indicating that additional processes are required to explain the geometry of the Rawil depression.
Directory of Open Access Journals (Sweden)
Rasool Alizadeh
2016-06-01
Full Text Available Existing solutions of the problem of axisymmetric stagnation-point flow and heat transfer on either a cylinder or a flat plate are for incompressible fluid. Here, fluid with viscosity proportional to a linear function of temperature is considered in the problem of an unaxisymmetric stagnation-point flow and heat transfer of an infinite stationary cylinder with non-uniform normal transpiration U0(φ and constant heat flux. The impinging free-stream is steady and with a constant strain rate k¯. A reduction of Navier–Stokes and energy equations is obtained by use of appropriate similarity transformations. The semi-similar solution of the Navier–Stokes equations and energy equation has been obtained numerically using an implicit finite-difference scheme. All the solutions aforesaid are presented for Reynolds numbers, Re=k¯a2/2υ∞, ranging from 0.01 to 100 for different values of Prandtl number and viscosity-variation parameter and for selected values of transpiration rate function, S(φ=U0(φ/k¯a, where a is cylinder radius and υ∞ is the reference kinematic viscosity of the fluid. Dimensionless shear-stresses corresponding to all the cases increase with the increase in Reynolds number and transpiration rate function while dimensionless shear stresses decrease with the increase in viscosity-variation parameter. The local coefficient of heat transfer (Nusselt number increases with increasing the transpiration rate function and Prandtl number.
黏性泥石流沟床冲刷深度试验研究%Experimental study on gully bed erosion depth of viscous debris flow
Institute of Scientific and Technical Information of China (English)
赵彦波; 游勇; 柳金峰; 林雪平
2012-01-01
黏性泥石流冲刷沟床，会导致建筑物构筑物基础失稳，从而毁坏工程设施。本文通过室内水槽试验探究黏性泥石流沟床冲刷深度规律。试验结果表明：黏性泥石流沟床冲刷深度主要受沟床坡度、泥石流容重以及沟床物质容重的影响；黏性泥石流冲刷沟床的深度与沟床坡度成正相关，与泥石流容重或沟床物质容重成负相关；沟床平均冲刷深度与沟床坡度成线性正比关系，与泥石流容重成线性反比关系，与沟床物质容重的自然对数成线性反比关系。最后，分析得到黏性泥石流沟床平均冲刷深度经验公式。% It is very common that the buildings and engineering facilities collapsed due to the instability of their foundations caused by viscous debris flow in eroding gully bed. In order to explore the law of gully bed erosion depth,three groups of flume experiments were carried out. Experimental results show that (1) Erosion depth of gully bed mainly influenced by slope gradient,density of debris flow and density of gully bed materials;(2) Erosion depth of gully bed increases with increase of slope gradient and decreases with increase of density of debris flow or density of gully bed materials;(3) Average erosion depth of gully bed increases with the increase of slope gradient and has a linear relation, decreases with the increase of density of debris flow and has a linear relation and the increase of density of gully bed materials and has a logarithmic relationship. Finally,a prediction formula of the average erosion depth of gully bed due to vis⁃cous debris flow based on the experiment data was posed.
Turbulent Boundary Layer Flow over Superhydrophobic Surfaces
2013-05-10
Figure 1 were a highly viscous fluid, such as honey , the boundary layer would be thick while if the fluid were water, a low-viscosity fluid, the boundary...drag has become even more important. In response to this need, and with the benefit of modern technology, the drag-reduction field is replete with...manufactured with “riblets,” small ridges on the order of fractions of millimeters, built-into the hull or skin that seek to reduce frictional drag. The
Directory of Open Access Journals (Sweden)
R. Fares
2012-01-01
Full Text Available We study the nonsteady Stokes flow in a thin tube structure composed by two thin rectangles with lateral elastic boundaries which are connected by a domain with rigid boundaries. After a variational approach of the problem which gives us existence, uniqueness, regularity results, and some a priori estimates, we construct an asymptotic solution. The existence of a junction region between the two rectangles imposes to consider, as part of the asymptotic solution, some boundary layer correctors that correspond to this region. We present and solve the problems for all the terms of the asymptotic expansion. For two different cases, we describe the order of steps of the algorithm of solving the problem and we construct the main term of the asymptotic expansion. By means of the a priori estimates, we justify our asymptotic construction, by obtaining a small error between the exact and the asymptotic solutions.
Directory of Open Access Journals (Sweden)
A. M. Salem
2013-01-01
Full Text Available A numerical model is developed to study the effects of temperature-dependent viscosity on heat and mass transfer flow of magnetohydrodynamic(MHD micropolar fluids with medium molecular weight along a permeable stretching surface embedded in a non-Darcian porous medium in the presence of viscous dissipation and chemical reaction. The governing boundary equations for momentum, angular momentum (microrotation, and energy and mass transfer are transformed to a set of nonlinear ordinary differential equations by using similarity solutions which are then solved numerically by shooting technique. A comparison between the analytical and the numerical solutions has been included. The effects of the various physical parameters entering into the problem on velocity, microrotation, temperature and concentration profiles are presented graphically. Finally, the effects of pertinent parameters on local skin-friction coefficient, local Nusselt number and local Sherwood number are also presented graphically. One important observation is that for some kinds of mixtures (e.g., H2, air with light and medium molecular weight, the magnetic field and temperature-dependent viscosity effects play a significant role and should be taken into consideration as well.
Directory of Open Access Journals (Sweden)
A.A. Boroujerdi
2015-12-01
Full Text Available In this paper, new relations for calculating heat transfer and pressure drop characteristics of oscillatory flow through wire-mesh screen regenerator such as Darcy permeability, Forchheimer’s inertial coefficient, and heat transfer area per unit volume, as a function of the wire diameter are presented. According to the derived relations, thinner wires have higher pressure drop and higher heat transfer rate. The relations are applicable for all regenerative cryocoolers. Embedding the new relations into a numerical model, three Stirling-type orifice pulse tube cryocoolers with three regenerators different in length and diameter but same volume in a variety of wire diameters, have been modeled. The results achieved by the model reveal that the local heat transfer coefficient decreases with increase of the wire diameter and the length-to-diameter ratio. In addition, it was shown that the mean absolute gas–solid wire temperature difference is a linear function of wire diameter in the range investigated. The results show that for larger length-to-diameter ratios, Forchheimer’s effect will dominate frictional losses, and the variations of the frictional losses are proportional to the inverse of the wire diameter. Wire diameter has been optimized to maximize the coefficient of performance of the cryocooler. Shorter regenerators have thinner optimum wires.
Slow Motion of a Sphere Away from a Wall: Effect of Surface Roughness on the Viscous Force
Indian Academy of Sciences (India)
Sunil Datta; Manju Shukla
2002-11-01
An asymptotic analysis is given for the effect of roughness exhibited through the slip parameter on the motion of the sphere, moving away from a plane surface with velocity . The method replaces the no-slip condition at the rough surface by slip condition and employs the method of inner and outer regions on the sphere surface. For > 0, we have the classical slip boundary condition and the results of the paper are then of interest in the microprocessor industry.
Directory of Open Access Journals (Sweden)
S.P. Anjali Devi
2010-01-01
Full Text Available Viscous and Joule dissipation effects are considered on MHD nonlinear flow and heat transfer past a stretching porous surface embedded in a porous medium under a transverse magnetic field. Analytical solutions of highly nonlinear momentum equation and confluent hypergeometric similarity solution of heat transfer equations in the case when the plate stretches with velocity varying linearly with distance are obtained. The effect of various parameters like suction parameter, Prandtl number, Magnetic parameter, and Eckert number entering into the velocity field, temperature distribution and skin friction co-efficient at the wall are discussed with the aid of graphs.
Directory of Open Access Journals (Sweden)
Kazi Humayun Kabir
2015-01-01
Full Text Available An analysis is presented to investigate the influences of viscous and pressure stress work on MHD natural convection flow along a uniformly heated vertical wavy surface. The governing equations are first modified and then transformed into dimensionless non-similar equations by using set of suitable transformations. The transformed boundary layer equations are solved numerically using the implicit finite difference method, known as Keller-box scheme. Numerical results for the velocity profiles, temperature profiles, skin friction coefficient, the rate of heat transfers, streamlines and isotherms are shown graphically. Some results of skin friction, rate of heat transfer are presented in tabular form for selected values of physical parameters.
Chatelin, Robin; Poncet, Philippe
2014-07-01
Particle methods are very convenient to compute transport equations in fluid mechanics as their computational cost is linear and they are not limited by convection stability conditions. To achieve large 3D computations the method must be coupled to efficient algorithms for velocity computations, including a good treatment of non-homogeneities and complex moving geometries. The Penalization method enables to consider moving bodies interaction by adding a term in the conservation of momentum equation. This work introduces a new computational algorithm to solve implicitly in the same step the Penalization term and the Laplace operators, since explicit computations are limited by stability issues, especially at low Reynolds number. This computational algorithm is based on the Sherman-Morrison-Woodbury formula coupled to a GMRES iterative method to reduce the computations to a sequence of Poisson problems: this allows to formulate a penalized Poisson equation as a large perturbation of a standard Poisson, by means of algebraic relations. A direct consequence is the possibility to use fast solvers based on Fast Fourier Transforms for this problem with good efficiency from both the computational and the memory consumption point of views, since these solvers are recursive and they do not perform any matrix assembling. The resulting fluid mechanics computations are very fast and they consume a small amount of memory, compared to a reference solver or a linear system resolution. The present applications focus mainly on a coupling between transport equation and 3D Stokes equations, for studying biological organisms motion in a highly viscous flows with variable viscosity.
Adhesion to model surfaces in a flow through system
Energy Technology Data Exchange (ETDEWEB)
Habeger, C.F.; Linhart, R.V.; Adair, J.H. [Univ. of Florida, Gainesville, FL (United States)
1995-12-31
A hydrodynamic method for measuring the adhesion of particles to a surface has been designed. By using hydrodynamic flow to remove particles from a model surface, the adhesive strength of particles to the surface can be measured using a flow-through cell. The hydrodynamic force required to displace a particle is calculated using the cell dimensions and the flow rate in Poiseuille`s equation.
Institute of Scientific and Technical Information of China (English)
凌锦龙; 徐敏虹; 俞丽丽
2012-01-01
The viscosity (77) and surface tension (σ) of ethyl acetate (EA) + isopropanol (IPA) binary mixture were measured over the entire composition range at 298. 15-323. 15 K and atmospheric pressure using Ubbelohde viscometer and pendant drop method, respectively. Viscosity deviations (Δ η)> excess Gibbs energy of activation of viscous flow (ΔG*E) and surface tension deviations (Δσ) were calculated from the experimental data. The excess thermodynamic properties, A17, AG*E and Act were correlated by the Redlich-Kister equation, and fitted parameters and standard deviations were obtained. The results show that Δη, ΔG*E and Δσ are negative over the whole mole fraction range in the temperature range studied, and all deviations become larger as temperature decreases. The surface tension values were further used to calculate the surface entropies (Ss) and surface enthalpies ( Hs) per unit surface area. The lyophobicity (β) and the surface mole fraction (x2s) of IPA were also derived using the extended Langmuir model. The obtained x2s values indicate that the surface concentration of IPA is always higher than its bulk concentration and consequently confirm that the surface is enriched with IPA.%常压下测定了乙酸乙酯和异丙醇二元系在298.15～323.15 K下的黏度和表面张力,计算了黏度偏差、过量流动活化自由能和表面张力偏差,采用Redlich-Kister方程进行了关联.结果表明,黏度偏差、过量流动活化自由能和表面张力偏差均为负值,且显示了相同的变化趋势,随温度降低而偏差增大.利用表面张力数据进一步考察了混合液表面熵和表面焓,并基于扩展的Langmuir模型,计算了异丙醇的疏液性β及其表面组成.β值表明异丙醇对表面有更大的亲和力,其表面组成始终高于在溶液本体中的组成.
Mahanthesh, B.; Gireesha, B. J.; Gorla, R. S. Reddy; Abbasi, F. M.; Shehzad, S. A.
2016-11-01
Numerical solutions of three-dimensional flow over a non-linear stretching surface are developed in this article. An electrically conducting flow of viscous nanoliquid is considered. Heat transfer phenomenon is accounted under thermal radiation, Joule heating and viscous dissipation effects. We considered the variable heat flux condition at the surface of sheet. The governing mathematical equations are reduced to nonlinear ordinary differential systems through suitable dimensionless variables. A well-known shooting technique is implemented to obtain the results of dimensionless velocities and temperature. The obtained results are plotted for multiple values of pertinent parameters to discuss the salient features of these parameters on fluid velocity and temperature. The expressions of skin-friction coefficient and Nusselt number are computed and analyzed comprehensively through numerical values. A comparison of present results with the previous results in absence of nanoparticle volume fraction, mixed convection and magnetic field is computed and an excellent agreement noticed. We also computed the results for both linear and non-linear stretching sheet cases.
Viscous fluid dynamics in Au+Au collisions at RHIC
Chaudhuri, A K
2008-01-01
We have studied the space-time evolution of minimally viscous ($\\frac{\\eta}{s}$=0.08) QGP fluid, undergoing boost-invariant longitudinal motion and arbitrary transverse expansion. Relaxation equations for the shear stress tensor components, derived from the phenomenological Israel-Stewart's theory of dissipative relativistic fluid, are solved simultaneously with the energy-momentum conservation equations. Comparison of evolution of ideal and viscous fluid, both initialized under the similar conditions, e.g. same equilibration time, energy density and velocity profile, indicate that in viscous fluid, energy density or temperature of the fluid evolve slowly than in an ideal fluid. Transverse expansion is also more in viscous evolution. We have also studied particle production in viscous dynamics. Compared to ideal dynamics, in viscous dynamics, particle yield at high $p_T$ is increased. Elliptic flow on the other hand decreases. Minimally viscous QGP fluid, initialized at entropy density $s_{ini}$=110 $fm^{-3}$...
Institute of Scientific and Technical Information of China (English)
杨琼方; 王永生; 张志宏
2012-01-01
After RANS simulation of full appended SUBOFF submarine＇s viscous flow with four groups of grids of the same mesh block topology and close mesh quality and five turbulent models, effects of mesh density and nodes distribution and turbulent models on calculation precision were analyzed, and detailed validation of force integral variables and velocity field variables and vorticity of viscous flow were completed at last. Results show that G4 （1.4 million） with the most mesh density can get the high- est precision,which calculated total drag just differ by 0. 723% to the experiment. As for the G4 mesh, choosing the SST model in the calculation is the best. Using G4, the predicted pressure coefficient and wall shear stress coefficient distribution both fit very well with the experiment; The numerical precision of the velocity profiles on propeller disk plane is near to the reference,and the calculated radial position for dimensional axial velocity over 0.9 is a little bigger than the experiment,while the rest is good agree- ment with the data; The precision of the three velocity components at r/R=0. 25 is higher than refer- ence too as a whole, and its axial component fits well with the experiment, the radial components＇ peak is a little lower while its circumferential position is coincident with the measure. What＇s more important, RANS simulation of the G4 successfully captures the complexity vorticity structures,including counter- rotating vortex induced by flow over fairwater cap and stern fin＇s tip surface, necklace-shaped vortex pair downstream of the appendages＇ root section,shoe-shaped vortex attached upwards of stern fin＇s tip sur- face trailing edge, horse-shoe vortex system induced by the flow around the appendages, vortex induced by flow extrusion within the passages of stern appendages, and the vortex concentration phenomenon on propeller disk plane,even the phenomenon of counter-rotating vortex induced by flow over fairwater cap being stable
Molecular dynamics of fluid flow at solid surfaces
Koplik, Joel; Banavar, Jayanth R.; Willemsen, Jorge F.
1989-05-01
Molecular dynamics techniques are used to study the microscopic aspects of several slow viscous flows past a solid wall, where both fluid and wall have a molecular structure. Systems of several thousand molecules are found to exhibit reasonable continuum behavior, albeit with significant thermal fluctuations. In Couette and Poiseuille flow of liquids it is found that the no-slip boundary condition arises naturally as a consequence of molecular roughness, and that the velocity and stress fields agree with the solutions of the Stokes equations. At lower densities slip appears, which can be incorporated into a flow-independent slip-length boundary condition. The trajectories of individual molecules in Poiseuille flow are examined, and it is also found that their average behavior is given by Taylor-Aris hydrodynamic dispersion. An immiscible two-fluid system is simulated by a species-dependent intermolecular interaction. A static meniscus is observed whose contact angle agrees with simple estimates and, when motion occurs, velocity-dependent advancing and receding angles are observed. The local velocity field near a moving contact line shows a breakdown of the no-slip condition and, up to substantial statistical fluctuations, is consistent with earlier predictions of Dussan [AIChE J. 23, 131 (1977)].
Inelastic non-Newtonian flow over heterogeneously slippery surfaces
Haase, A. Sander; Wood, Jeffery A.; Sprakel, Lisette M.J.; Lammertink, Rob G.H.
2017-01-01
In this study, we investigated inelastic non-Newtonian fluid flow over heterogeneously slippery surfaces. First, we simulated the flow of aqueous xanthan gum solutions over a bubble mattress, which is a superhydrophobic surface consisting of transversely positioned no-slip walls and no-shear gas bub
Dynamics and Instabilities of Free Surface and Vortex Flows
DEFF Research Database (Denmark)
Tophøj, Laust Emil Hjerrild
2012-01-01
This PhD thesis consists of two main parts. The first part describes the dynamics of an ideal fluid on a stationary free surface of a given shape. It turns out that one can formulate a set of self-contained equations of momentum conservation for the tangential flow, with no reference to the flow...... of the fluid bulk. With these equations, one can in principle predict the surface flow on a given free surface, once its shape has been measured. The equations are expressed for a general surface using Riemannian geometry and their solutions are discussed, including some difficulties that may arise...
Stokes’ and Lamb's viscous drag laws
Eames, I.; Klettner, C. A.
2017-03-01
Since Galileo used his pulse to measure the time period of a swinging chandelier in the 17th century, pendulums have fascinated scientists. It was not until Stokes' (1851 Camb. Phil. Soc. 9 8-106) (whose interest was spurred by the pendulur time pieces of the mid 19th century) treatise on viscous flow that a theoretical framework for the drag on a sphere at low Reynolds number was laid down. Stokes' famous drag law has been used to determine two fundamental physical constants—the charge on an electron and Avogadro's constant—and has been used in theories which have won three Nobel prizes. Considering its illustrious history it is then not surprising that the flow past a sphere and its two-dimensional analog, the flow past a cylinder, form the starting point of teaching flow past a rigid body in undergraduate level fluid mechanics courses. Usually starting with the two-dimensional potential flow past a cylinder, students progress to the three-dimensional potential flow past a sphere. However, when the viscous flow past rigid bodies is taught, the three-dimensional example of a sphere is first introduced, and followed by (but not often), the two-dimensional viscous flow past a cylinder. The reason why viscous flow past a cylinder is generally not taught is because it is usually explained from an asymptotic analysis perspective. In fact, this added mathematical complexity is why the drag on a cylinder was only solved in 1911, 60 years after the drag on a sphere. In this note, we show that the viscous flow past a cylinder can be explained without the need to introduce any asymptotic analysis while still capturing all the physical insight of this classic fluid mechanics problem.
Hydrodynamics of the free surface flow in Pelton turbine buckets
Perrig, Alexandre; Avellan, François; Farhat, Mohamed
2008-01-01
The design of Pelton turbines has always been more difficult than that of reaction turbines, and their performances lower. Indeed, the Pelton turbines combine 4 types of flows: (i) confined, steady-state flow in the piping systems and injector, (ii) free water jets, (iii) 3D unsteady free surface flows in the buckets, and (iv) dispersed 2-phase flows in the casing. The flow in Pelton turbines has not been analyzed so far with such detail as the flow in the reaction turbines, thus the understa...
Hydrodynamics of the free surface flow in Pelton turbine buckets
Perrig, Alexandre
2007-01-01
The design of Pelton turbines has always been more difficult than that of reaction turbines, and their performances lower. Indeed, the Pelton turbines combine 4 types of flows: (i) confined, steady-state flow in the piping systems and injector, (ii) free water jets, (iii) 3D unsteady free surface flows in the buckets, and (iv) dispersed 2-phase flows in the casing. The flow in Pelton turbines has not been analyzed so far with such detail as the flow in the reaction turbines, thus the understa...
Ricci flow on Kaehler-Einstein surfaces
Chen, Xiuxiong; Tian, Gang
2000-01-01
In this paper, we construct a set of new functionals of Ricci curvature on any Kaehler manifolds which are invariant under holomorphic transfermations in Kaehler Einstein manifolds and essentially decreasing under the Kaehler Ricci flow. Moreover, if the initial metric has non-negative bisectional curvature, using Tian's inequality, we can prove that each of the functionals has uniform lower bound along the flow which gives a set of integral estimates on curvature. Using this set of integral ...
Improving longitudinal motion prediction of hybrid monohulls with the viscous effect
Institute of Scientific and Technical Information of China (English)
ZHANG Heng; LI Ji-de
2007-01-01
A new method improves prediction of the motion of a hybrid monohull in regular waves. Stem section hydrodynamic coefficients of a hybrid monohull with harmonic oscillation were computed using the Reynolds Averaged Navier-Stokes Equations (RANSE). The governing equations were solved using the finite volume method. The VOF method was used for free surface treatment, and RNGK-ε turbulence model was employed in viscous flow calculation. The whole computational domain was divided into many blocks each with structured grids, and the dynamic process was treated with moving grids. Using a 2-D strip method and 2.5D theory with the correction hydrodynamic coefficients allows consideration of the viscous effect when predicting longitudinal motion of a hybrid monohull in regular waves. The method is effective at predicting motion of a hybrid monohull, showing that the viscous effect on a semi-submerged body cannot be ignored.
Directory of Open Access Journals (Sweden)
Mariano A.
2000-01-01
Full Text Available Kinematic viscosities of binary mixtures composed of tetrahydrofuran with 1-butanol, 2-butanol and 1-chlorobutane have been measured at 283.15, 298.15 and 313.15 K and atmospheric pressure for the whole range of compositions. The dynamic viscosity, the excess viscosity and the excess energy of activation for viscous flow were also calculated. The excess viscosity shows negative deviations from ideal behavior for the mixtures tetrahydrofuran with 1-butanol and 2-butanol and a small positive deviation for the binary tetrahydrofuran + 1-chlorobutane system. The experimental results have also been used to test some empirical and semiempirical equations adopted previously to correlate viscosity - composition data.
Lubricated viscous gravity currents
Kowal, Katarzyna N.; Worster, M. Grae
2015-01-01
This is the author accepted manuscript. The final version is available via CUP at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9553100&fileId=S0022112015000300. We present a theoretical and experimental study of viscous gravity currents lubricated by another viscous fluid from below. We use lubrication theory to model both layers as Newtonian fluids spreading under their own weight in two-dimensional and axisymmetric settings over a smooth rigid horizontal surfa...
Qu, Mengmeng; Jiang, Dazhi; Lu, Lucy X.
2016-11-01
To address the multiscale deformation and fabric development in Earth's ductile lithosphere, micromechanics-based self-consistent homogenization is commonly used to obtain macroscale rheological properties from properties of constituent elements. The homogenization is heavily based on the solution of an Eshelby viscous inclusion in a linear viscous medium and the extension of the solution to nonlinear viscous materials. The homogenization requires repeated numerical evaluation of Eshelby tensors for constituent elements and becomes ever more computationally challenging as the elements are deformed to more elongate or flattened shapes. In this paper, we develop an optimal scheme for evaluating Eshelby tensors, using a combination of a product Gaussian quadrature and the Lebedev quadrature. We first establish, through numerical experiments, an empirical relationship between the inclusion shape and the computational time it takes to evaluate its Eshelby tensors. We then use the relationship to develop an optimal scheme for selecting the most efficient quadrature to obtain the Eshelby tensors. The optimal scheme is applicable to general homogenizations. In this paper, it is implemented in a MATLAB package for investigating the evolution of solitary rigid or deformable inclusions and the development of shape preferred orientations in multi-inclusion systems during deformation. The MATLAB package, upgrading an earlier effort written in MathCad, can be downloaded online.