Bubble dynamics equations in Newton fluid
International Nuclear Information System (INIS)
Xiao, J
2008-01-01
For the high-speed flow of Newton fluid, bubble is produced and expanded when it moves toward the surface of fluid. Bubble dynamics is a very important research field to understand the intrinsic feature of bubble production and motion. This research formulates the bubble expansion by expansion-local rotation transformation, which can be calculated by the measured velocity field. Then, the related dynamic equations are established to describe the interaction between the fluid and the bubble. The research shows that the bubble production condition can be expressed by critical vortex value and fluid pressure; and the bubble expansion rate can be obtained by solving the non-linear dynamic equation of bubble motion. The results may help the related research as it shows a special kind of fluid motion in theoretic sense. As an application example, the nanofiber radium-voltage relation and threshold voltage-surface tension relation in electrospinning process are discussed
Attractors of equations of non-Newtonian fluid dynamics
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Zvyagin, V G; Kondrat'ev, S K
2014-01-01
This survey describes a version of the trajectory-attractor method, which is applied to study the limit asymptotic behaviour of solutions of equations of non-Newtonian fluid dynamics. The trajectory-attractor method emerged in papers of the Russian mathematicians Vishik and Chepyzhov and the American mathematician Sell under the condition that the corresponding trajectory spaces be invariant under the translation semigroup. The need for such an approach was caused by the fact that for many equations of mathematical physics for which the Cauchy initial-value problem has a global (weak) solution with respect to the time, the uniqueness of such a solution has either not been established or does not hold. In particular, this is the case for equations of fluid dynamics. At the same time, trajectory spaces invariant under the translation semigroup could not be constructed for many equations of non-Newtonian fluid dynamics. In this connection, a different approach to the construction of trajectory attractors for dissipative systems was proposed in papers of Zvyagin and Vorotnikov without using invariance of trajectory spaces under the translation semigroup and is based on the topological lemma of Shura-Bura. This paper presents examples of equations of non-Newtonian fluid dynamics (the Jeffreys system describing movement of the Earth's crust, the model of motion of weak aqueous solutions of polymers, a system with memory) for which the aforementioned construction is used to prove the existence of attractors in both the autonomous and the non-autonomous cases. At the beginning of the paper there is also a brief exposition of the results of Ladyzhenskaya on the existence of attractors of the two-dimensional Navier-Stokes system and the result of Vishik and Chepyzhov for the case of attractors of the three-dimensional Navier-Stokes system. Bibliography: 34 titles
International Nuclear Information System (INIS)
Myeong, Hyeon Guk
1999-06-01
This book deals with computational fluid dynamics with basic and history of numerical fluid dynamics, introduction of finite volume method using one-dimensional heat conduction equation, solution of two-dimensional heat conduction equation, solution of Navier-Stokes equation, fluid with heat transport, turbulent flow and turbulent model, Navier-Stokes solution by generalized coordinate system such as coordinate conversion, conversion of basic equation, program and example of calculation, application of abnormal problem and high speed solution of numerical fluid dynamics.
On the Schrodinger equation in fluid-dynamical form
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Wong, C.Y.
1976-01-01
The fluid-dynamical form of the Schrodinger equations is studied to examine the nature of the quantum forces arising from the quantum potential of Madelung and Bohm. It is found that they are in the form of a stress tensor having diagonal and nondiagonal components. Future studies of these quantum stress tensors in a many-body system may shed some light on the mechanism of spontaneous symmetry breaking and the generation of vorticity in many nuclear systems
Conservation form of the equations of fluid dynamics in general nonsteady coordinates
Zhang, H.; Camarero, R.; Kahawita, R.
1985-11-01
Many of the differential equations arising in fluid dynamics may be stated in conservation-law form. A number of investigations have been conducted with the aim to derive the conservation-law form of the Navier-Stokes equations in general nonsteady coordinate systems. The present note has the objective to illustrate a mathematical methodology with which such forms of the equations may be derived in an easier and more general fashion. For numerical applications, the scalar form of the equations is eventually provided. Attention is given to the conservation form of equations in curvilinear coordinates and numerical considerations.
Conservation form of the equations of fluid dynamics in general nonsteady coordinates
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Zhang, H.; Camarero, R.; Kahawita, R.
1985-01-01
Many of the differential equations arising in fluid dynamics may be stated in conservation-law form. A number of investigations have been conducted with the aim to derive the conservation-law form of the Navier-Stokes equations in general nonsteady coordinate systems. The present note has the objective to illustrate a mathematical methodology with which such forms of the equations may be derived in an easier and more general fashion. For numerical applications, the scalar form of the equations is eventually provided. Attention is given to the conservation form of equations in curvilinear coordinates and numerical considerations. 6 references
Euler's fluid equations: Optimal control vs optimization
International Nuclear Information System (INIS)
Holm, Darryl D.
2009-01-01
An optimization method used in image-processing (metamorphosis) is found to imply Euler's equations for incompressible flow of an inviscid fluid, without requiring that the Lagrangian particle labels exactly follow the flow lines of the Eulerian velocity vector field. Thus, an optimal control problem and an optimization problem for incompressible ideal fluid flow both yield the same Euler fluid equations, although their Lagrangian parcel dynamics are different. This is a result of the gauge freedom in the definition of the fluid pressure for an incompressible flow, in combination with the symmetry of fluid dynamics under relabeling of their Lagrangian coordinates. Similar ideas are also illustrated for SO(N) rigid body motion.
Cotter, C J; Gottwald, G A; Holm, D D
2017-09-01
In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.
Bernard, Peter S
2015-01-01
This book presents a focused, readable account of the principal physical and mathematical ideas at the heart of fluid dynamics. Graduate students in engineering, applied math, and physics who are taking their first graduate course in fluids will find this book invaluable in providing the background in physics and mathematics necessary to pursue advanced study. The book includes a detailed derivation of the Navier-Stokes and energy equations, followed by many examples of their use in studying the dynamics of fluid flows. Modern tensor analysis is used to simplify the mathematical derivations, thus allowing a clearer view of the physics. Peter Bernard also covers the motivation behind many fundamental concepts such as Bernoulli's equation and the stream function. Many exercises are designed with a view toward using MATLAB or its equivalent to simplify and extend the analysis of fluid motion including developing flow simulations based on techniques described in the book.
Phase space density representations in fluid dynamics
International Nuclear Information System (INIS)
Ramshaw, J.D.
1989-01-01
Phase space density representations of inviscid fluid dynamics were recently discussed by Abarbanel and Rouhi. Here it is shown that such representations may be simply derived and interpreted by means of the Liouville equation corresponding to the dynamical system of ordinary differential equations that describes fluid particle trajectories. The Hamiltonian and Poisson bracket for the phase space density then emerge as immediate consequences of the corresponding structure of the dynamics. For barotropic fluids, this approach leads by direct construction to the formulation presented by Abarbanel and Rouhi. Extensions of this formulation to inhomogeneous incompressible fluids and to fluids in which the state equation involves an additional transported scalar variable are constructed by augmenting the single-particle dynamics and phase space to include the relevant additional variable
FDTD for Hydrodynamic Electron Fluid Maxwell Equations
Directory of Open Access Journals (Sweden)
Yingxue Zhao
2015-05-01
Full Text Available In this work, we develop a numerical method for solving the three dimensional hydrodynamic electron fluid Maxwell equations that describe the electron gas dynamics driven by an external electromagnetic wave excitation. Our numerical approach is based on the Finite-Difference Time-Domain (FDTD method for solving the Maxwell’s equations and an explicit central finite difference method for solving the hydrodynamic electron fluid equations containing both electron density and current equations. Numerical results show good agreement with the experiment of studying the second-harmonic generation (SHG from metallic split-ring resonator (SRR.
Application of coarse-mesh methods to fluid dynamics equations
International Nuclear Information System (INIS)
Romstedt, P.; Werner, W.
1977-01-01
An Asymmetric Weighted Residual (ASWR) method for fluid dynamics equations is described. It leads to local operators with a 7-point Finite Difference (FD) structure, which is independent of the degree of the approximating polynomials. An 1-dimensional problem was solved by both this ASWR-method and a commonly used FD-method. The numerical results demonstrate that the ASWR-method combines high accuracy on a coarse computational mesh with short computing time per space point. The posibility of using fewer space points consequently brings about a considerable reduction in total running time for the ASWR-method as compared with conventional FD-methods. (orig.) [de
International Nuclear Information System (INIS)
Elfelsoufi, Z.; Azrar, L.
2016-01-01
In this paper, a mathematical modeling of flutter and divergence analyses of fluid conveying pipes based on integral equation formulations is presented. Dynamic stability problems related to fluid pressure, velocity, tension, topography slope and viscoelastic supports and foundations are formulated. A methodological approach is presented and the required matrices, associated to the influencing fluid and pipe parameters, are explicitly given. Internal discretizations are used allowing to investigate the deformation, the bending moment, slope and shear force at internal points. Velocity–frequency, pressure-frequency and tension-frequency curves are analyzed for various fluid parameters and internal elastic supports. Critical values of divergence and flutter behaviors with respect to various fluid parameters are investigated. This model is general and allows the study of dynamic stability of tubes crossed by stationary and instationary fluid on various types of supports. Accurate predictions can be obtained and are of particular interest for a better performance and for an optimal safety of piping system installations. - Highlights: • Modeling the flutter and divergence of fluid conveying pipes based on RBF. • Dynamic analysis of a fluid conveying pipe with generalized boundary conditions. • Considered parameters fluid are the pressure, tension, slopes topography, velocity. • Internal support increase the critical velocity value. • This methodologies determine the fluid parameters effects.
Euler's fluid equations: Optimal control vs optimization
Energy Technology Data Exchange (ETDEWEB)
Holm, Darryl D., E-mail: d.holm@ic.ac.u [Department of Mathematics, Imperial College London, SW7 2AZ (United Kingdom)
2009-11-23
An optimization method used in image-processing (metamorphosis) is found to imply Euler's equations for incompressible flow of an inviscid fluid, without requiring that the Lagrangian particle labels exactly follow the flow lines of the Eulerian velocity vector field. Thus, an optimal control problem and an optimization problem for incompressible ideal fluid flow both yield the same Euler fluid equations, although their Lagrangian parcel dynamics are different. This is a result of the gauge freedom in the definition of the fluid pressure for an incompressible flow, in combination with the symmetry of fluid dynamics under relabeling of their Lagrangian coordinates. Similar ideas are also illustrated for SO(N) rigid body motion.
International Nuclear Information System (INIS)
Turner, L.
1996-01-01
Adhering to the lore that vorticity is a critical ingredient of fluid turbulence, a triad of coupled helicity (vorticity) states of the incompressible Navier-Stokes fluid are followed. Effects of the remaining states of the fluid on the triad are then modeled as a simple driving term. Numerical solution of the equations yield attractors that seem strange and chaotic. This suggests that the unpredictability of nonlinear fluid dynamics (i.e., turbulence) may be traced back to the most primordial structure of the Navier-Stokes equation; namely, the driven triadic interaction. copyright 1996 The American Physical Society
Elizarova, Tatiana G
2009-01-01
This book presents two interconnected mathematical models generalizing the Navier-Stokes system. The models, called the quasi-gas-dynamic and quasi-hydrodynamic equations, are then used as the basis of numerical methods solving gas- and fluid-dynamic problems.
Ogilvie, Gordon I.
2016-06-01
> These lecture notes and example problems are based on a course given at the University of Cambridge in Part III of the Mathematical Tripos. Fluid dynamics is involved in a very wide range of astrophysical phenomena, such as the formation and internal dynamics of stars and giant planets, the workings of jets and accretion discs around stars and black holes and the dynamics of the expanding Universe. Effects that can be important in astrophysical fluids include compressibility, self-gravitation and the dynamical influence of the magnetic field that is `frozen in' to a highly conducting plasma. The basic models introduced and applied in this course are Newtonian gas dynamics and magnetohydrodynamics (MHD) for an ideal compressible fluid. The mathematical structure of the governing equations and the associated conservation laws are explored in some detail because of their importance for both analytical and numerical methods of solution, as well as for physical interpretation. Linear and nonlinear waves, including shocks and other discontinuities, are discussed. The spherical blast wave resulting from a supernova, and involving a strong shock, is a classic problem that can be solved analytically. Steady solutions with spherical or axial symmetry reveal the physics of winds and jets from stars and discs. The linearized equations determine the oscillation modes of astrophysical bodies, as well as their stability and their response to tidal forcing.
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Mihalas, D.; Weaver, R.
1982-01-01
The purpose of this paper is to give an overview of the role of radiation in the transport of energy and momentum in a combined matter-radiation fluid. The transport equation for a moving radiating fluid is presented in both a fully Eulerian and a fully Lagrangian formulation, along with conservation equations describing the dynamics of the fluid. Special attention is paid to the problem of deriving equations that are mutually consistent in each frame, and between frames, to 0(v/c). A detailed analysis is made to show that in situations of broad interest, terms that are formally of 0(v/c) actually dominate the solution, demonstrating that it is essential (1) to pay scrupulous attention to the question of the frame dependence in formulating the equations, and (2) to solve the equations to 0(v/c) in quite general circumstances. These points are illustrated in the context of the nonequilibrium radiation diffusion limit, and a sketch of how the Lagrangian equations are to be solved is presented
Molecular dynamics studies of transport properties and equation of state of supercritical fluids
Nwobi, Obika C.
Many chemical propulsion systems operate with one or more of the reactants above the critical point in order to enhance their performance. Most of the computational fluid dynamics (CFD) methods used to predict these flows require accurate information on the transport properties and equation of state at these supercritical conditions. This work involves the determination of transport coefficients and equation of state of supercritical fluids by equilibrium molecular dynamics (MD) simulations on parallel computers using the Green-Kubo formulae and the virial equation of state, respectively. MD involves the solution of equations of motion of a system of molecules that interact with each other through an intermolecular potential. Provided that an accurate potential can be found for the system of interest, MD can be used regardless of the phase and thermodynamic conditions of the substances involved. The MD program uses the effective Lennard-Jones potential, with system sizes of 1000-1200 molecules and, simulations of 2,000,000 time-steps for computing transport coefficients and 200,000 time-steps for pressures. The computer code also uses linked cell lists for efficient sorting of molecules, periodic boundary conditions, and a modified velocity Verlet algorithm for particle displacement. Particle decomposition is used for distributing the molecules to different processors of a parallel computer. Simulations have been carried out on pure argon, nitrogen, oxygen and ethylene at various supercritical conditions, with self-diffusion coefficients, shear viscosity coefficients, thermal conductivity coefficients and pressures computed for most of the conditions. Results compare well with experimental and the National Institute of Standards and Technology (NIST) values. The results show that the number of molecules and the potential cut-off radius have no significant effect on the computed coefficients, while long-time integration is necessary for accurate determination of the
Ruban, Anatoly I
This is the first book in a four-part series designed to give a comprehensive and coherent description of Fluid Dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture course, and then progressing through more advanced material up to the level of modern research in the field. The present Part 1 consists of four chapters. Chapter 1 begins with a discussion of Continuum Hypothesis, which is followed by an introduction to macroscopic functions, the velocity vector, pressure, density, and enthalpy. We then analyse the forces acting inside a fluid, and deduce the Navier-Stokes equations for incompressible and compressible fluids in Cartesian and curvilinear coordinates. In Chapter 2 we study the properties of a number of flows that are presented by the so-called exact solutions of the Navier-Stokes equations, including the Couette flow between two parallel plates, Hagen-Poiseuille flow through a pipe, and Karman flow above an infinite rotating disk. Chapter 3 is d...
BMS3 invariant fluid dynamics at null infinity
Penna, Robert F.
2018-02-01
We revisit the boundary dynamics of asymptotically flat, three dimensional gravity. The boundary is governed by a momentum conservation equation and an energy conservation equation, which we interpret as fluid equations, following the membrane paradigm. We reformulate the boundary’s equations of motion as Hamiltonian flow on the dual of an infinite-dimensional, semi-direct product Lie algebra equipped with a Lie–Poisson bracket. This gives the analogue for boundary fluid dynamics of the Marsden–Ratiu–Weinstein formulation of the compressible Euler equations on a manifold, M, as Hamiltonian flow on the dual of the Lie algebra of \
Coupled problems in transient fluid and structural dynamics in nuclear engineering
International Nuclear Information System (INIS)
Krieg, R.
1978-01-01
Some important problems in coupled fluid-structural dynamics which occur in safety investigations of liquid metal fast breeder reactors (LMFBR). light water reactors and nuclear reprocessing plants are discussed and a classification of solution methods is introduced. A distinction is made between the step by step solution procedure, where available computer codes in fluid and structural dynamics are coupled, and advanced simultaneous solution methods, where the coupling is carried out at the level of the fundamental equations. Results presented include the transient deformation of a two-row pin bundle surrounded by an infinite fluid field, vapour explosions in a fluid container and containment distortions due to bubble collapse in the pressure suppression system of a boiling water reactor. A recently developed simultaneous solution method is presented in detail. Here the fluid dynamics (inviscid, incompressible fluid) is described by a singularity method which reduces the three-dimensional fluid dynamics problems to a two-dimensional formulation. In this way the three-dynamics fluid dynamics as well as the structural (shell) dynamics can be described essentially by common unknowns at the fluid-structural interface. The resulting equations for the coupled fluid-structural dynamics are analogous to to the equations of motion of the structural dynamics alone. (author)
arXiv (3+1)-dimensional anisotropic fluid dynamics with a lattice QCD equation of state
McNelis, M.; Heinz, U.
2018-06-01
Anisotropic hydrodynamics improves upon standard dissipative fluid dynamics by treating certain large dissipative corrections non-perturbatively. Relativistic heavy-ion collisions feature two such large dissipative effects: (i) Strongly anisotropic expansion generates a large shear stress component which manifests itself in very different longitudinal and transverse pressures, especially at early times. (ii) Critical fluctuations near the quark-hadron phase transition lead to a large bulk viscous pressure on the conversion surface between hydrodynamics and a microscopic hadronic cascade description of the final collision stage. We present a new dissipative hydrodynamic formulation for non-conformal fluids where both of these effects are treated nonperturbatively. The evolution equations are derived from the Boltzmann equation in the 14-moment approximation, using an expansion around an anisotropic leading-order distribution function with two momentum-space deformation parameters, accounting for the longitudin...
Noncommutative geometry and fluid dynamics
International Nuclear Information System (INIS)
Das, Praloy; Ghosh, Subir
2016-01-01
In the present paper we have developed a Non-Commutative (NC) generalization of perfect fluid model from first principles, in a Hamiltonian framework. The noncommutativity is introduced at the Lagrangian (particle) coordinate space brackets and the induced NC fluid bracket algebra for the Eulerian (fluid) field variables is derived. Together with a Hamiltonian this NC algebra generates the generalized fluid dynamics that satisfies exact local conservation laws for mass and energy, thereby maintaining mass and energy conservation. However, nontrivial NC correction terms appear in the charge and energy fluxes. Other non-relativistic spacetime symmetries of the NC fluid are also discussed in detail. This constitutes the study of kinematics and dynamics of NC fluid. In the second part we construct an extension of the Friedmann-Robertson-Walker (FRW) cosmological model based on the NC fluid dynamics presented here. We outline the way in which NC effects generate cosmological perturbations bringing about anisotropy and inhomogeneity in the model. We also derive a NC extended Friedmann equation. (orig.)
Noncommutative geometry and fluid dynamics
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Das, Praloy; Ghosh, Subir [Indian Statistical Institute, Physics and Applied Mathematics Unit, Kolkata (India)
2016-11-15
In the present paper we have developed a Non-Commutative (NC) generalization of perfect fluid model from first principles, in a Hamiltonian framework. The noncommutativity is introduced at the Lagrangian (particle) coordinate space brackets and the induced NC fluid bracket algebra for the Eulerian (fluid) field variables is derived. Together with a Hamiltonian this NC algebra generates the generalized fluid dynamics that satisfies exact local conservation laws for mass and energy, thereby maintaining mass and energy conservation. However, nontrivial NC correction terms appear in the charge and energy fluxes. Other non-relativistic spacetime symmetries of the NC fluid are also discussed in detail. This constitutes the study of kinematics and dynamics of NC fluid. In the second part we construct an extension of the Friedmann-Robertson-Walker (FRW) cosmological model based on the NC fluid dynamics presented here. We outline the way in which NC effects generate cosmological perturbations bringing about anisotropy and inhomogeneity in the model. We also derive a NC extended Friedmann equation. (orig.)
International Conference on Mathematical Fluid Dynamics
Suzuki, Yukihito
2016-01-01
This volume presents original papers ranging from an experimental study on cavitation jets to an up-to-date mathematical analysis of the Navier-Stokes equations for free boundary problems, reflecting topics featured at the International Conference on Mathematical Fluid Dynamics, Present and Future, held 11–14 November 2014 at Waseda University in Tokyo. The contributions address subjects in one- and two-phase fluid flows, including cavitation, liquid crystal flows, plasma flows, and blood flows. Written by internationally respected experts, these papers highlight the connections between mathematical, experimental, and computational fluid dynamics. The book is aimed at a wide readership in mathematics and engineering, including researchers and graduate students interested in mathematical fluid dynamics.
New derivation of relativistic dissipative fluid dynamics
International Nuclear Information System (INIS)
Jaiswal, Amaresh; Bhalerao, Rajeev S.; Pal, Subrata
2012-01-01
Relativistic dissipative hydrodynamics has been quite successful in explaining the spectra and azimuthal anisotropy of particles produced in heavy-ion collisions at the RHIC and recently at the LHC. The first-order dissipative fluid dynamics or the relativistic Navier-Stokes (NS) theory involves parabolic differential equations and suffers from a causality and instability. The second-order or Israel-Stewart (IS) theory with its hyperbolic equations restores causality but may not guarantee stability. The correct formulation of relativistic viscous fluid dynamics is far from settled and is under intense investigation
Coarse-grained forms for equations describing the microscopic motion of particles in a fluid.
Das, Shankar P; Yoshimori, Akira
2013-10-01
Exact equations of motion for the microscopically defined collective density ρ(x,t) and the momentum density ĝ(x,t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations.
A stochastic differential equation analysis of cerebrospinal fluid dynamics.
Raman, Kalyan
2011-01-18
Clinical measurements of intracranial pressure (ICP) over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data. The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE) that accommodates the fluctuations in ICP. The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise. Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.
A stochastic differential equation analysis of cerebrospinal fluid dynamics
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Raman Kalyan
2011-01-01
Full Text Available Abstract Background Clinical measurements of intracranial pressure (ICP over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data. Methods The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE that accommodates the fluctuations in ICP. Results The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise. Conclusions Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.
Direct modeling for computational fluid dynamics
Xu, Kun
2015-06-01
All fluid dynamic equations are valid under their modeling scales, such as the particle mean free path and mean collision time scale of the Boltzmann equation and the hydrodynamic scale of the Navier-Stokes (NS) equations. The current computational fluid dynamics (CFD) focuses on the numerical solution of partial differential equations (PDEs), and its aim is to get the accurate solution of these governing equations. Under such a CFD practice, it is hard to develop a unified scheme that covers flow physics from kinetic to hydrodynamic scales continuously because there is no such governing equation which could make a smooth transition from the Boltzmann to the NS modeling. The study of fluid dynamics needs to go beyond the traditional numerical partial differential equations. The emerging engineering applications, such as air-vehicle design for near-space flight and flow and heat transfer in micro-devices, do require further expansion of the concept of gas dynamics to a larger domain of physical reality, rather than the traditional distinguishable governing equations. At the current stage, the non-equilibrium flow physics has not yet been well explored or clearly understood due to the lack of appropriate tools. Unfortunately, under the current numerical PDE approach, it is hard to develop such a meaningful tool due to the absence of valid PDEs. In order to construct multiscale and multiphysics simulation methods similar to the modeling process of constructing the Boltzmann or the NS governing equations, the development of a numerical algorithm should be based on the first principle of physical modeling. In this paper, instead of following the traditional numerical PDE path, we introduce direct modeling as a principle for CFD algorithm development. Since all computations are conducted in a discretized space with limited cell resolution, the flow physics to be modeled has to be done in the mesh size and time step scales. Here, the CFD is more or less a direct
Nonlinear transport processes and fluid dynamics: Cylindrical Couette flow of Lennard-Jones fluids
International Nuclear Information System (INIS)
Khayat, R.E.; Eu, B.C.
1988-01-01
In this paper we report on calculations of flow profiles for cylindrical Couette flow of a Lennard-Jones fluid. The flow is subjected to a temperature gradient and thermoviscous effects are taken into consideration. We apply the generalized fluid dynamic equations which are provided by the modified moment method for the Boltzmann equation reported previously. The results of calculations are in good agreement with the Monte Carlo direct simulation method by K. Nanbu [Phys. Fluids 27, 2632 (1984)] for most of Knudsen numbers for which the simulation data are available
Book review: Partial Differential Equations and Fluid Mechanics
Muntean, A.
2011-01-01
The baak is the result of the workshop Partial Differential Equations and Fluid Dynamics that look place at the Mathematics Institute of the University of Warwick. May 21st - 23rd, 2007. It contains ten review and research papers which provide an accessible summary of a wide range of active research
Lattice fluid dynamics from perfect discretizations of continuum flows
International Nuclear Information System (INIS)
Katz, E.; Wiese, U.
1998-01-01
We use renormalization group methods to derive equations of motion for large scale variables in fluid dynamics. The large scale variables are averages of the underlying continuum variables over cubic volumes and naturally exist on a lattice. The resulting lattice dynamics represents a perfect discretization of continuum physics, i.e., grid artifacts are completely eliminated. Perfect equations of motion are derived for static, slow flows of incompressible, viscous fluids. For Hagen-Poiseuille flow in a channel with a square cross section the equations reduce to a perfect discretization of the Poisson equation for the velocity field with Dirichlet boundary conditions. The perfect large scale Poisson equation is used in a numerical simulation and is shown to represent the continuum flow exactly. For nonsquare cross sections one can use a numerical iterative procedure to derive flow equations that are approximately perfect. copyright 1998 The American Physical Society
Mathematical geophysics an introduction to rotating fluids and the Navier-Stokes equations
Chemin, Jean-Yves; Gallagher, Isabelle; Grenier, Emmanuel
2006-01-01
Aimed at graduate students and researchers in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The Navier-Stokes equations are examined in both incompressible and rapidly rotating forms.
The numerical dynamic for highly nonlinear partial differential equations
Lafon, A.; Yee, H. C.
1992-01-01
Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.
Knotted solutions for linear and nonlinear theories: Electromagnetism and fluid dynamics
Directory of Open Access Journals (Sweden)
Daniel W.F. Alves
2017-10-01
Full Text Available We examine knotted solutions, the most simple of which is the “Hopfion”, from the point of view of relations between electromagnetism and ideal fluid dynamics. A map between fluid dynamics and electromagnetism works for initial conditions or for linear perturbations, allowing us to find new knotted fluid solutions. Knotted solutions are also found to be solutions of nonlinear generalizations of electromagnetism, and of quantum-corrected actions for electromagnetism coupled to other modes. For null configurations, electromagnetism can be described as a null pressureless fluid, for which we can find solutions from the knotted solutions of electromagnetism. We also map them to solutions of Euler's equations, obtained from a type of nonrelativistic reduction of the relativistic fluid equations.
International Nuclear Information System (INIS)
Núñez, Jóse; Ramos, Eduardo; Lopez, Juan M
2012-01-01
We describe a hybrid method based on the combined use of the Fourier Galerkin and finite-volume techniques to solve the fluid dynamics equations in cylindrical geometries. A Fourier expansion is used in the angular direction, partially translating the problem to the Fourier space and then solving the resulting equations using a finite-volume technique. We also describe an algorithm required to solve the coupled mass and momentum conservation equations similar to a pressure-correction SIMPLE method that is adapted for the present formulation. Using the Fourier–Galerkin method for the azimuthal direction has two advantages. Firstly, it has a high-order approximation of the partial derivatives in the angular direction, and secondly, it naturally satisfies the azimuthal periodic boundary conditions. Also, using the finite-volume method in the r and z directions allows one to handle boundary conditions with discontinuities in those directions. It is important to remark that with this method, the resulting linear system of equations are band-diagonal, leading to fast and efficient solvers. The benefits of the mixed method are illustrated with example problems. (paper)
Thermo-Fluid Dynamics of Two-Phase Flow
Ishii, Mamrou
2011-01-01
"Thermo-fluid Dynamics of Two-Phase Flow, Second Edition" is focused on the fundamental physics of two-phase flow. The authors present the detailed theoretical foundation of multi-phase flow thermo-fluid dynamics as they apply to: Nuclear reactor transient and accident analysis; Energy systems; Power generation systems; Chemical reactors and process systems; Space propulsion; Transport processes. This edition features updates on two-phase flow formulation and constitutive equations and CFD simulation codes such as FLUENT and CFX, new coverage of the lift force model, which is of part
Dynamics of fluid lines, sheets, filaments and membranes
International Nuclear Information System (INIS)
Coutris, N.
1988-01-01
We establish the dynamic equations of two types of fluid structures: 1) lines-filaments and 2) sheets-membranes. In the first part, we consider one-dimensional (line) and two-dimensional (sheet) fluid structures. The second part concerns the associated three- dimensional structures: filaments and membranes. In the third part, we establish the equations for thickened lines and thickened sheets. For that purpose, we introduce a thickness in the models of the first part. The fourth part concerns the thinning of the filament and the membrane. Then, by an asymptotic process, we deduce the corresponding equations from the equations of the second part in order to show the purely formal equivalence of the equations of the third and fourth parts. To obtain the equations, we make use of theorems whose proofs can be found in the appendices. The equations can be applied to many areas of interest: instabilities of liquid jets and liquid films, modelisation of interfaces between two different fluids as sheets or membranes, modelisation with the averaged equations over a cross section of single phase flows and two-phase flows in channels with a nonrectilinear axis such as bends or pump casings [fr
Pesch, L.; van der Vegt, Jacobus J.W.
2008-01-01
Using the generalized variable formulation of the Euler equations of fluid dynamics, we develop a numerical method that is capable of simulating the flow of fluids with widely differing thermodynamic behavior: ideal and real gases can be treated with the same method as an incompressible fluid. The
Derivation of fluid dynamics from kinetic theory with the 14-moment approximation
International Nuclear Information System (INIS)
Denicol, G.S.; Molnar, E.; Niemi, H.; Rischke, D.H.
2012-01-01
We review the traditional derivation of the fluid-dynamical equations from kinetic theory according to Israel and Stewart. We show that their procedure to close the fluid-dynamical equations of motion is not unique. Their approach contains two approximations, the first being the so-called 14-moment approximation to truncate the single-particle distribution function. The second consists in the choice of equations of motion for the dissipative currents. Israel and Stewart used the second moment of the Boltzmann equation, but this is not the only possible choice. In fact, there are infinitely many moments of the Boltzmann equation which can serve as equations of motion for the dissipative currents. All resulting equations of motion have the same form, but the transport coefficients are different in each case. (orig.)
Issues in computational fluid dynamics code verification and validation
Energy Technology Data Exchange (ETDEWEB)
Oberkampf, W.L.; Blottner, F.G.
1997-09-01
A broad range of mathematical modeling errors of fluid flow physics and numerical approximation errors are addressed in computational fluid dynamics (CFD). It is strongly believed that if CFD is to have a major impact on the design of engineering hardware and flight systems, the level of confidence in complex simulations must substantially improve. To better understand the present limitations of CFD simulations, a wide variety of physical modeling, discretization, and solution errors are identified and discussed. Here, discretization and solution errors refer to all errors caused by conversion of the original partial differential, or integral, conservation equations representing the physical process, to algebraic equations and their solution on a computer. The impact of boundary conditions on the solution of the partial differential equations and their discrete representation will also be discussed. Throughout the article, clear distinctions are made between the analytical mathematical models of fluid dynamics and the numerical models. Lax`s Equivalence Theorem and its frailties in practical CFD solutions are pointed out. Distinctions are also made between the existence and uniqueness of solutions to the partial differential equations as opposed to the discrete equations. Two techniques are briefly discussed for the detection and quantification of certain types of discretization and grid resolution errors.
Numerical schemes for dynamically orthogonal equations of stochastic fluid and ocean flows
International Nuclear Information System (INIS)
Ueckermann, M.P.; Lermusiaux, P.F.J.; Sapsis, T.P.
2013-01-01
The quantification of uncertainties is critical when systems are nonlinear and have uncertain terms in their governing equations or are constrained by limited knowledge of initial and boundary conditions. Such situations are common in multiscale, intermittent and non-homogeneous fluid and ocean flows. The dynamically orthogonal (DO) field equations provide an adaptive methodology to predict the probability density functions of such flows. The present work derives efficient computational schemes for the DO methodology applied to unsteady stochastic Navier–Stokes and Boussinesq equations, and illustrates and studies the numerical aspects of these schemes. Semi-implicit projection methods are developed for the mean and for the DO modes, and time-marching schemes of first to fourth order are used for the stochastic coefficients. Conservative second-order finite-volumes are employed in physical space with new advection schemes based on total variation diminishing methods. Other results include: (i) the definition of pseudo-stochastic pressures to obtain a number of pressure equations that is linear in the subspace size instead of quadratic; (ii) symmetric advection schemes for the stochastic velocities; (iii) the use of generalized inversion to deal with singular subspace covariances or deterministic modes; and (iv) schemes to maintain orthonormal modes at the numerical level. To verify our implementation and study the properties of our schemes and their variations, a set of stochastic flow benchmarks are defined including asymmetric Dirac and symmetric lock-exchange flows, lid-driven cavity flows, and flows past objects in a confined channel. Different Reynolds number and Grashof number regimes are employed to illustrate robustness. Optimal convergence under both time and space refinements is shown as well as the convergence of the probability density functions with the number of stochastic realizations.
TDHF and fluid dynamics of nuclear collective motions
International Nuclear Information System (INIS)
Di Nardo, M.; Di Toro, M.; Giansiracusa, G.; Lombardo, U.; Russo, G.
1983-01-01
The nuclear fluid dynamical equations are derived from a mean field description of the nuclear dynamics. Simple approximate solutions, corresponding to generalized scaling modes, are worked out for rotations and vibrations, with the evaluation of inertial parameters and flow patterns. Giant resonances are shown to be quite well described within an irrotational ansatz, which is equivalent to a lowest multipoles (up to lsub(max)=2) distortion of the momentum distribution. The physical meaning of a higher order truncation of the TDHF-Fluid-Dynamics chain is finally discussed with its implication on low lying states and on some description of the Landau damping. (author)
Computational Fluid Dynamics and Room Air Movement
DEFF Research Database (Denmark)
Nielsen, Peter Vilhelm
2004-01-01
on the mass fraction transport equation. The importance of ?false? or numerical diffusion is also addressed in connection with the simple description of a supply opening. The different aspects of boundary conditions in the indoor environment as e.g. the simulation of Air Terminal Devices and the simulation......Nielsen, P.V. Computational Fluid Dynamics and Room Air Movement. Indoor Air, International Journal of Indoor Environment and Health, Vol. 14, Supplement 7, pp. 134-143, 2004. ABSTRACT Computational Fluid Dynamics (CFD) and new developments of CFD in the indoor environment as well as quality...... considerations are important elements in the study of energy consumption, thermal comfort and indoor air quality in buildings. The paper discusses the quality level of Computational Fluid Dynamics and the involved schemes (first, second and third order schemes) by the use of the Smith and Hutton problem...
Phase portrait methods for verifying fluid dynamic simulations
Energy Technology Data Exchange (ETDEWEB)
Stewart, H.B.
1989-01-01
As computing resources become more powerful and accessible, engineers more frequently face the difficult and challenging engineering problem of accurately simulating nonlinear dynamic phenomena. Although mathematical models are usually available, in the form of initial value problems for differential equations, the behavior of the solutions of nonlinear models is often poorly understood. A notable example is fluid dynamics: while the Navier-Stokes equations are believed to correctly describe turbulent flow, no exact mathematical solution of these equations in the turbulent regime is known. Differential equations can of course be solved numerically, but how are we to assess numerical solutions of complex phenomena without some understanding of the mathematical problem and its solutions to guide us
Conformal symmetry and non-relativistic second-order fluid dynamics
International Nuclear Information System (INIS)
Chao Jingyi; Schäfer, Thomas
2012-01-01
We study the constraints imposed by conformal symmetry on the equations of fluid dynamics at second order in the gradients of the hydrodynamic variables. At zeroth order, conformal symmetry implies a constraint on the equation of state, E 0 =2/3 P, where E 0 is the energy density and P is the pressure. At first order, conformal symmetry implies that the bulk viscosity must vanish. We show that at second order, conformal invariance requires that two-derivative terms in the stress tensor must be traceless, and that it determines the relaxation of dissipative stresses to the Navier–Stokes form. We verify these results by solving the Boltzmann equation at second order in the gradient expansion. We find that only a subset of the terms allowed by conformal symmetry appear. - Highlights: ► We derive conformal constraints for the stress tensor of a scale invariant fluid. ► We determine the relaxation time in kinetic theory. ► We compute the rate of entropy production in second-order fluid dynamics.
Analytic solution of integral equations for molecular fluids
International Nuclear Information System (INIS)
Cummings, P.T.
1984-01-01
We review some recent progress in the analytic solution of integral equations for molecular fluids. The site-site Ornstein-Zernike (SSOZ) equation with approximate closures appropriate to homonuclear diatomic fluids both with and without attractive dispersion-like interactions has recently been solved in closed form analytically. In this paper, the close relationship between the SSOZ equation for homonuclear dumbells and the usual Ornstein-Zernike (OZ) equation for atomic fluids is carefully elucidated. This relationship is a key motivation for the analytic solutions of the SSOZ equation that have been obtained to date. (author)
Kleinstreuer, Clement
2018-01-01
Modern Fluid Dynamics, Second Edition provides up-to-date coverage of intermediate and advanced fluids topics. The text emphasizes fundamentals and applications, supported by worked examples and case studies. Scale analysis, non-Newtonian fluid flow, surface coating, convection heat transfer, lubrication, fluid-particle dynamics, microfluidics, entropy generation, and fluid-structure interactions are among the topics covered. Part A presents fluids principles, and prepares readers for the applications of fluid dynamics covered in Part B, which includes computer simulations and project writing. A review of the engineering math needed for fluid dynamics is included in an appendix.
International Nuclear Information System (INIS)
Donea, J.; Fasoli-Stella, P.; Giuliani, S.; Halleux, J.P.; Jones, A.V.
1980-01-01
This report describes the governing equations and the finite element modelling used in the computer code EURDYN - 1 M. The code is a non-linear transient dynamic program for the analysis of coupled fluid-structure systems; It is designed for safety studies on LMFBR components (primary containment and fuel subassemblies)
Meteorological fluid dynamics asymptotic modelling, stability and chaotic atmospheric motion
Zeytounian, Radyadour K
1991-01-01
The author considers meteorology as a part of fluid dynamics. He tries to derive the properties of atmospheric flows from a rational analysis of the Navier-Stokes equations, at the same time analyzing various types of initial and boundary problems. This approach to simulate nature by models from fluid dynamics will be of interest to both scientists and students of physics and theoretical meteorology.
A new formulation of equations of compressible fluids by analogy with Maxwell's equations
International Nuclear Information System (INIS)
Kambe, Tsutomu
2010-01-01
A compressible ideal fluid is governed by Euler's equation of motion and equations of continuity, entropy and vorticity. This system can be reformulated in a form analogous to that of electromagnetism governed by Maxwell's equations with source terms. The vorticity plays the role of magnetic field, while the velocity field plays the part of a vector potential and the enthalpy (of isentropic flows) plays the part of a scalar potential in electromagnetism. The evolution of source terms of fluid Maxwell equations is determined by solving the equations of motion and continuity. The equation of sound waves can be derived from this formulation, where time evolution of the sound source is determined by the equation of motion. The theory of vortex sound of aeroacoustics is included in this formulation. It is remarkable that the forces acting on a point mass moving in a velocity field of an inviscid fluid are analogous in their form to the electric force and Lorentz force in electromagnetism. The significance of the reformulation is interpreted by examples taken from fluid mechanics. This formulation can be extended to viscous fluids without difficulty. The Maxwell-type equations are unchanged by the viscosity effect, although the source terms have additional terms due to viscosities.
The nonlinear dynamics of a spacecraft coupled to the vibration of a contained fluid
Peterson, Lee D.; Crawley, Edward F.; Hansman, R. John
1988-01-01
The dynamics of a linear spacecraft mode coupled to a nonlinear low gravity slosh of a fluid in a cylindrical tank is investigated. Coupled, nonlinear equations of motion for the fluid-spacecraft dynamics are derived through an assumed mode Lagrangian method. Unlike linear fluid slosh models, this nonlinear slosh model retains two fundamental slosh modes and three secondary modes. An approximate perturbation solution of the equations of motion indicates that the nonlinear coupled system response involves fluid-spacecraft modal resonances not predicted by either a linear, or a nonlinear, uncoupled slosh analysis. Experimental results substantiate the analytical predictions.
A parametric study of a solar calcinator using computational fluid dynamics
International Nuclear Information System (INIS)
Fidaros, D.K.; Baxevanou, C.A.; Vlachos, N.S.
2007-01-01
In this work a horizontal rotating solar calcinator is studied numerically using computational fluid dynamics. The specific solar reactor is a 10 kW model designed and used for efficiency studies. The numerical model is based on the solution of the Navier-Stokes equations for the gas flow, and on Lagrangean dynamics for the discrete particles. All necessary mathematical models were developed and incorporated into a computational fluid dynamics model with the influence of turbulence simulated by a two-equation (RNG k-ε) model. The efficiency of the reactor was calculated for different thermal inputs, feed rates, rotational speeds and particle diameters. The numerically computed degrees of calcination compared well with equivalent experimental results
Fluid dynamics in porous media with Sailfish
Coelho, Rodrigo C. V.; Neumann, Rodrigo F.
2016-09-01
In this work we show the application of Sailfish to the study of fluid dynamics in porous media. Sailfish is an open-source software based on the lattice-Boltzmann method. This application of computational fluid dynamics is of particular interest to the oil and gas industry and the subject could be a starting point for an undergraduate or graduate student in physics or engineering. We built artificial samples of porous media with different porosities and used Sailfish to simulate the fluid flow through them in order to calculate their permeability and tortuosity. We also present a simple way to obtain the specific superficial area of porous media using Python libraries. To contextualise these concepts, we analyse the applicability of the Kozeny-Carman equation, which is a well-known permeability-porosity relation, to our artificial samples.
Blending and nudging in fluid dynamics: some simple observations
Energy Technology Data Exchange (ETDEWEB)
Germano, M, E-mail: mg234@duke.edu [Department of Civil and Environmental Engineering, Duke University, Durham, NC 27708, United States of America (United States)
2017-10-15
Blending and nudging methods have been recently applied in fluid dynamics, particularly regarding the assimilation of experimental data into the computations. In the paper we formally derive the differential equation associated to blending and compare it to the standard nudging equation. Some simple considerations related to these techniques and their mutual relations are exposed. (paper)
Blending and nudging in fluid dynamics: some simple observations
International Nuclear Information System (INIS)
Germano, M
2017-01-01
Blending and nudging methods have been recently applied in fluid dynamics, particularly regarding the assimilation of experimental data into the computations. In the paper we formally derive the differential equation associated to blending and compare it to the standard nudging equation. Some simple considerations related to these techniques and their mutual relations are exposed. (paper)
Blending and nudging in fluid dynamics: some simple observations
Germano, M.
2017-10-01
Blending and nudging methods have been recently applied in fluid dynamics, particularly regarding the assimilation of experimental data into the computations. In the paper we formally derive the differential equation associated to blending and compare it to the standard nudging equation. Some simple considerations related to these techniques and their mutual relations are exposed.
The maximal kinematical invariance group of fluid dynamics and explosion-implosion duality
International Nuclear Information System (INIS)
O'Raifeartaigh, L.; Sreedhar, V.V.
2001-01-01
It has recently been found that supernova explosions can be simulated in the laboratory by implosions induced in a plasma by intense lasers. A theoretical explanation is that the inversion transformation, (Σ:t→-1/t, x→x/t), leaves the Euler equations of fluid dynamics, with standard polytropic exponent, invariant. This implies that the kinematical invariance group of the Euler equations is larger than the Galilei group. In this paper we determine, in a systematic manner, the maximal invariance group G of general fluid dynamics and show that it is a semi-direct product G=SL(2, R) three G, where the SL(2, R) group contains the time-translations, dilations, and the inversion Σ, and G is the static (nine-parameter) Galilei group. A subtle aspect of the inclusion of viscosity fields is discussed and it is shown that the Navier-Stokes assumption of constant viscosity breaks the SL(2, R) group to a two-parameter group of time translations and dilations in a tensorial way. The 12-parameter group G is also known to be the maximal invariance group of the free Schroedinger equation. It originates in the free Hamilton-Jacobi equation which is central to both fluid dynamics and the Schroedinger equation
Statistically derived conservation equations for fluid particle flows
International Nuclear Information System (INIS)
Reyes, J.N. Jr.
1989-01-01
The behavior of water droplets in a heated nuclear fuel channel is of significant interest to nuclear reactor safety studies pertaining to loss-of-coolant accidents. This paper presents the derivation of the mass, momentum, and energy conservation equations for a distribution of fluid particles (bubbles or droplets) transported by a continuous fluid medium. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior
On the variational principle for the equations of perfect fluid dynamics
International Nuclear Information System (INIS)
Serre, D.
1993-01-01
One gives a new version of the variational principle δL = 0, L being the usual Lagrangian, for the perfect fluid mechanics. It is formally equivalent to the well-known principle but it gives the first rigorous derivation of the conservation laws (momentum and energy), including the discontinuous case (shock waves, contact discontinuities). Thanks to a new formulation of the constraints, we do not involve any Lagrange multiplier, which in previous works were neither physically relevant, since they do not appear in the Euler equations, nor mathematically relevant. We even give a variational interpretation of the entropy inequality when shock waves occur. Our method covers all aspects of the perfect fluids, including stationary and unstationary motion, compressible and incompressible fluids, axisymmetric case. When the velocity field admits a stream function, the variational principle gives rise to extremal points of the Lagrangian on various infinite dimensional manifolds. For a suitable choice of this manifold, the flow is itself periodic, that is all the fluid particles have a periodic motion with the same period. The flow describes a closed geodesic on some group of diffeomorphisms. (author). 10 refs
Entropy equilibrium equation and dynamic entropy production in environment liquid
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The entropy equilibrium equation is the basis of the nonequilibrium state thermodynamics. But the internal energy implies the kinetic energy of the fluid micelle relative to mass center in the classical entropy equilibrium equation at present. This internal energy is not the mean kinetic energy of molecular movement in thermodynamics. Here a modified entropy equilibrium equation is deduced, based on the concept that the internal energy is just the mean kinetic energy of the molecular movement. A dynamic entropy production is introduced into the entropy equilibrium equation to describe the dynamic process distinctly. This modified entropy equilibrium equation can describe not only the entropy variation of the irreversible processes but also the reversible processes in a thermodynamic system. It is more reasonable and suitable for wider applications.
AFDM: An Advanced Fluid-Dynamics Model
International Nuclear Information System (INIS)
Bohl, W.R.; Parker, F.R.; Wilhelm, D.; Goutagny, L.; Ninokata, H.
1990-09-01
AFDM, or the Advanced Fluid-Dynamics Model, is a computer code that investigates new approaches simulating the multiphase-flow fluid-dynamics aspects of severe accidents in fast reactors. The AFDM formalism starts with differential equations similar to those in the SIMMER-II code. These equations are modified to treat three velocity fields and supplemented with a variety of new models. The AFDM code has 12 topologies describing what material contacts are possible depending on the presence or absence of a given material in a computational cell, on the dominant liquid, and on the continuous phase. Single-phase, bubbly, churn-turbulent, cellular, and dispersed flow regimes are permitted for the pool situations modeled. Virtual mass terms are included for vapor in liquid-continuous flow. Interfacial areas between the continuous and discontinuous phases are convected to allow some tracking of phenomenological histories. Interfacial areas are also modified by models of nucleation, dynamic forces, turbulence, flashing, coalescence, and mass transfer. Heat transfer is generally treated using engineering correlations. Liquid-vapor phase transitions are handled with the nonequilibrium, heat-transfer-limited model, whereas melting and freezing processes are based on equilibrium considerations. Convection is treated using a fractional-step method of time integration, including a semi-implicit pressure iteration. A higher-order differencing option is provided to control numerical diffusion. The Los Alamos SESAME equation-of-state has been implemented using densities and temperatures as the independent variables. AFDM programming has vectorized all computational loops consistent with the objective of producing an exportable code. 24 refs., 4 figs
A symbiotic approach to fluid equations and non-linear flux-driven simulations of plasma dynamics
Halpern, Federico
2017-10-01
The fluid framework is ubiquitous in studies of plasma transport and stability. Typical forms of the fluid equations are motivated by analytical work dating several decades ago, before computer simulations were indispensable, and can be, therefore, not optimal for numerical computation. We demonstrate a new first-principles approach to obtaining manifestly consistent, skew-symmetric fluid models, ensuring internal consistency and conservation properties even in discrete form. Mass, kinetic, and internal energy become quadratic (and always positive) invariants of the system. The model lends itself to a robust, straightforward discretization scheme with inherent non-linear stability. A simpler, drift-ordered form of the equations is obtained, and first results of their numerical implementation as a binary framework for bulk-fluid global plasma simulations are demonstrated. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, Theory Program, under Award No. DE-FG02-95ER54309.
Fluid dynamics in porous media with Sailfish
International Nuclear Information System (INIS)
Coelho, Rodrigo C V; Neumann, Rodrigo F
2016-01-01
In this work we show the application of Sailfish to the study of fluid dynamics in porous media. Sailfish is an open-source software based on the lattice-Boltzmann method. This application of computational fluid dynamics is of particular interest to the oil and gas industry and the subject could be a starting point for an undergraduate or graduate student in physics or engineering. We built artificial samples of porous media with different porosities and used Sailfish to simulate the fluid flow through them in order to calculate their permeability and tortuosity. We also present a simple way to obtain the specific superficial area of porous media using Python libraries. To contextualise these concepts, we analyse the applicability of the Kozeny–Carman equation, which is a well-known permeability–porosity relation, to our artificial samples. (paper)
Fundamentals of Geophysical Fluid Dynamics
McWilliams, James C.
2006-07-01
Earth's atmosphere and oceans exhibit complex patterns of fluid motion over a vast range of space and time scales. These patterns combine to establish the climate in response to solar radiation that is inhomogeneously absorbed by the materials comprising air, water, and land. Spontaneous, energetic variability arises from instabilities in the planetary-scale circulations, appearing in many different forms such as waves, jets, vortices, boundary layers, and turbulence. Geophysical fluid dynamics (GFD) is the science of all these types of fluid motion. This textbook is a concise and accessible introduction to GFD for intermediate to advanced students of the physics, chemistry, and/or biology of Earth's fluid environment. The book was developed from the author's many years of teaching a first-year graduate course at the University of California, Los Angeles. Readers are expected to be familiar with physics and mathematics at the level of general dynamics (mechanics) and partial differential equations. Covers the essential GFD required for atmospheric science and oceanography courses Mathematically rigorous, concise coverage of basic theory and applications to both oceans and atmospheres Author is a world expert; this book is based on the course he has taught for many years Exercises are included, with solutions available to instructors from solutions@cambridge.org
Nonlinear quantum fluid equations for a finite temperature Fermi plasma
International Nuclear Information System (INIS)
Eliasson, Bengt; Shukla, Padma K
2008-01-01
Nonlinear quantum electron fluid equations are derived, taking into account the moments of the Wigner equation and by using the Fermi-Dirac equilibrium distribution for electrons with an arbitrary temperature. A simplified formalism with the assumptions of incompressibility of the distribution function is used to close the moments in velocity space. The nonlinear quantum diffraction effects into the fluid equations are incorporated. In the high-temperature limit, we retain the nonlinear fluid equations for a dense hot plasma and in the low-temperature limit, we retain the correct fluid equations for a fully degenerate plasma
International Nuclear Information System (INIS)
Brechet, S D; Hobson, M P; Lasenby, A N
2008-01-01
A dynamical analysis of an effective homogeneous and irrotational Weyssenhoff fluid in general relativity is performed using the 1 + 3 covariant approach that enables the dynamics of the fluid to be determined without assuming any particular form for the spacetime metric. The spin contributions to the field equations produce a bounce that averts an initial singularity, provided that the spin density exceeds the rate of shear. At later times, when the spin contribution can be neglected, a Weyssenhoff fluid reduces to a standard cosmological fluid in general relativity. Numerical solutions for the time evolution of the generalized scale factor R(t) in spatially curved models are presented, some of which exhibit eternal oscillatory behaviour without any singularities. In spatially flat models, analytical solutions for particular values of the equation-of-state parameter are derived. Although the scale factor of a Weyssenhoff fluid generically has a positive temporal curvature near a bounce, it requires unreasonable fine tuning of the equation-of-state parameter to produce a sufficiently extended period of inflation to fit the current observational data
Flexible equation of state for a hard sphere and Lennard–Jones fluid ...
Indian Academy of Sciences (India)
Equation of state; Lennard–Jones potential; hard-sphere potential; liquid mixture; computer simulation. ... deviation than Barker–Henderson BH2 for LJ fluids, and results are much closer to molecular dynamics (MD) simulations than expectations and reproduce the existing simulation data and present EoS for LJ potential, ...
Simulating coupled dynamics of a rigid-flexible multibody system and compressible fluid
Hu, Wei; Tian, Qiang; Hu, HaiYan
2018-04-01
As a subsequent work of previous studies of authors, a new parallel computation approach is proposed to simulate the coupled dynamics of a rigid-flexible multibody system and compressible fluid. In this approach, the smoothed particle hydrodynamics (SPH) method is used to model the compressible fluid, the natural coordinate formulation (NCF) and absolute nodal coordinate formulation (ANCF) are used to model the rigid and flexible bodies, respectively. In order to model the compressible fluid properly and efficiently via SPH method, three measures are taken as follows. The first is to use the Riemann solver to cope with the fluid compressibility, the second is to define virtual particles of SPH to model the dynamic interaction between the fluid and the multibody system, and the third is to impose the boundary conditions of periodical inflow and outflow to reduce the number of SPH particles involved in the computation process. Afterwards, a parallel computation strategy is proposed based on the graphics processing unit (GPU) to detect the neighboring SPH particles and to solve the dynamic equations of SPH particles in order to improve the computation efficiency. Meanwhile, the generalized-alpha algorithm is used to solve the dynamic equations of the multibody system. Finally, four case studies are given to validate the proposed parallel computation approach.
Poiseuille equation for steady flow of fractal fluid
Tarasov, Vasily E.
2016-07-01
Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.
Static/dynamic fluid-structure interaction analysis for 3-D rotary blade model
International Nuclear Information System (INIS)
Kim, Dong Hyun; Kim, Yu Sung; Kim, Dong Man; Park, Kang Kyun
2009-01-01
In this study, static/dynamic fluid-structure interaction analyses have been conducted for a 3D rotary blade model like a turbo-machinery or wind turbine blade. Advanced computational analysis system based on Computational Fluid Dynamics (CFD) and Computational Structural Dynamics (CSD) has been developed in order to investigate detailed dynamic responses of rotary type models. Fluid domains are modeled using the computational grid system with local grid deforming techniques. Reynolds-averaged Navier-Stokes equations with various turbulence model are solved for unsteady flow problems of the rotating blade model. Detailed static/dynamic responses and instantaneous pressure contours on the blade surfaces considering flow-separation effects are presented to show the multi-physical phenomenon of the rotating blades.
Improved Fluid Perturbation Theory: Equation of state for Fluid Xenon
Li, Qiong; Liu, Hai-Feng; Zhang, Gong-Mu; Zhao, Yan-Hong; Tian, Ming-Feng; Song, Hai-Feng
2016-01-01
The traditional fluid perturbation theory is improved by taking electronic excitations and ionizations into account, in the framework of average ion spheres. It is applied to calculate the equation of state for fluid Xenon, which turns out in good agreement with the available shock data.
Zonal methods and computational fluid dynamics
International Nuclear Information System (INIS)
Atta, E.H.
1985-01-01
Recent advances in developing numerical algorithms for solving fluid flow problems, and the continuing improvement in the speed and storage of large scale computers have made it feasible to compute the flow field about complex and realistic configurations. Current solution methods involve the use of a hierarchy of mathematical models ranging from the linearized potential equation to the Navier Stokes equations. Because of the increasing complexity of both the geometries and flowfields encountered in practical fluid flow simulation, there is a growing emphasis in computational fluid dynamics on the use of zonal methods. A zonal method is one that subdivides the total flow region into interconnected smaller regions or zones. The flow solutions in these zones are then patched together to establish the global flow field solution. Zonal methods are primarily used either to limit the complexity of the governing flow equations to a localized region or to alleviate the grid generation problems about geometrically complex and multicomponent configurations. This paper surveys the application of zonal methods for solving the flow field about two and three-dimensional configurations. Various factors affecting their accuracy and ease of implementation are also discussed. From the presented review it is concluded that zonal methods promise to be very effective for computing complex flowfields and configurations. Currently there are increasing efforts to improve their efficiency, versatility, and accuracy
Mathematical problems of the dynamics of incompressible fluid on a rotating sphere
Skiba, Yuri N
2017-01-01
This book presents selected mathematical problems involving the dynamics of a two-dimensional viscous and ideal incompressible fluid on a rotating sphere. In this case, the fluid motion is completely governed by the barotropic vorticity equation (BVE), and the viscosity term in the vorticity equation is taken in its general form, which contains the derivative of real degree of the spherical Laplace operator. This work builds a bridge between basic concepts and concrete outcomes by pursuing a rich combination of theoretical, analytical and numerical approaches, and is recommended for specialists developing mathematical methods for application to problems in physics, hydrodynamics, meteorology and geophysics, as well for upper undergraduate or graduate students in the areas of dynamics of incompressible fluid on a rotating sphere, theory of functions on a sphere, and flow stability.
Dark energy from cosmological fluids obeying a Shan-Chen non-ideal equation of state
Bini, Donato; Geralico, Andrea; Gregoris, Daniele; Succi, Sauro
2014-01-01
We consider a Friedmann-Robertson-Walker universe with a fluid source obeying a nonideal equation of state with ‘‘asymptotic freedom,’’ namely ideal gas behavior (pressure changes directly proportional to density changes) both at low and high density regimes, following a fluid dynamical model due to Shan and Chen. It is shown that, starting from an ordinary energy density component, such fluids naturally evolve towards a universe with a substantial ‘‘dark energy’’ component at the present tim...
Fiszdon, W
1965-01-01
Fluid Dynamics Transactions, Volume 2 compiles 46 papers on fluid dynamics, a subdiscipline of fluid mechanics that deals with fluid flow. The topics discussed in this book include developments in interference theory for aeronautical applications; diffusion from sources in a turbulent boundary layer; unsteady motion of a finite wing span in a compressible medium; and wall pressure covariance and comparison with experiment. The certain classes of non-stationary axially symmetric flows in magneto-gas-dynamics; description of the phenomenon of secondary flows in curved channels by means of co
Shivamoggi, Bhimsen K
1998-01-01
"Although there are many texts and monographs on fluid dynamics, I do not know of any which is as comprehensive as the present book. It surveys nearly the entire field of classical fluid dynamics in an advanced, compact, and clear manner, and discusses the various conceptual and analytical models of fluid flow." - Foundations of Physics on the first edition. Theoretical Fluid Dynamics functions equally well as a graduate-level text and a professional reference. Steering a middle course between the empiricism of engineering and the abstractions of pure mathematics, the author focuses
Four-fluid description of turbulent plasma focus dynamics
International Nuclear Information System (INIS)
Hayd, A.; Maurer, M.; Meinke, P.; Kaeppeler, H.J.
1984-06-01
The dynamic phenomena in the compression, pinch and late phases of the plasma focus experiment POSEIDON in its operational mode at 60 kV, 280 kJ, were previously calculated from a two-fluid theory using the new hybrid code REDUCE/FORTRAN. Two important results were found: the neutron production already in the pinch phase for currents larger than 500 kA and filamentary structures on and around the pinch axis. In a continuation of this work, a four-fluid system of dynamical equations was formulated and programmed with the REDUCE/FORTRAN code. Besides macro-turbulence, the new four-fluid theory includes micro-instabilities and anomalous transport properties, as well as the runaway effect for electrons and ions. First results from calculations with this new theory are presented and are compared with previous calculations and with recent experimental observations. (orig.)
Experimental investigation of unsteady fluid dynamic forces acting on tube array
International Nuclear Information System (INIS)
Tanaka, Hiroki; Takahara, Shigeru; Tanaka, Mitsutoshi
1981-01-01
It is well-known that the cylinder bundle vibrates in cross flow. Many studies of the vibration have been made, and it has been clarified that the vibration is caused by fluid-elastic vibration coupling to neighboring cylinders. The theory given in this paper considers unsteady fluid dynamic forces to be composed of inertia forces due to added mass of fluid, damping forces of fluid which are in phase to cylinder vibrating velocity, and stiffness forces which are proportional to cylinder displacements. Furthermore, taking account of the influences of neighboring cylinder vibrations, ten kinds of unsteady fluid dynamic forces are considered to act on a cylinder in cylinder bundles. Equations of motion of cylinders were deduced and the critical velocities were calculated with the measured unsteady fluid dynamic forces. Critical velocity tests were also conducted with cylinders which were supported with elastic spars. The calculated critical velocities coincided well with the test results. (author)
A dynamic neutral fluid model for the PIC scheme
Wu, Alan; Lieberman, Michael; Verboncoeur, John
2010-11-01
Fluid diffusion is an important aspect of plasma simulation. A new dynamic model is implemented using the continuity and boundary equations in OOPD1, an object oriented one-dimensional particle-in-cell code developed at UC Berkeley. The model is described and compared with analytical methods given in [1]. A boundary absorption parameter can be adjusted from ideal absorption to ideal reflection. Simulations exhibit good agreement with analytic time dependent solutions for the two ideal cases, as well as steady state solutions for mixed cases. For the next step, fluid sources and sinks due to particle-particle or particle-fluid collisions within the simulation volume and to surface reactions resulting in emission or absorption of fluid species will be implemented. The resulting dynamic interaction between particle and fluid species will be an improvement to the static fluid in the existing code. As the final step in the development, diffusion for multiple fluid species will be implemented. [4pt] [1] M.A. Lieberman and A.J. Lichtenberg, Principles of Plasma Discharges and Materials Processing, 2nd Ed, Wiley, 2005.
Molecular dynamics on diffusive time scales from the phase-field-crystal equation.
Chan, Pak Yuen; Goldenfeld, Nigel; Dantzig, Jon
2009-03-01
We extend the phase-field-crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of them. By solving the dynamical equation of the model, which is a partial differential equation, we are essentially performing molecular dynamics simulations on diffusive time scales. To illustrate this approach, we calculate the two-point correlation function of a fluid.
Free vibration analysis of multi-span pipe conveying fluid with dynamic stiffness method
International Nuclear Information System (INIS)
Li Baohui; Gao Hangshan; Zhai Hongbo; Liu Yongshou; Yue Zhufeng
2011-01-01
Research highlights: → The dynamic stiffness method was proposed to analysis the free vibration of multi-span pipe conveying fluid. → The main advantage of the proposed method is that it can hold a high precision even though the element size is large. → The flowing fluid can weaken the pipe stiffness, when the fluid velocity increases, the natural frequencies of pipe are decreasing. - Abstract: By taking a pipe as Timoshenko beam, in this paper the original 4-equation model of pipe conveying fluid was modified by taking the dynamic effects of fluid into account. The shape function that always used in the finite element method was replaced by the exact wave solution of the modified four equations. And then the dynamic stiffness was deduced for the free vibration of pipe conveying fluid. The proposed method was validated by comparing the results of critical velocity with analytical solution for a simply supported pipe at both ends. In the example, the proposed method was applied to calculate the first three natural frequencies of a three span pipe with twelve meters long in three different cases. The results of natural frequency for the pipe conveying stationary fluid fitted well with that calculated by finite element software Abaqus. It was shown that the dynamic stiffness method can still hold high precision even though the element's size was quite large. And this is the predominant advantage of the proposed method comparing with conventional finite element method.
Xiao, Zi-Jian; Tian, Bo; Sun, Yan
2018-01-01
In this paper, we investigate a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili (mKP) equation in fluid dynamics. With the binary Bell-polynomial and an auxiliary function, bilinear forms for the equation are constructed. Based on the bilinear forms, multi-soliton solutions and Bell-polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton interactions are presented. Based on the graphic analysis, Parametric conditions for the existence of the shock waves, elevation solitons and depression solitons are given, and it is shown that under the condition of keeping the wave vectors invariable, the change of α(t) and β(t) can lead to the change of the solitonic velocities, but the shape of each soliton remains unchanged, where α(t) and β(t) are the variable coefficients in the equation. Oblique elastic interactions can exist between the (i) two shock waves, (ii) two elevation solitons, and (iii) elevation and depression solitons. However, oblique interactions between (i) shock waves and elevation solitons, (ii) shock waves and depression solitons are inelastic.
General solution of the aerosol dynamic equation: growth and diffusion processes
International Nuclear Information System (INIS)
Elgarayhi, A.; Elhanbaly, A.
2004-01-01
The dispersion of aerosol particles in a fluid media is studied considering the main mechanism for condensation and diffusion. This has been done when the technique of Lie is used for solving the aerosol dynamic equation. This method is very useful in sense that it reduces the partial differential equation to some ordinary differential equations. So, different classes of similarity solutions have been obtained. The quantity of well-defined physical interest is the mean particle volume has been calculated
Discovering governing equations from data by sparse identification of nonlinear dynamical systems.
Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan
2016-04-12
Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.
International Nuclear Information System (INIS)
Lue Xing; Zhu Hongwu; Yao Zhenzhi; Meng Xianghua; Zhang Cheng; Zhang Chunyi; Tian Bo
2008-01-01
In this paper, the multisoliton solutions in terms of double Wronskian determinant are presented for a generalized variable-coefficient nonlinear Schroedinger equation, which appears in space and laboratory plasmas, arterial mechanics, fluid dynamics, optical communications and so on. By means of the particularly nice properties of Wronskian determinant, the solutions are testified through direct substitution into the bilinear equations. Furthermore, it can be proved that the bilinear Baecklund transformation transforms between (N - 1)- and N-soliton solutions
Nonequilibrium chiral fluid dynamics including dissipation and noise
International Nuclear Information System (INIS)
Nahrgang, Marlene; Herold, Christoph; Bleicher, Marcus; Leupold, Stefan
2011-01-01
We present a consistent theoretical approach for the study of nonequilibrium effects in chiral fluid dynamics within the framework of the linear σ model with constituent quarks. Treating the quarks as an equilibrated heat bath, we use the influence functional formalism to obtain a Langevin equation for the σ field. This allows us to calculate the explicit form of the damping coefficient and the noise correlators. For a self-consistent derivation of both the dynamics of the σ field and the quark fluid, we have to employ the 2PI (two-particle irreducible) effective action formalism. The energy dissipation from the field to the fluid is treated in the exact formalism of the 2PI effective action where a conserved energy-momentum tensor can be constructed. We derive its form and comment on approximations generating additional terms in the energy-momentum balance of the entire system.
General particle transport equation. Final report
International Nuclear Information System (INIS)
Lafi, A.Y.; Reyes, J.N. Jr.
1994-12-01
The general objectives of this research are as follows: (1) To develop fundamental models for fluid particle coalescence and breakage rates for incorporation into statistically based (Population Balance Approach or Monte Carlo Approach) two-phase thermal hydraulics codes. (2) To develop fundamental models for flow structure transitions based on stability theory and fluid particle interaction rates. This report details the derivation of the mass, momentum and energy conservation equations for a distribution of spherical, chemically non-reacting fluid particles of variable size and velocity. To study the effects of fluid particle interactions on interfacial transfer and flow structure requires detailed particulate flow conservation equations. The equations are derived using a particle continuity equation analogous to Boltzmann's transport equation. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior. Unlike the Eulerian volume and time averaged conservation equations, the statistically averaged conservation equations contain additional terms that take into account the change due to fluid particle interfacial acceleration and fluid particle dynamics. Two types of particle dynamics are considered; coalescence and breakage. Therefore, the rate of change due to particle dynamics will consider the gain and loss involved in these processes and implement phenomenological models for fluid particle breakage and coalescence
Fluid dynamics applications of the Illiac IV computer
Maccormack, R. W.; Stevens, K. G., Jr.
1976-01-01
The Illiac IV is a parallel-structure computer with computing power an order of magnitude greater than that of conventional computers. It can be used for experimental tasks in fluid dynamics which can be simulated more economically, for simulating flows that cannot be studied by experiment, and for combining computer and experimental simulations. The architecture of Illiac IV is described, and the use of its parallel operation is demonstrated on the example of its solution of the one-dimensional wave equation. For fluid dynamics problems, a special FORTRAN-like vector programming language was devised, called CFD language. Two applications are described in detail: (1) the determination of the flowfield around the space shuttle, and (2) the computation of transonic turbulent separated flow past a thick biconvex airfoil.
Dynamic analysis of structures with solid-fluid interaction
International Nuclear Information System (INIS)
Nahavandi, A.N.; Pedrido, R.R.; Cloud, R.L.
1977-01-01
This study develops a finite element model for interaction between an elastic solid and fluid medium (flow-induced vibrations in nuclear reactor components). Plane triangular finite elements have been used separately for fluid, solid, and solid-fluid continuua and the equivalent mass, damping, and stiffness matrices and interaction load arrays for all elements are derived and assembled into global matrices. The global matrix differential equation of motion developed is solved in time to obtain the pressure and velocity distributions in the fluid, as well as the displacements in the solid. Two independent computer programs are used to obtain the dynamic solution. The first program is a finite element program developed for solid-fluid interaction studies. This program uses the modal superposition technique in which the eigenvalues and eigenvectors for the system are found and used to uncouple the equations. This approach allows an analytic solution in each integration time step. The second program is WECAN finite element program in which a new element library subroutine for solid-fluid interaction was incorporated. This program can employ a NASTRAN direct integration scheme based on a central difference formula for the acceleration and velocity terms and an implicit representation of the displacement term. This reduces the problem to a matrix equation whose right hand side is updated in every time step and is solved by a variation of the Gaussian elimination method known as the wave front technique. Results have been obtained for the case of water, between two flat elastic parallel plates, initially at rest and accelerated suddenly by applying a step pressure. The results obtained from the above-mentioned two independent finite element programs are in full agreement. This verification provides the confidence needed to initiate parametric studies. Both rigid wall (no solid-fluid interaction) and flexible wall (including solid-fluid interaction) cases were examined
Relativistic nuclear fluid dynamics and VUU kinetic theory
International Nuclear Information System (INIS)
Molitoris, J.J.; Hahn, D.; Alonso, C.; Collazo, I.; D'Alessandris, P.; McAbee, T.; Wilson, J.; Zingman, J.
1987-01-01
Relativistic kinetic theory may be used to understand hot dense hadronic matter. We address the questions of collective flow and pion production in a 3 D relativistic fluid dynamic model and in the VUU microscopic theory. The GSI/LBL collective flow and pion data point to a stiff equation of state. The effect of the nuclear equation of state on the thermodynamic parameters is discussed. The properties of dense hot hadronic matter are studied in Au + Au collisions from 0.1 to 10 GeV/nucleon. 22 refs., 5 figs
Poisson structure of the equations of ideal multispecies fluid electrodynamics
International Nuclear Information System (INIS)
Spencer, R.G.
1984-01-01
The equations of the two- (or multi-) fluid model of plasma physics are recast in Hamiltonian form, following general methods of symplectic geometry. The dynamical variables are the fields of physical interest, but are noncanonical, so that the Poisson bracket in the theory is not the standard one. However, it is a skew-symmetric bilinear form which, from the method of derivation, automatically satisfies the Jacobi identity; therefore, this noncanonical structure has all the essential properties of a canonical Poisson bracket
The coupling of fluids, dynamics, and controls on advanced architecture computers
Atwood, Christopher
1995-01-01
This grant provided for the demonstration of coupled controls, body dynamics, and fluids computations in a workstation cluster environment; and an investigation of the impact of peer-peer communication on flow solver performance and robustness. The findings of these investigations were documented in the conference articles.The attached publication, 'Towards Distributed Fluids/Controls Simulations', documents the solution and scaling of the coupled Navier-Stokes, Euler rigid-body dynamics, and state feedback control equations for a two-dimensional canard-wing. The poor scaling shown was due to serialized grid connectivity computation and Ethernet bandwidth limits. The scaling of a peer-to-peer communication flow code on an IBM SP-2 was also shown. The scaling of the code on the switched fabric-linked nodes was good, with a 2.4 percent loss due to communication of intergrid boundary point information. The code performance on 30 worker nodes was 1.7 (mu)s/point/iteration, or a factor of three over a Cray C-90 head. The attached paper, 'Nonlinear Fluid Computations in a Distributed Environment', documents the effect of several computational rate enhancing methods on convergence. For the cases shown, the highest throughput was achieved using boundary updates at each step, with the manager process performing communication tasks only. Constrained domain decomposition of the implicit fluid equations did not degrade the convergence rate or final solution. The scaling of a coupled body/fluid dynamics problem on an Ethernet-linked cluster was also shown.
Test of a new heat-flow equation for dense-fluid shock waves.
Holian, Brad Lee; Mareschal, Michel; Ravelo, Ramon
2010-09-21
Using a recently proposed equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, we model shockwave propagation in the dense Lennard-Jones fluid. Disequilibrium among the three components of temperature, namely, the difference between the kinetic temperature in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, gives rise to a new transport (equilibration) mechanism not seen in usual one-dimensional heat-flow situations. The modification of the heat-flow equation was tested earlier for the case of strong shock waves in the ideal gas, which had been studied in the past and compared to Navier-Stokes-Fourier solutions. Now, the Lennard-Jones fluid, whose equation of state and transport properties have been determined from independent calculations, allows us to study the case where potential, as well as kinetic contributions are important. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations under strong shock wave conditions, compared to Navier-Stokes.
On the Dynamic Programming Approach for the 3D Navier-Stokes Equations
International Nuclear Information System (INIS)
Manca, Luigi
2008-01-01
The dynamic programming approach for the control of a 3D flow governed by the stochastic Navier-Stokes equations for incompressible fluid in a bounded domain is studied. By a compactness argument, existence of solutions for the associated Hamilton-Jacobi-Bellman equation is proved. Finally, existence of an optimal control through the feedback formula and of an optimal state is discussed
Common intersection points in dense fluids via equations of state
International Nuclear Information System (INIS)
Parsafar, G. A.; Noorian, R.
2001-01-01
Some new of state which are derived for dense fluids in recent years, namely the linear isotherm regularity, the dense system equation of state, Ihm-Song-Mason equation of state, and a newly derived semi-empirical equation of state have used to investigate the common intersection point of isobaric expansivity (α p ) in dense fluids. We have shown that the accuracy of these equations of state in predicting such a common intersection point is reduced from the new semi-imperial equation of state, dense system equation of state, linear isotherm regularity, to Ihm-Song-Mason equation of state. respectively. Form physical point of view, the van der Waals equation of state is used to investigate such an intersection point. It is shown that the van der Waals repulsion forces and temperature dependency of the effective molecular diameter are important for existence of this common point. Finally, we have shown that the common intersection points of the isotherms of thermal pressure coefficient, the isotherms of heat capacity at constant volume, and the iso chores of internal pressure for a fluid are related to each other. Also, the common intersection points of the reduced bulk modulus and 1/(Tα p ) for isotherms of a fluid both appear at the same density
Lagrangian fluid description with simple applications in compressible plasma and gas dynamics
International Nuclear Information System (INIS)
Schamel, Hans
2004-01-01
The Lagrangian fluid description, in which the dynamics of fluids is formulated in terms of trajectories of fluid elements, not only presents an alternative to the more common Eulerian description but has its own merits and advantages. This aspect, which seems to be not fully explored yet, is getting increasing attention in fluid dynamics and related areas as Lagrangian codes and experimental techniques are developed utilizing the Lagrangian point of view with the ultimate goal of a deeper understanding of flow dynamics. In this tutorial review we report on recent progress made in the analysis of compressible, more or less perfect flows such as plasmas and dilute gases. The equations of motion are exploited to get further insight into the formation and evolution of coherent structures, which often exhibit a singular or collapse type behavior occurring in finite time. It is argued that this technique of solution has a broad applicability due to the simplicity and generality of equations used. The focus is on four different topics, the physics of which being governed by simple fluid equations subject to initial and/or boundary conditions. Whenever possible also experimental results are mentioned. In the expansion of a semi-infinite plasma into a vacuum the energetic ion peak propagating supersonically towards the vacuum--as seen in laboratory experiments--is interpreted by means of the Lagrangian fluid description as a relic of a wave breaking scenario of the corresponding inviscid ion dynamics. The inclusion of viscosity is shown numerically to stabilize the associated density collapse giving rise to a well defined fast ion peak reminiscent of adhesive matter. In purely convection driven flows the Lagrangian flow velocity is given by its initial value and hence the Lagrangian velocity gradient tensor can be evaluated accurately to find out the appearance of singularities in density and vorticity and the emergence of new structures such as wavelets in one
Lagrangian fluid description with simple applications in compressible plasma and gas dynamics
Schamel, Hans
2004-03-01
The Lagrangian fluid description, in which the dynamics of fluids is formulated in terms of trajectories of fluid elements, not only presents an alternative to the more common Eulerian description but has its own merits and advantages. This aspect, which seems to be not fully explored yet, is getting increasing attention in fluid dynamics and related areas as Lagrangian codes and experimental techniques are developed utilizing the Lagrangian point of view with the ultimate goal of a deeper understanding of flow dynamics. In this tutorial review we report on recent progress made in the analysis of compressible, more or less perfect flows such as plasmas and dilute gases. The equations of motion are exploited to get further insight into the formation and evolution of coherent structures, which often exhibit a singular or collapse type behavior occurring in finite time. It is argued that this technique of solution has a broad applicability due to the simplicity and generality of equations used. The focus is on four different topics, the physics of which being governed by simple fluid equations subject to initial and/or boundary conditions. Whenever possible also experimental results are mentioned. In the expansion of a semi-infinite plasma into a vacuum the energetic ion peak propagating supersonically towards the vacuum-as seen in laboratory experiments-is interpreted by means of the Lagrangian fluid description as a relic of a wave breaking scenario of the corresponding inviscid ion dynamics. The inclusion of viscosity is shown numerically to stabilize the associated density collapse giving rise to a well defined fast ion peak reminiscent of adhesive matter. In purely convection driven flows the Lagrangian flow velocity is given by its initial value and hence the Lagrangian velocity gradient tensor can be evaluated accurately to find out the appearance of singularities in density and vorticity and the emergence of new structures such as wavelets in one-dimension (1D
Phase-resolved fluid dynamic forces of a flapping foil energy harvester based on PIV measurements
Liburdy, James
2017-11-01
Two-dimensional particle image velocimetry measurements are performed in a wind tunnel to evaluate the spatial and temporal fluid dynamic forces acting on a flapping foil operating in the energy harvesting regime. Experiments are conducted at reduced frequencies (k = fc/U) of 0.05 - 0.2, pitching angle of, and heaving amplitude of A / c = 0.6. The phase-averaged pressure field is obtained by integrating the pressure Poisson equation. Fluid dynamic forces are then obtained through the integral momentum equation. Results are compared with a simple force model based on the concept of flow impulse. These results help to show the detailed force distributions, their transient nature and aide in understanding the impact of the fluid flow structures that contribute to the power production.
Directory of Open Access Journals (Sweden)
Zhang Sheng
2015-01-01
Full Text Available In this paper, Painleve analysis is used to test the Painleve integrability of a forced variable-coefficient extended Korteveg-de Vries equation which can describe the weakly-non-linear long internal solitary waves in the fluid with continuous stratification on density. The obtained results show that the equation is integrable under certain conditions. By virtue of the truncated Painleve expansion, a pair of new exact solutions to the equation is obtained.
International Nuclear Information System (INIS)
Khasare, S.B.
2012-01-01
The present work uses the concept of a scaled particle along with the perturbation and variation approach, to develop an equation of state (EOS) for a mixture of hard sphere (HS), Lennard—Jones (LJ) fluids. A suitable flexible functional form for the radial distribution function G(R) is assumed for the mixture, with R as a variable. The function G(R) has an arbitrary parameter m and a different equation of state can be obtained with a suitable choice of m. For m = 0.75 and m = 0.83 results are close to molecular dynamics (MD) result for pure HS and LJ fluid respectively. (physics of gases, plasmas, and electric discharges)
Cosmological model with viscosity media (dark fluid) described by an effective equation of state
International Nuclear Information System (INIS)
Ren Jie; Meng Xinhe
2006-01-01
A generally parameterized equation of state (EOS) is investigated in the cosmological evolution with bulk viscosity media modelled as dark fluid, which can be regarded as a unification of dark energy and dark matter. Compared with the case of the perfect fluid, this EOS has possessed four additional parameters, which can be interpreted as the case of the non-perfect fluid with time-dependent viscosity or the model with variable cosmological constant. From this general EOS, a completely integrable dynamical equation to the scale factor is obtained with its solution explicitly given out. (i) In this parameterized model of cosmology, for a special choice of the parameters we can explain the late-time accelerating expansion universe in a new view. The early inflation, the median (relatively late time) deceleration, and the recently cosmic acceleration may be unified in a single equation. (ii) A generalized relation of the Hubble parameter scaling with the redshift is obtained for some cosmology interests. (iii) By using the SNe Ia data to fit the effective viscosity model we show that the case of matter described by p=0 plus with effective viscosity contributions can fit the observational gold data in an acceptable level
Multimedia in physics education: teaching videos about aero and fluid dynamics
International Nuclear Information System (INIS)
Wagner, Andreas; Altherr, Stefan; Eckert, Bodo; Jodl, Hans Joerg
2007-01-01
In a series of letters, we present teaching videos on topics which are difficult to understand for students, or which are difficult to realize experimentally in school, if at all. These videos can be used for quantitative analysis or visualization of phenomena. Here we present videos on aero and fluid dynamics which deal with the Navier-Stokes equation, the continuity equation and Karman's vortex street. (letters and comments)
Byun, Chansup; Guruswamy, Guru P.; Kutler, Paul (Technical Monitor)
1994-01-01
In recent years significant advances have been made for parallel computers in both hardware and software. Now parallel computers have become viable tools in computational mechanics. Many application codes developed on conventional computers have been modified to benefit from parallel computers. Significant speedups in some areas have been achieved by parallel computations. For single-discipline use of both fluid dynamics and structural dynamics, computations have been made on wing-body configurations using parallel computers. However, only a limited amount of work has been completed in combining these two disciplines for multidisciplinary applications. The prime reason is the increased level of complication associated with a multidisciplinary approach. In this work, procedures to compute aeroelasticity on parallel computers using direct coupling of fluid and structural equations will be investigated for wing-body configurations. The parallel computer selected for computations is an Intel iPSC/860 computer which is a distributed-memory, multiple-instruction, multiple data (MIMD) computer with 128 processors. In this study, the computational efficiency issues of parallel integration of both fluid and structural equations will be investigated in detail. The fluid and structural domains will be modeled using finite-difference and finite-element approaches, respectively. Results from the parallel computer will be compared with those from the conventional computers using a single processor. This study will provide an efficient computational tool for the aeroelastic analysis of wing-body structures on MIMD type parallel computers.
Two-fluid equations for a nuclear system with arbitrary motions
Energy Technology Data Exchange (ETDEWEB)
Kim, Byoung Jae [Chungnam National University, Daejeon (Korea, Republic of); Kim, Kyung Doo [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2016-10-15
Ocean nuclear systems include a seabed-type plant, a floating-type plant, and a nuclear-propulsion ship. We asked ourselves, 'What governing equations should be used for ocean nuclear systems?' Since ocean nuclear systems are apt to move arbitrarily, the two-fluid model must be formulated in the non-inertial frame of reference that is undergoing acceleration with respect to an inertial frame. Two-phase flow systems with arbitrary motions are barely reported. Kim et al. (1996) added the centripetal and Euler acceleration forces to the homogeneous equilibrium momentum equation embedded in the RETRAN code. However, they did not look into the mass and energy equations. The purpose of this study is to derive general two-fluid equations in the non-inertial frame of reference, which can be used for safety analysis of ocean nuclear systems. The two-fluid equation forms for scalar properties such as mass, internal energy, and enthalpy equation in the moving frame are the same as those in the absolute frame. On the other hand, the fictitious effect must be included in the momentum equation.
Regularity criteria for the 3D magneto-micropolar fluid equations via ...
Indian Academy of Sciences (India)
3D magneto-micropolar fluid equations. It involves only the direction of the velocity and the magnetic field. Our result extends to the cases of Navier–Stokes and MHD equations. Keywords. Magneto-micropolar fluid equations; regularity criteria; direction of velocity. 2010 Mathematics Subject Classification. 35Q35, 76W05 ...
Fluid dynamics following flow shut-off in bottle filling
Thete, Sumeet; Appathurai, Santosh; Gao, Haijing; Basaran, Osman
2012-11-01
Bottle filling is ubiquitous in industry. Examples include filling of bottles with shampoos and cleaners, engine oil and pharmaceuticals. In these examples, fluid flows out of a nozzle to fill bottles in an assembly line. Once the required volume of fluid has flowed out of the nozzle, the flow is shut off. However, an evolving fluid thread or string may remain suspended from the nozzle following flow shut-off and persist. This stringing phenomenon can be detrimental to a bottle filling operation because it can adversely affect line speed and filling accuracy by causing uncertainty in fill volume, product loss and undesirable marring of the bottles' exterior surfaces. The dynamics of stringing are studied numerically primarily by using the 1D, slender-jet approximation of the flow equations. A novel feature entails development and use of a new boundary condition downstream of the nozzle exit to expedite the computations. While the emphasis is on stringing of Newtonian fluids and use of 1D approximations, results will also be presented for situations where (a) the fluids are non-Newtonian and (b) the full set of equations are solved without invoking the 1D approximation. Phase diagrams will be presented that identify conditions for which stringing can be problematic.
Bazaz Behbahani, Sanaz; Tan, Xiaobo
2017-08-01
Fish actively control their stiffness in different swimming conditions. Inspired by such an adaptive behavior, in this paper we study the design, prototyping, and dynamic modeling of compact, tunable-stiffness fins for robotic fish, where electrorheological (ER) fluid serves as the enabling element. A multi-layer composite fin with an ER fluid core is prototyped and utilized to investigate the influence of electrical field on its performance. Hamilton's principle is used to derive the dynamic equations of motion of the flexible fin, and Lighthill's large-amplitude elongated-body theory is adopted to estimate the hydrodynamic force when the fin undergoes base-actuated rotation. The dynamic equations are then discretized using the finite element method, to obtain an approximate numerical solution. Experiments are conducted on the prototyped flexible ER fluid-filled beam for parameter identification and validation of the proposed model, and for examining the effectiveness of electrically controlled stiffness tuning. In particular, it is found that the natural frequency is increased by almost 40% when the applied electric field changes from 0 to 1.5× {10}6 {{V}} {{{m}}}-1.
Dynamic Stability of Pipe Conveying Fluid with Crack and Attached Masses
International Nuclear Information System (INIS)
Ahn, Tae Soo; Yoon, Han Ik; Son, In Soo; Ahn, Sung Jin
2007-01-01
In this paper, the dynamic stability of a cracked simply supported pipe conveying fluid with an attached mass is investigated. Also, the effect of attached masses on the dynamic stability of a simply supported pipe conveying fluid is presented for the different positions and depth of the crack. Based on the Euler-Bernoulli beam theory, the equation of motion can be constructed by the energy expressions using extended Hamilton's principle. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The crack is assumed to be in the first mode of a fracture and to be always opened during the vibrations. Finally, the critical flow velocities and stability maps of the pipe conveying fluid are obtained by changing the attached masses and crack severity
Global Solutions to the Coupled Chemotaxis-Fluid Equations
Duan, Renjun
2010-08-10
In this paper, we are concerned with a model arising from biology, which is a coupled system of the chemotaxis equations and the viscous incompressible fluid equations through transport and external forcing. The global existence of solutions to the Cauchy problem is investigated under certain conditions. Precisely, for the Chemotaxis-Navier-Stokes system over three space dimensions, we obtain global existence and rates of convergence on classical solutions near constant states. When the fluid motion is described by the simpler Stokes equations, we prove global existence of weak solutions in two space dimensions for cell density with finite mass, first-order spatial moment and entropy provided that the external forcing is weak or the substrate concentration is small. © Taylor & Francis Group, LLC.
Integral transform solutions of dynamic response of a clamped–clamped pipe conveying fluid
International Nuclear Information System (INIS)
Gu Jijun; An Chen; Duan Menglan; Levi, Carlos; Su Jian
2013-01-01
Highlights: ► Dynamic response of pipe conveying fluid was studied numerically. ► The generalized integral transform technique (GITT) was applied. ► Numerical solutions with automatic global accuracy control were obtained. ► Excellent convergence behavior was shown. ► Modal separation analysis was carried out and the influence of mass ratio was analyzed. - Abstract: Analysis of dynamic response of pipe conveying fluid is an important aspect in nuclear power plant design. In the present paper, dynamic response of a clamped–clamped pipe conveying fluid was solved by the generalized integral transform technique (GITT). The governing partial differential equation was transformed into a set of second-order ordinary differential equations which is then numerically solved by making use of the subroutine DIVPAG from IMSL Library. A thorough convergence analysis was performed to yield sets of reference results of the transverse deflection at different time and spanwise position. We found good agreement between the computed natural frequencies at mode 1–3 and those obtained by previous theoretical study. Besides, modal separation analysis was carried out and the influence of mass ratio on deflection and natural frequencies was qualitatively and quantitatively assessed.
NASA-VOF2D, 2-D Transient Free Surface Incompressible Fluid Dynamic
International Nuclear Information System (INIS)
Torrey, M.D.
1988-01-01
1 - Description of program or function: NASA-VOF2D is a two- dimensional, transient, free surface incompressible fluid dynamics program. It allows multiple free surfaces with surface tension and wall adhesion forces and has a partial cell treatment which allows curved boundaries and interior obstacles. 2 - Method of solution: NASA-VOF2D simulates incompressible flows with free surfaces using the volume-of-fluid (VOF) algorithm. This technique is based on the use of donor-acceptor differencing to track the free surface across an Eulerian grid. The complete Navier-Stokes equations in primitive variables for an incompressible fluid are solved by finite differences with surface tension and wall adhesion included. Optionally the pressure equation can be solved by a conjugate residual method rather than the successive over-relaxation (SOR) method
Geophysical fluid dynamics understanding (almost) everything with rotating shallow water models
Zeitlin, Vladimir
2018-01-01
The book explains the key notions and fundamental processes in the dynamics of the fluid envelopes of the Earth (transposable to other planets), and methods of their analysis, from the unifying viewpoint of rotating shallow-water model (RSW). The model, in its one- or two-layer versions, plays a distinguished role in geophysical fluid dynamics, having been used for around a century for conceptual understanding of various phenomena, for elaboration of approaches and methods, to be applied later in more complete models, for development and testing of numerical codes and schemes of data assimilations, and many other purposes. Principles of modelling of large-scale atmospheric and oceanic flows, and corresponding approximations, are explained and it is shown how single- and multi-layer versions of RSW arise from the primitive equations by vertical averaging, and how further time-averaging produces celebrated quasi-geostrophic reductions of the model. Key concepts of geophysical fluid dynamics are exposed and inte...
Mean field theory for non-abelian gauge theories and fluid dynamics. A brief progress report
International Nuclear Information System (INIS)
Wadia, Spenta R.
2009-01-01
We review the long standing problem of 'mean field theory' for non-abelian gauge theories. As a consequence of the AdS/CFT correspondence, in the large N limit, at strong coupling, and high temperatures and density, the 'mean field theory' is described by the Navier-Stokes equations of fluid dynamics. We also discuss and present results on the non-conformal fluid dynamics of the D1 brane in 1+1 dim. (author)
A fluid dynamic approach to the dust-acoustic soliton
International Nuclear Information System (INIS)
McKenzie, J.F.; Doyle, T.B.
2002-01-01
The properties of dust-acoustic solitons are derived from a fluid dynamic viewpoint in which conservation of total momentum, combined with the Bernoulli-like energy equations for each species, yields the structure equation for the heavy (or dust) speed in the stationary wave. This fully nonlinear approach reveals the crucial role played by the heavy sonic point in limiting the collective dust-acoustic Mach number, above which solitons cannot exist. An exact solution illustrates that the cold heavy species is compressed and this implies concomitant contraints on the potential and on the flow speed of the electrons and protons in the wave
A Fluid Dynamic Approach to the Dust-Acoustic Soliton
McKenzie, J. F.; Doyle, T. B.
2002-12-01
The properties of dust-acoustic solitons are derived from a fluid dynamic viewpoint in which conservation of total momentum, combined with the Bernoulli-like energy equations for each species, yields the structure equation for the heavy (or dust) speed in the stationary wave. This fully nonlinear approach reveals the crucial role played by the heavy sonic point in limiting the collective dust-acoustic Mach number, above which solitons cannot exist. An exact solution illustrates that the cold heavy species is compressed and this implies concomitant contraints on the potential and on the flow speed of the electrons and protons in the wave.
International Nuclear Information System (INIS)
Farinnas Wong, E. Y.; Jauregui Rigo, S.; Betancourt Mena, J.
2009-01-01
In this paper we describe different approaches to solving problems computational fluid dynamics using the finite element method, there is a perspective what are the different problems that must be addressed when choose a path to develop a code that solves the problems of boundary layer and turbulence to simulate the transport equipment and fluid handling. In principle, the turbulent flow is governed by the equations of dynamics fluids. The nonlinearity of the Navier-Stokes equations, make the solution analytical is only possible in a few very specific cases and for senior Reynolds numbers the flow equations become a more complex, for it is necessary to use certain models dependent on some settings, usually obtained experimentally. Existing in the powerful techniques present numerical resolution of these equations such as the direct numerical simulation (DNS) and large eddy simulation or vertices (RES), discussed for use in solving problems flow machines. (author)
Stochastic Ocean Predictions with Dynamically-Orthogonal Primitive Equations
Subramani, D. N.; Haley, P., Jr.; Lermusiaux, P. F. J.
2017-12-01
The coastal ocean is a prime example of multiscale nonlinear fluid dynamics. Ocean fields in such regions are complex and intermittent with unstationary heterogeneous statistics. Due to the limited measurements, there are multiple sources of uncertainties, including the initial conditions, boundary conditions, forcing, parameters, and even the model parameterizations and equations themselves. For efficient and rigorous quantification and prediction of these uncertainities, the stochastic Dynamically Orthogonal (DO) PDEs for a primitive equation ocean modeling system with a nonlinear free-surface are derived and numerical schemes for their space-time integration are obtained. Detailed numerical studies with idealized-to-realistic regional ocean dynamics are completed. These include consistency checks for the numerical schemes and comparisons with ensemble realizations. As an illustrative example, we simulate the 4-d multiscale uncertainty in the Middle Atlantic/New York Bight region during the months of Jan to Mar 2017. To provide intitial conditions for the uncertainty subspace, uncertainties in the region were objectively analyzed using historical data. The DO primitive equations were subsequently integrated in space and time. The probability distribution function (pdf) of the ocean fields is compared to in-situ, remote sensing, and opportunity data collected during the coincident POSYDON experiment. Results show that our probabilistic predictions had skill and are 3- to 4- orders of magnitude faster than classic ensemble schemes.
Methods and models for accelerating dynamic simulation of fluid power circuits
Energy Technology Data Exchange (ETDEWEB)
Aaman, R.
2011-07-01
The objective of this dissertation is to improve the dynamic simulation of fluid power circuits. A fluid power circuit is a typical way to implement power transmission in mobile working machines, e.g. cranes, excavators etc. Dynamic simulation is an essential tool in developing controllability and energy-efficient solutions for mobile machines. Efficient dynamic simulation is the basic requirement for the real-time simulation. In the real-time simulation of fluid power circuits there exist numerical problems due to the software and methods used for modelling and integration. A simulation model of a fluid power circuit is typically created using differential and algebraic equations. Efficient numerical methods are required since differential equations must be solved in real time. Unfortunately, simulation software packages offer only a limited selection of numerical solvers. Numerical problems cause noise to the results, which in many cases leads the simulation run to fail. Mathematically the fluid power circuit models are stiff systems of ordinary differential equations. Numerical solution of the stiff systems can be improved by two alternative approaches. The first is to develop numerical solvers suitable for solving stiff systems. The second is to decrease the model stiffness itself by introducing models and algorithms that either decrease the highest eigenvalues or neglect them by introducing steady-state solutions of the stiff parts of the models. The thesis proposes novel methods using the latter approach. The study aims to develop practical methods usable in dynamic simulation of fluid power circuits using explicit fixed-step integration algorithms. In this thesis, two mechanisms which make the system stiff are studied. These are the pressure drop approaching zero in the turbulent orifice model and the volume approaching zero in the equation of pressure build-up. These are the critical areas to which alternative methods for modelling and numerical simulation
Modeling quantum fluid dynamics at nonzero temperatures
Berloff, Natalia G.; Brachet, Marc; Proukakis, Nick P.
2014-01-01
The detailed understanding of the intricate dynamics of quantum fluids, in particular in the rapidly growing subfield of quantum turbulence which elucidates the evolution of a vortex tangle in a superfluid, requires an in-depth understanding of the role of finite temperature in such systems. The Landau two-fluid model is the most successful hydrodynamical theory of superfluid helium, but by the nature of the scale separations it cannot give an adequate description of the processes involving vortex dynamics and interactions. In our contribution we introduce a framework based on a nonlinear classical-field equation that is mathematically identical to the Landau model and provides a mechanism for severing and coalescence of vortex lines, so that the questions related to the behavior of quantized vortices can be addressed self-consistently. The correct equation of state as well as nonlocality of interactions that leads to the existence of the roton minimum can also be introduced in such description. We review and apply the ideas developed for finite-temperature description of weakly interacting Bose gases as possible extensions and numerical refinements of the proposed method. We apply this method to elucidate the behavior of the vortices during expansion and contraction following the change in applied pressure. We show that at low temperatures, during the contraction of the vortex core as the negative pressure grows back to positive values, the vortex line density grows through a mechanism of vortex multiplication. This mechanism is suppressed at high temperatures. PMID:24704874
Self-similarity in the equation of motion of a ship
Directory of Open Access Journals (Sweden)
Gyeong Joong Lee
2014-06-01
Full Text Available If we want to analyze the motion of a body in fluid, we should use rigid-body dynamics and fluid dynamics together. Even if the rigid-body and fluid dynamics are each self-consistent, there arises the problem of self-similar structure in the equation of motion when the two dynamics are coupled with each other. When the added mass is greater than the mass of a body, the calculated motion is divergent because of its self-similar structure. This study showed that the above problem is an inherent problem. This problem of self-similar structure may arise in the equation of motion in which the fluid dynamic forces are treated as external forces on the right hand side of the equation. A reconfiguration technique for the equation of motion using pseudo-added-mass was proposed to resolve the self-similar structure problem; specifically for the case when the fluid force is expressed by integration of the fluid pressure.
International Nuclear Information System (INIS)
Ezaki, Masahiro; Mitake, Susumu; Ozawa, Tamotsu
1979-06-01
The SCOTCH program solves the one-dimensional (R or Z), two-group reactor kinetics equations with multi-channel temperature transients and fluid dynamics. Sub-program SCOTCH-RX simulates the space-time neutron diffusion in radial direction, and sub-program SCOTCH-AX simulates the same in axial direction. The program has about 8,000 steps of FORTRAN statement and requires about 102 kilo-words of computer memory. (author)
Ha, Seung-Yeal; Xiao, Qinghua; Zhang, Xiongtao
2018-04-01
We study the dynamics of infinitely many Cucker-Smale (C-S) flocking particles under the interplay of random communication and incompressible fluids. For the dynamics of an ensemble of flocking particles, we use the kinetic Cucker-Smale-Fokker-Planck (CS-FP) equation with a degenerate diffusion, whereas for the fluid component, we use the incompressible Navier-Stokes (N-S) equations. These two subsystems are coupled via the drag force. For this coupled model, we present the global existence of weak and strong solutions in Rd (d = 2 , 3). Under the extra regularity assumptions of the initial data, the unique solvability of strong solutions is also established in R2. In a large coupling regime and periodic spatial domain T2 : =R2 /Z2, we show that the velocities of C-S particles and fluids are asymptotically aligned to two constant velocities which may be different.
Relativistic fluid dynamics with spin
Florkowski, Wojciech; Friman, Bengt; Jaiswal, Amaresh; Speranza, Enrico
2018-04-01
Using the conservation laws for charge, energy, momentum, and angular momentum, we derive hydrodynamic equations for the charge density, local temperature, and fluid velocity, as well as for the polarization tensor, starting from local equilibrium distribution functions for particles and antiparticles with spin 1/2. The resulting set of differential equations extends the standard picture of perfect-fluid hydrodynamics with a conserved entropy current in a minimal way. This framework can be used in space-time analyses of the evolution of spin and polarization in various physical systems including high-energy nuclear collisions. We demonstrate that a stationary vortex, which exhibits vorticity-spin alignment, corresponds to a special solution of the spin-hydrodynamical equations.
A Van der Pol-Mathieu equation for the dynamics of dust grain charge in dusty plasmas
International Nuclear Information System (INIS)
Momeni, M; Kourakis, I; Moslehi-Fard, M; Shukla, P K
2007-01-01
The chaotic profile of dust grain dynamics associated with dust-acoustic oscillations in a dusty plasma is considered. The collective behaviour of the dust plasma component is described via a multi-fluid model, comprising Boltzmann distributed electrons and ions, as well as an equation of continuity possessing a source term for the dust grains, the dust momentum and Poisson's equations. A Van der Pol-Mathieu-type nonlinear ordinary differential equation for the dust grain density dynamics is derived. The dynamical system is cast into an autonomous form by employing an averaging method. Critical stability boundaries for a particular trivial solution of the governing equation with varying parameters are specified. The equation is analysed to determine the resonance region, and finally numerically solved by using a fourth-order Runge-Kutta method. The presence of chaotic limit cycles is pointed out. (fast track communication)
Eight equation model for arbitrary shaped pipe conveying fluid
International Nuclear Information System (INIS)
Gale, J.; Tiselj, I.
2006-01-01
Linear eight-equation system for two-way coupling of single-phase fluid transient and arbitrary shaped one-dimensional pipeline movement is described and discussed. The governing phenomenon described with this system is also known as Fluid-Structure Interaction. Standard Skalak's four-equation model for axial coupling was improved with additional four Timoshenko's beam equations for description of flexural displacements and rotations. In addition to the conventional eight-equation system that enables coupling of straight sections, the applied mathematical model was improved for description of the arbitrary shaped pipeline located in two-dimensional plane. The applied model was solved with second-order accurate numerical method that is based on Godounov's characteristic upwind schemes. The model was successfully used for simulation of the rod impact induced transient and conventional instantaneous valve closure induced transient in the tank-pipe-valve system. (author)
Pedlosky, Joseph
1982-01-01
The content of this book is based, largely, on the core curriculum in geophys ical fluid dynamics which land my colleagues in the Department of Geophysical Sciences at The University of Chicago have taught for the past decade. Our purpose in developing a core curriculum was to provide to advanced undergraduates and entering graduate students a coherent and systematic introduction to the theory of geophysical fluid dynamics. The curriculum and the outline of this book were devised to form a sequence of courses of roughly one and a half academic years (five academic quarters) in length. The goal of the sequence is to help the student rapidly advance to the point where independent study and research are practical expectations. It quickly became apparent that several topics (e. g. , some aspects of potential theory) usually thought of as forming the foundations of a fluid-dynamics curriculum were merely classical rather than essential and could be, however sadly, dispensed with for our purposes. At the same tim...
Pedlosky, Joseph
1979-01-01
The content of this book is based, largely, on the core curriculum in geophys ical fluid dynamics which I and my colleagues in the Department of Geophysical Sciences at The University of Chicago have taught for the past decade. Our purpose in developing a core curriculum was to provide to advanced undergraduates and entering graduate students a coherent and systematic introduction to the theory of geophysical fluid dynamics. The curriculum and the outline of this book were devised to form a sequence of courses of roughly one and a half academic years (five academic quarters) in length. The goal of the sequence is to help the student rapidly advance to the point where independent study and research are practical expectations. It quickly became apparent that several topics (e. g. , some aspects of potential theory) usually thought of as forming the foundations of a fluid-dynamics curriculum were merely classical rather than essential and could be, however sadly, dispensed with for our purposes. At the same ti...
Exact solutions for a system of nonlinear plasma fluid equations
International Nuclear Information System (INIS)
Prahovic, M.G.; Hazeltine, R.D.; Morrison, P.J.
1991-04-01
A method is presented for constructing exact solutions to a system of nonlinear plasma fluid equations that combines the physics of reduced magnetohydrodynamics and the electrostatic drift-wave description of the Charney-Hasegawa-Mima equation. The system has nonlinearities that take the form of Poisson brackets involving the fluid field variables. The method relies on modifying a class of simple equilibrium solutions, but no approximations are made. A distinguishing feature is that the original nonlinear problem is reduced to the solution of two linear partial differential equations, one fourth-order and the other first-order. The first-order equation has Hamiltonian characteristics and is easily integrated, supplying information about the general structure of solutions. 6 refs
Implementing a Loosely Coupled Fluid Structure Interaction Finite Element Model in PHASTA
Pope, David
Fluid Structure Interaction problems are an important multi-physics phenomenon in the design of aerospace vehicles and other engineering applications. A variety of computational fluid dynamics solvers capable of resolving the fluid dynamics exist. PHASTA is one such computational fluid dynamics solver. Enhancing the capability of PHASTA to resolve Fluid-Structure Interaction first requires implementing a structural dynamics solver. The implementation also requires a correction of the mesh used to solve the fluid equations to account for the deformation of the structure. This results in mesh motion and causes the need for an Arbitrary Lagrangian-Eulerian modification to the fluid dynamics equations currently implemented in PHASTA. With the implementation of both structural dynamics physics, mesh correction, and the Arbitrary Lagrangian-Eulerian modification of the fluid dynamics equations, PHASTA is made capable of solving Fluid-Structure Interaction problems.
Static, Dynamic, and Thermal Properties of Compressible Fluid Film Journal Bearings
DEFF Research Database (Denmark)
Paulsen, Bo Terp; Morosi, Stefano; Santos, Ilmar
2011-01-01
fluid film journal bearing, in order to identify when this type of analysis should be of concern. Load capacity, stiffness, and damping coefficients are determined by the solution of the standard Reynolds equation coupled to the energy equation. Numerical investigations show how bearing geometry......, and work great efficiency. A great deal of literature has concentrated on the analysis and prediction of the static and dynamic performance of gas bearings, assuming isothermal conditions. The present contribution presents a detailed mathematical modeling for nonisothermal lubrication of a compressible...
Viscous-elastic dynamics of power-law fluids within an elastic cylinder
Boyko, Evgeniy; Bercovici, Moran; Gat, Amir D.
2017-07-01
In a wide range of applications, microfluidic channels are implemented in soft substrates. In such configurations, where fluidic inertia and compressibility are negligible, the propagation of fluids in channels is governed by a balance between fluid viscosity and elasticity of the surrounding solid. The viscous-elastic interactions between elastic substrates and non-Newtonian fluids are particularly of interest due to the dependence of viscosity on the state of the system. In this work, we study the fluid-structure interaction dynamics between an incompressible non-Newtonian fluid and a slender linearly elastic cylinder under the creeping flow regime. Considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a nonhomogeneous p-Laplacian equation governing the viscous-elastic dynamics. We present exact solutions for the pressure and deformation fields for various initial and boundary conditions for both shear-thinning and shear-thickening fluids. We show that in contrast to Stokes' problem where a compactly supported front is obtained for shear-thickening fluids, here the role of viscosity is inversed and such fronts are obtained for shear-thinning fluids. Furthermore, we demonstrate that for the case of a step in inlet pressure, the propagation rate of the front has a tn/n +1 dependence on time (t ), suggesting the ability to indirectly measure the power-law index (n ) of shear-thinning liquids through measurements of elastic deformation.
Faber, T. E.
1995-08-01
This textbook provides an accessible and comprehensive account of fluid dynamics that emphasizes fundamental physical principles and stresses connections with other branches of physics. Beginning with a basic introduction, the book goes on to cover many topics not typically treated in texts, such as compressible flow and shock waves, sound attenuation and bulk viscosity, solitary waves and ship waves, thermal convection, instabilities, turbulence, and the behavior of anisotropic, non-Newtonian and quantum fluids. Undergraduate or graduate students in physics or engineering who are taking courses in fluid dynamics will find this book invaluable.
Balance equations for a viscous fluid from a Hamilton type variational principle
International Nuclear Information System (INIS)
Fierros Palacios, A.
1992-01-01
The partial differential field equations for any viscous fluid are obtained from the Lagrangian formalism as in classical field theory. An action functional is introduced as a space-time integral over a region of three-dimensional Euclidean space, of a Lagrangian density function of certain field variables. A Hamilton type extremum action principle is postulated with adequate boundary conditions, and a set of differential field equations is derived. With an appropriate Lagrangian density of the T-V type, the equation of motion for any viscous fluid is reproduced. A theorem referring to the invariance of the action under time variations lead to the generalized energy balance equation for the viscous fluid and to the energy balance equation proper. The same theoretical approach can be used to solve the problem of potential flow. (Author)
The Kerr/fluid duality and the singularity of solutions to the fluid equation
International Nuclear Information System (INIS)
Fujisawa, Ippei; Nakayama, Ryuichi
2016-01-01
An equation for a viscous incompressible fluid on a spheroidal surface that is dual to the perturbation around the near-near-horizon extreme Kerr (near-NHEK) black hole is derived. It is also shown that an expansion scalar θ of a congruence of null geodesics on the perturbed horizon of the perturbed near-NHEK spacetime, which is dual to a viscous incompressible fluid, is not in general positive semidefinite, even if initial conditions on the velocity are smooth. Unless the initial conditions are appropriately adjusted, caustics of null congruence will occur on the perturbed horizon in the future. A similar result is obtained for a perturbed Schwarzschild black hole spacetime, which is dual to a viscous incompressible fluid on S 2 . An initial condition that θ be positive semidefinite at any point on S 2 is a necessary condition for the existence of smooth solutions to the incompressible Navier-Stokes equation on S 2
Vortex dynamics in the two-fluid model
International Nuclear Information System (INIS)
Thouless, D. J.; Geller, M. R.; Vinen, W. F.; Fortin, J.-Y.; Rhee, S. W.
2001-01-01
We have used two-fluid dynamics to study the discrepancy between the work of Thouless, Ao, and Niu (TAN) and that of Iordanskii. In TAN no transverse force on a vortex due to normal fluid flow was found, whereas the earlier work found a transverse force proportional to normal fluid velocity u n and normal fluid density ρ n . We have linearized the time-independent two-fluid equations about the exact solution for a vortex, and find three solutions that are important in the region far from the vortex. Uniform superfluid flow gives rise to the usual superfluid Magnus force. Uniform normal fluid flow gives rise to no forces in the linear region, but does not satisfy reasonable boundary conditions at short distances. A logarithmically increasing normal fluid flow gives a viscous force. As in classical hydrodynamics, and as in the early work of Hall and Vinen, this logarithmic increase must be cut off by nonlinear effects at large distances; this gives a viscous force proportional to u n /lnu n , and a transverse contribution that goes like u n /(lnu n ) 2 , even in the absence of an explicit Iordanskii force. In the limit u n ->0 the TAN result is obtained, but at nonzero u n there are important corrections that were not found in TAN. We argue that the Magnus force in a superfluid at nonzero temperature is an example of a topological relation for which finite-size corrections may be large
Sparse dynamics for partial differential equations.
Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D; Osher, Stanley
2013-04-23
We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms.
The real gas dynamics of the fluids of high specific heat
International Nuclear Information System (INIS)
Meier, G.E.A.
1987-01-01
The gas dynamics of real fluids show several new effects beyond the gas dynamics of ideal substances. Many of these effects rely on phase changes in the flow fields and can be explained with the help of more complicated thermal and caloric state equations of the real fluids. Complete adiabatic liquefaction and evaporation are possible for those substances whose specific heat exceeds a limit of about twenty gas constants. These fluids consisting of great molecules have so much internal energy storage capacity in their numerous vibrational degrees of freedom that the heat of evaporation can be supplied or also stored in the case of condensation. So liquefaction shock waves, which transform a gas completely or partly into a liquid, are possible. The shock front becomes thereby the surface of a liquid. Partial liquefaction with droplet condensation occurs in weaker shock waves. On the other hand a superheated liquid with high specific heat can be changed into a gas or mixture state in expansion waves or flows. (orig.)
Computational fluid dynamics incompressible turbulent flows
Kajishima, Takeo
2017-01-01
This textbook presents numerical solution techniques for incompressible turbulent flows that occur in a variety of scientific and engineering settings including aerodynamics of ground-based vehicles and low-speed aircraft, fluid flows in energy systems, atmospheric flows, and biological flows. This book encompasses fluid mechanics, partial differential equations, numerical methods, and turbulence models, and emphasizes the foundation on how the governing partial differential equations for incompressible fluid flow can be solved numerically in an accurate and efficient manner. Extensive discussions on incompressible flow solvers and turbulence modeling are also offered. This text is an ideal instructional resource and reference for students, research scientists, and professional engineers interested in analyzing fluid flows using numerical simulations for fundamental research and industrial applications. • Introduces CFD techniques for incompressible flow and turbulence with a comprehensive approach; • Enr...
Energy Technology Data Exchange (ETDEWEB)
Barbante, Paolo [Dipartimento di Matematica, Politecnico di Milano - Piazza Leonardo da Vinci 32 - 20133 Milano (Italy); Frezzotti, Aldo; Gibelli, Livio [Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano - Via La Masa 34 - 20156 Milano (Italy)
2014-12-09
The unsteady evaporation of a thin planar liquid film is studied by molecular dynamics simulations of Lennard-Jones fluid. The obtained results are compared with the predictions of a diffuse interface model in which capillary Korteweg contributions are added to hydrodynamic equations, in order to obtain a unified description of the liquid bulk, liquid-vapor interface and vapor region. Particular care has been taken in constructing a diffuse interface model matching the thermodynamic and transport properties of the Lennard-Jones fluid. The comparison of diffuse interface model and molecular dynamics results shows that, although good agreement is obtained in equilibrium conditions, remarkable deviations of diffuse interface model predictions from the reference molecular dynamics results are observed in the simulation of liquid film evaporation. It is also observed that molecular dynamics results are in good agreement with preliminary results obtained from a composite model which describes the liquid film by a standard hydrodynamic model and the vapor by the Boltzmann equation. The two mathematical model models are connected by kinetic boundary conditions assuming unit evaporation coefficient.
Quantum molecular dynamics simulations of thermophysical properties of fluid ethane.
Zhang, Yujuan; Wang, Cong; Zheng, Fawei; Zhang, Ping
2012-12-01
We have performed first-principles molecular-dynamics simulations based on density-functional theory to study the thermophysical properties of ethane under extreme conditions. We present results for the equation of state of fluid ethane in the warm dense region. The optical conductivity is calculated via the Kubo-Greenwood formula from which the dc conductivity and optical reflectivity are derived. The close correlation between the nonmetal-metal transition of ethane and its decomposition, that ethane dissociates significantly into molecular and/or atomic hydrogen and some long alkane chains, has been systematically studied by analyzing the optical conductivity spectra, pair correlation functions, electronic density of states, and charge density distribution of fluid ethane.
Relativistic quantum vorticity of the quadratic form of the Dirac equation
International Nuclear Information System (INIS)
Asenjo, Felipe A; Mahajan, Swadesh M
2015-01-01
We explore the fluid version of the quadratic form of the Dirac equation, sometimes called the Feynman–Gell-Mann equation. The dynamics of the quantum spinor field is represented by equations of motion for the fluid density, the velocity field, and the spin field. In analogy with classical relativistic and non-relativistic quantum theories, the fully relativistic fluid formulation of this equation allows a vortex dynamics. The vortical form is described by a total tensor field that is the weighted combination of the inertial, electromagnetic and quantum forces. The dynamics contrives the quadratic form of the Dirac equation as a total vorticity free system. (paper)
Lorentz-like covariant equations of non-relativistic fluids
International Nuclear Information System (INIS)
Montigny, M de; Khanna, F C; Santana, A E
2003-01-01
We use a geometrical formalism of Galilean invariance to build various hydrodynamics models. It consists in embedding the Newtonian spacetime into a non-Euclidean 4 + 1 space and provides thereby a procedure that unifies models otherwise apparently unrelated. After expressing the Navier-Stokes equation within this framework, we show that slight modifications of its Lagrangian allow us to recover the Chaplygin equation of state as well as models of superfluids for liquid helium (with both its irrotational and rotational components). Other fluid equations are also expressed in a covariant form
A hybrid Eulerian–Lagrangian numerical scheme for solving prognostic equations in fluid dynamics
Directory of Open Access Journals (Sweden)
E. Kaas
2013-11-01
Full Text Available A new hybrid Eulerian–Lagrangian numerical scheme (HEL for solving prognostic equations in fluid dynamics is proposed. The basic idea is to use an Eulerian as well as a fully Lagrangian representation of all prognostic variables. The time step in Lagrangian space is obtained as a translation of irregularly spaced Lagrangian parcels along downstream trajectories. Tendencies due to other physical processes than advection are calculated in Eulerian space, interpolated, and added to the Lagrangian parcel values. A directionally biased mixing amongst neighboring Lagrangian parcels is introduced. The rate of mixing is proportional to the local deformation rate of the flow. The time stepping in Eulerian representation is achieved in two steps: first a mass-conserving Eulerian or semi-Lagrangian scheme is used to obtain a provisional forecast. This forecast is then nudged towards target values defined from the irregularly spaced Lagrangian parcel values. The nudging procedure is defined in such a way that mass conservation and shape preservation is ensured in Eulerian space. The HEL scheme has been designed to be accurate, multi-tracer efficient, mass conserving, and shape preserving. In Lagrangian space only physically based mixing takes place; i.e., the problem of artificial numerical mixing is avoided. This property is desirable in atmospheric chemical transport models since spurious numerical mixing can impact chemical concentrations severely. The properties of HEL are here verified in two-dimensional tests. These include deformational passive transport on the sphere, and simulations with a semi-implicit shallow water model including topography.
Palazzi, Elisa; Fraedrich, Klaus
2016-01-01
This volume provides an overview of the fluid aspects of the climate system, focusing on basic aspects as well as recent research developments. It will bring together contributions from diverse fields of the physical, mathematical and engineering sciences. The volume will be useful to doctorate students, postdocs and researchers working on different aspects of atmospheric, oceanic and environmental fluid dynamics. It will also be of interest to researchers interested in quantitatively understanding how fluid dynamics can be applied to the climate system, and to climate scientists willing to gain a deeper insight into the fluid mechanics underlying climate processes.
Fractional dynamic calculus and fractional dynamic equations on time scales
Georgiev, Svetlin G
2018-01-01
Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on time scales and examines recent developments within the field of fractional calculus and fractional equations. Useful tools are provided for solving differential and integral equations as well as various problems involving special functions of mathematical physics and their extensions and generalizations in one and more variables. Much discussion is devoted to Riemann-Liouville fractional dynamic equations and Caputo fractional dynamic equations. Intended for use in the field and designed for students without an extensive mathematical background, this book is suitable for graduate courses and researchers looking for an introduction to fractional dynamic calculus and equations on time scales. .
Dynamic modeling of interfacial structures via interfacial area transport equation
International Nuclear Information System (INIS)
Seungjin, Kim; Mamoru, Ishii
2004-01-01
Full text of publication follows:In the current thermal-hydraulic system analysis codes using the two-fluid model, the empirical correlations that are based on the two-phase flow regimes and regime transition criteria are being employed as closure relations for the interfacial transfer terms. Due to its inherent shortcomings, however, such static correlations are inaccurate and present serious problems in the numerical analysis. In view of this, a new dynamic approach employing the interfacial area transport equation has been studied. The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Therefore, the interfacial area transport equation can make a leapfrog improvement in the current capability of the two-fluid model from both scientific and practical point of view. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right hand-side of the transport equations have been established by mechanistically modeling the creation and destruction of bubbles due to major bubble interaction mechanisms. The coalescence mechanisms include the random collision driven by turbulence, and the entrainment of trailing bubbles in the wake region of the preceding bubble. The disintegration mechanisms include the break-up by turbulence impact, shearing-off at the rim of large cap bubbles and the break-up of large cap
Dynamical equations for the optical potential
International Nuclear Information System (INIS)
Kowalski, K.L.
1981-01-01
Dynamical equations for the optical potential are obtained starting from a wide class of N-particle equations. This is done with arbitrary multiparticle interactions to allow adaptation to few-body models of nuclear reactions and including all effects of nucleon identity. Earlier forms of the optical potential equations are obtained as special cases. Particular emphasis is placed upon obtaining dynamical equations for the optical potential from the equations of Kouri, Levin, and Tobocman including all effects of particle identity
Dutta, Jibitesh; Khyllep, Wompherdeiki; Tamanini, Nicola
2018-01-01
We consider scalar field models of dark energy interacting with dark matter through a coupling proportional to the contraction of the four-derivative of the scalar field with the four-velocity of the dark matter fluid. The coupling is realized at the Lagrangian level employing the formalism of Scalar-Fluid theories, which use a consistent Lagrangian approach for relativistic fluid to describe dark matter. This framework produces fully covariant field equations, from which we can derive unequivocal cosmological equations at both background and linear perturbations levels. The background evolution is analyzed in detail applying dynamical systems techniques, which allow us to find the complete asymptotic behavior of the universe given any set of model parameters and initial conditions. Furthermore we study linear cosmological perturbations investigating the growth of cosmic structures within the quasi-static approximation. We find that these interacting dark energy models give rise to interesting phenomenological dynamics, including late-time transitions from dark matter to dark energy domination, matter and accelerated scaling solutions and dynamical crossing of the phantom barrier. Moreover we obtain possible deviations from standard ΛCDM behavior at the linear perturbations level, which have an impact on the dynamics of structure formation and might provide characteristic observational signatures.
Parallel processing for fluid dynamics applications
International Nuclear Information System (INIS)
Johnson, G.M.
1989-01-01
The impact of parallel processing on computational science and, in particular, on computational fluid dynamics is growing rapidly. In this paper, particular emphasis is given to developments which have occurred within the past two years. Parallel processing is defined and the reasons for its importance in high-performance computing are reviewed. Parallel computer architectures are classified according to the number and power of their processing units, their memory, and the nature of their connection scheme. Architectures which show promise for fluid dynamics applications are emphasized. Fluid dynamics problems are examined for parallelism inherent at the physical level. CFD algorithms and their mappings onto parallel architectures are discussed. Several example are presented to document the performance of fluid dynamics applications on present-generation parallel processing devices
Quantum molecular dynamics simulations of thermophysical properties of fluid ethane
Zhang, Yujuan; Wang, Cong; Zheng, Fawei; Zhang, Ping
2012-01-01
We have performed first-principles molecular-dynamics simulations based on density-functional theory to study the thermophysical properties of ethane under extreme conditions. We present new results for the equation of state of fluid ethane in the warm dense region. The optical conductivity is calculated via the Kubo-Greenwood formula from which the dc conductivity and optical reflectivity are derived. The close correlation between the nonmetal-metal transition of ethane and its decomposition...
Modified two-fluid model for the two-group interfacial area transport equation
International Nuclear Information System (INIS)
Sun Xiaodong; Ishii, Mamoru; Kelly, Joseph M.
2003-01-01
This paper presents a modified two-fluid model that is ready to be applied in the approach of the two-group interfacial area transport equation. The two-group interfacial area transport equation was developed to provide a mechanistic constitutive relation for the interfacial area concentration in the two-fluid model. In the two-group transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 while cap/slug/churn-turbulent bubbles as Group 2. Therefore, this transport equation can be employed in the flow regimes spanning from bubbly, cap bubbly, slug to churn-turbulent flows. However, the introduction of the two groups of bubbles requires two gas velocity fields. Yet it is not practical to solve two momentum equations for the gas phase alone. In the current modified two-fluid model, a simplified approach is proposed. The momentum equation for the averaged velocity of both Group-1 and Group-2 bubbles is retained. By doing so, the velocity difference between Group-1 and Group-2 bubbles needs to be determined. This may be made either based on simplified momentum equations for both Group-1 and Group-2 bubbles or by a modified drift-flux model
International Nuclear Information System (INIS)
Yan, Yang; Yong-Liang, Yu; Bing-Gang, Tong; Guan-Hao, Wu
2008-01-01
We present (1) the dynamical equations of deforming body and (2) an integrated method for deforming body dynamics and unsteady fluid dynamics, to investigate a modelled freely self-propelled fish. The theoretical model and practical method is applicable for studies on the general mechanics of animal locomotion such as flying in air and swimming in water, particularly of free self-propulsion. The present results behave more credibly than the previous numerical studies and are close to the experimental results, and the aligned vortices pattern is discovered in cruising swimming
Fermionic corrections to fluid dynamics from BTZ black hole
Energy Technology Data Exchange (ETDEWEB)
Gentile, L.G.C. [DISIT, Università del Piemonte Orientale,via T. Michel, 11, Alessandria, 15120 (Italy); Dipartimento di Fisica “Galileo Galilei”,Università di Padova, via Marzolo 8, 35131 Padova (Italy); INFN - Sezione di Padova,via Marzolo 8, 35131, Padova (Italy); Grassi, P.A. [DISIT, Università del Piemonte Orientale,via T. Michel, 11, Alessandria, 15120 (Italy); INFN - Gruppo Collegato di Alessandria, Sezione di Torino,Alessandria (Italy); PH-TH Department, CERN,CH-1211 Geneva 23 (Switzerland); Mezzalira, A. [Dipartimento di Fisica Teorica, Università di Torino,via P. Giuria, 1, Torino, 10125 (Italy); INFN - Gruppo Collegato di Alessandria, Sezione di Torino,Alessandria (Italy)
2015-11-23
We reconstruct the complete fermionic orbit of the non-extremal BTZ black hole by acting with finite supersymmetry transformations. The solution satisfies the exact supergravity equations of motion to all orders in the fermonic expansion and the final result is given in terms of fermionic bilinears. By fluid/gravity correspondence, we derive linearized Navier-Stokes equations and a set of new differential equations from Rarita-Schwinger equation. We compute the boundary energy-momentum tensor and we interpret the result as a perfect fluid with a modified definition of fluid velocity. Finally, we derive the modified expression for the entropy of the black hole in terms of the fermionic bilinears.
Analytical, Computational Fluid Dynamics and Flight Dynamics of Coandă MAV
Djojodihardjo, H.; Ahmed, RI
2016-11-01
The paper establishes the basic working relationships among various relevant variables and parameters governing the aerodynamics forces and performance measures of Coandă MAV in hover and translatory motion. With such motivation, capitalizing on the basic fundamental principles, the Fluid Dynamics and Flight Mechanics of semi-spherical Coandă MAV configurations are revisited and analyzed as a baseline. To gain better understanding on the principle of Coandă MAV lift generation, a mathematical model for a spherical Coandă MAV is developed and analyzed from first physical principles. To gain further insight into the prevailing flow field around a Coandă MAV, as well as to verify the theoretical prediction presented in the work, a computational fluid dynamic CFD simulation for a Coandă MAV generic model are elaborated using commercial software FLUENT®. In addition, the equation of motion for translatory motion of Coandă MAV is elaborated. The mathematical model and derived performance measures are shown to be capable in describing the physical phenomena of the flow field of the semi-spherical Coandă MAV. The relationships between the relevant parameters of the mathematical model of the Coandă MAV to the forces acting on it are elaborated subsequently.
Technical fluid dynamics. 7. rev. ed.
International Nuclear Information System (INIS)
Becker, E.; Piltz, E.
1993-01-01
An introductory textbook for students of engineering containing the following subjects: Definition and properties of fluids, hydrostatics, Bernoulli's equation, theorem of momentum for steadystate flows, wing lattice and single wing, plane parallel flow of a viscous fluid, pipe flow, boundary layers, gas flows. (orig.) [de
Hamilton's equations for a fluid membrane
International Nuclear Information System (INIS)
Capovilla, R; Guven, J; Rojas, E
2005-01-01
Consider a homogeneous fluid membrane described by the Helfrich-Canham energy, quadratic in the mean curvature of the membrane surface. The shape equation that determines equilibrium configurations is fourth order in derivatives and cubic in the mean curvature. We introduce a Hamiltonian formulation of this equation which dismantles it into a set of coupled first-order equations. This involves interpreting the Helfrich-Canham energy as an action; equilibrium surfaces are generated by the evolution of space curves. Two features complicate the implementation of a Hamiltonian framework. (i) The action involves second derivatives. This requires treating the velocity as a phase-space variable and the introduction of its conjugate momentum. The canonical Hamiltonian is constructed on this phase space. (ii) The action possesses a local symmetry-reparametrization invariance. The two labels we use to parametrize points on the surface are themselves physically irrelevant. This symmetry implies primary constraints, one for each label, that need to be implemented within the Hamiltonian. The two Lagrange multipliers associated with these constraints are identified as the components of the acceleration tangential to the surface. The conservation of the primary constraints implies two secondary constraints, fixing the tangential components of the momentum conjugate to the position. Hamilton's equations are derived and the appropriate initial conditions on the phase-space variables are identified. Finally, it is shown how the shape equation can be reconstructed from these equations
DEFF Research Database (Denmark)
Svec, Oldrich; Skoček, Jan
2013-01-01
The ability of the Lattice Boltzmann method, as the fluid dynamics solver, to properly simulate macroscopic Navier’s slip boundary condition is investigated. An approximate equation relating the Lattice Boltzmann variable slip boundary condition with the macroscopic Navier’s slip boundary condition...
Symbolic dynamics of the Lorenz equations
International Nuclear Information System (INIS)
Fang Hai-ping; Hao Bailin.
1994-07-01
The Lorenz equations are investigated in a wide range of parameters by using the method of symbolic dynamics. First, the systematics of stable periodic orbits in the Lorenz equations is compared with that of the one-dimensional cubic map, which shares the same discrete symmetry with the Lorenz model. The systematics is then ''corrected'' in such a way as to encompass all the known periodic windows of the Lorenz equations with only one exception. Second, in order to justify the above approach and to understand the exceptions, another 1D map with a discontinuity is extracted from an extension of the geometric Lorenz attractor and its symbolic dynamics is constructed. All this has to be done in light of symbolic dynamics of two-dimensional maps. Finally, symbolic dynamics for the actual Poincare return map of the Lorenz equations is constructed in a heuristic way. New periodic windows of the Lorenz equations and their parameters can be predicted from this symbolic dynamics in combination with the 1D cubic map. The extended geometric 2D Lorenz map and the 1D antisymmetric map with a discontinuity describe the topological aspects of the Lorenz equations to high accuracy. (author). 44 refs, 17 figs, 8 tabs
Active Polar Two-Fluid Macroscopic Dynamics
Pleiner, Harald; Svensek, Daniel; Brand, Helmut R.
2014-03-01
We study the dynamics of systems with a polar dynamic preferred direction. Examples include the pattern-forming growth of bacteria (in a solvent, shoals of fish (moving in water currents), flocks of birds and migrating insects (flying in windy air). Because the preferred direction only exists dynamically, but not statically, the macroscopic variable of choice is the macroscopic velocity associated with the motion of the active units. We derive the macroscopic equations for such a system and discuss novel static, reversible and irreversible cross-couplings connected to this second velocity. We find a normal mode structure quite different compared to the static descriptions, as well as linear couplings between (active) flow and e.g. densities and concentrations due to the genuine two-fluid transport derivatives. On the other hand, we get, quite similar to the static case, a direct linear relation between the stress tensor and the structure tensor. This prominent ``active'' term is responsible for many active effects, meaning that our approach can describe those effects as well. In addition, we also deal with explicitly chiral systems, which are important for many active systems. In particular, we find an active flow-induced heat current specific for the dynamic chiral polar order.
Institute of Scientific and Technical Information of China (English)
2008-01-01
Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.
Full-scale HDR blowdown experiments as a tool for investigating dynamic fluid-structural coupling
International Nuclear Information System (INIS)
Krieg, R.; Schlechtendahl, E.G.; Scholl, K.-H.; Schumann, U.
1977-01-01
As an answer to rigorous safety requirements in reactor technology an experimental-theoretical program has been established to investigate safety-relevant mechanical aspects of LWR-blowdown accidents. Part of the program are several full-scale blowdown experiments which will be performed in the former HDR-reactor. As the conceptional study confirms, the primary goal is to find out, how big the safety margins of present LWR's in the case of a blowdown actually are, rather than simply to show that essential parts of the reactor will withstand such an accident. However, to determine the safety margins, the physical phenomena involved in the blowdown process must be understood and appropriate wave of description must be found. Therefore the experimental program is accompanied by the development of theoretical models and computer codes. A survey is given over existing methods for coupled fluid structural dynamics. The following approaches are used: - Specific finite difference-code for integrated treatment of both fluid and structure in 3D-geometry using the fast cyclic reduction scheme for solving Poisson's equation. - Modification of mass and stiffness matrices of FEM-models for shell dynamics by reducing the 3D incompressible fluid problem to 2D with the boundary integral equation method. This presently developed method has the capacity to deal with general problems in fluid-structural coupling. (Auth.)
Fluid Dynamics Theory, Computation, and Numerical Simulation
Pozrikidis, Constantine
2009-01-01
Fluid Dynamics: Theory, Computation, and Numerical Simulation is the only available book that extends the classical field of fluid dynamics into the realm of scientific computing in a way that is both comprehensive and accessible to the beginner. The theory of fluid dynamics, and the implementation of solution procedures into numerical algorithms, are discussed hand-in-hand and with reference to computer programming. This book is an accessible introduction to theoretical and computational fluid dynamics (CFD), written from a modern perspective that unifies theory and numerical practice. There are several additions and subject expansions in the Second Edition of Fluid Dynamics, including new Matlab and FORTRAN codes. Two distinguishing features of the discourse are: solution procedures and algorithms are developed immediately after problem formulations are presented, and numerical methods are introduced on a need-to-know basis and in increasing order of difficulty. Matlab codes are presented and discussed for ...
Fast reactor safety and computational thermo-fluid dynamics approaches
International Nuclear Information System (INIS)
Ninokata, Hisashi; Shimizu, Takeshi
1993-01-01
This article provides a brief description of the safety principle on which liquid metal cooled fast breeder reactors (LMFBRs) is based and the roles of computations in the safety practices. A number of thermohydraulics models have been developed to date that successfully describe several of the important types of fluids and materials motion encountered in the analysis of postulated accidents in LMFBRs. Most of these models use a mixture of implicit and explicit numerical solution techniques in solving a set of conservation equations formulated in Eulerian coordinates, with special techniques included to specific situations. Typical computational thermo-fluid dynamics approaches are discussed in particular areas of analyses of the physical phenomena relevant to the fuel subassembly thermohydraulics design and that involve describing the motion of molten materials in the core over a large scale. (orig.)
Dynamics of partial differential equations
Wayne, C Eugene
2015-01-01
This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties, and results about radiation damping where waves lose energy through radiation. The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equ...
An introduction to Computational Fluid Dynamics
DEFF Research Database (Denmark)
Sørensen, Lars Schiøtt
1999-01-01
CFD is the shortname for Computational Fluid Dynamics and is a numerical method by means of which we can analyze systems containing fluids. For instance systems dealing with heat flow or smoke control systems acting when a fire occur in a building.......CFD is the shortname for Computational Fluid Dynamics and is a numerical method by means of which we can analyze systems containing fluids. For instance systems dealing with heat flow or smoke control systems acting when a fire occur in a building....
Energy Technology Data Exchange (ETDEWEB)
Denicol, G.S. [Department of Physics, McGill University, 3600 University Street, Montreal, Quebec, H3A2T8 (Canada); Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main (Germany); Niemi, H. [Department of Physics, P.O. Box 35, FI-40014 University of Jyväskylä (Finland)
2013-05-02
We derive the non-equilibrium single-particle momentum distribution function of a hadron resonance gas. We then study the effects that this newly derived expression can have in the freeze-out description of fluid-dynamical models of heavy ion collisions and compare it with the method traditionally employed, the 14-moment approximation.
Algorithms for computational fluid dynamics n parallel processors
International Nuclear Information System (INIS)
Van de Velde, E.F.
1986-01-01
A study of parallel algorithms for the numerical solution of partial differential equations arising in computational fluid dynamics is presented. The actual implementation on parallel processors of shared and nonshared memory design is discussed. The performance of these algorithms is analyzed in terms of machine efficiency, communication time, bottlenecks and software development costs. For elliptic equations, a parallel preconditioned conjugate gradient method is described, which has been used to solve pressure equations discretized with high order finite elements on irregular grids. A parallel full multigrid method and a parallel fast Poisson solver are also presented. Hyperbolic conservation laws were discretized with parallel versions of finite difference methods like the Lax-Wendroff scheme and with the Random Choice method. Techniques are developed for comparing the behavior of an algorithm on different architectures as a function of problem size and local computational effort. Effective use of these advanced architecture machines requires the use of machine dependent programming. It is shown that the portability problems can be minimized by introducing high level operations on vectors and matrices structured into program libraries
Numerical implication of Riemann problem theory for fluid dynamics
International Nuclear Information System (INIS)
Menikoff, R.
1988-01-01
The Riemann problem plays an important role in understanding the wave structure of fluid flow. It is also crucial step in some numerical algorithms for accurately and efficiently computing fluid flow; Godunov method, random choice method, and from tracking method. The standard wave structure consists of shock and rarefaction waves. Due to physical effects such as phase transitions, which often are indistinguishable from numerical errors in an equation of state, anomalkous waves may occur, ''rarefaction shocks'', split waves, and composites. The anomalous waves may appear in numerical calculations as waves smeared out by either too much artificial viscosity or insufficient resolution. In addition, the equation of state may lead to instabilities of fluid flow. Since these anomalous effects due to the equation of state occur for the continuum equations, they can be expected to occur for all computational algorithms. The equation of state may be characterized by three dimensionless variables: the adiabatic exponent γ, the Grueneisen coefficient Γ, and the fundamental derivative G. The fluid flow anomalies occur when inequalities relating these variables are violated. 18 refs
Fluid dynamics theory, computation, and numerical simulation
Pozrikidis, C
2001-01-01
Fluid Dynamics Theory, Computation, and Numerical Simulation is the only available book that extends the classical field of fluid dynamics into the realm of scientific computing in a way that is both comprehensive and accessible to the beginner The theory of fluid dynamics, and the implementation of solution procedures into numerical algorithms, are discussed hand-in-hand and with reference to computer programming This book is an accessible introduction to theoretical and computational fluid dynamics (CFD), written from a modern perspective that unifies theory and numerical practice There are several additions and subject expansions in the Second Edition of Fluid Dynamics, including new Matlab and FORTRAN codes Two distinguishing features of the discourse are solution procedures and algorithms are developed immediately after problem formulations are presented, and numerical methods are introduced on a need-to-know basis and in increasing order of difficulty Matlab codes are presented and discussed for a broad...
Generalised fluid dynamics and quantum mechanics
Broer, L.J.F.
1974-01-01
A generalised theory of irrotational fluid flow is developed in hamiltonian form. This allows a systematic derivation of equations for momentum, energy and the rate of work. It is shown that a nonlinear field equation for weakly interacting condensed bosons as given by Gross1) and the one-electron
Equation-of-State Modeling of Phase Equilibria in Petroleum Fluids
DEFF Research Database (Denmark)
Jørgensen, Marianne
1996-01-01
The Soave-Redlich-Kwong (SRK) equation of state was used to investigate and develop several aspects of the modeling of natural petroleum fluids.A new method was presented for numerical evaluation of PVT experiments. This method was used in the estimation of binary interaction parameters. A comphr......The Soave-Redlich-Kwong (SRK) equation of state was used to investigate and develop several aspects of the modeling of natural petroleum fluids.A new method was presented for numerical evaluation of PVT experiments. This method was used in the estimation of binary interaction parameters....... A comphrensive study of pseudoization procedures is presented. It is concluded that the compared methods exhibit results of comparable accuracy, and that six to eight pseudocomponents are needed for optimal representation of petroleum fluids.Finally, it is investigated how well the EOS can represent the VLLE...
Principles of computational fluid dynamics
Wesseling, Pieter
2001-01-01
The book is aimed at graduate students, researchers, engineers and physicists involved in flow computations. An up-to-date account is given of the present state-of-the-art of numerical methods employed in computational fluid dynamics. The underlying numerical principles are treated with a fair amount of detail, using elementary mathematical analysis. Attention is given to difficulties arising from geometric complexity of the flow domain and of nonuniform structured boundary-fitted grids. Uniform accuracy and efficiency for singular perturbation problems is studied, pointing the way to accurate computation of flows at high Reynolds number. Much attention is given to stability analysis, and useful stability conditions are provided, some of them new, for many numerical schemes used in practice. Unified methods for compressible and incompressible flows are discussed. Numerical analysis of the shallow-water equations is included. The theory of hyperbolic conservation laws is treated. Godunov's order barrier and ho...
Electron transfer dynamics: Zusman equation versus exact theory
International Nuclear Information System (INIS)
Shi Qiang; Chen Liping; Nan Guangjun; Xu Ruixue; Yan Yijing
2009-01-01
The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations.
Extensive use of computational fluid dynamics in the upgrading of hydraulic turbines
Energy Technology Data Exchange (ETDEWEB)
Sabourin, M.; De Henau, V. [GEC Alsthom Electromechanical Inc., Tracy, PQ (Canada); Eremeef, R. [GEC Alsthom Neyrpic, Grenoble (France)
1995-12-31
The use of computational fluid flow dynamics (CFD) and the Navier Stokes equations by GEC Alsthom for turbine rehabilitation were discussed. The process of runner rehabilitation was discussed from a fluid flow perspective, which accounts for the spiral case-distributor set and draft tube. The Kootenay turbine rehabilitation was described with regard to it spiral case and stay vane. The numerical analysis used to model upstream components was explained. The influence of draft tube effects was emphasized as an important efficiency factor. The differences between draft tubes at Sir Adam Beck 2 and La Grande 2 were discussed. Computational fluid flow modelling was claimed to have produced global performance enhancements in a reasonably short time, and at a reasonable cost. 6 refs., 6 figs., 4 tabs.
Computational Fluid Dynamics (CFD) simulations of a Heisenberg Vortex Tube
Bunge, Carl; Sitaraman, Hariswaran; Leachman, Jake
2017-11-01
A 3D Computational Fluid Dynamics (CFD) simulation of a Heisenberg Vortex Tube (HVT) is performed to estimate cooling potential with cryogenic hydrogen. The main mechanism driving operation of the vortex tube is the use of fluid power for enthalpy streaming in a highly turbulent swirl in a dual-outlet tube. This enthalpy streaming creates a temperature separation between the outer and inner regions of the flow. Use of a catalyst on the peripheral wall of the centrifuge enables endothermic conversion of para-ortho hydrogen to aid primary cooling. A κ- ɛ turbulence model is used with a cryogenic, non-ideal equation of state, and para-orthohydrogen species evolution. The simulations are validated with experiments and strategies for parametric optimization of this device are presented.
Investigation of two and three parameter equations of state for cryogenic fluids
International Nuclear Information System (INIS)
Jenkins, S.L.; Majumdar, A.K.; Hendricks, R.C.
1990-01-01
Two-phase flows are a common occurrence in cryogenic engines and an accurate evaluation of the heat-transfer coefficient in two-phase flow is of significant importance in their analysis and design. The thermodynamic equation of state plays a key role in calculating the heat transfer coefficient which is a function of thermodynamic and thermophysical properties. An investigation has been performed to study the performance of two- and three-parameter equations of state to calculate the compressibility factor of cryogenic fluids along the saturation loci. The two-parameter equations considered here are van der Waals and Redlich-Kwong equations of state. The three-parameter equation represented here is the generalized Benedict-Webb-Rubin (BWR) equation of Lee and Kesler. Results have been compared with the modified BWR equation of Bender and the extended BWR equations of Stewart. Seven cryogenic fluids have been tested; oxygen, hydrogen, helium, nitrogen, argon, neon, and air. The performance of the generalized BWR equation is poor for hydrogen and helium. The van der Waals equation is found to be inaccurate for air near the critical point. For helium, all three equations of state become inaccurate near the critical point. 13 refs
DEFF Research Database (Denmark)
Estupinan, Edgar Alberto; Santos, Ilmar
2009-01-01
elements are supported by fluid film bearings, where the hydrodynamic interaction forces are described by the Reynolds equation. The system of nonlinear equations is numerically solved for three different restrictive conditions of the motion of the crank, where the third case takes into account lateral...... and tilting oscillations of the extremity of the crankshaft. The numerical results of the behaviour of the journal bearings for each case are presented giving some insights into design parameters such as, maximum oil film pressure, minimum oil film thickness, maximum vibration levels and dynamic reaction...
Regularity criteria for the 3D magneto-micropolar fluid equations via ...
Indian Academy of Sciences (India)
We consider sufficient conditions to ensure the smoothness of solutions to 3D magneto-micropolar fluid equations. It involves only the direction of the velocity and the magnetic field. Our result extends to the cases of Navier–Stokes and MHD equations.
Directory of Open Access Journals (Sweden)
Panayotounakos D. E.
1996-01-01
Full Text Available We develop a new unique technique in constructing closed-form solutions for several nonlinear partial differential systems appearing in fluid mechanics and gas dynamics. The obtained solutions include fewer arbitrary functions than needed for general solutions, fact that permits us to specify them according to the initial state, or the geometry, of each specific problem under consideration. In order to apply the before mentioned technique we construct closed-form solutions concerning the gas-dynamic equations with constant pressure, the dynamic equations of an ideal gas in isentropic flow, and the two-dimensional incompressible boundary layer flow.
Extensive use of computational fluid dynamics in the upgrading of hydraulic turbines
Energy Technology Data Exchange (ETDEWEB)
Sabourin, M.; Eremeef, R.; De Henau, V.
1995-12-31
Computational fluid dynamics codes, based on turbulent Navier-Stokes equations, allow evaluation of the hydraulic losses of each turbine component with precision. Using those codes with the new generation of computers enables a wide variety of component geometries to be modelled and compared to the original designs under flow conditions obtained from testing, at a reasonable cost and in a relatively short time. This paper reviews the actual method used in the design of a solution to a turbine rehabilitation project involving runner replacement, redesign of upstream components (stay vanes and wicket gates), and downstream components (draft tubes and runner outlets). The paper shows how computational fluid dynamics can help hydraulic engineers to obtain valuable information not only on performance enhancement but also on the phenomena that produce the enhancement, and to reduce the variety of modifications to be tested.
The effect of sediments on turbulent plume dynamics in a stratified fluid
Stenberg, Erik; Ezhova, Ekaterina; Brandt, Luca
2017-11-01
We report large eddy simulation results of sediment-loaded turbulent plumes in a stratified fluid. The configuration, where the plume is discharged from a round source, provides an idealized model of subglacial discharge from a submarine tidewater glacier and is a starting point for understanding the effect of sediments on the dynamics of the rising plume. The transport of sediments is modeled by means of an advection-diffusion equation where sediment settling velocity is taken into account. We initially follow the experimental setup of Sutherland (Phys. Rev. Fluids, 2016), considering uniformly stratified ambients and further extend the work to pycnocline-type stratifications typical of Greenland fjords. Apart from examining the rise height, radial spread and intrusion of the rising plume, we gain further insights of the plume dynamics by extracting turbulent characteristics and the distribution of the sediments inside the plume.
Aerodynamic research of a racing car based on wind tunnel test and computational fluid dynamics
Directory of Open Access Journals (Sweden)
Wang Jianfeng
2018-01-01
Full Text Available Wind tunnel test and computational fluid dynamics (CFD simulation are two main methods for the study of automotive aerodynamics. CFD simulation software solves the results in calculation by using the basic theory of aerodynamic. Calculation will inevitably lead to bias, and the wind tunnel test can effectively simulate the real driving condition, which is the most effective aerodynamics research method. This paper researches the aerodynamic characteristics of the wing of a racing car. Aerodynamic model of a racing car is established. Wind tunnel test is carried out and compared with the simulation results of computational fluid dynamics. The deviation of the two methods is small, and the accuracy of computational fluid dynamics simulation is verified. By means of CFD software simulation, the coefficients of six aerodynamic forces are fitted and the aerodynamic equations are obtained. Finally, the aerodynamic forces and torques of the racing car travel in bend are calculated.
Computational fluid dynamic applications
Energy Technology Data Exchange (ETDEWEB)
Chang, S.-L.; Lottes, S. A.; Zhou, C. Q.
2000-04-03
The rapid advancement of computational capability including speed and memory size has prompted the wide use of computational fluid dynamics (CFD) codes to simulate complex flow systems. CFD simulations are used to study the operating problems encountered in system, to evaluate the impacts of operation/design parameters on the performance of a system, and to investigate novel design concepts. CFD codes are generally developed based on the conservation laws of mass, momentum, and energy that govern the characteristics of a flow. The governing equations are simplified and discretized for a selected computational grid system. Numerical methods are selected to simplify and calculate approximate flow properties. For turbulent, reacting, and multiphase flow systems the complex processes relating to these aspects of the flow, i.e., turbulent diffusion, combustion kinetics, interfacial drag and heat and mass transfer, etc., are described in mathematical models, based on a combination of fundamental physics and empirical data, that are incorporated into the code. CFD simulation has been applied to a large variety of practical and industrial scale flow systems.
Multicomponent fluid flow analysis using a new set of conservation equations
International Nuclear Information System (INIS)
Kamali, Reza; Emdad, Homayoon; Alishahi, Mohammad M
2008-01-01
In this work hydrodynamics of multicomponent ideal gas mixtures have been studied. Starting from the kinetic equations, the Eulerian approach is used to derive a new set of conservation equations for the multicomponent system where each component may have different velocity and kinetic temperature. The equations are based on the Grad's method of moment derived from the kinetic model in a relaxation time approximation (RTA). Based on this model which contains separate equation sets for each component of the system, a computer code has been developed for numerical computation of compressible flows of binary gas mixture in generalized curvilinear boundary conforming coordinates. Since these equations are similar to the Navier-Stokes equations for the single fluid systems, the same numerical methods are applied to these new equations. The Roe's numerical scheme is used to discretize the convective terms of governing fluid flow equations. The prepared algorithm and the computer code are capable of computing and presenting flow fields of each component of the system separately as well as the average flow field of the multicomponent gas system as a whole. Comparison of the present code results with those of a more common algorithm based on the mixture theory in a supersonic converging-diverging nozzle provides the validation of the present formulation. Afterwards, a more involved nozzle cooling problem with a binary ideal gas (helium-xenon) is chosen to compare the present results with those of the ordinary mixture theory. The present model provides the details of the flow fields of each component separately which is not available otherwise. It is also shown that the separate fluids treatment, such as the present study, is crucial when considering time scales on the order of (or shorter than) the intercollisions relaxation times.
Approaching multiphase flows from the perspective of computational fluid dynamics
International Nuclear Information System (INIS)
Banas, A.O.
1992-01-01
Thermalhydraulic simulation methodologies based on subchannel and porous-medium concepts are briefly reviewed and contrasted with the general approach of Computational Fluid Dynamics (CFD). An outline of the advanced CFD methods for single-phase turbulent flows is followed by a short discussion of the unified formulation of averaged equations for turbulent and multiphase flows. Some of the recent applications of CFD at Chalk River Laboratories are discussed, and the complementary role of CFD with regard to the established thermalhydraulic methods of analysis is indicated. (author). 8 refs
Computational fluid dynamics modeling of mixed convection flows in buildings enclosures
Energy Technology Data Exchange (ETDEWEB)
Kayne, Alexander; Agarwal, Ramesh K. [Department of Mechanical Engineering and Materials Science, Washington University, St. Louis, MO 63130 (United States)
2013-07-01
In recent years Computational Fluid Dynamics (CFD) simulations are increasingly used to model the air circulation and temperature environment inside the rooms of residential and office buildings to gain insight into the relative energy consumptions of various HVAC systems for cooling/heating for climate control and thermal comfort. This requires accurate simulation of turbulent flow and heat transfer for various types of ventilation systems using the Reynolds-Averaged Navier-Stokes (RANS) equations of fluid dynamics. Large Eddy Simulation (LES) or Direct Numerical Simulation (DNS) of Navier-Stokes equations is computationally intensive and expensive for simulations of this kind. As a result, vast majority of CFD simulations employ RANS equations in conjunction with a turbulence model. In order to assess the modeling requirements (mesh, numerical algorithm, turbulence model etc.) for accurate simulations, it is critical to validate the calculations against the experimental data. For this purpose, we use three well known benchmark validation cases, one for natural convection in 2D closed vertical cavity, second for forced convection in a 2D rectangular cavity and the third for mixed convection in a 2D square cavity. The simulations are performed on a number of meshes of different density using a number of turbulence models. It is found that k-epsilon two-equation turbulence model with a second-order algorithm on a reasonable mesh gives the best results. This information is then used to determine the modeling requirements (mesh, numerical algorithm, turbulence model etc.) for flows in 3D enclosures with different ventilation systems. In particular two cases are considered for which the experimental data is available. These cases are (1) air flow and heat transfer in a naturally ventilated room and (2) airflow and temperature distribution in an atrium. Good agreement with the experimental data and computations of other investigators is obtained.
Energy Technology Data Exchange (ETDEWEB)
Xiao, Jianjun; Travis, Jack; Royl, Peter; Necker, Gottfried; Svishchev, Anatoly; Jordan, Thomas
2016-07-01
Karlsruhe Institute of Technology (KIT) is developing the parallel computational fluid dynamics code GASFLOW-MPI as a best-estimate tool for predicting transport, mixing, and combustion of hydrogen and other gases in nuclear reactor containments and other facility buildings. GASFLOW-MPI is a finite-volume code based on proven computational fluid dynamics methodology that solves the compressible Navier-Stokes equations for three-dimensional volumes in Cartesian or cylindrical coordinates.
Probing the Chaotic Dynamics of Fluids using Insights from Coupled Map Lattices
Barbish, Johnathon; Xu, Mu; Paul, Mark
2017-11-01
Many difficult fluid challenges exhibit high-dimensional spatiotemporal chaos. Natural examples include the dynamics of the atmosphere and oceans. New insights have been gained by studying canonical fluid problems such as Rayleigh-Bénard convection where significant progress has been made using large-scale computations of the partial differential equations that describe the fluid flow. However, these computations remain very expensive which makes it difficult, if not currently impossible, to explore new ideas that require large sample sets, vast sweeps of parameter space, and long-time statistics. We study these questions using coupled map lattices (CML) in one and two dimensions. We compute the covariant Lyapunov vectors to probe fundamental features of the CML's including the Lyapunov spectrum, fractal dimension, and the principal angle between the stable and unstable manifolds. We are particularly interested in the role of a conservation law on the chaotic dynamics, the use of ideas from equilibrium thermodynamics to yield a coarse-grained representation, and in the development of reduced order models. This work is supported by NSF DMS-1622299.
Theoretical equation of state for classical fluids. I. Test by perturbation theory
International Nuclear Information System (INIS)
Gil-Villegas, A.; Chavez, M.; Del Rio, F.
1993-01-01
This paper shows how to construct the theoretical equation of state (TEOS) of a classical simple fluid. The theory relies on the mean collisional diameter and range, and maps the thermodynamical properties of the fluid into those of an equivalent square-well (ESW) fluid of appropriate depth ε , diameter σ and range R. It is shown that the ESW has the same pressure as the fluid of interest. Hence the THEOS of any simple fluid takes the form of a SW EOS of the given ε , σ and R. The theory is applied to a Lennard-Jones (LJ) system in a first-order perturbation. The mapping equation have a physical solution for densities where the SW EOS is accurate; the resulting LJ TEOS agrees very well with the results of computer simulations, and compares favorably with the recent TEOS developed by Song and Mason. (Author). 17 refs, 7 figs, 1 tab
Superfluid kinetic equation approach to the dynamics of the 3He A-B phase boundary
International Nuclear Information System (INIS)
Palmeri, J.
1990-01-01
The dynamics of the A-B phase boundary is studied using a nonequilibrium theory inspired by the microscopic approach to flux flow in type-II superconductors, namely a generalized two-fluid model consisting of coupled dynamical equations for the superfluid order parameter and the quasiparticle fluid. The interface mobility is obtained to lowest order in the front velocity in three different dynamical regimes: the gapless, hydrodynamic, and ballistic. Experiments have so far only been performed in the ballistic regime, and in this regime we find that, if only Andreev scattering processes are accounted for in the interface mobility, then the theoretical predictions for the terminal velocity of the planar interface are too big by a factor ∼2. From this we conclude that there may be other important contributions to the interface mobility in the ballistic regime, and we discuss a few possibilities
Strongly Coupled Fluid-Body Dynamics in the Immersed Boundary Projection Method
Wang, Chengjie; Eldredge, Jeff D.
2014-11-01
A computational algorithm is developed to simulate dynamically coupled interaction between fluid and rigid bodies. The basic computational framework is built upon a multi-domain immersed boundary method library, whirl, developed in previous work. In this library, the Navier-Stokes equations for incompressible flow are solved on a uniform Cartesian grid by the vorticity-based immersed boundary projection method of Colonius and Taira. A solver for the dynamics of rigid-body systems is also included. The fluid and rigid-body solvers are strongly coupled with an iterative approach based on the block Gauss-Seidel method. Interfacial force, with its intimate connection with the Lagrange multipliers used in the fluid solver, is used as the primary iteration variable. Relaxation, developed from a stability analysis of the iterative scheme, is used to achieve convergence in only 2-4 iterations per time step. Several two- and three-dimensional numerical tests are conducted to validate and demonstrate the method, including flapping of flexible wings, self-excited oscillations of a system of linked plates and three-dimensional propulsion of flexible fluked tail. This work has been supported by AFOSR, under Award FA9550-11-1-0098.
Energy Technology Data Exchange (ETDEWEB)
Lee, Seung Jun; Park, Ik Kyu; Yoon, Han Young [Thermal-Hydraulic Safety Research Division, Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Jae, Byoung [School of Mechanical Engineering, Chungnam National University, Daejeon (Korea, Republic of)
2017-01-15
Two-fluid equations are widely used to obtain averaged behaviors of two-phase flows. This study addresses a problem that may arise when the two-fluid equations are used for multi-dimensional bubbly flows. If steady drag is the only accounted force for the interfacial momentum transfer, the disperse-phase velocity would be the same as the continuous-phase velocity when the flow is fully developed without gravity. However, existing momentum equations may show unphysical results in estimating the relative velocity of the disperse phase against the continuous-phase. First, we examine two types of existing momentum equations. One is the standard two-fluid momentum equation in which the disperse-phase is treated as a continuum. The other is the averaged momentum equation derived from a solid/ fluid particle motion. We show that the existing equations are not proper for multi-dimensional bubbly flows. To resolve the problem mentioned above, we modify the form of the Reynolds stress terms in the averaged momentum equation based on the solid/fluid particle motion. The proposed equation shows physically correct results for both multi-dimensional laminar and turbulent flows.
Hyperbolic partial differential equations
Witten, Matthew
1986-01-01
Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M
Brehm, Christoph; Barad, Michael F.; Kiris, Cetin C.
2016-01-01
An immersed boundary method for the compressible Navier-Stokes equation and the additional infrastructure that is needed to solve moving boundary problems and fully coupled fluid-structure interaction is described. All the methods described in this paper were implemented in NASA's LAVA solver framework. The underlying immersed boundary method is based on the locally stabilized immersed boundary method that was previously introduced by the authors. In the present paper this method is extended to account for all aspects that are involved for fluid structure interaction simulations, such as fast geometry queries and stencil computations, the treatment of freshly cleared cells, and the coupling of the computational fluid dynamics solver with a linear structural finite element method. The current approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems in 2D and 3D. As part of the validation procedure, results from the second AIAA aeroelastic prediction workshop are also presented. The current paper is regarded as a proof of concept study, while more advanced methods for fluid structure interaction are currently being investigated, such as geometric and material nonlinearities, and advanced coupling approaches.
International Nuclear Information System (INIS)
Yoon, Han Ik; Son, In Soo
2005-01-01
In this paper, we studied about the effect of the open crack and a tip mass on the dynamic behavior of a cantilever pipe conveying fluid with a moving mass. The equation of motion is derived by using Lagrange's equation and analyzed by numerical method. The cantilever pipe is modelled by the Euler-Bernoulli beam theory. The crack section is represented by a local flexibility matrix connecting two undamaged pipe segments. The influences of the crack, the moving mass, the tip mass and its moment of inertia, the velocity of fluid, and the coupling of these factors on the vibration mode, the frequency, and the tip-displacement of the cantilever pipe are analytically clarified
Travelling wave solutions for a surface wave equation in fluid mechanics
Directory of Open Access Journals (Sweden)
Tian Yi
2016-01-01
Full Text Available This paper considers a non-linear wave equation arising in fluid mechanics. The exact traveling wave solutions of this equation are given by using G'/G-expansion method. This process can be reduced to solve a system of determining equations, which is large and difficult. To reduce this process, we used Wu elimination method. Example shows that this method is effective.
MINI-TRAC code: a driver program for assessment of constitutive equations of two-fluid model
International Nuclear Information System (INIS)
Akimoto, Hajime; Abe, Yutaka; Ohnuki, Akira; Murao, Yoshio
1991-05-01
MINI-TRAC code, a driver program for assessment of constitutive equations of two-fluid model, has been developed to perform assessment and improvement of constitutive equations of two-fluid model widely and efficiently. The MINI-TRAC code uses one-dimensional conservation equations for mass, momentum and energy based on the two-fluid model. The code can work on a personal computer because it can be operated with a core memory size less than 640 KB. The MINI-TRAC code includes constitutive equations of TRAC-PF1/MOD1 code, TRAC-BF1 code and RELAP5/MOD2 code. The code is modulated so that one can easily change constitutive equations to perform a test calculation. This report is a manual of the MINI-TRAC code. The basic equations, numerics, constitutive, equations included in the MINI-TRAC code will be described. The user's manual such as input description will be presented. The program structure and contents of main variables will also be mentioned in this report. (author)
Relativistic Fluid Dynamics Far From Local Equilibrium
Romatschke, Paul
2018-01-01
Fluid dynamics is traditionally thought to apply only to systems near local equilibrium. In this case, the effective theory of fluid dynamics can be constructed as a gradient series. Recent applications of resurgence suggest that this gradient series diverges, but can be Borel resummed, giving rise to a hydrodynamic attractor solution which is well defined even for large gradients. Arbitrary initial data quickly approaches this attractor via nonhydrodynamic mode decay. This suggests the existence of a new theory of far-from-equilibrium fluid dynamics. In this Letter, the framework of fluid dynamics far from local equilibrium for a conformal system is introduced, and the hydrodynamic attractor solutions for resummed Baier-Romatschke-Son-Starinets-Stephanov theory, kinetic theory in the relaxation time approximation, and strongly coupled N =4 super Yang-Mills theory are identified for a system undergoing Bjorken flow.
Collisional drift fluid equations and implications for drift waves
International Nuclear Information System (INIS)
Pfirsch, Dieter; Correa-Restrepo, Dario
1996-01-01
The usual theoretical description of drift-wave turbulence (considered to be one possible cause of anomalous transport in a plasma), e.g. the Hasegawa-Wakatani theory, makes use of various approximations, the effects of which are extremely difficult to assess. This concerns in particular the conservation laws for energy and momentum. The latter law is important in relation to charge separation and the resulting electric fields, which are possibly related to the L-H transition. Energy conservation is crucial to the stability behaviour, it will be discussed by means of an example. New collisional multi-species drift-fluid equations were derived by a new method which yields, in a transparent way, conservation of energy and total angular momentum and the law for energy dissipation. Both electrostatic and electromagnetic field variations are considered. The only restriction involved is the validity of the drift approximation; in particular, there are no assumptions restricting the geometry of the system. The method is based primarily on a Lagrangian for dissipationless fluids in the drift approximation with isotropic pressures. The dissipative terms are introduced by adding corresponding terms to the ideal equations of motion and of the pressures. The equations of motion, of course, no longer result from a Lagrangian via Hamilton's principle. However, their relation to the ideal equations also implies a relation to the ideal Lagrangian, which can be used to advantage. Instead of introducing heat conduction one can also assume isothermal behaviour, e.g. T v (x) = constant. Assumptions of this kind are often made in the literature. The new method of introducing dissipation is not restricted to the present kind of theory; it can equally well be applied to theories such as multi-fluid theories without using the drift approximation of the present paper. (author)
Conservation properties and potential systems of vorticity-type equations
International Nuclear Information System (INIS)
Cheviakov, Alexei F.
2014-01-01
Partial differential equations of the form divN=0, N t +curl M=0 involving two vector functions in R 3 depending on t, x, y, z appear in different physical contexts, including the vorticity formulation of fluid dynamics, magnetohydrodynamics (MHD) equations, and Maxwell's equations. It is shown that these equations possess an infinite family of local divergence-type conservation laws involving arbitrary functions of space and time. Moreover, it is demonstrated that the equations of interest have a rather special structure of a lower-degree (degree two) conservation law in R 4 (t,x,y,z). The corresponding potential system has a clear physical meaning. For the Maxwell's equations, it gives rise to the scalar electric and the vector magnetic potentials; for the vorticity equations of fluid dynamics, the potentialization inverts the curl operator to yield the fluid dynamics equations in primitive variables; for MHD equations, the potential equations yield a generalization of the Galas-Bogoyavlenskij potential that describes magnetic surfaces of ideal MHD equilibria. The lower-degree conservation law is further shown to yield curl-type conservation laws and determined potential equations in certain lower-dimensional settings. Examples of new nonlocal conservation laws, including an infinite family of nonlocal material conservation laws of ideal time-dependent MHD equations in 2+1 dimensions, are presented
Experimental and theoretical advances in fluid dynamics
Klapp, Jaime; Fuentes, Oscar Velasco
2011-01-01
The book is comprised of lectures and selected contributions presented at the Enzo Levi and XVI Annual Meeting of the Fluid Dynamic Division of the Mexican Physical Society in 2010. It is aimed at fourth year undergraduate and graduate students, as well as scientists in the fields of physics, engineering and chemistry with an interest in fluid dynamics from the experimental and theoretical point of view. The lectures are introductory and avoid the use of complicated mathematics. The other selected contributions are also geared to fourth year undergraduate and graduate students. The fluid dynam
Dynamics of two coaxial cylindrical shells containing viscous fluid
International Nuclear Information System (INIS)
Yeh, T.T.; Chen, S.S.
1976-09-01
This study was motivated by the need to design the thermal shield in reactor internals and other system components to avoid detrimental flow-induced vibrations. The system component is modeled as two coaxial shells separated by a viscous fluid. In the analysis, Flugge's shell equations of motion and linearized Navier-Stokes equation for viscous fluid are employed. First, a traveling-wave type solution is taken for shells and fluid. Then, from the interface conditions between the shells and fluid, the solution for the fluid medium is expressed in terms of shell displacements. Finally, using the shell equations of motion gives the frequency equation, from which the natural frequency, mode shape, and modal damping ratio of coupled modes can be calculated. The analytical results show a fairly good qualitative agreement with the published experimental data. Some important conclusions are as follows: (1) In computing the natural frequencies and mode shapes of uncoupled modes and coupled modes, the fluid may be considered inviscid and incompressible. (2) There exists out-of-phase and in-phase modes. The lowest natural frequency is always associated with the out-of-phase mode. (3) The lowest natural frequency of coupled modes is lower than the uncoupled modes. (4) The fluid viscosity contributes significantly to damping, in particular, the modal damping of the out-of-phase modes isrelatively large for small gaps. (5) If the fluid gap is small, or the fluid viscosity is relatively high, the simulation of the vibration Reynolds number should be included to ensure that modal damping of the model is properly accounted for. With the presented analysis and results, the frequency and damping characteristics can be analyzed and design parameters can be related to frequency and damping
Applied Computational Fluid Dynamics at NASA Ames Research Center
Holst, Terry L.; Kwak, Dochan (Technical Monitor)
1994-01-01
The field of Computational Fluid Dynamics (CFD) has advanced to the point where it can now be used for many applications in fluid mechanics research and aerospace vehicle design. A few applications being explored at NASA Ames Research Center will be presented and discussed. The examples presented will range in speed from hypersonic to low speed incompressible flow applications. Most of the results will be from numerical solutions of the Navier-Stokes or Euler equations in three space dimensions for general geometry applications. Computational results will be used to highlight the presentation as appropriate. Advances in computational facilities including those associated with NASA's CAS (Computational Aerosciences) Project of the Federal HPCC (High Performance Computing and Communications) Program will be discussed. Finally, opportunities for future research will be presented and discussed. All material will be taken from non-sensitive, previously-published and widely-disseminated work.
Energy Technology Data Exchange (ETDEWEB)
Xiao, Jianjun; Travis, Jack; Royl, Peter; Necker, Gottfried; Svishchev, Anatoly; Jordan, Thomas
2016-07-01
Karlsruhe Institute of Technology (KIT) is developing the parallel computational fluid dynamics code GASFLOW-MPI as a best-estimate tool for predicting transport, mixing, and combustion of hydrogen and other gases in nuclear reactor containments and other facility buildings. GASFLOW-MPI is a finite-volume code based on proven computational fluid dynamics methodology that solves the compressible Navier-Stokes equations for three-dimensional volumes in Cartesian or cylindrical coordinates.
Dynamic analysis of electro- and magneto-rheological fluid dampers using duct flow models
International Nuclear Information System (INIS)
Esteki, Kambiz; Bagchi, Ashutosh; Sedaghati, Ramin
2014-01-01
Magneto-rheological (MR) and electro-rheological (ER) fluid dampers provide a semi-active control mechanism for suppressing vibration responses of a structure. MR and ER fluids change their viscosity under the influence of magnetic and electrical fields, respectively, which facilitates automatic control when these fluids are used in damping devices. The existing models, namely the phenomenological models for simulating the behavior of MR and ER dampers, rely on various parameters determined experimentally by the manufacturers for each damper configuration. It is of interest to develop mechanistic models of these dampers which can be applied to various configurations so that their fundamental characteristics can be studied to develop flexible design solutions for smart structures. This paper presents a formulation for dynamic analysis of electro-rheological (ER) and magneto-rheological (MR) fluid dampers in flow and mix mode configurations under harmonic and random excitations. The procedure employs the vorticity transport equation and the regularization function to deal with the unsteady flow and nonlinear behavior of ER/MR fluid in general motion. The finite difference method has been used to solve the governing differential equations. Using the developed approach, the damping force of ER/MR dampers can be calculated under any type of excitation. (paper)
Hamiltonian models for the Madelung fluid and generalized Langevin equations
International Nuclear Information System (INIS)
Nonnenmacher, T.F.
1985-01-01
We present a Hamiltonian formulation of some type of an 'electromagnetic' Madelung fluid leading to a fluid mechanics interpretation of the Aharonov-Bohm effect and to a subsidary condition to be required in order to make the correspondence between Schroedinger's quantum mechanics and Madelung's fluid mechanics unique. Then we discuss some problems related with the Brownian oscillator. Our aim is to start out with a Hamiltonian for the composite system with surrounding heat bath) and to finally arrive at a stochastic differential equation with completely determined statistical properties. (orig./HSI)
Dissipative fluid mechanics of nuclei
International Nuclear Information System (INIS)
Morgenstern, B.
1987-11-01
With the aim to describe nucleus-nucleus collisions at low energies in the present thesis for the first time dissipative fluid dynamics for large-amplitude nuclear motion have been formulated. Thereby the collective dynamics are described in a scaling approximation in which the wave function of the system is distorted by a vortex-free velocity field. For infintely extended nuclear matter this scaling of the wave functions leads to a deformation of the Fermi sphere. Two-body collisions destroy the collective deformation of the Fermi sphere and yield so the dissipative contribution of the motion. Equations of motion for a finite set of collective variables and a field equation for the collective velocity potential in the limit of infinitely many degrees of freedom were developed. In the elastic limit oscillations around the equilibrium position are described. For small collective amplitudes and vortex-free velocity fields the integrodifferential equation for the velocity potential in the elastic limit could be transformed to the divergence of the field equation of fluid dynamics. In the dissipative limit an equation results which is similar to the Navier-Stokes equation and transforms to the divergence of the Navier-Stokes equation for vortex-free fields. It was shown that generally the dynamics of the many-body system is described by non-Markovian equations. (orig./HSI) [de
International Nuclear Information System (INIS)
Melo, Ana Cristina Bezerra Azedo de
2004-12-01
The fluid dynamic behavior of a riser in a cold type FCC model was investigated by means of catalyst concentration distribution measured with gamma attenuation and simulated with a mathematical model. In the riser of the cold model, MEF, 0,032 m in diameter, 2,30 m in length the fluidized bed, whose components are air and FCC catalyst, circulates. The MEF is operated by automatic control and instruments for measuring fluid dynamic variables. An axial catalyst concentration distribution was measured using an Am-241 gamma source and a NaI detector coupled to a multichannel provided with a software for data acquisition and evaluation. The MEF was adapted for a fluid dynamic model validation which describes the flow in the riser, for example, by introducing an injector for controlling the solid flow in circulation. Mathematical models were selected from literature, analyzed and tested to simulate the fluid dynamic of the riser. A methodology for validating fluid dynamic models was studied and implemented. The stages of the work were developed according to the validation methodology, such as data planning experiments, study of the equations which describe the fluidodynamic, computational solvers application and comparison with experimental data. Operational sequences were carried out keeping the MEF conditions for measuring catalyst concentration and simultaneously measuring the fluid dynamic variables, velocity of the components and pressure drop in the riser. Following this, simulated and experimental values were compared and statistical data treatment done, aiming at the required precision to validate the fluid dynamic model. The comparison tests between experimental and simulated data were carried out under validation criteria. The fluid dynamic behavior of the riser was analyzed and the results and the agreement with literature were discussed. The adopt model was validated under the MEF operational conditions, for a 3 to 6 m/s gas velocity in the riser and a slip
Nambu brackets in fluid mechanics and magnetohydrodynamics
International Nuclear Information System (INIS)
Salazar, Roberto; Kurgansky, Michael V
2010-01-01
Concrete examples of the construction of Nambu brackets for equations of motion (both 3D and 2D) of Boussinesq stratified fluids and also for magnetohydrodynamical equations are given. It serves a generalization of Hamiltonian formulation for the considered equations of motion. Two alternative Nambu formulations are proposed, first by using fluid dynamical (kinetic) helicity and/or enstrophy as constitutive elements and second, by using the existing conservation laws of the governing equation.
Thermodynamic Fluid Equations-of-State
Directory of Open Access Journals (Sweden)
Leslie V. Woodcock
2018-01-01
Full Text Available As experimental measurements of thermodynamic properties have improved in accuracy, to five or six figures, over the decades, cubic equations that are widely used for modern thermodynamic fluid property data banks require ever-increasing numbers of terms with more fitted parameters. Functional forms with continuity for Gibbs density surface ρ(p,T which accommodate a critical-point singularity are fundamentally inappropriate in the vicinity of the critical temperature (Tc and pressure (pc and in the supercritical density mid-range between gas- and liquid-like states. A mesophase, confined within percolation transition loci that bound the gas- and liquid-state by third-order discontinuities in derivatives of the Gibbs energy, has been identified. There is no critical-point singularity at Tc on Gibbs density surface and no continuity of gas and liquid. When appropriate functional forms are used for each state separately, we find that the mesophase pressure functions are linear. The negative and positive deviations, for both gas and liquid states, on either side of the mesophase, are accurately represented by three or four-term virial expansions. All gaseous states require only known virial coefficients, and physical constants belonging to the fluid, i.e., Boyle temperature (TB, critical temperature (Tc, critical pressure (pc and coexisting densities of gas (ρcG and liquid (ρcL along the critical isotherm. A notable finding for simple fluids is that for all gaseous states below TB, the contribution of the fourth virial term is negligible within experimental uncertainty. Use may be made of a symmetry between gas and liquid states in the state function rigidity (dp/dρT to specify lower-order liquid-state coefficients. Preliminary results for selected isotherms and isochores are presented for the exemplary fluids, CO2, argon, water and SF6, with focus on the supercritical mesophase and critical region.
International Nuclear Information System (INIS)
Jordan, T.
1996-01-01
Some aspects concerning the coupling of quasi-stationary electromagnetics and the dynamics of structure and fluid are investigated. The necessary equations are given in a dimensionless form. The dimensionless parameters in these equations are used to evaluate the importance of the different coupling effects. A finite element formulation of the eddy-current damping in solid structures is developed. With this formulation, an existing finite element method (FEM) structural dynamics code is extended and coupled to an FEM eddy-current code. With this program system, the influence of the eddy-current damping on the dynamic loading of the dual coolant blanket during a centered plasma disruption is determined. The analysis proves that only in loosely fixed or soft structures will eddy-current damping considerably reduce the resulting stresses. Additionally, the dynamic behavior of the liquid metal in the blankets' poloidal channels is described with a simple two-dimensional magnetohydrodynamic approach. The analysis of the dimensionless parameters shows that for small-scale experiments, which are designed to model the coupled electromagnetic and structural/fluid dynamic effects in such a blanket, the same magnetic fields must be applied as in the real fusion device. This will be the easiest way to design experiments that produce transferable results. 10 refs., 7 figs
Linking rigid multibody systems via controllable thin fluid films
DEFF Research Database (Denmark)
Estupinan, Edgar Alberto; Santos, Ilmar
2009-01-01
, this paper gives a theoretical contribution to the combined fields of fluid–structure interaction and vibration control. The methodology is applied to a reciprocating linear compressor, where the dynamics of the mechanical components are described with help of multibody dynamics. The crank is linked......This work deals with the mathematical modelling of multibody systems interconnected via thin fluid films. The dynamics of the fluid films can be actively controlled by means of different types of actuators, allowing significant vibration reduction of the system components. In this framework...... to the rotor via a thin fluid film, where the hydrodynamic pressure is described by the Reynolds equation, which is modified to accommodate the controllable lubrication conditions. The fluid film forces are coupled to the set of nonlinear equations that describes the dynamics of the reciprocating linear...
Effective equations for fluid-structure interaction with applications to poroelasticity
Brown, Donald; Popov, Peter V.; Efendiev, Yalchin R.
2012-01-01
Modeling of fluid-solid interactions in porous media is a challenging and computationally demanding task. Due to the multiscale nature of the problem, simulating the flow and mechanics by direct numerical simulation is often not feasible and an effective model is preferred. In this work, we formally derive an effective model for Fluid-Structure Interaction (FSI). In earlier work, assuming infinitesimal pore-scale deformations, an effective poroelastic model of Biot was derived. We extend this model to a nonlinear Biot model that includes pore-scale deformation into the effective description. The main challenge is the difference in coordinate systems of the fluid and solid equations. This is circumvented by utilizing the Arbitrary Lagrange-Eulerian (ALE) formulation of the FSI equations, giving a unified frame in which to apply two-scale asymptotic techniques. In the derived nonlinear Biot model, the local cell problem are coupled to the macroscopic equations via the effective coefficients. These coefficients may be viewed as tabular functions of the macroscopic parameters. After simplifying this dependence, we assume the coefficients depend on macroscopic pressure only. Using a three dimensional pore geometry we calculate, as a proof-of-concept example, the effective permeability and Biot coefficients for various values or pressure. We observe that, for this geometry, a stronger pressure dependence on flow quantities than on mechanically based effective quantities. © 2014 Taylor & Francis Group, LLC.
Effective equations for fluid-structure interaction with applications to poroelasticity
Brown, Donald
2012-11-05
Modeling of fluid-solid interactions in porous media is a challenging and computationally demanding task. Due to the multiscale nature of the problem, simulating the flow and mechanics by direct numerical simulation is often not feasible and an effective model is preferred. In this work, we formally derive an effective model for Fluid-Structure Interaction (FSI). In earlier work, assuming infinitesimal pore-scale deformations, an effective poroelastic model of Biot was derived. We extend this model to a nonlinear Biot model that includes pore-scale deformation into the effective description. The main challenge is the difference in coordinate systems of the fluid and solid equations. This is circumvented by utilizing the Arbitrary Lagrange-Eulerian (ALE) formulation of the FSI equations, giving a unified frame in which to apply two-scale asymptotic techniques. In the derived nonlinear Biot model, the local cell problem are coupled to the macroscopic equations via the effective coefficients. These coefficients may be viewed as tabular functions of the macroscopic parameters. After simplifying this dependence, we assume the coefficients depend on macroscopic pressure only. Using a three dimensional pore geometry we calculate, as a proof-of-concept example, the effective permeability and Biot coefficients for various values or pressure. We observe that, for this geometry, a stronger pressure dependence on flow quantities than on mechanically based effective quantities. © 2014 Taylor & Francis Group, LLC.
Equations of radiation hydrodynamics
International Nuclear Information System (INIS)
Mihalas, D.
1982-01-01
The purpose of this paper is to give an overview of the role of radiation in the transport of energy and momentum in a combined matter-radiation fluid. The transport equation for a moving radiating fluid is presented in both a fully Eulerian and a fully Lagrangian formulation, along with conservation equations describing the dynamics of the fluid. Special attention is paid to the problem of deriving equations that are mutually consistent in each frame, and between frames, to 0(v/c). A detailed analysis is made to show that in situations of broad interest, terms that are formally of 0(v/c) actually dominate the solution, demonstrating that it is esential (1) to pay scrupulous attention to the question of the frame dependence in formulating the equations; and (2) to solve the equations to 0(v/c) in quite general circumstances. These points are illustrated in the context of the nonequilibrium radiation diffusion limit, and a sketch of how the Lagrangian equations are to be solved will be presented
Fach, S; Sitzenfrei, R; Rauch, W
2009-01-01
It is state of the art to evaluate and optimise sewer systems with urban drainage models. Since spill flow data is essential in the calibration process of conceptual models it is important to enhance the quality of such data. A wide spread approach is to calculate the spill flow volume by using standard weir equations together with measured water levels. However, these equations are only applicable to combined sewer overflow (CSO) structures, whose weir constructions correspond with the standard weir layout. The objective of this work is to outline an alternative approach to obtain spill flow discharge data based on measurements with a sonic depth finder. The idea is to determine the relation between water level and rate of spill flow by running a detailed 3D computational fluid dynamics (CFD) model. Two real world CSO structures have been chosen due to their complex structure, especially with respect to the weir construction. In a first step the simulation results were analysed to identify flow conditions for discrete steady states. It will be shown that the flow conditions in the CSO structure change after the spill flow pipe acts as a controlled outflow and therefore the spill flow discharge cannot be described with a standard weir equation. In a second step the CFD results will be used to derive rating curves which can be easily applied in everyday practice. Therefore the rating curves are developed on basis of the standard weir equation and the equation for orifice-type outlets. Because the intersection of both equations is not known, the coefficients of discharge are regressed from CFD simulation results. Furthermore, the regression of the CFD simulation results are compared with the one of the standard weir equation by using historic water levels and hydrographs generated with a hydrodynamic model. The uncertainties resulting of the wide spread use of the standard weir equation are demonstrated.
Navier-Stokes equations an introduction with applications
Łukaszewicz, Grzegorz
2016-01-01
This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from students to engineers and mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier–Stokes equations. Incompressible Navier–Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior o...
Long-Term Dynamics of Autonomous Fractional Differential Equations
Liu, Tao; Xu, Wei; Xu, Yong; Han, Qun
This paper aims to investigate long-term dynamic behaviors of autonomous fractional differential equations with effective numerical method. The long-term dynamic behaviors predict where systems are heading after long-term evolution. We make some modification and transplant cell mapping methods to autonomous fractional differential equations. The mapping time duration of cell mapping is enlarged to deal with the long memory effect. Three illustrative examples, i.e. fractional Lotka-Volterra equation, fractional van der Pol oscillator and fractional Duffing equation, are studied with our revised generalized cell mapping method. We obtain long-term dynamics, such as attractors, basins of attraction, and saddles. Compared with some existing stability and numerical results, the validity of our method is verified. Furthermore, we find that the fractional order has its effect on the long-term dynamics of autonomous fractional differential equations.
Institute of Scientific and Technical Information of China (English)
WANG; Shunjin; ZHANG; Hua
2006-01-01
The problem of preserving fidelity in numerical computation of nonlinear ordinary differential equations is studied in terms of preserving local differential structure and approximating global integration structure of the dynamical system.The ordinary differential equations are lifted to the corresponding partial differential equations in the framework of algebraic dynamics,and a new algorithm-algebraic dynamics algorithm is proposed based on the exact analytical solutions of the ordinary differential equations by the algebraic dynamics method.In the new algorithm,the time evolution of the ordinary differential system is described locally by the time translation operator and globally by the time evolution operator.The exact analytical piece-like solution of the ordinary differential equations is expressd in terms of Taylor series with a local convergent radius,and its finite order truncation leads to the new numerical algorithm with a controllable precision better than Runge Kutta Algorithm and Symplectic Geometric Algorithm.
Liang, Feng; Yang, Xiao-Dong; Zhang, Wei; Qian, Ying-Jing
2018-03-01
In this paper, a dynamical model of simply-supported spinning pipes conveying fluid with axial deployment is proposed and the transverse free vibration and stability for such a doubly gyroscopic system involving time-dependent parameters are investigated. The partial differential equations of motion are derived by the extended Hamilton principle and then truncated by the Galerkin technique. The time-variant frequencies, mode shapes and responses to initial conditions are comprehensively investigated to reveal the dynamical essence of the system. It is indicated that the qualitative stability evolution of the system mainly depends on the effect of fluid-structure interaction (FSI), while the spinning motion will enhance the pipe rigidity and eliminate the buckling instability. The dynamical evolution of a retracting pipe is almost inverse to that of the deploying one. The pipe possesses different mode configurations of spatial curves as the pipe length increases and some modal and response characteristics of the present system are found rather distinct from those of deploying cantilevered structures.
Meniscal Tear Film Fluid Dynamics Near Marx’s Line
Zubkov, V. S.
2013-07-03
Extensive studies have explored the dynamics of the ocular surface fluid, though theoretical investigations are typically limited to the use of the lubrication approximation, which is not guaranteed to be uniformly valid a-priori throughout the tear meniscus. However, resolving tear film behaviour within the meniscus and especially its apices is required to characterise the flow dynamics where the tear film is especially thin, and thus most susceptible to evaporatively induced hyperosmolarity and subsequent epithelial damage. Hence, we have explored the accuracy of the standard lubrication approximation for the tear film by explicit comparisons with the 2D Navier-Stokes model, considering both stationary and moving eyelids. Our results demonstrate that the lubrication model is qualitatively accurate except in the vicinity of the eyelids. In particular, and in contrast to lubrication theory, the solution of the full Navier-Stokes equations predict a distinct absence of fluid flow, and thus convective mixing in the region adjacent to the tear film contact line. These observations not only support emergent hypotheses concerning the formation of Marx\\'s line, a region of epithelial cell staining adjacent to the contact line on the eyelid, but also enhance our understanding of the pathophysiological consequences of the flow profile near the tear film contact line. © 2013 Society for Mathematical Biology.
Fluid bed porosity equation for an inverse fluidized bed bioreactor with particles growing biofilm
International Nuclear Information System (INIS)
Campos-Diaz, K. E.; Limas-Ballesteros, R.
2009-01-01
Fluid Bed Bioreactor performance is strongly affected by bed void fraction or bed porosity fluctuations. Particle size enlargement due to biofilm growth is an important factor that is involved in these variations and until now there are no mathematical equations that consider biofilm growth. In this work a mathematical equation is proposed to calculate bed void fraction in an inverse fluid bed bioreactor. (Author)
Post-Newtonian celestial dynamics in cosmology: Field equations
Kopeikin, Sergei M.; Petrov, Alexander N.
2013-02-01
Post-Newtonian celestial dynamics is a relativistic theory of motion of massive bodies and test particles under the influence of relatively weak gravitational forces. The standard approach for development of this theory relies upon the key concept of the isolated astronomical system supplemented by the assumption that the background spacetime is flat. The standard post-Newtonian theory of motion was instrumental in the explanation of the existing experimental data on binary pulsars, satellite, and lunar laser ranging, and in building precise ephemerides of planets in the Solar System. Recent studies of the formation of large-scale structures in our Universe indicate that the standard post-Newtonian mechanics fails to describe more subtle dynamical effects in motion of the bodies comprising the astronomical systems of larger size—galaxies and clusters of galaxies—where the Riemann curvature of the expanding Friedmann-Lemaître-Robertson-Walker universe interacts with the local gravitational field of the astronomical system and, as such, cannot be ignored. The present paper outlines theoretical principles of the post-Newtonian mechanics in the expanding Universe. It is based upon the gauge-invariant theory of the Lagrangian perturbations of cosmological manifold caused by an isolated astronomical N-body system (the Solar System, a binary star, a galaxy, and a cluster of galaxies). We postulate that the geometric properties of the background manifold are described by a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker metric governed by two primary components—the dark matter and the dark energy. The dark matter is treated as an ideal fluid with the Lagrangian taken in the form of pressure along with the scalar Clebsch potential as a dynamic variable. The dark energy is associated with a single scalar field with a potential which is hold unspecified as long as the theory permits. Both the Lagrangians of the dark matter and the scalar field are
Departure of microscopic friction from macroscopic drag in molecular fluid dynamics
Energy Technology Data Exchange (ETDEWEB)
Hanasaki, Itsuo [Institute of Engineering, Tokyo University of Agriculture and Technology, Naka-cho 2-24-16, Koganei, Tokyo 184-8588 (Japan); Fujiwara, Daiki; Kawano, Satoyuki, E-mail: kawano@me.es.osaka-u.ac.jp [Graduate School of Engineering Science, Osaka University, Machikaneyama-cho 1-3, Toyonaka, Osaka 560-8531 (Japan)
2016-03-07
Friction coefficient of the Langevin equation and drag of spherical macroscopic objects in steady flow at low Reynolds numbers are usually regarded as equivalent. We show that the microscopic friction can be different from the macroscopic drag when the mass is taken into account for particles with comparable scale to the surrounding fluid molecules. We illustrate it numerically by molecular dynamics simulation of chloride ion in water. Friction variation by the atomistic mass effect beyond the Langevin regime can be of use in the drag reduction technology as well as the electro or thermophoresis.
Smoothed particle hydrodynamics model for phase separating fluid mixtures. I. General equations
Thieulot, C; Janssen, LPBM; Espanol, P
We present a thermodynamically consistent discrete fluid particle model for the simulation of a recently proposed set of hydrodynamic equations for a phase separating van der Waals fluid mixture [P. Espanol and C.A.P. Thieulot, J. Chem. Phys. 118, 9109 (2003)]. The discrete model is formulated by
Directory of Open Access Journals (Sweden)
Andrei Khrennikov
2016-07-01
Full Text Available We present a new conceptual approach for modeling of fluid flows in random porous media based on explicit exploration of the treelike geometry of complex capillary networks. Such patterns can be represented mathematically as ultrametric spaces and the dynamics of fluids by ultrametric diffusion. The images of p-adic fields, extracted from the real multiscale rock samples and from some reference images, are depicted. In this model the porous background is treated as the environment contributing to the coefficients of evolutionary equations. For the simplest trees, these equations are essentially less complicated than those with fractional differential operators which are commonly applied in geological studies looking for some fractional analogs to conventional Euclidean space but with anomalous scaling and diffusion properties. It is possible to solve the former equation analytically and, in particular, to find stationary solutions. The main aim of this paper is to attract the attention of researchers working on modeling of geological processes to the novel utrametric approach and to show some examples from the petroleum reservoir static and dynamic characterization, able to integrate the p-adic approach with multifractals, thermodynamics and scaling. We also present a non-mathematician friendly review of trees and ultrametric spaces and pseudo-differential operators on such spaces.
A modified two-fluid model for the application of two-group interfacial area transport equation
International Nuclear Information System (INIS)
Sun, X.; Ishii, M.; Kelly, J.
2003-01-01
This paper presents the modified two-fluid model that is ready to be applied in the approach of the two-group interfacial area transport equation. The two-group interfacial area transport equation was developed to provide a mechanistic constitutive relation for the interfacial area concentration in the two-fluid model. In the two-group transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 while cap/slug/churn-turbulent bubbles as Group 2. Therefore, this transport equation can be employed in the flow regimes spanning from bubbly, cap bubbly, slug to churn-turbulent flows. However, the introduction of the two groups of bubbles requires two gas velocity fields. Yet it is not desirable to solve two momentum equations for the gas phase alone. In the current modified two-fluid model, a simplified approach is proposed. The momentum equation for the averaged velocity of both Group-1 and Group-2 bubbles is retained. By doing so, the velocity difference between Group-1 and Group-2 bubbles needs to be determined. This may be made either based on simplified momentum equations for both Group-1 and Group-2 bubbles or by a modified drift-flux model
Geophysical aspects of underground fluid dynamics and mineral transformation process
Khramchenkov, Maxim; Khramchenkov, Eduard
2014-05-01
The description of processes of mass exchange between fluid and poly-minerals material in porous media from various kinds of rocks (primarily, sedimentary rocks) have been examined. It was shown that in some important cases there is a storage equation of non-linear diffusion equation type. In addition, process of filtration in un-swelling soils, swelling porous rocks and coupled process of consolidation and chemical interaction between fluid and particles material were considered. In the latter case equations of physical-chemical mechanics of conservation of mass for fluid and particles material were used. As it is well known, the mechanics of porous media is theoretical basis of such branches of science as rock mechanics, soil physics and so on. But at the same moment some complex processes in the geosystems lacks full theoretical description. The example of such processes is metamorphosis of rocks and correspondent variations of stress-strain state. In such processes chemical transformation of solid and fluid components, heat release and absorption, phase transitions, rock destruction occurs. Extensive usage of computational resources in limits of traditional models of the mechanics of porous media cannot guarantee full correctness of obtained models and results. The process of rocks consolidation which happens due to filtration of underground fluids is described from the position of rock mechanics. As an additional impact, let us consider the porous media consolidating under the weight of overlying rock with coupled complex geological processes, as a continuous porous medium of variable mass. Problems of obtaining of correct storage equations for coupled processes of consolidation and mass exchange between underground fluid and skeleton material are often met in catagenesi processes description. The example of such processes is metamorphosis of rocks and correspondent variations of stress-strain state. In such processes chemical transformation of solid and fluid
On some properties of Einstein equations with the perfect fluid energy-momentum tensor
International Nuclear Information System (INIS)
Biesiada, M.; Szydlowski, M.; Szczesny, J.
1989-01-01
We discuss the symmetries of Einstein equations with the perfect fluid energy momentum tensor. We show that the symmetries inherited from vacuum equations enforce the equation of state in the form p p 0 = γρ which is the most often used one and contains models with the cosmological constant. 9 refs. (author)
Khan, Aamir; Shah, Rehan Ali; Shuaib, Muhammad; Ali, Amjad
2018-06-01
The effects of magnetic field dependent (MFD) thermosolutal convection and MFD viscosity of the fluid dynamics are investigated between squeezing discs rotating with different velocities. The unsteady constitutive expressions of mass conservation, modified Navier-Stokes, Maxwell and MFD thermosolutal convection are coupled as a system of ordinary differential equations. The corresponding solutions for the transformed radial and azimuthal momentum as well as solutions for the azimuthal and axial induced magnetic field equations are determined, also the MHD pressure and torque which the fluid exerts on the upper disc is derived and discussed in details. In the case of smooth discs the self-similar equations are solved using Homotopy Analysis Method (HAM) with appropriate initial guesses and auxiliary parameters to produce an algorithm with an accelerated and assured convergence. The validity and accuracy of HAM results is proved by comparison of the HAM solutions with numerical solver package BVP4c. It has been shown that magnetic Reynolds number causes to decrease magnetic field distributions, fluid temperature, axial and tangential velocity. Also azimuthal and axial components of magnetic field have opposite behavior with increase in MFD viscosity. Applications of the study include automotive magneto-rheological shock absorbers, novel aircraft landing gear systems, heating up or cooling processes, biological sensor systems and biological prosthetic etc.
Matsumoto, Daichi; Fukudome, Koji; Wada, Hirofumi
2016-10-01
Understanding the hydrodynamic properties of fluid flow in a curving pipe and channel is important for controlling the flow behavior in technologies and biomechanics. The nature of the resulting flow in a bent pipe is extremely complicated because of the presence of a cross-stream secondary flow. In an attempt to disentangle this complexity, we investigate the fluid dynamics in a bent channel via the direct numerical simulation of the Navier-Stokes equation in two spatial dimensions. We exploit the absence of secondary flow from our model and systematically investigate the flow structure along the channel as a function of both the bend angle and Reynolds number of the laminar-to-turbulent regime. We numerically suggest a scaling relation between the shape of the separation bubble and the flow conductance, and construct an integrated phase diagram.
Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas
International Nuclear Information System (INIS)
Zawaideh, E.; Najmabadi, F.; Conn, R.W.
1986-01-01
A new set of two-fluid equations that are valid from collisional to weakly collisional limits is derived. Starting from gyrokinetic equations in flux coordinates with no zero-order drifts, a set of moment equations describing plasma transport along the field lines of a space- and time-dependent magnetic field is derived. No restriction on the anisotropy of the ion distribution function is imposed. In the highly collisional limit, these equations reduce to those of Braginskii, while in the weakly collisional limit they are similar to the double adiabatic or Chew, Goldberger, and Low (CGL) equations [Proc. R. Soc. London, Ser. A 236, 112 (1956)]. The new set of equations also exhibits a physical singularity at the sound speed. This singularity is used to derive and compute the sound speed. Numerical examples comparing these equations with conventional transport equations show that in the limit where the ratio of the mean free path lambda to the scale length of the magnetic field gradient L/sub B/ approaches zero, there is no significant difference between the solution of the new and conventional transport equations. However, conventional fluid equations, ordinarily expected to be correct to the order (lambda/L/sub B/) 2 , are found to have errors of order (lambda/L/sub u/) 2 = (lambda/L/sub B/) 2 /(1-M 2 ) 2 , where L/sub u/ is the scale length of the flow velocity gradient and M is the Mach number. As such, the conventional equations may contain large errors near the sound speed (Mroughly-equal1)
Computational fluid dynamics principles and applications
Blazek, J
2005-01-01
Computational Fluid Dynamics (CFD) is an important design tool in engineering and also a substantial research tool in various physical sciences as well as in biology. The objective of this book is to provide university students with a solid foundation for understanding the numerical methods employed in today's CFD and to familiarise them with modern CFD codes by hands-on experience. It is also intended for engineers and scientists starting to work in the field of CFD or for those who apply CFD codes. Due to the detailed index, the text can serve as a reference handbook too. Each chapter includes an extensive bibliography, which provides an excellent basis for further studies. The accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) as well as of grid generators. Provided are also tools for Von Neumann stability analysis of 1-D model equations. Finally, the companion website includes the source code of a dedicated visualisation so...
Modern fluid dynamics for physics and astrophysics
Regev, Oded; Yecko, Philip A
2016-01-01
This book grew out of the need to provide students with a solid introduction to modern fluid dynamics. It offers a broad grounding in the underlying principles and techniques used, with some emphasis on applications in astrophysics and planetary science. The book comprehensively covers recent developments, methods and techniques, including, for example, new ideas on transitions to turbulence (via transiently growing stable linear modes), new approaches to turbulence (which remains the enigma of fluid dynamics), and the use of asymptotic approximation methods, which can give analytical or semi-analytical results and complement fully numerical treatments. The authors also briefly discuss some important considerations to be taken into account when developing a numerical code for computer simulation of fluid flows. Although the text is populated throughout with examples and problems from the field of astrophysics and planetary science, the text is eminently suitable as a general introduction to fluid dynamics. It...
Optics and Fluid Dynamics Department annual progress report for 1995
Energy Technology Data Exchange (ETDEWEB)
Hanson, S.G.; Lading, L.; Lynov, J.P.; Skaarup, B. [eds.
1996-01-01
Research in the Optics and Fluid Dynamics Department has been performed within the following two programme areas: (1) optical diagnostics and information processing and (2) plasma and fluid dynamics. The optical activities are concentrated on optical materials, diagnostics and sensors. The plasma and fluid dynamics activities are concentrated on nonlinear dynamics in fluids, plasmas and optics as well as on plasma and fluid diagnostics. Scientific computing is an integral part of the work. The activities are supported by several EU programmes, including EURATOM, by research councils and by industry. A summary of the activities in 1995 is presented. (au) 36 ills., 166 refs.
Optics and Fluid Dynamics Department annual progress report for 1995
International Nuclear Information System (INIS)
Hanson, S.G.; Lading, L.; Lynov, J.P.; Skaarup, B.
1996-01-01
Research in the Optics and Fluid Dynamics Department has been performed within the following two programme areas: (1) optical diagnostics and information processing and (2) plasma and fluid dynamics. The optical activities are concentrated on optical materials, diagnostics and sensors. The plasma and fluid dynamics activities are concentrated on nonlinear dynamics in fluids, plasmas and optics as well as on plasma and fluid diagnostics. Scientific computing is an integral part of the work. The activities are supported by several EU programmes, including EURATOM, by research councils and by industry. A summary of the activities in 1995 is presented. (au) 36 ills., 166 refs
Spreading dynamics of power-law fluid droplets
International Nuclear Information System (INIS)
Liang Zhanpeng; Peng Xiaofeng; Wang Xiaodong; Lee, D-J; Su Ay
2009-01-01
This paper aims at providing a summary of the theoretical models available for non-Newtonian fluid spreading dynamics. Experimental findings and model predictions for a Newtonian fluid spreading test are briefly reviewed. Then how the complete wetting and partial wetting power-law fluids spread over a solid substrate is examined. The possible extension of Newtonian fluid models to power-law fluids is also discussed.
Stability theory for dynamic equations on time scales
Martynyuk, Anatoly A
2016-01-01
This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems. In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Ma...
Differential equation models for sharp threshold dynamics.
Schramm, Harrison C; Dimitrov, Nedialko B
2014-01-01
We develop an extension to differential equation models of dynamical systems to allow us to analyze probabilistic threshold dynamics that fundamentally and globally change system behavior. We apply our novel modeling approach to two cases of interest: a model of infectious disease modified for malware where a detection event drastically changes dynamics by introducing a new class in competition with the original infection; and the Lanchester model of armed conflict, where the loss of a key capability drastically changes the effectiveness of one of the sides. We derive and demonstrate a step-by-step, repeatable method for applying our novel modeling approach to an arbitrary system, and we compare the resulting differential equations to simulations of the system's random progression. Our work leads to a simple and easily implemented method for analyzing probabilistic threshold dynamics using differential equations. Published by Elsevier Inc.
Simulating Smoke Filling in Big Halls by Computational Fluid Dynamics
Directory of Open Access Journals (Sweden)
W. K. Chow
2011-01-01
Full Text Available Many tall halls of big space volume were built and, to be built in many construction projects in the Far East, particularly Mainland China, Hong Kong, and Taiwan. Smoke is identified to be the key hazard to handle. Consequently, smoke exhaust systems are specified in the fire code in those areas. An update on applying Computational Fluid Dynamics (CFD in smoke exhaust design will be presented in this paper. Key points to note in CFD simulations on smoke filling due to a fire in a big hall will be discussed. Mathematical aspects concerning of discretization of partial differential equations and algorithms for solving the velocity-pressure linked equations are briefly outlined. Results predicted by CFD with different free boundary conditions are compared with those on room fire tests. Standards on grid size, relaxation factors, convergence criteria, and false diffusion should be set up for numerical experiments with CFD.
Longwave instabilities and patterns in fluids
Shklyaev, Sergey
2017-01-01
This book summarizes the main advances in the field of nonlinear evolution and pattern formation caused by longwave instabilities in fluids. It will allow readers to master the multiscale asymptotic methods and become familiar with applications of these methods in a variety of physical problems. Longwave instabilities are inherent to a variety of systems in fluid dynamics, geophysics, electrodynamics, biophysics, and many others. The techniques of the derivation of longwave amplitude equations, as well as the analysis of numerous nonlinear equations, are discussed throughout. This book will be of value to researchers and graduate students in applied mathematics, physics, and engineering, in particular within the fields of fluid mechanics, heat and mass transfer theory, and nonlinear dynamics. .
Fluid dynamics an introduction
Rieutord, Michel
2015-01-01
This book is dedicated to readers who want to learn fluid dynamics from the beginning. It assumes a basic level of mathematics knowledge that would correspond to that of most second-year undergraduate physics students and examines fluid dynamics from a physicist’s perspective. As such, the examples used primarily come from our environment on Earth and, where possible, from astrophysics. The text is arranged in a progressive and educational format, aimed at leading readers from the simplest basics to more complex matters like turbulence and magnetohydrodynamics. Exercises at the end of each chapter help readers to test their understanding of the subject (solutions are provided at the end of the book), and a special chapter is devoted to introducing selected aspects of mathematics that beginners may not be familiar with, so as to make the book self-contained.
Fluid dynamic propagation of initial baryon number perturbations on a Bjorken flow background
Floerchinger, Stefan
2015-01-01
Baryon number density perturbations offer a possible route to experimentally measure baryon number susceptibilities and heat conductivity of the quark gluon plasma. We study the fluid dynamical evolution of local and event-by-event fluctuations of baryon number density, flow velocity and energy density on top of a (generalized) Bjorken expansion. To that end we use a background-fluctuation splitting and a Bessel-Fourier decomposition for the fluctuating part of the fluid dynamical fields with respect to the azimuthal angle, the radius in the transverse plane and rapidity. We examine how the time evolution of linear perturbations depends on the equation of state as well as on shear viscosity, bulk viscosity and heat conductivity for modes with different azimuthal, radial and rapidity wave numbers. Finally we discuss how this information is accessible to experiments in terms of the transverse and rapidity dependence of correlation functions for baryonic particles in high energy nuclear collisions.
Partial chemical equilibrium in fluid dynamics
International Nuclear Information System (INIS)
Ramshaw, J.D.
1980-01-01
An analysis is given for the flow of a multicomponent fluid in which an arbitrary number of chemical reactions may occur, some of which are in equilibrium while the others proceed kinetically. The primitive equations describing this situation are inconvenient to use because the progress rates omega-dot/sub s/ for the equilibrium reactions are determined implicitly by the associated equilibrium constraint conditions. Two alternative equivalent equation systems that are more pleasant to deal with are derived. In the first system, the omega-dot/sub s/ are eliminated by replacing the transport equations for the chemical species involved in the equilibrium reactions with transport equations for the basic components of which these species are composed. The second system retains the usual species transport equations, but eliminates the nonlinear algebraic equilibrium constraint conditions by deriving an explicit expression for the omega-dot/sub s/. Both systems are specialized to the case of an ideal gas mixture. Considerations involved in solving these equation systems numerically are discussed briefly
Multitasking the code ARC3D. [for computational fluid dynamics
Barton, John T.; Hsiung, Christopher C.
1986-01-01
The CRAY multitasking system was developed in order to utilize all four processors and sharply reduce the wall clock run time. This paper describes the techniques used to modify the computational fluid dynamics code ARC3D for this run and analyzes the achieved speedup. The ARC3D code solves either the Euler or thin-layer N-S equations using an implicit approximate factorization scheme. Results indicate that multitask processing can be used to achieve wall clock speedup factors of over three times, depending on the nature of the program code being used. Multitasking appears to be particularly advantageous for large-memory problems running on multiple CPU computers.
Stability of non-linear constitutive formulations for viscoelastic fluids
Siginer, Dennis A
2014-01-01
Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids provides a complete and up-to-date view of the field of constitutive equations for flowing viscoelastic fluids, in particular on their non-linear behavior, the stability of these constitutive equations that is their predictive power, and the impact of these constitutive equations on the dynamics of viscoelastic fluid flow in tubes. This book gives an overall view of the theories and attendant methodologies developed independently of thermodynamic considerations as well as those set within a thermodynamic framework to derive non-linear rheological constitutive equations for viscoelastic fluids. Developments in formulating Maxwell-like constitutive differential equations as well as single integral constitutive formulations are discussed in the light of Hadamard and dissipative type of instabilities.
Dynamics of polymeric liquids. Vol. 1, 2nd Ed.: Fluid mechanics
International Nuclear Information System (INIS)
Bird, R.B.; Armstrong, R.C.; Hassager, O.
1987-01-01
This book examines Newtonian liquids and polymer fluid mechanics. It begins with a review of the main ideas of fluid dynamics as well as key points of Newtonian fluids. Major revisions include extensive updating of all material and a greater emphasis on fluid dynamics problem solving. It presents summaries of experiments describing the difference between polymeric and simple fluids. In addition, it traces, roughly in historical order, various methods for solving polymer fluid dynamics problems
Numerical solution of plasma fluid equations using locally refined grids
International Nuclear Information System (INIS)
Colella, P.
1997-01-01
This paper describes a numerical method for the solution of plasma fluid equations on block-structured, locally refined grids. The plasma under consideration is typical of those used for the processing of semiconductors. The governing equations consist of a drift-diffusion model of the electrons and an isothermal model of the ions coupled by Poisson's equation. A discretization of the equations is given for a uniform spatial grid, and a time-split integration scheme is developed. The algorithm is then extended to accommodate locally refined grids. This extension involves the advancement of the discrete system on a hierarchy of levels, each of which represents a degree of refinement, together with synchronization steps to ensure consistency across levels. A brief discussion of a software implementation is followed by a presentation of numerical results
Moving interfaces and quasilinear parabolic evolution equations
Prüss, Jan
2016-01-01
In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions...
Langevin equation of a fluid particle in wall-induced turbulence
Brouwers, J.J.H.
2010-01-01
We derive the Langevin equation describing the stochastic process of fluid particle motion in wall-inducedturbulence (turbulent flow in pipes, channels, and boundary layers including the atmospheric surface layer).The analysis is based on the asymptotic behavior at a large Reynolds number. We use
Fluid/Structure Interaction Studies of Aircraft Using High Fidelity Equations on Parallel Computers
Guruswamy, Guru; VanDalsem, William (Technical Monitor)
1994-01-01
Abstract Aeroelasticity which involves strong coupling of fluids, structures and controls is an important element in designing an aircraft. Computational aeroelasticity using low fidelity methods such as the linear aerodynamic flow equations coupled with the modal structural equations are well advanced. Though these low fidelity approaches are computationally less intensive, they are not adequate for the analysis of modern aircraft such as High Speed Civil Transport (HSCT) and Advanced Subsonic Transport (AST) which can experience complex flow/structure interactions. HSCT can experience vortex induced aeroelastic oscillations whereas AST can experience transonic buffet associated structural oscillations. Both aircraft may experience a dip in the flutter speed at the transonic regime. For accurate aeroelastic computations at these complex fluid/structure interaction situations, high fidelity equations such as the Navier-Stokes for fluids and the finite-elements for structures are needed. Computations using these high fidelity equations require large computational resources both in memory and speed. Current conventional super computers have reached their limitations both in memory and speed. As a result, parallel computers have evolved to overcome the limitations of conventional computers. This paper will address the transition that is taking place in computational aeroelasticity from conventional computers to parallel computers. The paper will address special techniques needed to take advantage of the architecture of new parallel computers. Results will be illustrated from computations made on iPSC/860 and IBM SP2 computer by using ENSAERO code that directly couples the Euler/Navier-Stokes flow equations with high resolution finite-element structural equations.
Numerical study of coupled fluid-structure interaction for combustion system
Khatir, Z.; Pozarlik, Artur Krzysztof; Cooper, R.K.; Watterson, J.W.; Kok, Jacobus B.W.
2007-01-01
The computation of fluid–structure interaction (FSI) problems requires solving simultaneously the coupled fluid and structure equations. A partitioned approach using a volume spline solution procedure is applied for the coupling of fluid dynamics and structural dynamics codes. For comparative study,
International Nuclear Information System (INIS)
Guo, Shimin; Mei, Liquan; Li, Ying; Sun, Youfa
2012-01-01
By introducing a new general ansätz, the improved fractional sub-equation method is proposed to construct analytical solutions of nonlinear evolution equations involving Jumarie's modified Riemann–Liouville derivative. By means of this method, the space–time fractional Whitham–Broer–Kaup and generalized Hirota–Satsuma coupled KdV equations are successfully solved. The obtained results show that the proposed method is quite effective, promising and convenient for solving nonlinear fractional differential equations. -- Highlights: ► We propose a novel method for nonlinear fractional differential equations. ► Two important fractional differential equations in fluid mechanics are solved successfully. ► Some new exact solutions of the fractional differential equations are obtained. ► These solutions will advance the understanding of nonlinear physical phenomena.
SALE-3D, 3-D Fluid Flow, Navier Stokes Equation Using Lagrangian or Eulerian Method
International Nuclear Information System (INIS)
Amsden, A.A.; Ruppel, H.M.
1991-01-01
1 - Description of problem or function: SALE-3D calculates three- dimensional fluid flows at all speeds, from the incompressible limit to highly supersonic. An implicit treatment of the pressure calculation similar to that in the Implicit Continuous-fluid Eulerian (ICE) technique provides this flow speed flexibility. In addition, the computing mesh may move with the fluid in a typical Lagrangian fashion, be held fixed in an Eulerian manner, or move in some arbitrarily specified way to provide a continuous rezoning capability. This latitude results from use of an Arbitrary Lagrangian-Eulerian (ALE) treatment of the mesh. The partial differential equations solved are the Navier-Stokes equations and the mass and internal energy equations. The fluid pressure is determined from an equation of state and supplemented with an artificial viscous pressure for the computation of shock waves. The computing mesh consists of a three-dimensional network of arbitrarily shaped, six-sided deformable cells, and a variety of user-selectable boundary conditions are provided in the program. 2 - Method of solution: SALE3D uses an ICED-ALE technique, which combines the ICE method of treating flow speeds and the ALE mesh treatment to calculate three-dimensional fluid flow. The finite- difference approximations to the conservation of mass, momentum, and specific internal energy differential equations are solved in a sequence of time steps on a network of deformable computational cells. The basic hydrodynamic part of each cycle is divided into three phases: (1) an explicit solution of the Lagrangian equations of motion updating the velocity field by the effects of all forces, (2) an implicit calculation using Newton-Raphson iterative scheme that provides time-advanced pressures and velocities, and (3) the addition of advective contributions for runs that are Eulerian or contain some relative motion of grid and fluid. A powerful feature of this three-phases approach is the ease with which
Mathematical well-posedness of a two-fluid equations for bubbly two-phase flows
International Nuclear Information System (INIS)
Okawa, Tomio; Kataoka, Isao
2000-01-01
It is widely known that two-fluid equations used in most engineering applications do not satisfy the necessary condition for being mathematical well-posed as initial-value problems. In the case of stratified two-phase flows, several researchers have revealed that differential models satisfying the necessary condition are to be derived if the pressure difference between the phases is related to the spatial gradient of the void fraction through the effects of gravity or surface tension. While, in the case of dispersed two-phase flows, no physically reasonable method to derive mathematically well-posed two-fluid model has been proposed. In the present study, particularly focusing on the effect of interfacial pressure terms, we derived the mathematically closed form of the volume-averaged two-fluid model for bubbly two-phase flows. As a result of characteristic analyses, it was shown that the proposed two-fluid equations satisfy the necessary condition of mathematical well-posedness if the void fraction is sufficiently small. (author)
Introduction to differential equations with dynamical systems
Campbell, Stephen L
2011-01-01
Many textbooks on differential equations are written to be interesting to the teacher rather than the student. Introduction to Differential Equations with Dynamical Systems is directed toward students. This concise and up-to-date textbook addresses the challenges that undergraduate mathematics, engineering, and science students experience during a first course on differential equations. And, while covering all the standard parts of the subject, the book emphasizes linear constant coefficient equations and applications, including the topics essential to engineering students. Stephen Campbell and Richard Haberman--using carefully worded derivations, elementary explanations, and examples, exercises, and figures rather than theorems and proofs--have written a book that makes learning and teaching differential equations easier and more relevant. The book also presents elementary dynamical systems in a unique and flexible way that is suitable for all courses, regardless of length.
Differential equations a dynamical systems approach ordinary differential equations
Hubbard, John H
1991-01-01
This is a corrected third printing of the first part of the text Differential Equations: A Dynamical Systems Approach written by John Hubbard and Beverly West. The authors' main emphasis in this book is on ordinary differential equations. The book is most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as the life sciences, physics and economics. Traditional courses on differential equations focus on techniques leading to solutions. Yet most differential equations do not admit solutions which can be written in elementary terms. The authors have taken the view that a differential equations defines functions; the object of the theory is to understand the behavior of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods. The companion software, MacMath, is designed to bring these notions to life.
International Nuclear Information System (INIS)
Kawashima, S.; Matsumara, A.; Nishida, T.
1979-01-01
The compressible and heat-conductive Navier-Stokes equation obtained as the second approximation of the formal Chapman-Enskog expansion is investigated on its relations to the original nonlinear Boltzmann equation and also to the incompressible Navier-Stokes equation. The solutions of the Boltzmann equation and the incompressible Navier-Stokes equation for small initial data are proved to be asymptotically equivalent (mod decay rate tsup(-5/4)) as t → + infinitely to that of the compressible Navier-Stokes equation for the corresponding initial data. (orig.) 891 HJ/orig. 892 MKO
International Nuclear Information System (INIS)
Lo, C.-Y.; Chang-Jian, C.-W.
2008-01-01
This study presents a dynamic analysis of a rotor supported by two turbulent flow model journal bearings and lubricated with couple stress fluid under nonlinear suspension. The dynamics of the rotor center and bearing center is studied. The dynamic equations are solved using the Runge-Kutta method. The analysis methods employed in this study is inclusive of the dynamic trajectories of the rotor center and bearing center, power spectra, Poincare maps and bifurcation diagrams. The maximum Lyapunov exponent analysis is also used to identify the onset of chaotic motion. The results show that the values of dimensionless parameters l* strongly influence dynamic motions of bearing and rotor centre. It is found that couple stress fluid improve the stability of the system when l* > 0.4 even if the flow of this system is turbulent. We also demonstrated that the dimensionless rotational speed ratios s and the dimensionless unbalance parameter β are also significant system parameters. The modeling results thus obtained by using the method proposed in this paper can be employed to predict the stability of the rotor-bearing system and the undesirable behavior of the rotor and bearing center can be avoided
Energetics and dynamics of excess electrons in simple fluids
International Nuclear Information System (INIS)
Space, B.
1992-01-01
Excess electronic dynamical and equilibrium properties are modeled in both polarizable and nonpolarizable noble gas fluids. Explicit dynamical calculations are carried out for excess electrons in fluid helium, where excess electronic eigenstates are localized. Energetics and dynamics are considered for fluids which span the entire range of polarizability present in the rare gases. Excess electronic eigenstates and eigenvalues are calculated for fluids of helium, argon and xenon. Both equilibrium and dynamical information is obtained from the calculation of these wavefunctions. A surface hopping trajectory method for studying nonadiabatic excess electronic relaxation in condensed systems is used to explore the nonadiabatic relaxation after photoexciting an equilibrated excess electron in dense fluid helium. The different types on nonadiabatic phenomena which are important in excess electronic relaxation are surveyed. The same surface hopping trajectory method is also used to study the rapid nonadiabatic relaxation after an excess electron is injected into unperturbed fluid helium. Several distinctively different relaxation processes, characterized by their relative importance at different times during the relaxation to a localized equilibrium state, are detailed. Though the dynamical properties of excess electrons under the conditions considered here have never been studied before, the behavior is remarkably similar to that observed in both experimental and theoretical studies of electron hydration dynamics, indicating that the processes described may be very general relaxation mechanisms for localization and trapping in fluids. Additionally, ground state energies of an excess electron, e 0 , are computed as a function of solvent density using model electron-atom pseudopotentials in fluid helium, argon, and xenon. The nonuniqueness of the pseudopotential description of electron-molecule interactions is demonstrated
Hamilton's equations for a fluid membrane
Energy Technology Data Exchange (ETDEWEB)
Capovilla, R [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados, Apdo. Postal 14-740, 07000 Mexico, DF (Mexico); Guven, J [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo. Postal 70-543, 04510 Mexico, DF (Mexico); Rojas, E [Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico)
2005-10-14
Consider a homogeneous fluid membrane described by the Helfrich-Canham energy, quadratic in the mean curvature of the membrane surface. The shape equation that determines equilibrium configurations is fourth order in derivatives and cubic in the mean curvature. We introduce a Hamiltonian formulation of this equation which dismantles it into a set of coupled first-order equations. This involves interpreting the Helfrich-Canham energy as an action; equilibrium surfaces are generated by the evolution of space curves. Two features complicate the implementation of a Hamiltonian framework. (i) The action involves second derivatives. This requires treating the velocity as a phase-space variable and the introduction of its conjugate momentum. The canonical Hamiltonian is constructed on this phase space. (ii) The action possesses a local symmetry-reparametrization invariance. The two labels we use to parametrize points on the surface are themselves physically irrelevant. This symmetry implies primary constraints, one for each label, that need to be implemented within the Hamiltonian. The two Lagrange multipliers associated with these constraints are identified as the components of the acceleration tangential to the surface. The conservation of the primary constraints implies two secondary constraints, fixing the tangential components of the momentum conjugate to the position. Hamilton's equations are derived and the appropriate initial conditions on the phase-space variables are identified. Finally, it is shown how the shape equation can be reconstructed from these equations.
The use of computers for instruction in fluid dynamics
Watson, Val
1987-01-01
Applications for computers which improve instruction in fluid dynamics are examined. Computers can be used to illustrate three-dimensional flow fields and simple fluid dynamics mechanisms, to solve fluid dynamics problems, and for electronic sketching. The usefulness of computer applications is limited by computer speed, memory, and software and the clarity and field of view of the projected display. Proposed advances in personal computers which will address these limitations are discussed. Long range applications for computers in education are considered.
Principles of computational fluid dynamics
International Nuclear Information System (INIS)
Wesseling, P.
2001-01-01
The book is aimed at graduate students, researchers, engineers and physicists involved in flow computations. An up-to-date account is given of the present state- of-the-art of numerical methods employed in computational fluid dynamics. The underlying numerical principles are treated with a fair amount of detail, using elementary mathematical analysis. Attention is given to difficulties arising from geometric complexity of the flow domain and of nonuniform structured boundary-fitted grids. Uniform accuracy and efficiency for singular perturbation problems is studied, pointing the way to accurate computation of flows at high Reynolds number. Much attention is given to stability analysis, and useful stability conditions are provided, some of them new, for many numerical schemes used in practice. Unified methods for compressible and incompressible flows are discussed. Numerical analysis of the shallow-water equations is included. The theory of hyperbolic conservation laws is treated. Godunov's order barrier and how to overcome it by means of slope-limited schemes is discussed. An introduction is given to efficient iterative solution methods, using Krylov subspace and multigrid acceleration. Many pointers are given to recent literature, to help the reader to quickly reach the current research frontier. (orig.)
Technical Competencies Applied in Experimental Fluid Dynamics
Tagg, Randall
2017-11-01
The practical design, construction, and operation of fluid dynamics experiments require a broad range of competencies. Three types are instrumental, procedural, and design. Respective examples would be operation of a spectrum analyzer, soft-soldering or brazing flow plumbing, and design of a small wind tunnel. Some competencies, such as the selection and installation of pumping systems, are unique to fluid dynamics and fluids engineering. Others, such as the design and construction of electronic amplifiers or optical imaging systems, overlap with other fields. Thus the identification and development of learning materials and methods for instruction are part of a larger effort to identify competencies needed in active research and technical innovation.
Quinoa - Adaptive Computational Fluid Dynamics, 0.2
Energy Technology Data Exchange (ETDEWEB)
2017-09-22
Quinoa is a set of computational tools that enables research and numerical analysis in fluid dynamics. At this time it remains a test-bed to experiment with various algorithms using fully asynchronous runtime systems. Currently, Quinoa consists of the following tools: (1) Walker, a numerical integrator for systems of stochastic differential equations in time. It is a mathematical tool to analyze and design the behavior of stochastic differential equations. It allows the estimation of arbitrary coupled statistics and probability density functions and is currently used for the design of statistical moment approximations for multiple mixing materials in variable-density turbulence. (2) Inciter, an overdecomposition-aware finite element field solver for partial differential equations using 3D unstructured grids. Inciter is used to research asynchronous mesh-based algorithms and to experiment with coupling asynchronous to bulk-synchronous parallel code. Two planned new features of Inciter, compared to the previous release (LA-CC-16-015), to be implemented in 2017, are (a) a simple Navier-Stokes solver for ideal single-material compressible gases, and (b) solution-adaptive mesh refinement (AMR), which enables dynamically concentrating compute resources to regions with interesting physics. Using the NS-AMR problem we plan to explore how to scale such high-load-imbalance simulations, representative of large production multiphysics codes, to very large problems on very large computers using an asynchronous runtime system. (3) RNGTest, a test harness to subject random number generators to stringent statistical tests enabling quantitative ranking with respect to their quality and computational cost. (4) UnitTest, a unit test harness, running hundreds of tests per second, capable of testing serial, synchronous, and asynchronous functions. (5) MeshConv, a mesh file converter that can be used to convert 3D tetrahedron meshes from and to either of the following formats: Gmsh
International Nuclear Information System (INIS)
Pana, P.
1975-12-01
A mathematical model is derived to describe the fluid-dynamics for the region of subcooled water. The qualitative changes, when crossing the saturation line, from the wet-steam region to the subcooled region, are discussed with respect to thermodynamical considerations, and the change of state in the subcooled region is treated detailled, showing the limitation of validity for the theoretical model. (orig./TK) [de
Hoover, Wm G; Hoover, Carol G
2010-04-01
Guided by molecular dynamics simulations, we generalize the Navier-Stokes-Fourier constitutive equations and the continuum motion equations to include both transverse and longitudinal temperatures. To do so we partition the contributions of the heat transfer, the work done, and the heat flux vector between the longitudinal and transverse temperatures. With shockwave boundary conditions time-dependent solutions of these equations converge to give stationary shockwave profiles. The profiles include anisotropic temperature and can be fitted to molecular dynamics results, demonstrating the utility and simplicity of a two-temperature description of far-from-equilibrium states.
Fluid dynamics of moving fish in a two-dimensional multiparticle collision dynamics model
Reid, Daniel A. P.; Hildenbrandt, H.; Hemelrijk, C. K.; Padding, J.T.
2012-01-01
The fluid dynamics of animal locomotion, such as that of an undulating fish, are of great interest to both biologists and engineers. However, experimentally studying these fluid dynamics is difficult and time consuming. Model studies can be of great help because of their simpler and more detailed
DEFF Research Database (Denmark)
Larsson, Hilde Kristina
the velocity and pressure distributions in a fluid. CFD also enables the modelling of several fluids simultaneously, e.g. gas bubbles in a liquid, as well as the presence of turbulence and dissolved chemicals in a fluid, and many other phenomena. This makes CFD an appreciated tool for studying flow structures......, mixing, and other mass transfer phenomena in chemical and biochemical reactor systems. In this project, four selected case studies are investigated in order to explore the capabilities of CFD. The selected cases are a 1 ml stirred microbioreactor, an 8 ml magnetically stirred reactor, a Rushton impeller...... and an ion-exchange reaction are also modelled and compared to experimental data. The thesis includes a comprehensive overview of the fundamentals behind a CFD software, as well as a more detailed review of the fluid dynamic phenomena investigated in this project. The momentum and continuity equations...
AFDM: An advanced fluid-dynamics model
International Nuclear Information System (INIS)
Henneges, G.; Kleinheins, S.
1994-01-01
This volume of the Advanced Fluid-Dynamics Model (AFDM) documents the modeling of the equation of state (EOS) in the code. The authors present an overview of the basic concepts underlying the thermodynamics modeling and resulting EOS, which is a set of relations between the thermodynamic properties of materials. The AFDM code allows for multiphase-multimaterial systems, which they explore in three phase models: two-material solid, two-material liquid, and three-material vapor. They describe and compare two ways of specifying the EOS of materials: (1) as simplified analytic expressions, or (2) as tables that precisely describe the properties of materials and their interactions for mechanical equilibrium. Either of the two EOS models implemented in AFDM can be selected by specifying the option when preprocessing the source code for compilation. Last, the authors determine thermophysical properties such as surface tension, thermal conductivities, and viscosities in the model for the intracell exchanges of AFDM. Specific notations, routines, EOS data, plots, test results, and corrections to the code are available in the appendices
Fluid dynamics theory, computation, and numerical simulation
Pozrikidis, C
2017-01-01
This book provides an accessible introduction to the basic theory of fluid mechanics and computational fluid dynamics (CFD) from a modern perspective that unifies theory and numerical computation. Methods of scientific computing are introduced alongside with theoretical analysis and MATLAB® codes are presented and discussed for a broad range of topics: from interfacial shapes in hydrostatics, to vortex dynamics, to viscous flow, to turbulent flow, to panel methods for flow past airfoils. The third edition includes new topics, additional examples, solved and unsolved problems, and revised images. It adds more computational algorithms and MATLAB programs. It also incorporates discussion of the latest version of the fluid dynamics software library FDLIB, which is freely available online. FDLIB offers an extensive range of computer codes that demonstrate the implementation of elementary and advanced algorithms and provide an invaluable resource for research, teaching, classroom instruction, and self-study. This ...
Computational fluid dynamics (CFD) modelling of coal/biomass co-firing in pulverised fuel boilers
Energy Technology Data Exchange (ETDEWEB)
Moghtaderi, B.; Meesri, C. [University of Newcastle, Callaghan, NSW (Australia). CRC for Coal in Sustainable Development, Dept. of Chemical Engineering
2002-07-01
The present study is concerned with computational fluid dynamics (CFD) modelling of coal/biomass blends co-fired under conditions pertinent to pulverised fuel (PF) boilers. The attention is particularly focused on the near burner zone to examine the impact of biomass on the flame geometry and temperature. The predictions are obtained by numerical solution of the conservation equations for the gas and particle phases. The gas phase is solved in the Eulerian domain using steady-state time-averaged Navier-Stokes equations while the solution of the particle phase is obtained from a series of Lagrangian particle tracking equations. Turbulence is modelled using the {kappa}-{epsilon} and Reynolds Stress models. The comparison between the predictions and experimental measurement reported in the literature resulted in a good agreement. Other influences of biomass co-firing are observed for fuel devolatilisation and burnout. 19 refs., 6 figs.
The fluid-dynamic paradigm of the dust-acoustic soliton
McKenzie, J. F.
2002-06-01
In most studies, the properties of dust-acoustic solitons are derived from the first integral of the Poisson equation, in which the shape of the pseudopotential determines both the conditions in which a soliton may exist and its amplitude. Here this first integral is interpreted as conservation of total momentum, which, along with the Bernoulli-like energy equations for each species, may be cast as the structure equation for the dust (or heavy-ion) speed in the wave. In this fluid-dynamic picture, the significance of the sonic points of each species becomes apparent. In the wave, the heavy-ion (or dust) flow speed is supersonic (relative to its sound speed), whereas the protons and electrons are subsonic (relative to their sound speeds), and the dust flow is driven towards its sonic point. It is this last feature that limits the strength (amplitude) of the wave, since the equilibrium point (the centre of the wave) must be reached before the dust speed becomes sonic. The wave is characterized by a compression in the heavies and a compression (rarefaction) in the electrons and a rarefaction (compression) in the protons if the heavies have positive (negative) charge, and the corresponding potential is a hump (dip). These features are elucidated by an exact analytical soliton, in a special case, which provides the fully nonlinear counterpoint to the weakly nonlinear sech2-type solitons associated with the Korteweg de Vries equation, and indicates the parameter regimes in which solitons may exist.
DEFF Research Database (Denmark)
Rasmussen, Anders Rønne; Sørensen, Mads Peter; Gaididei, Yuri Borisovich
2011-01-01
A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves the Hami...... is proposed. The dynamics of the rarefaction wave is approximated by a collective coordinate approach in the energy balance equation. © 2010 Springer Science+Business Media B.V.......A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves...... the Hamiltonian structure, in contrast to the Kuznetsov equation, a model often used in nonlinear acoustics. An exact traveling wave front solution is derived from a generalized traveling wave assumption for the velocity potential. Numerical studies of the evolution of a number of arbitrary initial conditions...
Dynamical TAP equations for non-equilibrium Ising spin glasses
DEFF Research Database (Denmark)
Roudi, Yasser; Hertz, John
2011-01-01
We derive and study dynamical TAP equations for Ising spin glasses obeying both synchronous and asynchronous dynamics using a generating functional approach. The system can have an asymmetric coupling matrix, and the external fields can be time-dependent. In the synchronously updated model, the TAP...... equations take the form of self consistent equations for magnetizations at time t+1, given the magnetizations at time t. In the asynchronously updated model, the TAP equations determine the time derivatives of the magnetizations at each time, again via self consistent equations, given the current values...... of the magnetizations. Numerical simulations suggest that the TAP equations become exact for large systems....
Structural priority approach to fluid-structure interaction problems
International Nuclear Information System (INIS)
Au-Yang, M.K.; Galford, J.E.
1981-01-01
In a large class of dynamic problems occurring in nuclear reactor safety analysis, the forcing function is derived from the fluid enclosed within the structure itself. Since the structural displacement depends on the fluid pressure, which in turn depends on the structural boundaries, a rigorous approach to this class of problems involves simultaneous solution of the coupled fluid mechanics and structural dynamics equations with the structural response and the fluid pressure as unknowns. This paper offers an alternate approach to the foregoing problems. 8 refs
Vortex dynamics in plasmas and fluids
DEFF Research Database (Denmark)
Juul Rasmussen, J.; Lynov, Jens-Peter; Hesthaven, J.S.
1994-01-01
The existence and dynamics of vortical structures in both homogeneous and inhomogeneous systems will be discussed. In particular the dynamics of monopolar and dipolar vortices in a plasma with nonuniform density and in a rotating fluid with varying Coriolis force is described. The role of vortica...
Time-nonlocal kinetic equations, jerk and hyperjerk in plasmas and solar physics
El-Nabulsi, Rami Ahmad
2018-06-01
The simulation and analysis of nonlocal effects in fluids and plasmas is an inherently complicated problem due to the massive breadth of physics required to describe the nonlocal dynamics. This is a multi-physics problem that draws upon various miscellaneous fields, such as electromagnetism and statistical mechanics. In this paper we strive to focus on one narrow but motivating mathematical way: the derivation of nonlocal plasma-fluid equations from a generalized nonlocal Liouville derivative operator motivated from Suykens's nonlocal arguments. The paper aims to provide a guideline toward modeling nonlocal effects occurring in plasma-fluid systems by means of a generalized nonlocal Boltzmann equation. The generalized nonlocal equations of fluid dynamics are derived and their implications in plasma-fluid systems are addressed, discussed and analyzed. Three main topics were discussed: Landau damping in plasma electrodynamics, ideal MHD and solar wind. A number of features were revealed, analyzed and confronted with recent research results and observations.
Local invariants in non-ideal flows of neutral fluids and two-fluid plasmas
Zhu, Jian-Zhou
2018-03-01
The main objective is the locally invariant geometric object of any (magneto-)fluid dynamics with forcing and damping (nonideal), while more attention is paid to the untouched dynamical properties of two-fluid fashion. Specifically, local structures, beyond the well-known "frozen-in" to the barotropic flows of the generalized vorticities, of the two-fluid model of plasma flows are presented. More general non-barotropic situations are also considered. A modified Euler equation [T. Tao, "Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation," Ann. PDE 2, 9 (2016)] is also accordingly analyzed and remarked from the angle of view of the two-fluid model, with emphasis on the local structures. The local constraints of high-order differential forms such as helicity, among others, find simple formulation for possible practices in modeling the dynamics. Thus, the Cauchy invariants equation [N. Besse and U. Frisch, "Geometric formulation of the Cauchy invariants for incompressible Euler flow in flat and curved spaces," J. Fluid Mech. 825, 412 (2017)] may be enabled to find applications in non-ideal flows. Some formal examples are offered to demonstrate the calculations, and particularly interestingly the two-dimensional-three-component (2D3C) or the 2D passive scalar problem presents that a locally invariant Θ = 2θζ, with θ and ζ being, respectively, the scalar value of the "vertical velocity" (or the passive scalar) and the "vertical vorticity," may be used as if it were the spatial density of the globally invariant helicity, providing a Lagrangian prescription to control the latter in some situations of studying its physical effects in rapidly rotating flows (ubiquitous in atmosphere of astrophysical objects) with marked 2D3C vortical modes or in purely 2D passive scalars.
Associative Yang-Baxter equation for quantum (semi-)dynamical R-matrices
International Nuclear Information System (INIS)
Sechin, Ivan; Zotov, Andrei
2016-01-01
In this paper we propose versions of the associative Yang-Baxter equation and higher order R-matrix identities which can be applied to quantum dynamical R-matrices. As is known quantum non-dynamical R-matrices of Baxter-Belavin type satisfy this equation. Together with unitarity condition and skew-symmetry it provides the quantum Yang-Baxter equation and a set of identities useful for different applications in integrable systems. The dynamical R-matrices satisfy the Gervais-Neveu-Felder (or dynamical Yang-Baxter) equation. Relation between the dynamical and non-dynamical cases is described by the IRF (interaction-round-a-face)-Vertex transformation. An alternative approach to quantum (semi-)dynamical R-matrices and related quantum algebras was suggested by Arutyunov, Chekhov, and Frolov (ACF) in their study of the quantum Ruijsenaars-Schneider model. The purpose of this paper is twofold. First, we prove that the ACF elliptic R-matrix satisfies the associative Yang-Baxter equation with shifted spectral parameters. Second, we directly prove a simple relation of the IRF-Vertex type between the Baxter-Belavin and the ACF elliptic R-matrices predicted previously by Avan and Rollet. It provides the higher order R-matrix identities and an explanation of the obtained equations through those for non-dynamical R-matrices. As a by-product we also get an interpretation of the intertwining transformation as matrix extension of scalar theta function likewise R-matrix is interpreted as matrix extension of the Kronecker function. Relations to the Gervais-Neveu-Felder equation and identities for the Felder’s elliptic R-matrix are also discussed.
Distributed Approximating Functional Approach to Burgers' Equation ...
African Journals Online (AJOL)
This equation is similar to, but simpler than, the Navier-Stokes equation in fluid dynamics. To verify this advantage through some comparison studies, an exact series solution are also obtained. In addition, the presented scheme has numerically stable behavior. After demonstrating the convergence and accuracy of the ...
Two-equation and multi-fluid turbulence models for Rayleigh–Taylor mixing
International Nuclear Information System (INIS)
Kokkinakis, I.W.; Drikakis, D.; Youngs, D.L.; Williams, R.J.R.
2015-01-01
Highlights: • We present a new improved version of the K–L model. • The improved K–L is found in good agreement with the multi-fluid model and ILES. • The study concerns Rayleigh–Taylor flows at initial density ratios 3:1 and 20:1. - Abstract: This paper presents a new, improved version of the K–L model, as well as a detailed investigation of K–L and multi-fluid models with reference to high-resolution implicit large eddy simulations of compressible Rayleigh–Taylor mixing. The accuracy of the models is examined for different interface pressures and specific heat ratios for Rayleigh–Taylor flows at initial density ratios 3:1 and 20:1. It is shown that the original version of the K–L model requires modifications in order to provide comparable results to the multi-fluid model. The modifications concern the addition of an enthalpy diffusion term to the energy equation; the formulation of the turbulent kinetic energy (source) term in the K equation; and the calculation of the local Atwood number. The proposed modifications significantly improve the results of the K–L model, which are found in good agreement with the multi-fluid model and implicit large eddy simulations with respect to the self-similar mixing width; peak turbulent kinetic energy growth rate, as well as volume fraction and turbulent kinetic energy profiles. However, a key advantage of the two-fluid model is that it can represent the degree of molecular mixing in a direct way, by transferring mass between the two phases. The limitations of the single-fluid K–L model as well as the merits of more advanced Reynolds-averaged Navier–Stokes models are also discussed throughout the paper.
Duran-Olivencia, Miguel A.; Goddard, Ben; Kalliadasis, Serafim
2015-11-01
Over the last few decades the classical density-functional theory (DFT) and its dynamic extensions (DDFTs) have become a remarkably powerful tool in the study of colloidal fluids. Recently there has been extensive research to generalise all previous DDFTs finally yielding a general DDFT equation (for spherical particles) which takes into account both inertia and hydrodynamic interactions (HI) which strongly influence non-equilibrium properties. The present work will be devoted to a further generalisation of such a framework to systems of anisotropic particles. To this end, the kinetic equation for the Brownian particle distribution function is derived starting from the Liouville equation and making use of Zwanzig's projection-operator techniques. By averaging over all but one particle, a DDFT equation is finally obtained with some similarities to that for spherical colloids. However, there is now an inevitable translational-rotational coupling which affects the diffusivity of asymmetric particles. Lastly, in the overdamped (high friction) limit the theory is notably simplified leading to a DDFT equation which agrees with previous derivations. We acknowledge financial support from European Research Council via Advanced Grant No. 247031.
International Nuclear Information System (INIS)
Sabundjian, Gaiane
1999-01-01
This work presents a novel numeric method, based on the finite element method, applied for the solution of the Navier-Stokes equations for incompressible fluids in two dimensions in laminar flow. The method is based on the expansion of the variables in almost hierarchical functions. The used expansion functions are based on Legendre polynomials, adjusted in the rectangular elements in a such a way that corner, side and area functions are defined. The order of the expansion functions associated with the sides and with the area of the elements can be adjusted to the necessary or desired degree. This novel numeric method is denominated by Hierarchical Expansion Method. In order to validate the proposed numeric method three well-known problems of the literature in two dimensions are analyzed. The results show the method capacity in supplying precise results. From the results obtained in this thesis it is possible to conclude that the hierarchical expansion method can be applied successfully for the solution of fluid dynamic problems that involve incompressible fluids. (author)
Xiao, Li; Cai, Qin; Li, Zhilin; Zhao, Hongkai; Luo, Ray
2014-11-25
A multi-scale framework is proposed for more realistic molecular dynamics simulations in continuum solvent models by coupling a molecular mechanics treatment of solute with a fluid mechanics treatment of solvent. This article reports our initial efforts to formulate the physical concepts necessary for coupling the two mechanics and develop a 3D numerical algorithm to simulate the solvent fluid via the Navier-Stokes equation. The numerical algorithm was validated with multiple test cases. The validation shows that the algorithm is effective and stable, with observed accuracy consistent with our design.
Effect of centrifugation on dynamic susceptibility of magnetic fluids
International Nuclear Information System (INIS)
Pshenichnikov, Alexander; Lebedev, Alexander; Lakhtina, Ekaterina; Kuznetsov, Andrey
2017-01-01
Highlights: • Six samples of magnetic fluid were obtained by centrifuging two base ferrocolloids. • Aggregates in magnetic fluids are main reason of dynamic susceptibility dispersion. • Centrifugation is an effective way of changing the dynamic susceptibility. - Abstract: The dispersive composition, dynamic susceptibility and spectrum of times of magnetization relaxation for six samples of magnetic fluid obtained by centrifuging two base colloidal solutions of the magnetite in kerosene was investigated experimentally. The base solutions differed by the concentration of the magnetic phase and the width of the particle size distribution. The procedure of cluster analysis allowing one to estimate the characteristic sizes of aggregates with uncompensated magnetic moments was described. The results of the magnetogranulometric and cluster analyses were discussed. It was shown that centrifugation has a strong effect on the physical properties of the separated fractions, which is related to the spatial redistribution of particles and multi-particle aggregates. The presence of aggregates in magnetic fluids is interpreted as the main reason of low-frequency (0.1–10 kHz) dispersion of the dynamic susceptibility. The obtained results count in favor of using centrifugation as an effective means of changing the dynamic susceptibility over wide limits and obtaining fluids with the specified type of susceptibility dispersion.
Effect of centrifugation on dynamic susceptibility of magnetic fluids
Energy Technology Data Exchange (ETDEWEB)
Pshenichnikov, Alexander, E-mail: pshenichnikov@icmm.ru; Lebedev, Alexander; Lakhtina, Ekaterina; Kuznetsov, Andrey
2017-06-15
Highlights: • Six samples of magnetic fluid were obtained by centrifuging two base ferrocolloids. • Aggregates in magnetic fluids are main reason of dynamic susceptibility dispersion. • Centrifugation is an effective way of changing the dynamic susceptibility. - Abstract: The dispersive composition, dynamic susceptibility and spectrum of times of magnetization relaxation for six samples of magnetic fluid obtained by centrifuging two base colloidal solutions of the magnetite in kerosene was investigated experimentally. The base solutions differed by the concentration of the magnetic phase and the width of the particle size distribution. The procedure of cluster analysis allowing one to estimate the characteristic sizes of aggregates with uncompensated magnetic moments was described. The results of the magnetogranulometric and cluster analyses were discussed. It was shown that centrifugation has a strong effect on the physical properties of the separated fractions, which is related to the spatial redistribution of particles and multi-particle aggregates. The presence of aggregates in magnetic fluids is interpreted as the main reason of low-frequency (0.1–10 kHz) dispersion of the dynamic susceptibility. The obtained results count in favor of using centrifugation as an effective means of changing the dynamic susceptibility over wide limits and obtaining fluids with the specified type of susceptibility dispersion.
Partial differential equations for scientists and engineers
Farlow, Stanley J
1993-01-01
Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing th
The Price Equation, Gradient Dynamics, and Continuous Trait Game Theory.
Lehtonen, Jussi
2018-01-01
A recent article convincingly nominated the Price equation as the fundamental theorem of evolution and used it as a foundation to derive several other theorems. A major section of evolutionary theory that was not addressed is that of game theory and gradient dynamics of continuous traits with frequency-dependent fitness. Deriving fundamental results in these fields under the unifying framework of the Price equation illuminates similarities and differences between approaches and allows a simple, unified view of game-theoretical and dynamic concepts. Using Taylor polynomials and the Price equation, I derive a dynamic measure of evolutionary change, a condition for singular points, the convergence stability criterion, and an alternative interpretation of evolutionary stability. Furthermore, by applying the Price equation to a multivariable Taylor polynomial, the direct fitness approach to kin selection emerges. Finally, I compare these results to the mean gradient equation of quantitative genetics and the canonical equation of adaptive dynamics.
Conjugate Compressible Fluid Flow and Heat Transfer in Ducts
Cross, M. F.
2011-01-01
A computational approach to modeling transient, compressible fluid flow with heat transfer in long, narrow ducts is presented. The primary application of the model is for analyzing fluid flow and heat transfer in solid propellant rocket motor nozzle joints during motor start-up, but the approach is relevant to a wide range of analyses involving rapid pressurization and filling of ducts. Fluid flow is modeled through solution of the spatially one-dimensional, transient Euler equations. Source terms are included in the governing equations to account for the effects of wall friction and heat transfer. The equation solver is fully-implicit, thus providing greater flexibility than an explicit solver. This approach allows for resolution of pressure wave effects on the flow as well as for fast calculation of the steady-state solution when a quasi-steady approach is sufficient. Solution of the one-dimensional Euler equations with source terms significantly reduces computational run times compared to general purpose computational fluid dynamics packages solving the Navier-Stokes equations with resolved boundary layers. In addition, conjugate heat transfer is more readily implemented using the approach described in this paper than with most general purpose computational fluid dynamics packages. The compressible flow code has been integrated with a transient heat transfer solver to analyze heat transfer between the fluid and surrounding structure. Conjugate fluid flow and heat transfer solutions are presented. The author is unaware of any previous work available in the open literature which uses the same approach described in this paper.
APS presents prizes in fluid dynamics and plasma physics
International Nuclear Information System (INIS)
Anon.
1992-01-01
This article reviews the presentation of the American Physical Society awards in fluid dynamics and plasma physics. The recipient of the plasma physics James Clerk Maxwell Prize was John M. Green for contributions to the theory of magnetohydrodynamics equilibria and ideal and resistive instabilities, for discovering the inverse scattering transform leading to soliton solutions of many nonlinear partial differential equations and for inventing the residue method of determining the transition to global chaos. The excellence in Plasma Physics Research Award was presented to Nathaniel A. Fisch for theoretical investigations of noninductive current generation in toroidally confined plasma. Wim Pieter Leemans received the Simon Ramo Award for experimental and simulational contributions to laser-plasma physics. William R. Sears was given the 1992 Fuid Dynamics Prize for contributions to the study of steady and unsteady aerodynamics, aeroacoustics, magnetoaerodynamics,and wind tunnel design. William C. Reynolds received the Otto Laporte Award for experimental, theoretical, and computational work in turbulence modeling and control and leadership in direct numerical simulation and large eddy simulation
Dynamic data analysis modeling data with differential equations
Ramsay, James
2017-01-01
This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in...
Energy Technology Data Exchange (ETDEWEB)
Paolucci, S.
1982-12-01
An approximation leading to anelastic equations capable of describing thermal convection in a compressible fluid is given. These equations are more general than the Oberbeck-Boussinesq equations and different than the standard anelastic equations in that they can be used for the computation of convection in a fluid with large density gradients present. We show that the equations do not contain acoustic waves, while at the same time they can still describe the propagation of internal waves. Throughout we show that the filtering of acoustic waves, within the limits of the approximation, does not appreciably alter the description of the physics.
Implicit upwind schemes for computational fluid dynamics. Solution by domain decomposition
International Nuclear Information System (INIS)
Clerc, S.
1998-01-01
In this work, the numerical simulation of fluid dynamics equations is addressed. Implicit upwind schemes of finite volume type are used for this purpose. The first part of the dissertation deals with the improvement of the computational precision in unfavourable situations. A non-conservative treatment of some source terms is studied in order to correct some shortcomings of the usual operator-splitting method. Besides, finite volume schemes based on Godunov's approach are unsuited to compute low Mach number flows. A modification of the up-winding by preconditioning is introduced to correct this defect. The second part deals with the solution of steady-state problems arising from an implicit discretization of the equations. A well-posed linearized boundary value problem is formulated. We prove the convergence of a domain decomposition algorithm of Schwartz type for this problem. This algorithm is implemented either directly, or in a Schur complement framework. Finally, another approach is proposed, which consists in decomposing the non-linear steady state problem. (author)
The Fluid Dynamics of Competitive Swimming
Wei, Timothy; Mark, Russell; Hutchison, Sean
2014-01-01
Nowhere in sport is performance so dependent on the interaction of the athlete with the surrounding medium than in competitive swimming. As a result, understanding (at least implicitly) and controlling (explicitly) the fluid dynamics of swimming are essential to earning a spot on the medal stand. This is an extremely complex, highly multidisciplinary problem with a broad spectrum of research approaches. This review attempts to provide a historical framework for the fluid dynamics-related aspects of human swimming research, principally conducted roughly over the past five decades, with an emphasis on the past 25 years. The literature is organized below to show a continuous integration of computational and experimental technologies into the sport. Illustrations from the authors' collaborations over a 10-year period, coupling the knowledge and experience of an elite-level coach, a lead biomechanician at USA Swimming, and an experimental fluid dynamicist, are intended to bring relevance and immediacy to the review.
Ermakov-Pinney equation in scalar field cosmologies
International Nuclear Information System (INIS)
Hawkins, Rachael M.; Lidsey, James E.
2002-01-01
It is shown that the dynamics of cosmologies sourced by a mixture of perfect fluids and self-interacting scalar fields are described by the nonlinear, Ermakov-Pinney equation. The general solution of this equation can be expressed in terms of particular solutions to a related, linear differential equation. This characteristic is employed to derive exact cosmologies in the inflationary and quintessential scenarios. The relevance of the Ermakov-Pinney equation to the braneworld scenario is discussed
Directory of Open Access Journals (Sweden)
Mohsen Mehrabi
2012-01-01
Full Text Available This study focuses on the behavior of blood flow in the stenosed vessels. Blood is modelled as an incompressible non-Newtonian fluid which is based on the power law viscosity model. A numerical technique based on the finite difference method is developed to simulate the blood flow taking into account the transient periodic behaviour of the blood flow in cardiac cycles. Also, pulsatile blood flow in the stenosed vessel is based on the Womersley model, and fluid flow in the lumen region is governed by the continuity equation and the Navier-Stokes equations. In this study, the stenosis shape is cosine by using Tu and Devil model. Comparing the results obtained from three stenosed vessels with 30%, 50%, and 75% area severity, we find that higher percent-area severity of stenosis leads to higher extrapressure jumps and higher blood speeds around the stenosis site. Also, we observe that the size of the stenosis in stenosed vessels does influence the blood flow. A little change on the cross-sectional value makes vast change on the blood flow rate. This simulation helps the people working in the field of physiological fluid dynamics as well as the medical practitioners.
Analytical approach to linear fractional partial differential equations arising in fluid mechanics
International Nuclear Information System (INIS)
Momani, Shaher; Odibat, Zaid
2006-01-01
In this Letter, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving linear fractional partial differential equations arising in fluid mechanics. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these methods, the solution takes the form of a convergent series with easily computable components. The corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations. Some numerical examples are presented to illustrate the efficiency and reliability of the two methods
The Variety of Fluid Dynamics.
Barnes, Francis; And Others
1980-01-01
Discusses three research topics which are concerned with eminently practical problems and deal at the same time with fundamental fluid dynamical problems. These research topics come from the general areas of chemical and biological engineering, geophysics, and pure mathematics. (HM)
A conservative finite difference method for the numerical solution of plasma fluid equations
International Nuclear Information System (INIS)
Colella, P.; Dorr, M.R.; Wake, D.D.
1999-01-01
This paper describes a numerical method for the solution of a system of plasma fluid equations. The fluid model is similar to those employed in the simulation of high-density, low-pressure plasmas used in semiconductor processing. The governing equations consist of a drift-diffusion model of the electrons, together with an internal energy equation, coupled via Poisson's equation to a system of Euler equations for each ion species augmented with electrostatic force, collisional, and source/sink terms. The time integration of the full system is performed using an operator splitting that conserves space charge and avoids dielectric relaxation timestep restrictions. The integration of the individual ion species and electrons within the time-split advancement is achieved using a second-order Godunov discretization of the hyperbolic terms, modified to account for the significant role of the electric field in the propagation of acoustic waves, combined with a backward Euler discretization of the parabolic terms. Discrete boundary conditions are employed to accommodate the plasma sheath boundary layer on underresolved grids. The algorithm is described for the case of a single Cartesian grid as the first step toward an implementation on a locally refined grid hierarchy in which the method presented here may be applied on each refinement level
Two-Phase Fluid Simulation Using a Diffuse Interface Model with Peng--Robinson Equation of State
Qiao, Zhonghua; Sun, Shuyu
2014-01-01
In this paper, two-phase fluid systems are simulated using a diffusive interface model with the Peng-Robinson equation of state (EOS), a widely used realistic EOS for hydrocarbon fluid in the petroleum industry. We first utilize the gradient theory
Challenges in fluid dynamics a new approach
Zeytounian, R Kh
2017-01-01
This monograph presents a synopsis of fluid dynamics based on the personal scientific experience of the author who has contributed immensely to the field. The interested reader will also benefit from the general historical context in which the material is presented in the book. The book covers a wide range of relevant topics of the field, and the main tool being rational asymptotic modelling (RAM) approach. The target audience primarily comprises experts in the field of fluid dynamics, but the book may also be beneficial for graduate students.
Cardiac fluid dynamics meets deformation imaging.
Dal Ferro, Matteo; Stolfo, Davide; De Paris, Valerio; Lesizza, Pierluigi; Korcova, Renata; Collia, Dario; Tonti, Giovanni; Sinagra, Gianfranco; Pedrizzetti, Gianni
2018-02-20
Cardiac function is about creating and sustaining blood in motion. This is achieved through a proper sequence of myocardial deformation whose final goal is that of creating flow. Deformation imaging provided valuable contributions to understanding cardiac mechanics; more recently, several studies evidenced the existence of an intimate relationship between cardiac function and intra-ventricular fluid dynamics. This paper summarizes the recent advances in cardiac flow evaluations, highlighting its relationship with heart wall mechanics assessed through the newest techniques of deformation imaging and finally providing an opinion of the most promising clinical perspectives of this emerging field. It will be shown how fluid dynamics can integrate volumetric and deformation assessments to provide a further level of knowledge of cardiac mechanics.
Computational fluid dynamics study of viscous fingering in supercritical fluid chromatography.
Subraveti, Sai Gokul; Nikrityuk, Petr; Rajendran, Arvind
2018-01-26
Axi-symmetric numerical simulations are carried out to study the dynamics of a plug introduced through a mixed-stream injection in supercritical fluid chromatographic columns. The computational fluid dynamics model developed in this work takes into account both the hydrodynamics and adsorption equilibria to describe the phenomena of viscous fingering and plug effect that contribute to peak distortions in mixed-stream injections. The model was implemented into commercial computational fluid dynamics software using user-defined functions. The simulations describe the propagation of both the solute and modifier highlighting the interplay between the hydrodynamics and plug effect. The simulated peaks showed good agreement with experimental data published in the literature involving different injection volumes (5 μL, 50 μL, 1 mL and 2 mL) of flurbiprofen on Chiralpak AD-H column using a mobile phase of CO 2 and methanol. The study demonstrates that while viscous fingering is the main source of peak distortions for large-volume injections (1 mL and 2 mL) it has negligible impact on small-volume injections (5 μL and 50 μL). Band broadening in small-volume injections arise mainly due to the plug effect. Crown Copyright © 2017. Published by Elsevier B.V. All rights reserved.
On petroleum fluid characterization with the PC-SAFT equation of state
DEFF Research Database (Denmark)
Liang, Xiaodong; Yan, Wei; Thomsen, Kaj
2014-01-01
The perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state has shown promising results for describing complex phase behaviors and high pressure properties of various systems. It has been proposed as an alternative to the classical cubic equations of state in the petroleum...... industry. It is, however, far from a simple task to develop a sophisticated oil characterization method for the PC-SAFT EOS. In this work, in order to answer some fundamental questions of developing new characterization methods for PC-SAFT, six methods are proposed to estimate the model parameters...
EDITORIAL: Changes to Fluid Dynamics Research in 2009 Changes to Fluid Dynamics Research in 2009
Funakoshi, Mitsuaki
2009-02-01
Welcome to the first issue of the modified Fluid Dynamics Research (FDR) journal, which is now being published by IOP Publishing on behalf of the Japan Society of Fluid Mechanics. Since its launch in 1986, FDR has become a well-established international journal that publishes theoretical, numerical and experimental studies contributing to the fundamental understanding and application of fluid phenomena. It has also been an invaluable resource for physicists and researchers in engineering interested in problems relevant to the motion of fluids. From 2009, FDR will be edited by a new international Editorial Board, with the strong intention of establishing the journal further and bringing it to a wider audience. In this new-look FDR, which will be published six times per year, readers will find several special sections containing high quality invited reviews and papers written by leading researchers who have been selected by the international Editorial Board. This is in addition to the regular papers on a variety of topical subjects by active researchers in the field. As before, there are no publication charges for standard articles, and now article numbering has been adopted, enabling accepted papers to be published online more quickly, ahead of print publication. In order to maintain a balanced and up-to-date perspective, we welcome feedback from our readers regarding the content of the journal, as well as suggestions for topics to cover and areas to highlight. Finally, I would like to thank our authors, members of the international Editorial Board, and the staff at IOP Publishing for producing this first issue. We hope you will enjoy reading this renewed and exciting journal for the international fluid dynamics community.
Optimization-based Fluid Simulation on Unstructured Meshes
DEFF Research Database (Denmark)
Misztal, Marek Krzysztof; Bridson, Robert; Erleben, Kenny
2010-01-01
for solving the fluid dynamics equations as well as direct access to the interface geometry data, making in- clusion of a new surface energy term feasible. Furthermore, using an unstructured mesh makes it straightforward to handle curved solid boundaries and gives us a possibility to explore several fluid...
Meta fluid dynamic as a gauge field theory
International Nuclear Information System (INIS)
Mendes, A.C.R.; Neves, C.; Oliveira, W.; Takakura, F.I.
2003-01-01
In this paper, the analog of Maxwell electromagnetism for hydrodynamic turbulence, the meta fluid dynamics, is extended in order to reformulate the meta fluid dynamics as a gauge field theory. That analogy opens up the possibility to investigate this theory as a constrained system. Having this possibility in mind, we propose a Lagrangian to describe this new theory of turbulence and, subsequently, analyze it from the symplectic point of view. From this analysis, a hidden gauge symmetry is revealed, providing a clear interpretation and meaning of the physics behind the meta fluid theory. Also, the geometrical interpretation to the gauge symmetries is discussed. (author)
Articulated pipes conveying fluid pulsating with high frequency
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
1999-01-01
Stability and nonlinear dynamics of two articulated pipes conveying fluid with a high-frequency pulsating component is investigated. The non-autonomous model equations are converted into autonomous equations by approximating the fast excitation terms with slowly varying terms. The downward hanging...... pipe position will lose stability if the mean flow speed exceeds a certain critical value. Adding a pulsating component to the fluid flow is shown to stabilize the hanging position for high values of the ratio between fluid and pipe-mass, and to marginally destabilize this position for low ratios....... An approximate nonlinear solution for small-amplitude flutter oscillations is obtained using a fifth-order multiple scales perturbation method, and large-amplitude oscillations are examined by numerical integration of the autonomous model equations, using a path-following algorithm. The pulsating fluid component...
New Directions in Mathematical Fluid Mechanics
Fursikov, Andrei V
2010-01-01
The scientific interests of Professor A.V. Kazhikhov were fundamentally devoted to Mathematical Fluid Mechanics, where he achieved outstanding results that had, and still have, a significant influence on this field. This volume, dedicated to the memory of A.V. Kazhikhov, presents the latest contributions from renowned world specialists in a number of new important directions of Mathematical Physics, mostly of Mathematical Fluid Mechanics, and, more generally, in the field of nonlinear partial differential equations. These results are mostly related to boundary value problems and to control problems for the Navier-Stokes equations, and for equations of heat convection. Other important topics include non-equilibrium processes, Poisson-Boltzmann equations, dynamics of elastic body, and related problems of function theory and nonlinear analysis.
Development of multidimensional two-fluid model code ACE-3D for evaluation of constitutive equations
Energy Technology Data Exchange (ETDEWEB)
Ohnuki, Akira; Akimoto, Hajime [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment; Kamo, Hideki
1996-11-01
In order to perform design calculations for a passive safety reactor with good accuracy by a multidimensional two-fluid model, we developed an analysis code, ACE-3D, which can apply for evaluation of constitutive equations. The developed code has the following features: 1. The basic equations are based on 3-dimensional two-fluid model and the orthogonal or the cylindrical coordinate system can be selected. The fluid system is air-water or steam-water. 2. The basic equations are formulated by the finite-difference scheme of staggered mesh. The convection term is formulated by an upwind scheme and the diffusion term by a center-difference scheme. 3. Semi-implicit numerical scheme is adopted and the mass and the energy equations are treated equally in convergent steps for Jacobi equations. 4. The interfacial stress term consists of drag force, life force, turbulent dispersion force, wall force and virtual mass force. 5. A {kappa}-{epsilon} turbulent model for bubbly flow is incorporated as the turbulent model. The predictive capability of ACE-3D has been verified using a data-base for bubbly flow in a small-scale vertical pipe. In future, the constitutive equations will be improved with a data-base in a large vertical pipe developed in our laboratory and we have a plan to construct a reliable analytical tool through the improvement work, the progress of calculational speed with vector and parallel processing, the assessments for phase change terms and so on. This report describes the outline for the basic equations and the finite-difference equations in ACE-3D code and also the outline for the program structure. Besides, the results for the assessments of ACE-3D code for the small-scale pipe are summarized. (author)
Development of multidimensional two-fluid model code ACE-3D for evaluation of constitutive equations
International Nuclear Information System (INIS)
Ohnuki, Akira; Akimoto, Hajime; Kamo, Hideki.
1996-11-01
In order to perform design calculations for a passive safety reactor with good accuracy by a multidimensional two-fluid model, we developed an analysis code, ACE-3D, which can apply for evaluation of constitutive equations. The developed code has the following features: 1. The basic equations are based on 3-dimensional two-fluid model and the orthogonal or the cylindrical coordinate system can be selected. The fluid system is air-water or steam-water. 2. The basic equations are formulated by the finite-difference scheme of staggered mesh. The convection term is formulated by an upwind scheme and the diffusion term by a center-difference scheme. 3. Semi-implicit numerical scheme is adopted and the mass and the energy equations are treated equally in convergent steps for Jacobi equations. 4. The interfacial stress term consists of drag force, life force, turbulent dispersion force, wall force and virtual mass force. 5. A κ-ε turbulent model for bubbly flow is incorporated as the turbulent model. The predictive capability of ACE-3D has been verified using a data-base for bubbly flow in a small-scale vertical pipe. In future, the constitutive equations will be improved with a data-base in a large vertical pipe developed in our laboratory and we have a plan to construct a reliable analytical tool through the improvement work, the progress of calculational speed with vector and parallel processing, the assessments for phase change terms and so on. This report describes the outline for the basic equations and the finite-difference equations in ACE-3D code and also the outline for the program structure. Besides, the results for the assessments of ACE-3D code for the small-scale pipe are summarized. (author)
Gyro-Landau fluid model of tokamak core fluctuations
International Nuclear Information System (INIS)
Leboeuf, J.N.; Carreras, B.A.; Dominguez, N.; Hedrick, C.L.; Sidikman, K.L.; Lynch, V.E.; Drake, J.B.; Walker, D.W.
1992-01-01
Dissipative trapped electron modes (DTEM) may be one of the causes of deterioration of confinement in tokamak and stellatator plasmas. We have implemented a fluid model to study DTEM turbulence in slab geometry. The electron dynamics include in addition to the adiabatic part, a non-adiabatic piece modeled with an i-delta-type response. The ion dynamics include Landau damping and FLR corrections through Landau fluid approximate techniques and Pade approximants for Γ 0 (b)=I 0 (b)e -b . The model follows from the gyrokinetic equation. Evolution equations, which closely resemble those used in standard reduced MHD, are presented since these are better suited to non-linear calculations. The numerical results of radially resolved calculations will be discussed. A recently developed hybrid model, which consists of a gyrokinetic implementation for the ions using particles and the same description for the electron dynamics as in the fluid model, will also be presented
Optics and Fluid Dynamics Department annual progress report for 1999
DEFF Research Database (Denmark)
Hanson, Steen Grüner; Johansen, Per Michael; Lynov, Jens-Peter
2000-01-01
The Optics and Fluid Dynamics Department performs basic and applied research within the three programmes: (1) optical materials, (2) optical diagnostics and information processing and (3) plasma and fluid dynamics. The department has core competences in:optical sensors, optical materials, biooptics...
Systems of quasilinear equations and their applications to gas dynamics
Roždestvenskiĭ, B L; Schulenberger, J R
1983-01-01
This book is essentially a new edition, revised and augmented by results of the last decade, of the work of the same title published in 1968 by "Nauka." It is devoted to mathematical questions of gas dynamics. Topics covered include Foundations of the Theory of Systems of Quasilinear Equations of Hyperbolic Type in Two Independent Variables; Classical and Generalized Solutions of One-Dimensional Gas Dynamics; Difference Methods for Solving the Equations of Gas Dynamics; and Generalized Solutions of Systems of Quasilinear Equations of Hyperbolic Type.
Dynamic rheological properties of viscoelastic magnetic fluids in uniform magnetic fields
International Nuclear Information System (INIS)
Yamaguchi, Hiroshi; Niu Xiaodong; Ye Xiaojiang; Li Mingjun; Iwamoto, Yuhiro
2012-01-01
The dynamic rheological properties of viscoelastic magnetic fluids in externally applied uniform magnetic fields are investigated by a laboratory-made cone-plate rheometer in this study. In particular, the effects of the magnetic field on the viscoelastic properties (the complex dynamic modulus) of the viscoelastic magnetic fluids are studied. In the investigation, three viscoelastic magnetic fluids are made by mixing a magnetic fluid and a viscoelastic fluid with different mass ratios. As a supplementation to the experimental investigation, a theoretical analysis is also presented. The present study shows that the viscosity and elasticity of the viscoelastic magnetic fluids are significantly influenced by the magnetic field and the concentrations of the magnetic particles in the test fluids. Theoretical analysis qualitatively explains the present findings. - Highlights: ► The dynamic rheological properties of the viscoelastic magnetic fluids in uniform magnetic fields are investigated. ► Both the magnetic field strength and the concentration of the magnetic particles in the fluids have significant effects on the viscosity and elasticity of the viscoelastic magnetic fluids. ► Theoretical prediction and analysis qualitatively explains the present findings.
Energy Technology Data Exchange (ETDEWEB)
Shintaku, H; Kawano, S [Department of Mechanical Science and Bioengineering, Graduate School of Engineering Science, Osaka University, Machikaneyama-cho, Toyonaka, Osaka 560-8531 (Japan); Okitsu, T [Transplantation Unit, Kyoto University Hospital, Kawara-cho Shogoin, Sakyo-ku, Kyoto 606-8507 (Japan); Matsumoto, S [Baylor Research Institute Islet Cell Laboratory, 1400 Eight Avenue, Fort Worth, TX 76104 (United States); Suzuki, T; Kanno, I; Kotera, H [Department of Microengineering, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501 (Japan)], E-mail: shintaku@me.es.osaka-u.ac.jp
2008-06-07
Among clinical treatments for type 1 diabetes mellitus, the transplantation of islets of Langerhans to the portal vein of the hepar is a commonly used treatment for glucose homeostasis. Islet purification using the density gradient of a solution in a centrifuge separator is required for safety and efficiency. In the purification, the number of tissues to be transplanted is reduced by removing the acinar tissue and gathering the islet from the digest of pancreas. However, the mechanical effects on the fracture of islets in the centrifuge due to fluid dynamic stress are a serious problem in the purification process. In this study, a preliminary experiment using a cylindrical rotating viscometer with a simple geometry is conducted in order to systematically clarify the effect of fluid dynamic stress on the fracture of islets. The effects of fluid dynamic stress on the islet configuration is quantitatively measured for various flow conditions, and a predictive fracture model is developed based on the experimental results. Furthermore, in the practical purification process in the COBE (Gambro BCT), which is widely used in clinical applications, we perform a numerical analysis of the fluid dynamic stress based on Navier-Stokes equations to estimate the stress conditions for islets. Using the fracture model and numerical analysis, the islet fracture characteristics using the COBE are successfully investigated. The results obtained in this study provide crucial information for the purification of islets by centrifuge in practical and clinical applications.
International Nuclear Information System (INIS)
Shintaku, H; Kawano, S; Okitsu, T; Matsumoto, S; Suzuki, T; Kanno, I; Kotera, H
2008-01-01
Among clinical treatments for type 1 diabetes mellitus, the transplantation of islets of Langerhans to the portal vein of the hepar is a commonly used treatment for glucose homeostasis. Islet purification using the density gradient of a solution in a centrifuge separator is required for safety and efficiency. In the purification, the number of tissues to be transplanted is reduced by removing the acinar tissue and gathering the islet from the digest of pancreas. However, the mechanical effects on the fracture of islets in the centrifuge due to fluid dynamic stress are a serious problem in the purification process. In this study, a preliminary experiment using a cylindrical rotating viscometer with a simple geometry is conducted in order to systematically clarify the effect of fluid dynamic stress on the fracture of islets. The effects of fluid dynamic stress on the islet configuration is quantitatively measured for various flow conditions, and a predictive fracture model is developed based on the experimental results. Furthermore, in the practical purification process in the COBE (Gambro BCT), which is widely used in clinical applications, we perform a numerical analysis of the fluid dynamic stress based on Navier-Stokes equations to estimate the stress conditions for islets. Using the fracture model and numerical analysis, the islet fracture characteristics using the COBE are successfully investigated. The results obtained in this study provide crucial information for the purification of islets by centrifuge in practical and clinical applications
All static spherically symmetric perfect-fluid solutions of Einstein's equations
International Nuclear Information System (INIS)
Lake, Kayll
2003-01-01
An algorithm based on the choice of a single monotone function (subject to boundary conditions) is presented which generates all regular static spherically symmetric perfect-fluid solutions of Einstein's equations. For physically relevant solutions the generating functions must be restricted by nontrivial integral-differential inequalities. Nonetheless, the algorithm is demonstrated here by the construction of an infinite number of previously unknown physically interesting exact solutions
Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations
Lorz, Alexander
2011-01-17
Nonlocal Lotka-Volterra models have the property that solutions concentrate as Dirac masses in the limit of small diffusion. Is it possible to describe the dynamics of the limiting concentration points and of the weights of the Dirac masses? What is the long time asymptotics of these Dirac masses? Can several Dirac masses coexist? We will explain how these questions relate to the so-called "constrained Hamilton-Jacobi equation" and how a form of canonical equation can be established. This equation has been established assuming smoothness. Here we build a framework where smooth solutions exist and thus the full theory can be developed rigorously. We also show that our form of canonical equation comes with a kind of Lyapunov functional. Numerical simulations show that the trajectories can exhibit unexpected dynamics well explained by this equation. Our motivation comes from population adaptive evolution a branch of mathematical ecology which models Darwinian evolution. © Taylor & Francis Group, LLC.
The Fluid Dynamics Demo Kit: Part I
Flack, Karen; Underhill, Patrick; Prestridge, Kathy
2012-11-01
The goal of this project is to develop a fluid dynamics demonstration/experiment kit that can be used by professors and graduate students at high school outreach events. The demonstrations in the kit will be easy to use and true crowd pleasers in order to inspire understanding and pique curiosity about the physics of flow. The kits will be inexpensive, containing readily available materials so that teachers can duplicate the demonstrations and experiments. The kits will be left with the teachers as a gift from the American Physics Society. The experiments and demonstrations cover the concepts of conservation of mass, momentum, and energy, Bernoulli's equation, frictional losses and the ideal gas law. For each experiment, the teachers will receive presentation material, access to instructional videos, plus a worksheet that can be used in a high school physics classroom. This kit has been developed through the efforts of the APS-DFD Mentoring and Outreach Committee and has received funding from the APS-DFD. Work funded by the APS-DFD.
Development of a CFD Code for Analysis of Fluid Dynamic Forces in Seals
Athavale, Mahesh M.; Przekwas, Andrzej J.; Singhal, Ashok K.
1991-01-01
The aim is to develop a 3-D computational fluid dynamics (CFD) code for the analysis of fluid flow in cylindrical seals and evaluation of the dynamic forces on the seals. This code is expected to serve as a scientific tool for detailed flow analysis as well as a check for the accuracy of the 2D industrial codes. The features necessary in the CFD code are outlined. The initial focus was to develop or modify and implement new techniques and physical models. These include collocated grid formulation, rotating coordinate frames and moving grid formulation. Other advanced numerical techniques include higher order spatial and temporal differencing and an efficient linear equation solver. These techniques were implemented in a 2D flow solver for initial testing. Several benchmark test cases were computed using the 2D code, and the results of these were compared to analytical solutions or experimental data to check the accuracy. Tests presented here include planar wedge flow, flow due to an enclosed rotor, and flow in a 2D seal with a whirling rotor. Comparisons between numerical and experimental results for an annular seal and a 7-cavity labyrinth seal are also included.
Viriato: a Fourier-Hermite spectral code for strongly magnetised fluid-kinetic plasma dynamics
Loureiro, Nuno; Dorland, William; Fazendeiro, Luis; Kanekar, Anjor; Mallet, Alfred; Zocco, Alessandro
2015-11-01
We report on the algorithms and numerical methods used in Viriato, a novel fluid-kinetic code that solves two distinct sets of equations: (i) the Kinetic Reduced Electron Heating Model equations [Zocco & Schekochihin, 2011] and (ii) the kinetic reduced MHD (KRMHD) equations [Schekochihin et al., 2009]. Two main applications of these equations are magnetised (Alfvnénic) plasma turbulence and magnetic reconnection. Viriato uses operator splitting to separate the dynamics parallel and perpendicular to the ambient magnetic field (assumed strong). Along the magnetic field, Viriato allows for either a second-order accurate MacCormack method or, for higher accuracy, a spectral-like scheme. Perpendicular to the field Viriato is pseudo-spectral, and the time integration is performed by means of an iterative predictor-corrector scheme. In addition, a distinctive feature of Viriato is its spectral representation of the parallel velocity-space dependence, achieved by means of a Hermite representation of the perturbed distribution function. A series of linear and nonlinear benchmarks and tests are presented, with focus on 3D decaying kinetic turbulence. Work partially supported by Fundação para a Ciência e Tecnologia via Grants UID/FIS/50010/2013 and IF/00530/2013.
Coslovich, Daniele; Kahl, Gerhard; Krakoviack, Vincent
2011-06-01
Over the past two decades, the dynamics of fluids under nanoscale confinement has attracted much attention. Motivation for this rapidly increasing interest is based on both practical and fundamental reasons. On the practical and rather applied side, problems in a wide range of scientific topics, such as polymer and colloidal sciences, rheology, geology, or biophysics, benefit from a profound understanding of the dynamical behaviour of confined fluids. Further, effects similar to those observed in confinement are expected in fluids whose constituents have strong size or mass asymmetry, and in biological systems where crowding and obstruction phenomena in the cytosol are responsible for clear separations of time scales for macromolecular transport in the cell. In fundamental research, on the other hand, the interest focuses on the complex interplay between confinement and structural relaxation, which is responsible for the emergence of new phenomena in the dynamics of the system: in confinement, geometric constraints associated with the pore shape are imposed to the adsorbed fluids and an additional characteristic length scale, i.e. the pore size, comes into play. For many years, the topic has been mostly experimentally driven. Indeed, a broad spectrum of systems has been investigated by sophisticated experimental techniques, while theoretical and simulation studies were rather scarce due to conceptual and computational issues. In the past few years, however, theory and simulations could largely catch up with experiments. On one side, new theories have been put forward that duly take into account the porosity, the connectivity, and the randomness of the confinement. On the other side, the ever increasing available computational power now allows investigations that were far out of reach a few years ago. Nowadays, instead of isolated state points, systematic investigations on the dynamics of confined fluids, covering a wide range of system parameters, can be realized
Fractional neutron point kinetics equations for nuclear reactor dynamics
International Nuclear Information System (INIS)
Espinosa-Paredes, Gilberto; Polo-Labarrios, Marco-A.; Espinosa-Martinez, Erick-G.; Valle-Gallegos, Edmundo del
2011-01-01
The fractional point-neutron kinetics model for the dynamic behavior in a nuclear reactor is derived and analyzed in this paper. The fractional model retains the main dynamic characteristics of the neutron motion in which the relaxation time associated with a rapid variation in the neutron flux contains a fractional order, acting as exponent of the relaxation time, to obtain the best representation of a nuclear reactor dynamics. The physical interpretation of the fractional order is related with non-Fickian effects from the neutron diffusion equation point of view. The numerical approximation to the solution of the fractional neutron point kinetics model, which can be represented as a multi-term high-order linear fractional differential equation, is calculated by reducing the problem to a system of ordinary and fractional differential equations. The numerical stability of the fractional scheme is investigated in this work. Results for neutron dynamic behavior for both positive and negative reactivity and for different values of fractional order are shown and compared with the classic neutron point kinetic equations. Additionally, a related review with the neutron point kinetics equations is presented, which encompasses papers written in English about this research topic (as well as some books and technical reports) published since 1940 up to 2010.
Spinodal decomposition in fluid mixtures
International Nuclear Information System (INIS)
Kawasaki, Kyozi; Koga, Tsuyoshi
1993-01-01
We study the late stage dynamics of spinodal decomposition in binary fluids by the computer simulation of the time-dependent Ginzburg-Landau equation. We obtain a temporary linear growth law of the characteristic length of domains in the late stage. This growth law has been observed in many real experiments of binary fluids and indicates that the domain growth proceeds by the flow caused by the surface tension of interfaces. We also find that the dynamical scaling law is satisfied in this hydrodynamic domain growth region. By comparing the scaling functions for fluids with that for the case without hydrodynamic effects, we find that the scaling functions for the two systems are different. (author)
Multiscale Behavior of Viscous Fluids Dynamics: Experimental Observations
Arciniega-Ceballos, Alejandra; Spina, Laura; Scheu, Bettina; Dingwell, Donald B.
2016-04-01
The dynamics of Newtonian fluids with viscosities of mafic to intermediate silicate melts (10-1000 Pa s) during slow decompression present multi-time scale processes. To observe these processes we have performed several experiments on silicon oil saturated with Argon gas for 72 hours, in a Plexiglas autoclave. The slow decompression, dropping from 10 MPa to ambient pressure, acting as the excitation mechanism, triggered several processes with their own distinct timescales. These processes generate complex non-stationary microseismic signals, which have been recorded with 7 high-dynamic piezoelectric sensors located along the conduit flanked by high-speed video recordings. The analysis in time and frequency of these time series and their correlation with the associated high-speed imaging enables the characterization of distinct phases and the extraction of the individual processes during the evolution of decompression of these viscous fluids. We have observed fluid-solid elastic interaction, degassing, fluid mass expansion and flow, bubble nucleation, growth, coalescence and collapse, foam building and vertical wagging. All these processes (in fine and coarse scales) are sequentially coupled in time, occur within specific pressure intervals, and exhibit a localized distribution along the conduit. Their coexistence and interactions constitute the stress field and driving forces that determine the dynamics of the conduit system. Our observations point to the great potential of this experimental approach in the understanding of volcanic conduit dynamics and volcanic seismicity.
Dynamic reponse of a cylindrical shell immersed in a potential fluid
International Nuclear Information System (INIS)
Cummings, G.E.
1978-01-01
A numerical solution technique is presented for determining the dynamic response of a thin, elastic, circular, cylindrical shell of constant wall thickness and density, immersed in a potential fluid. The shell may be excited by an arbitrary radial forcing function with a specified time history and spatial distribution. In addition, a pressure history may be specified over a segment of the fluid outer boundary. Any of the natural shell end conditions may be prescribed. A numerical instability prevented direct solutions where the ratio of the hydrodynamic forces to shell inertial forces is greater than two. This instability is believed to be the result of the weak coupling between the equations describing the fluid to those describing the shell. To circumvent this instability, an effective mass was calculated and added to the shell. Comparison of numerical to experimental results are made using a 1 / 12 scale model of a nuclear reactor core support barrel. Natural frequencies and modes are determined for this model in air, water, and oil. The computed frequencies compare to experimental results to within 15%. The use of this numerical technique is illustrated by comparing it to an analytical solution for shell beam modes and an uncertainty in the analytical technique concerning the proper effective mass to use, is resolved
Dynamic reponse of a cylindrical shell immersed in a potential fluid
Energy Technology Data Exchange (ETDEWEB)
Cummings, G.E.
1978-04-18
A numerical solution technique is presented for determining the dynamic response of a thin, elastic, circular, cylindrical shell of constant wall thickness and density, immersed in a potential fluid. The shell may be excited by an arbitrary radial forcing function with a specified time history and spatial distribution. In addition, a pressure history may be specified over a segment of the fluid outer boundary. Any of the natural shell end conditions may be prescribed. A numerical instability prevented direct solutions where the ratio of the hydrodynamic forces to shell inertial forces is greater than two. This instability is believed to be the result of the weak coupling between the equations describing the fluid to those describing the shell. To circumvent this instability, an effective mass was calculated and added to the shell. Comparison of numerical to experimental results are made using a /sup 1///sub 12/ scale model of a nuclear reactor core support barrel. Natural frequencies and modes are determined for this model in air, water, and oil. The computed frequencies compare to experimental results to within 15%. The use of this numerical technique is illustrated by comparing it to an analytical solution for shell beam modes and an uncertainty in the analytical technique concerning the proper effective mass to use, is resolved.
Unsteady bio-fluid dynamics in flying and swimming
Liu, Hao; Kolomenskiy, Dmitry; Nakata, Toshiyuki; Li, Gen
2017-08-01
Flying and swimming in nature present sophisticated and exciting ventures in biomimetics, which seeks sustainable solutions and solves practical problems by emulating nature's time-tested patterns, functions, and strategies. Bio-fluids in insect and bird flight, as well as in fish swimming are highly dynamic and unsteady; however, they have been studied mostly with a focus on the phenomena associated with a body or wings moving in a steady flow. Characterized by unsteady wing flapping and body undulation, fluid-structure interactions, flexible wings and bodies, turbulent environments, and complex maneuver, bio-fluid dynamics normally have challenges associated with low Reynolds number regime and high unsteadiness in modeling and analysis of flow physics. In this article, we review and highlight recent advances in unsteady bio-fluid dynamics in terms of leading-edge vortices, passive mechanisms in flexible wings and hinges, flapping flight in unsteady environments, and micro-structured aerodynamics in flapping flight, as well as undulatory swimming, flapping-fin hydrodynamics, body-fin interaction, C-start and maneuvering, swimming in turbulence, collective swimming, and micro-structured hydrodynamics in swimming. We further give a perspective outlook on future challenges and tasks of several key issues of the field.
Dynamic dielectrophoresis model of multi-phase ionic fluids.
Directory of Open Access Journals (Sweden)
Ying Yan
Full Text Available Ionic-based dielectrophoretic microchips have attracted significant attention due to their wide-ranging applications in electro kinetic and biological experiments. In this work, a numerical method is used to simulate the dynamic behaviors of ionic droplets in a microchannel under the effect of dielectrophoresis. When a discrete liquid dielectric is encompassed within a continuous fluid dielectric placed in an electric field, an electric force is produced due to the dielectrophoresis effect. If either or both of the fluids are ionic liquids, the magnitude and even the direction of the force will be changed because the net ionic charge induced by an electric field can affect the polarization degree of the dielectrics. However, using a dielectrophoresis model, assuming ideal dielectrics, results in significant errors. To avoid the inaccuracy caused by the model, this work incorporates the electrode kinetic equation and defines a relationship between the polarization charge and the net ionic charge. According to the simulation conditions presented herein, the electric force obtained in this work has an error exceeding 70% of the actual value if the false effect of net ionic charge is not accounted for, which would result in significant issues in the design and optimization of experimental parameters. Therefore, there is a clear motivation for developing a model adapted to ionic liquids to provide precise control for the dielectrophoresis of multi-phase ionic liquids.
Dynamic dielectrophoresis model of multi-phase ionic fluids.
Yan, Ying; Luo, Jing; Guo, Dan; Wen, Shizhu
2015-01-01
Ionic-based dielectrophoretic microchips have attracted significant attention due to their wide-ranging applications in electro kinetic and biological experiments. In this work, a numerical method is used to simulate the dynamic behaviors of ionic droplets in a microchannel under the effect of dielectrophoresis. When a discrete liquid dielectric is encompassed within a continuous fluid dielectric placed in an electric field, an electric force is produced due to the dielectrophoresis effect. If either or both of the fluids are ionic liquids, the magnitude and even the direction of the force will be changed because the net ionic charge induced by an electric field can affect the polarization degree of the dielectrics. However, using a dielectrophoresis model, assuming ideal dielectrics, results in significant errors. To avoid the inaccuracy caused by the model, this work incorporates the electrode kinetic equation and defines a relationship between the polarization charge and the net ionic charge. According to the simulation conditions presented herein, the electric force obtained in this work has an error exceeding 70% of the actual value if the false effect of net ionic charge is not accounted for, which would result in significant issues in the design and optimization of experimental parameters. Therefore, there is a clear motivation for developing a model adapted to ionic liquids to provide precise control for the dielectrophoresis of multi-phase ionic liquids.
International Nuclear Information System (INIS)
Hasse, R.W.; Ghosh, G.
1982-01-01
The long-mean-free-path nuclear fluid dynamics is extended to include damping. First the damping stress is derived from the solution of the Boltzmann equation for a breathing spherical container filled with a Fermi gas. Then the corresponding damping force is incorporated into Euler equations of motion and energies and widths of low lying collective resonances are computed as eigenfrequencies of a vibrating nucleus under surface tension and Coulomb potential as well as the high lying isoscalar giant resonances as eigenfrequencies of an elastic nucleus. Maximum damping is obtained if the particle frequency approximately resonates with the wall frequency. Theoretical results are compared with experimental data and future improvements are indicated
Augmented Lagrangian methods to solve Navier-Stokes equations for a Bingham fluid flow
International Nuclear Information System (INIS)
Boscardin, Laetitia
1999-01-01
The objective of this research thesis is to develop one or more methods for the numerical resolution of equations of movement obtained for a Bingham fluid. The resolution of Navier-Stokes equations is processed by splitting elliptic and hyperbolic operators (Galerkin transport). In this purpose, the author first studied the Stokes problem, and then addressed issues of stability and consistency of the global scheme. The variational formulation of the Stokes problem can be expressed under the form of a minimisation problem under the constraint of non linear and non differentiable functions. Then, the author proposes a discretization of the Stokes problem based on a hybrid finite element method. Then he extends the demonstrations of stability and consistency of the Galerkin-transport scheme which have been established for a Newtonian fluid, to the case of a Bingham fluid. A relaxation algorithm and a Newton-GMRES algorithm are developed to solve the problem, and their convergence is studied. To ensure this convergence, some constraints must be verified. In order to do so, a specific speed element has been developed [fr
Multiscale functions, scale dynamics, and applications to partial differential equations
Cresson, Jacky; Pierret, Frédéric
2016-05-01
Modeling phenomena from experimental data always begins with a choice of hypothesis on the observed dynamics such as determinism, randomness, and differentiability. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following: "With a finite set of data concerning a phenomenon, can we recover its underlying nature? From this problem, we introduce in this paper the definition of multi-scale functions, scale calculus, and scale dynamics based on the time scale calculus [see Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Springer Science & Business Media, 2001)] which is used to introduce the notion of scale equations. These definitions will be illustrated on the multi-scale Okamoto's functions. Scale equations are analysed using scale regimes and the notion of asymptotic model for a scale equation under a particular scale regime. The introduced formalism explains why a single scale equation can produce distinct continuous models even if the equation is scale invariant. Typical examples of such equations are given by the scale Euler-Lagrange equation. We illustrate our results using the scale Newton's equation which gives rise to a non-linear diffusion equation or a non-linear Schrödinger equation as asymptotic continuous models depending on the particular fractional scale regime which is considered.
Optics and Fluid Dynamics Department annual progress report for 2003
Bindslev, H.; Hanson, Steen Grüner; Lynov, Jens-Peter; Petersen, Paul Michael; Skaarup, Bitten
2004-01-01
The Optics and Fluid Dynamics Department performs basic and applied research within three scientific programmes: (1) laser systems and optical materials, (2) optical diagnostics and information processing and (3) plasma and fluid dynamics. The departmenthas core competences in: optical sensors, optical materials, optical storage, biophotonics, numerical modelling and information processing, non-linear dynamics, fusion plasma physics and plasma technology. The research is supported by several ...
International Nuclear Information System (INIS)
Mulero, A.; Cuadros, F; Faundez, C.A.
1999-01-01
Vapour-liquid equilibrium properties for both three- and two-dimensional Lennard-Jones fluids were obtained using simple cubic-in-density equations of state proposed by the authors. Results were compared with those obtained by other workers from computer simulations and also with results given by other more complex semi-theoretical or semi-empirical equations of state. In the three-dimensional case good agreement is found for all properties and all temperatures. In the two-dimensional case only the coexistence densities were compared, producing good agreement for low temperatures only. The present work is the first to give numerical data for the vapour-liquid equilibrium properties of Lennard-Jones fluids calculated from equations of state. Copyright (1999) CSIRO Australia
Classical and quantum dynamics of a perfect fluid scalar-metric cosmology
International Nuclear Information System (INIS)
Vakili, Babak
2010-01-01
We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology, coupled to a perfect fluid, in the context of the scalar-metric gravity. Using the Schutz' representation for the perfect fluid, we show that, under a particular gauge choice, it may lead to the identification of a time parameter for the corresponding dynamical system. It is shown that the evolution of the universe based on the classical cosmology represents a late time power law expansion coming from a big-bang singularity in which the scale factor goes to zero while the scalar field blows up. Moreover, this formalism gives rise to a Schroedinger-Wheeler-DeWitt (SWD) equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave function in order to investigate the possibility of the avoidance of classical singularities due to quantum effects by means of the many-worlds and ontological interpretation of quantum cosmology.
Chaotic dynamics in the Maxwell-Bloch equations
International Nuclear Information System (INIS)
Holm, D.D.; Kovacic, G.
1992-01-01
In the slowly varying envelope approximation and the rotating wave approximation for the Maxwell-Bloch equations, we describe how the presence of a small-amplitude probe laser in an excited, two-level, resonant medium leads to homoclinic chaos in the laser-matter dynamics. We also describe a derivation of the Maxwell-Bloch equations from an action principle
Symmetry breaking in fluid dynamics: Lie group reducible motions for real fluids
International Nuclear Information System (INIS)
Holm, D.D.
1976-07-01
The physics of fluids is based on certain kinematical invariance principles, which refer to coordinate systems, dimensions, and Galilean reference frames. Other, thermodynamic, symmetry principles are introduced by the material description. In the present work, the interplay between these two kinds of invariance principles is used to solve for classes of one-dimensional non-steady isentropic motions of a fluid whose equation of state is of Mie-Gruneisen type. Also, the change in profile and attenuation of weak shock waves in a dissipative medium is studied at the level of Burgers' approximation from the viewpoint of its underlying symmetry structure. The mathematical method of approach is based on the theory of infinitesimal Lie groups. Fluid motions are characterized according to inequivalent subgroups of the full invariance group of the flow description and exact group reducible solutions are presented
Symmetry breaking in fluid dynamics: Lie group reducible motions for real fluids
Energy Technology Data Exchange (ETDEWEB)
Holm, D.D.
1976-07-01
The physics of fluids is based on certain kinematical invariance principles, which refer to coordinate systems, dimensions, and Galilean reference frames. Other, thermodynamic, symmetry principles are introduced by the material description. In the present work, the interplay between these two kinds of invariance principles is used to solve for classes of one-dimensional non-steady isentropic motions of a fluid whose equation of state is of Mie-Gruneisen type. Also, the change in profile and attenuation of weak shock waves in a dissipative medium is studied at the level of Burgers' approximation from the viewpoint of its underlying symmetry structure. The mathematical method of approach is based on the theory of infinitesimal Lie groups. Fluid motions are characterized according to inequivalent subgroups of the full invariance group of the flow description and exact group reducible solutions are presented.
Fluid Dynamics of Pressurized, Entrained Coal Gasifiers
International Nuclear Information System (INIS)
1997-01-01
Pressurized, entrained gasification is a promising new technology for the clean and efficient combustion of coal. Its principle is to operate a coal gasifier at a high inlet gas velocity to increase the inflow of reactants, and at an elevated pressure to raise the overall efficiency of the process. Unfortunately, because of the extraordinary difficulties involved in performing measurements in hot, pressurized, high-velocity pilot plants, its fluid dynamics are largely unknown. Thus the designer cannot predict with certainty crucial phenomena like erosion, heat transfer and solid capture. In this context, we are conducting a study of the fluid dynamics of Pressurized Entrained Coal Gasifiers (PECGs). The idea is to simulate the flows in generic industrial PECGs using dimensional similitude. To this end, we employ a unique entrained gas-solid flow facility with the flexibility to recycle--rather than discard--gases other than air. By matching five dimensionless parameters, suspensions in mixtures of helium, carbon dioxide and sulfur hexafluoride simulate the effects of pressure and scale-upon the fluid dynamics of PECGs. Because it operates under cold, atmospheric conditions, the laboratory facility is ideal for detailed measurements
Nonlinear fluid equations for fully toroidal electromagnetic waves for the core tokamak plasma
Weiland, J.; Liu, C. S.; Liu
2013-12-01
The rather general set of fluid equations with full curvature effects (Shukla and Weiland, Phys. Rev. A 40, 341 (1989)) has been modified to apply to the core and generalized to include also microtearing modes.
International Nuclear Information System (INIS)
Kunihiro, Teiji; Minami, Yuki; Tsumura, Kyosuke
2009-01-01
The dynamical density fluctuations around the QCD critical point (CP) are analyzed using relativistic dissipative fluid dynamics, and we show that the sound mode around the QCD CP is strongly attenuated whereas the thermal fluctuation stands out there. We speculate that if possible suppression or disappearance of a Mach cone, which seems to be created by the partonic jets at RHIC, is observed as the incident energy of the heavy-ion collisions is decreased, it can be a signal of the existence of the QCD CP. We have presented the Israel-Stewart type fluid dynamic equations that are derived rigorously on the basis of the (dynamical) renormalization group method in the second part of the talk, which we omit here because of a lack of space.
Kunihiro, Teiji; Minami, Yuki; Tsumura, Kyosuke
2009-11-01
The dynamical density fluctuations around the QCD critical point (CP) are analyzed using relativistic dissipative fluid dynamics, and we show that the sound mode around the QCD CP is strongly attenuated whereas the thermal fluctuation stands out there. We speculate that if possible suppression or disappearance of a Mach cone, which seems to be created by the partonic jets at RHIC, is observed as the incident energy of the heavy-ion collisions is decreased, it can be a signal of the existence of the QCD CP. We have presented the Israel-Stewart type fluid dynamic equations that are derived rigorously on the basis of the (dynamical) renormalization group method in the second part of the talk, which we omit here because of a lack of space.
Singular multiparameter dynamic equations with distributional ...
African Journals Online (AJOL)
Singular multiparameter dynamic equations with distributional potentials on time scales. ... In this paper, we consider both singular single and several multiparameter ... multiple function which is of one sign and nonzero on the given time scale.
Krekelberg, William P; Siderius, Daniel W; Shen, Vincent K; Truskett, Thomas M; Errington, Jeffrey R
2017-08-03
Using molecular simulations, we investigate how the range of fluid-fluid (adsorbate-adsorbate) interactions and the strength of fluid-solid (adsorbate-adsorbent) interactions impact the strong connection between distinct adsorptive regimes and distinct self-diffusivity regimes reported in [Krekelberg, W. P.; Siderius, D. W.; Shen, V. K.; Truskett, T. M.; Errington, J. R. Langmuir 2013 , 29 , 14527-14535]. Although increasing the fluid-fluid interaction range changes both the thermodynamics and the dynamic properties of adsorbed fluids, the previously reported connection between adsorptive filling regimes and self-diffusivity regimes remains. Increasing the fluid-fluid interaction range leads to enhanced layering and decreased self-diffusivity in the multilayer-formation regime but has little effect on the properties within film-formation and pore-filling regimes. We also find that weakly attractive adsorbents, which do not display distinct multilayer formation, are hard-sphere-like at super- and subcritical temperatures. In this case, the self-diffusivity of the confined and bulk fluid has a nearly identical scaling-relationship with effective density.
Energy Technology Data Exchange (ETDEWEB)
Kan, Kan; Liu, Huiwen; Yang, Chunxia [Hohai University, Nanjing (China); Zheng, Yuan [National Engineering Research Center of Water Resources Efficient Utilization and Engineering Safety, Nanjing (China); Fu, Shifeng; Zhang, Xin [Power China Huadong Engineering Corporation, Hangzhou (China)
2017-04-15
Current research on the stability of tubular pumps is mainly concerned with the transient hydrodynamic characteristics. However, the structural response under the influence of fluid-structure interaction hasn't been taken fully into consideration. The instability of the structure can cause vibration and cracks, which may threaten the safety of the unit. We used bidirectional fluid-structure interaction to comprehensively analyze the dynamic stress characteristics of the impeller blades of the shaft extension tubular pump device. Furthermore, dynamic stress of impeller blade of shaft extension tubular pump device was solved under different lift conditions of 0° blade angle. Based on Reynolds-average N-S equation and SST k-ω turbulence model, numerical simulation was carried out for three-dimensional unsteady incompressible turbulent flow field of the pump device whole flow passage. Meanwhile, the finite element method was used to calculate dynamic characteristics of the blade structure. The blade dynamic stress distribution was obtained on the basis of fourth strength theory. The research results indicate that the maximum blade dynamic stress appears at the joint between root of inlet side of the blade suction surface and the axis. Considering the influence of gravity, the fluctuation of the blade dynamic stress increases initially and decreases afterwards within a rotation period. In the meantime, the dynamic stress in the middle part of inlet edge presents larger relative fluctuation amplitude. Finally, a prediction method for dynamic stress distribution of tubular pump considering fluid-structure interaction and gravity effect was proposed. This method can be used in the design stage of tubular pump to predict dynamic stress distribution of the structure under different operating conditions, improve the reliability of pump impeller and analyze the impeller fatigue life.
International Nuclear Information System (INIS)
Webb, G M; Zank, G P
2007-01-01
We explore the role of the Lagrangian map for Lie symmetries in magnetohydrodynamics (MHD) and gas dynamics. By converting the Eulerian Lie point symmetries of the Galilei group to Lagrange label space, in which the Eulerian position coordinate x is regarded as a function of the Lagrange fluid labels x 0 and time t, one finds that there is an infinite class of symmetries in Lagrange label space that map onto each Eulerian Lie point symmetry of the Galilei group. The allowed transformation of the Lagrangian fluid labels x 0 corresponds to a fluid relabelling symmetry, including the case where there is no change in the fluid labels. We also consider a class of three, well-known, scaling symmetries for a gas with a constant adiabatic index γ. These symmetries map onto a modified form of the fluid relabelling symmetry determining equations, with non-zero source terms. We determine under which conditions these symmetries are variational or divergence symmetries of the action, and determine the corresponding Lagrangian and Eulerian conservation laws by use of Noether's theorem. These conservation laws depend on the initial entropy, density and magnetic field of the fluid. We derive the conservation law corresponding to the projective symmetry in gas dynamics, for the case γ = (n + 2)/n, where n is the number of Cartesian space coordinates, and the corresponding result for two-dimensional (2D) MHD, for the case γ = 2. Lie algebraic structures in Lagrange label space corresponding to the symmetries are investigated. The Lie algebraic symmetry relations between the fluid relabelling symmetries in Lagrange label space, and their commutators with a linear combination of the three symmetries with a constant adiabatic index are delineated
Review and limitations of 3D plasma blob modeling with reduced collisional fluid equations
Energy Technology Data Exchange (ETDEWEB)
Angus, Justin R., E-mail: jangus@ucsd.edu [University of California, San Diego, La Jolla, CA (United States); Umansky, Maxim V. [Lawrence Livermore National Laboratory, Livermore, CA (United States); Krashenninikov, Sergei I. [University of California, San Diego, La Jolla, CA (United States)
2013-07-15
Recent 3D studies on plasma blobs (coherent structures found in the edge region of magnetic confinement devices) have demonstrated that the drift wave instability can strongly limit the blob’s coherency and cross field convective nature that is predicted by 2D theory. However, the dominant unstable drift wave modes that effect plasma blobs were found to exist in parameter regimes that only marginally satisfied several of the major assumptions considered for the validity of the reduced collisional fluid equations used in the study. Namely, the neglect of electron heat flow, finite electron mean free path effects, and thermal ions. A follow up study demonstrated how the drift wave instability might change if a set of equations that does not suffer from the limitations mentioned above were considered. In the present paper, the results of this later work are used to discuss the limitations on using the collisional fluid equations for 3D studies of plasma blobs.
HIGH-FIDELITY SIMULATION-DRIVEN MODEL DEVELOPMENT FOR COARSE-GRAINED COMPUTATIONAL FLUID DYNAMICS
Energy Technology Data Exchange (ETDEWEB)
Hanna, Botros N.; Dinh, Nam T.; Bolotnov, Igor A.
2016-06-01
Nuclear reactor safety analysis requires identifying various credible accident scenarios and determining their consequences. For a full-scale nuclear power plant system behavior, it is impossible to obtain sufficient experimental data for a broad range of risk-significant accident scenarios. In single-phase flow convective problems, Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) can provide us with high fidelity results when physical data are unavailable. However, these methods are computationally expensive and cannot be afforded for simulation of long transient scenarios in nuclear accidents despite extraordinary advances in high performance scientific computing over the past decades. The major issue is the inability to make the transient computation parallel, thus making number of time steps required in high-fidelity methods unaffordable for long transients. In this work, we propose to apply a high fidelity simulation-driven approach to model sub-grid scale (SGS) effect in Coarse Grained Computational Fluid Dynamics CG-CFD. This approach aims to develop a statistical surrogate model instead of the deterministic SGS model. We chose to start with a turbulent natural convection case with volumetric heating in a horizontal fluid layer with a rigid, insulated lower boundary and isothermal (cold) upper boundary. This scenario of unstable stratification is relevant to turbulent natural convection in a molten corium pool during a severe nuclear reactor accident, as well as in containment mixing and passive cooling. The presented approach demonstrates how to create a correction for the CG-CFD solution by modifying the energy balance equation. A global correction for the temperature equation proves to achieve a significant improvement to the prediction of steady state temperature distribution through the fluid layer.
Prandtl, Ludwig
1953-01-01
Equilibrium of liquids and gases ; kinematics : dynamics of frictionless fluids ; motion of viscous fluids : turbulence : fluid resistance : practical applications ; flow with appreciable volume changes (dynamics of gases) ; miscellaneous topics.
Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas
International Nuclear Information System (INIS)
Zawaideh, E.S.
1985-01-01
A new set of two-fluid equations which are valid from collisional to weakly collisional limits are derived. Starting from gyrokinetic equations in flux coordinates with no zeroth order drifts, a set of moment equations describing plasma transport along the field lines of a space and time dependent magnetic field are derived. No restriction on the anisotropy of the ion distribution function is imposed. In the highly collisional limit, these equations reduce to those of Braginskii while in the weakly collisional limit, they are similar to the double adiabatic or Chew, Goldberger, and Low (CGL) equations. The new transport equations are used to study the effects of collisionality, magnetic field structure, and plasma anisotropy on plasma parallel transport. Numerical examples comparing these equations with conventional transport equations show that the conventional equations may contain large errors near the sound speed (M approx. = 1). It is also found that plasma anisotropy, which is not included in the conventional equations, is a critical parameter in determining plasma transport in varying magnetic field. The new transport equations are also used to study axial confinement in multiple mirror devices from the strongly to weakly collisional regime. A new ion conduction model was worked out to extend the regime of validity of the transport equations to the low density multiple mirror regime
High-precision numerical integration of equations in dynamics
Alesova, I. M.; Babadzanjanz, L. K.; Pototskaya, I. Yu.; Pupysheva, Yu. Yu.; Saakyan, A. T.
2018-05-01
An important requirement for the process of solving differential equations in Dynamics, such as the equations of the motion of celestial bodies and, in particular, the motion of cosmic robotic systems is high accuracy at large time intervals. One of effective tools for obtaining such solutions is the Taylor series method. In this connection, we note that it is very advantageous to reduce the given equations of Dynamics to systems with polynomial (in unknowns) right-hand sides. This allows us to obtain effective algorithms for finding the Taylor coefficients, a priori error estimates at each step of integration, and an optimal choice of the order of the approximation used. In the paper, these questions are discussed and appropriate algorithms are considered.
New formulation of Hardin-Pope equations for aeroacoustics
DEFF Research Database (Denmark)
Ekaterinaris, J.A.
1999-01-01
Dynamics, Vol. 6, No. 5-6, 1994, pp. 334-340). This method requires detailed information about the unsteady aerodynamic flowfield, which usually is obtained from a computational fluid dynamics solution. A new, conservative formulation of the equations governing acoustic disturbances is presented....... The conservative form of the governing equations is obtained after application of a transformation of variables that produces a set of inhomogeneous equations similar to the conservation-law form of the compressible Euler equations. The source term of these equations depends only on the derivatives...... of the hydrodynamic variables. Explicit time marching is performed. A high-order accurate, upwind-biased numerical scheme is used for numerical solution of the conservative equations. The convective fluxes are evaluated using upwind-biased formulas and flux-vector splitting. Solutions are obtained for the acoustic...
State-dependent neutral delay equations from population dynamics.
Barbarossa, M V; Hadeler, K P; Kuttler, C
2014-10-01
A novel class of state-dependent delay equations is derived from the balance laws of age-structured population dynamics, assuming that birth rates and death rates, as functions of age, are piece-wise constant and that the length of the juvenile phase depends on the total adult population size. The resulting class of equations includes also neutral delay equations. All these equations are very different from the standard delay equations with state-dependent delay since the balance laws require non-linear correction factors. These equations can be written as systems for two variables consisting of an ordinary differential equation (ODE) and a generalized shift, a form suitable for numerical calculations. It is shown that the neutral equation (and the corresponding ODE--shift system) is a limiting case of a system of two standard delay equations.
Landau fluid equations for electromagnetic and electrostatic fluctuations
International Nuclear Information System (INIS)
Hedrick, C.L.; Leboeuf, J.
1992-01-01
Closure relations are developed to allow approximate treatment of Landau damping and growth using fluid equations for both electrostatic and electromagnetic modes. The coefficients in these closure relations are related to approximations of the plasma dispersion function by ratios of polynomials. Thirteen different numerical sets of coefficients are given and explicitly related to previous fits to the plasma dispersion function. The application of the techniques presented in this paper is illustrated with the specific example of resistive g modes. Comparisons of full kinetic and approximate results are made for the solutions to the dispersion relation, radially resolved modes in sheared magnetic geometry, and the plasma dispersion function itself
Dynamic Characteristics of Rotors on Passive and Active Thrust Fluid-film Bearings with Fixed Pads
Directory of Open Access Journals (Sweden)
Babin Alexander
2018-01-01
Full Text Available Application of fluid-film bearings in rotor machines in many cases could have no alternative due to obvious advantages when compared to roller element bearings. Integration of information technology in mechanical engineering resulting in emergence of a new field of research – mechatronic bearings which allowed tracking condition of the most important parts of a machine and adjusting operational parameters of the system. Application of servo valves to control the flow rate through a fluid-film bearing is the most universal and simple way of rotor’s position control due to relative simplicity of modelling and absence of need to radically change the design of conventional hydrodynamic bearings. In the present paper numerical simulations of passive (conventional as opposed to mechatronic and active hybrid thrust fluid-film bearings with a central feeding chamber are presented, that are parts of a mechatronic rotor-bearing node. Numerical model of an active thrust bearing is based on solution of equations of hydrodynamics, rotor dynamics and an additional model of a servo valve. Various types of control have been investigated: P, PI and PID control, and the dynamic behaviour of a system has been estimated under various loads, namely static, periodic and impulse. A design of a test rig has been proposed to study passive and active thrust fluid-film bearings aimed at, among other, validation of numerical results of active bearings simulation.
Computational Fluid Dynamics in Ventilation
DEFF Research Database (Denmark)
Nielsen, Peter V.; Allard, Francis; Awbi, Hazim B.
2008-01-01
Computational Fluid Dynamics in Ventilation Design is a new title in the is a new title in the REHVA guidebook series. The guidebook is written for people who need to use and discuss results based on CFD predictions, and it gives insight into the subject for those who are not used to work with CFD...
Nonlinear dynamics in the Einstein-Friedmann equation
International Nuclear Information System (INIS)
Tanaka, Yosuke; Mizuno, Yuji; Ohta, Shigetoshi; Mori, Keisuke; Horiuchi, Tanji
2009-01-01
We have studied the gravitational field equations on the basis of general relativity and nonlinear dynamics. The space component of the Einstein-Friedmann equation shows the chaotic behaviours in case the following conditions are satisfied: (i)the expanding ratio: h=x . /x max = +0.14) for the occurrence of the chaotic behaviours in the Einstein-Friedmann equation (0 ≤ λ ≤ +0.14). The numerical calculations are performed with the use of the Microsoft EXCEL(2003), and the results are shown in the following cases; λ = 2b = +0.06 and +0.14.
Directory of Open Access Journals (Sweden)
Boričić Zoran
2005-01-01
Full Text Available This paper deals with laminar, unsteady flow of viscous, incompressible and electro conductive fluid caused by variable motion of flat plate. Fluid electro conductivity is variable. Velocity of the plate is time function. Plate moves in its own plane and in "still" fluid. Present external magnetic filed is perpendicular to the plate. Plate temperature is a function of longitudinal coordinate and time. Viscous dissipation, Joule heat, Hole and polarization effects are neglected. For obtaining of universal equations system general similarity method is used as well as impulse and energy equation of described problem.
Differential equations and applications recent advances
2014-01-01
Differential Equations and Applications : Recent Advances focus on the latest developments in Nonlinear Dynamical Systems, Neural Networks, Fluid Dynamics, Fractional Differential Systems, Mathematical Modelling and Qualitative Theory. Different aspects such as Existence, Stability, Controllability, Viscosity and Numerical Analysis for different systems have been discussed in this book. This book will be of great interest and use to researchers in Applied Mathematics, Engineering and Mathematical Physics.
Pieprzyk, S.; Brańka, A. C.; Maćkowiak, Sz.; Heyes, D. M.
2018-03-01
The equation of state (EoS) of the Lennard-Jones fluid is calculated using a new set of molecular dynamics data which extends to higher temperature than in previous studies. The modified Benedict-Webb-Rubin (MBWR) equation, which goes up to ca. T ˜ 6, is reparametrized with new simulation data. A new analytic form for the EoS, which breaks the fluid range into two regions with different analytic forms and goes up to ca. T ≃ 35, is also proposed. The accuracy of the new formulas is at least as good as the MBWR fit and goes to much higher temperature allowing it to now encompass the Amagat line. The fitted formula extends into the high temperature range where the system can be well represented by inverse power potential scaling, which means that our specification of the equation of state covers the entire (ρ, T) plane. Accurate analytic fit formulas for the Boyle, Amagat, and inversion curves are presented. Parametrizations of the extrema loci of the isochoric, CV, and isobaric, CP, heat capacities are given. As found by others, a line maxima of CP terminates in the critical point region, and a line of minima of CP terminates on the freezing line. The line of maxima of CV terminates close to or at the critical point, and a line of minima of CV terminates to the right of the critical point. No evidence for a divergence in CV in the critical region is found.
Molecular Dynamics Simulation of Binary Fluid in a Nanochannel
International Nuclear Information System (INIS)
Mullick, Shanta; Ahluwalia, P. K.; Pathania, Y.
2011-01-01
This paper presents the results from a molecular dynamics simulation of binary fluid (mixture of argon and krypton) in the nanochannel flow. The computational software LAMMPS is used for carrying out the molecular dynamics simulations. Binary fluids of argon and krypton with varying concentration of atom species were taken for two densities 0.65 and 0.45. The fluid flow takes place between two parallel plates and is bounded by horizontal walls in one direction and periodic boundary conditions are imposed in the other two directions. To drive the flow, a constant force is applied in one direction. Each fluid atom interacts with other fluid atoms and wall atoms through Week-Chandler-Anderson (WCA) potential. The velocity profile has been looked at for three nanochannel widths i.e for 12σ, 14σ and 16σ and also for the different concentration of two species. The velocity profile of the binary fluid predicted by the simulations agrees with the quadratic shape of the analytical solution of a Poiseuille flow in continuum theory.
Brito, Irene; Mena, Filipe C
2017-08-01
We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial space-like hypersurface with a time-like boundary, there exists a unique, local in time solution to the Einstein equations in a neighbourhood of the boundary. As an application, we consider a particular elastic fluid interior matched to a vacuum exterior.
Using Difference Equation to Model Discrete-time Behavior in System Dynamics Modeling
Hesan, R.; Ghorbani, A.; Dignum, M.V.
2014-01-01
In system dynamics modeling, differential equations have been used as the basic mathematical operator. Using difference equation to build system dynamics models instead of differential equation, can be insightful for studying small organizations or systems with micro behavior. In this paper we
Deriving the equations of motion of porous isotropic media
International Nuclear Information System (INIS)
Pride, S.R.; Gangi, A.F.; Morgan, F.D.
1992-01-01
The equations of motion and stress/strain relations for the linear dynamics of a two-phase, fluid/solid, isotropic, porous material have been derived by a direct volume averaging of the equations of motion and stress-strain relations known to apply in each phase. The equations thus obtained are shown to be consistent with Biot's equations of motion and stress/strain relations; however, the effective fluid density in the equation of relative flow has an unambiguous definition in terms of the tractions acting on the pore walls. The stress/strain relations of the theory correspond to 'quasistatic' stressing (i.e., inertial effects are ignored). It is demonstrated that using such quasistatic stress/strain relations in the equations of motion is justified whenever the wavelengths are greater than a length characteristic of the averaging volume size. 37 refs., 2 figs
Fluid dynamics of moving fish in a two-dimensional multiparticle collision dynamics model in 2D
Reid, D.A.P.; Hildenbrandt, H.; Padding, J.T.; Hemelrijk, C.K.
2012-01-01
The fluid dynamics of animal locomotion, such as that of an undulating fish, are of great interest to both biologists and engineers. However, experimentally studying these fluid dynamics is difficult and time consuming. Model studies can be of great help because of their simpler and more detailed
Solving the Fluid Pressure Poisson Equation Using Multigrid-Evaluation and Improvements.
Dick, Christian; Rogowsky, Marcus; Westermann, Rudiger
2016-11-01
In many numerical simulations of fluids governed by the incompressible Navier-Stokes equations, the pressure Poisson equation needs to be solved to enforce mass conservation. Multigrid solvers show excellent convergence in simple scenarios, yet they can converge slowly in domains where physically separated regions are combined at coarser scales. Moreover, existing multigrid solvers are tailored to specific discretizations of the pressure Poisson equation, and they cannot easily be adapted to other discretizations. In this paper we analyze the convergence properties of existing multigrid solvers for the pressure Poisson equation in different simulation domains, and we show how to further improve the multigrid convergence rate by using a graph-based extension to determine the coarse grid hierarchy. The proposed multigrid solver is generic in that it can be applied to different kinds of discretizations of the pressure Poisson equation, by using solely the specification of the simulation domain and pre-assembled computational stencils. We analyze the proposed solver in combination with finite difference and finite volume discretizations of the pressure Poisson equation. Our evaluations show that, despite the common assumption, multigrid schemes can exploit their potential even in the most complicated simulation scenarios, yet this behavior is obtained at the price of higher memory consumption.
Optics and Fluid Dynamics Department annual progress report for 2000
DEFF Research Database (Denmark)
Hanson, Steen Grüner; Johansen, Per Michael; Lynov, Jens-Peter
2001-01-01
The Optics and Fluid Dynamics Department performs basic and applied research within three scientific programmes: (1) optical materials, (2) optical diagnostics and information processing and (3) plasma and fluid dynamics. The department has corecompetences in: optical sensors, optical materials......, optical storage, biooptics, numerical modelling and information processing, non-linear dynamics and fusion plasma physics. The research is supported by several EU programmes, including EURATOM, by Danishresearch councils and by industry. A summary of the activities in 2000 is presented....
Molecular thermodynamics of nonideal fluids
Lee, Lloyd L
2013-01-01
Molecular Thermodynamics of Nonideal Fluids serves as an introductory presentation for engineers to the concepts and principles behind and the advances in molecular thermodynamics of nonideal fluids. The book covers related topics such as the laws of thermodynamics; entropy; its ensembles; the different properties of the ideal gas; and the structure of liquids. Also covered in the book are topics such as integral equation theories; theories for polar fluids; solution thermodynamics; and molecular dynamics. The text is recommended for engineers who would like to be familiarized with the concept
Dynamic analysis of a nuclear reactor with fluid-structure interaction
International Nuclear Information System (INIS)
Sigrist, Jean-Francois; Broc, Daniel; Laine, Christian
2007-01-01
The present paper is related to the dynamic (shock) analysis of a naval propulsion (on-board) reactor with fluid-structure interaction modelling. In a previous study, low frequency analysis has been performed; the present study deals with high frequency analysis, i.e. taking into account compressibility effects in the fluid medium. Elasto-acoustic coupling effects are studied and described in the industrial case. The coupled problem is formulated using the so-called (u, p, φ) formulation which yields symmetric matrices. A modal analysis is first performed on the fluid problem alone, then for the coupled fluid-structure problem in the following cases: (i) with incompressible fluid; (ii) with compressible fluid at standard pressure and temperature conditions; (iii) with compressible fluid at the operating pressure and temperature conditions. Elasto-coupling effects are then highlighted, in particular through the calculation of an elastic energy ratio. As a general conclusion, compressibility effects are proved significant in the dynamic response of the reactor in the high frequency range
The Direct Effect of Flexible Walls on Fontan Connection Fluid Dynamics
Tree, Mike; Fagan, Kiley; Yoganathan, Ajit
2014-11-01
The current standard treatment for sufferers of congenital heart defects is the palliative Fontan procedure. The Fontan procedure results in an anastomosis of major veins directly to the branched pulmonary arteries bypassing the dysfunctional ventricle. This total cavopulmonary connection (TCPC) extends life past birth, but Fontan patients still suffer long-term complications like decreased exercise capacity, protein-losing enteropathy, and pulmonary arteriovenous malformations (PAVM). These complications have direct ties to fluid dynamics within the connection. Previous experimental and computation studies of Fontan connection fluid dynamics employed rigid vessel models. More recent studies utilize flexible models, but a direct comparison of the fundamental fluid dynamics between rigid and flexible vessels only exists for a computational model, without a direct experimental validation. Thus, this study was a direct comparison of fluid dynamics within a rigid and two compliant idealized TCPCs. 2D particle image velocimetry measurements were collected at the connection center plane. Results include power loss, hepatic flow distribution, fluid shear stress, and flow structure recognition. The effect of flexible walls on these values and clinical impact will be discussed.
Symbolic-Numeric Integration of the Dynamical Cosserat Equations
Lyakhov, Dmitry A.
2017-08-29
We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized \\\\alpha -method illustrating the computational efficiency of our approach for problems in structural mechanics.
Symbolic-Numeric Integration of the Dynamical Cosserat Equations
Lyakhov, Dmitry A.; Gerdt, Vladimir P.; Weber, Andreas G.; Michels, Dominik L.
2017-01-01
We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized \\alpha -method illustrating the computational efficiency of our approach for problems in structural mechanics.
Perspectives in Fluid Dynamics
Batchelor, G. K.; Moffatt, H. K.; Worster, M. G.
2002-12-01
With applications ranging from modelling the environment to automotive design and physiology to astrophysics, conventional textbooks cannot hope to give students much information on what topics in fluid dynamics are currently being researched, or how to choose between them. This book rectifies matters. It consists of eleven chapters that introduce and review different branches of the subject for graduate-level courses, or for specialists seeking introductions to other areas. Hb ISBN (2001): 0-521-78061-6
International Nuclear Information System (INIS)
Jakubov, T.S.; Mainwaring, D.E.
2006-01-01
In the present work a generalized Kelvin equation for a fluid confined in thick-walled cylindrical capillary is developed. This has been accomplished by including the potential energy function for interaction between a solid wall of a capillary and a confined fluid into the Kelvin equation. Using the Lennard-Jones 12-6 potential, an explicit form of the potential energy functions as expressed by hypergeometrical functions have been derived-firstly, for the interaction between a solid wall and a test atom placed at an arbitrary point in a long open-end capillary, and thereafter for the body-body interaction between the solid wall and a confined Lennard-Jones fluid. Further, this generalized Kelvin equation has been applied to detailed description hysteresis phenomena in such capillaries. All numerical calculations have been carried out for the model argon-graphite system at 90 K
Application of Lie group analysis in geophysical fluid dynamics
Ibragimov, Ranis
2011-01-01
This is the first monograph dealing with the applications of the Lie group analysis to the modeling equations governing internal wave propagation in the deep ocean. A new approach to describe the nonlinear interactions of internal waves in the ocean is presented. While the central idea of the book is to investigate oceanic internal waves through the prism of Lie group analysis, it is also shown for the first time that internal wave beams, representing exact solutions to the equation of motion of stratified fluid, can be found by solving the given model as invariant solutions of nonlinear equat
Particle hopping vs. fluid-dynamical models for traffic flow
Energy Technology Data Exchange (ETDEWEB)
Nagel, K.
1995-12-31
Although particle hopping models have been introduced into traffic science in the 19509, their systematic use has only started recently. Two reasons for this are, that they are advantageous on modem computers, and that recent theoretical developments allow analytical understanding of their properties and therefore more confidence for their use. In principle, particle hopping models fit between microscopic models for driving and fluiddynamical models for traffic flow. In this sense, they also help closing the conceptual gap between these two. This paper shows connections between particle hopping models and traffic flow theory. It shows that the hydrodynamical limits of certain particle hopping models correspond to the Lighthill-Whitham theory for traffic flow, and that only slightly more complex particle hopping models produce already the correct traffic jam dynamics, consistent with recent fluid-dynamical models for traffic flow. By doing so, this paper establishes that, on the macroscopic level, particle hopping models are at least as good as fluid-dynamical models. Yet, particle hopping models have at least two advantages over fluid-dynamical models: they straightforwardly allow microscopic simulations, and they include stochasticity.
Nonlinear Dynamical Analysis for a Plain Bearing
Directory of Open Access Journals (Sweden)
Ali Belhamra
2014-03-01
Full Text Available This paper investigates the nonlinear dynamic behavior for a plain classic bearing (fluid bearing lubricated by a non-Newtonian fluid of a turbo machine rotating with high speed; this type of fluid contains additives viscosity (couple-stress fluid film. The solution of the nonlinear dynamic problem of this type of bearing is determined with a spatial discretisation of the modified Reynolds' equation written in dynamic mode by using the optimized short bearing theory and a temporal discretisation for equations of rotor motion by the help of Euler's explicit diagram. This study analyzes the dynamic behavior of a rotor supported by two couple-stress fluid film journal lubricant enhances the dynamic stability of the rotor-bearing system considerably compared to that obtained when using a traditional Newtonian lubricant. The analysis shows that the dynamic behavior of a shaft which turns with high velocities is strongly nonlinear even for poor eccentricities of unbalance; the presence of parameters of couple stress allows strongly attenuating the will synchrony (unbalance and asynchrony (whipping amplitudes of vibrations of the shaft which supports more severe conditions (large unbalances.
Optics and Fluid Dynamics Department annual progress report for 2000
International Nuclear Information System (INIS)
Hanson, S.G.; Johansen, P.M.; Lynov, J.P.; Skaarup, B.
2001-05-01
The Optics and Fluid Dynamics Department performs basic and applied research within three scientific programmes: (1) optical materials, (2) optical diagnostics and information processing and (3) plasma and fluid dynamics. The department has core competence in: optical sensors, optical materials, optical storage, bio-optics, numerical modelling and information processing, non-linear dynamics and fusion plasma physics. The research is supported by several EU programmes, including EURATOM, by Danish research councils and by industry. A summary of the activities in 2000 is presented. (au)
Optics and Fluid Dynamics Department annual progress report for 2003
DEFF Research Database (Denmark)
Bindslev, H.; Hanson, Steen Grüner; Lynov, Jens-Peter
2004-01-01
The Optics and Fluid Dynamics Department performs basic and applied research within three scientific programmes: (1) laser systems and optical materials, (2) optical diagnostics and information processing and (3) plasma and fluid dynamics. The departmenthas core competences in: optical sensors......, optical materials, optical storage, biophotonics, numerical modelling and information processing, non-linear dynamics, fusion plasma physics and plasma technology. The research is supported by several EUprogrammes, including EURATOM, by Danish research councils and by industry. A summary of the activities...
Optics and Fluid Dynamics Department annual progress report for 2001
DEFF Research Database (Denmark)
Bindslev, H.; Hanson, Steen Grüner; Lynov, Jens-Peter
2002-01-01
The Optics and Fluid Dynamics Department performs basic and applied research within three scientific programmes: (1) laser systems and optical materials, (2) optical diagnostics and information processing and (3) plasma and fluid dynamics. The departmenthas core competences in: optical sensors......, optical materials, optical storage, biooptics, numerical modelling and information processing, non-linear dynamics and fusion plasma physics. The research is supported by several EU programmes, including EURATOM,by Danish research councils and by industry. A summary of the activities in 2001 is presented....
Optics and Fluid Dynamics Department annual progress report for 2002
DEFF Research Database (Denmark)
Bindslev, H.; Hanson, Steen Grüner; Lynov, Jens-Peter
2003-01-01
The Optics and Fluid Dynamics Department performs basic and applied research within three scientific programmes: (1) laser systems and optical materials (2) optical diagnostics and information processing and (3) plasma and fluid dynamics. The departmenthas core competences in: optical sensors......, optical materials, optical storage, biophotonics, numerical modelling and information processing, non-linear dynamics and fusion plasma physics. The research is supported by several EU programmes, includingEURATOM, by Danish research councils and by industry. A summary of the activities in 2002...
Vortex dynamics equation in type-II superconductors in a temperature gradient
International Nuclear Information System (INIS)
Vega Monroy, R.; Sarmiento Castillo, J.; Puerta Torres, D.
2010-01-01
In this work we determined a vortex dynamics equation in a temperature gradient in the frame of the time dependent Ginzburg-Landau equation. In this sense, we derived a local solvability condition, which governs the vortex dynamics. Also, we calculated the explicit form for the force coefficients, which are the keys for the understanding of the balance equation due to vortex interactions with the environment. (author)
Vortex dynamics equation in type-II superconductors in a temperature gradient
Energy Technology Data Exchange (ETDEWEB)
Vega Monroy, R.; Sarmiento Castillo, J. [Universidad del Atlantico, Barranquilla (Colombia). Facultad de Ciencias Basicas; Puerta Torres, D. [Universidad de Cartagena (Colombia). Facultad de Ciencias Exactas
2010-12-15
In this work we determined a vortex dynamics equation in a temperature gradient in the frame of the time dependent Ginzburg-Landau equation. In this sense, we derived a local solvability condition, which governs the vortex dynamics. Also, we calculated the explicit form for the force coefficients, which are the keys for the understanding of the balance equation due to vortex interactions with the environment. (author)
Computational Fluid Dynamic Pressure Drop Estimation of Flow between Parallel Plates
Energy Technology Data Exchange (ETDEWEB)
Son, Hyung Min; Yang, Soo Hyung; Park, Jong Hark [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2014-10-15
Many pool type reactors have forced downward flows inside the core during normal operation; there is a chance of flow inversion when transients occur. During this phase, the flow undergo transition between turbulent and laminar regions where drastic changes take place in terms of momentum and heat transfer, and the decrease in safety margin is usually observed. Additionally, for high Prandtl number fluids such as water, an effect of the velocity profile inside the channel on the temperature distribution is more pronounced over the low Prandtl number ones. This makes the checking of its pressure drop estimation accuracy less important, assuming the code verification is complete. With an advent of powerful computer hardware, engineering applications of computational fluid dynamics (CFD) methods have become quite common these days. Especially for a fully-turbulent and single phase convective heat transfer, the predictability of the commercial codes has matured enough so that many well-known companies adopt those to accelerate a product development cycle and to realize an increased profitability. In contrast to the above, the transition models for the CFD code are still under development, and the most of the models show limited generality and prediction accuracy. Unlike the system codes, the CFD codes estimate the pressure drop from the velocity profile which is obtained by solving momentum conservation equations, and the resulting friction factor can be a representative parameter for a constant cross section channel flow. In addition, the flow inside a rectangular channel with a high span to gap ratio can be approximated by flow inside parallel plates. The computational fluid dynamics simulation on the flow between parallel plates showed reasonable prediction capability for the laminar and the turbulent regime.
Nonequilibrium Langevin dynamics: A demonstration study of shear flow fluctuations in a simple fluid
Belousov, Roman; Cohen, E. G. D.; Rondoni, Lamberto
2017-08-01
The present paper is based on a recent success of the second-order stochastic fluctuation theory in describing time autocorrelations of equilibrium and nonequilibrium physical systems. In particular, it was shown to yield values of the related deterministic parameters of the Langevin equation for a Couette flow in a microscopic molecular dynamics model of a simple fluid. In this paper we find all the remaining constants of the stochastic dynamics, which then is simulated numerically and compared directly with the original physical system. By using these data, we study in detail the accuracy and precision of a second-order Langevin model for nonequilibrium physical systems theoretically and computationally. We find an intriguing relation between an applied external force and cumulants of the resulting flow fluctuations. This is characterized by a linear dependence of an athermal cumulant ratio, an apposite quantity introduced here. In addition, we discuss how the order of a given Langevin dynamics can be raised systematically by introducing colored noise.
Computational Fluid Dynamics Methods and Their Applications in Medical Science
Directory of Open Access Journals (Sweden)
Kowalewski Wojciech
2016-12-01
Full Text Available As defined by the National Institutes of Health: “Biomedical engineering integrates physical, chemical, mathematical, and computational sciences and engineering principles to study biology, medicine, behavior, and health”. Many issues in this area are closely related to fluid dynamics. This paper provides an overview of the basic concepts concerning Computational Fluid Dynamics and its applications in medicine.
Activities and interconnections of thermal-fluid dynamics
International Nuclear Information System (INIS)
Celata, G.P.
1999-01-01
Thermal-fluid dynamics is a field of fundamental interest for a wide spectrum of past and present advanced 'applications': in nature, in the 'machines' of our everyday life and in industry. In particular, in today industry, its knowledge and the developments are of fundamental importance in understanding, modelling and in the advance design of heat and mass transfer process in energy conversion and transformation plants. Various examples of the role of the thermal-fluid dynamics to increase efficiency in energy utilization and in the design and in the development of new components and high performance system are exposed. New thermodynamic models and advanced analysis techniques together with necessary balance between theoretical advances codes for modelling and their experimental specific verifications are throughout discussed and illustrated
Atomic dynamics in fluids studied by inelastic x-ray scattering
International Nuclear Information System (INIS)
Inui, Masanori; Kajihara, Yukio; Matsuda, Kazuhiro; Ishikawa, Daisuke; Tsutsui, Satoshi; Baron, Alfred Q.
2010-01-01
Studies on atomic dynamics in supercritical fluids at high temperature and high pressure have remarkably been advanced by using an inelastic x-ray scattering technique that achieved a meV-energy resolution in the middle of 1990's. In this article, we describe a brief review of the theoretical background on liquid dynamics, our own high-temperature high-pressure technique and recent results of atomic dynamics in supercritical fluids. In particular, we report the results of inelastic x-ray scattering measurements for expanding fluid Hg at high temperature and high pressure, which were conduced at BL35XU/SPring-8. We found that in the metal-nonmetal transition in fluid Hg, the excitation energy of the acoustic mode disperses three times faster than the adiabatic sound velocity obtained by ultrasonic measurements. This phenomenon must be crucial to understand how a metallic state is formed during atomic condensation accurately. Finally we put a future development of this field in perspective. (author)
Relativistic three-particle dynamical equations: I. Theoretical development
International Nuclear Information System (INIS)
Adhikari, S.K.; Tomio, L.; Frederico, T.
1993-11-01
Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, three dimensional scattering integral equations satisfying constrains of relativistic unitarity and covariance are rederived. These equations were first derived by Weinberg and by Blankenbecler and Sugar. These two-particle equations are shown to be related by a transformation of variables. Hence it is shown to perform and relate dynamical calculation using these two equations. Similarly, starting from the Bethe-Salpeter-Faddeev equation for the three-particle system and integrating over the time component of momentum, several three dimensional three-particle scattering equations satisfying constraints of relativistic unitary and covariance are derived. Two of these three-particle equations are related by a transformation of variables as in the two-particle case. The three-particle equations obtained are very practical and suitable for performing relativistic scattering calculations. (author)
Andersson, Kennet
2011-01-01
Patients with idiopathic normal pressure hydrocephalus (INPH) have a disturbance in the cerebrospinal fluid (CSF) system. The treatment is neurosurgical – a shunt is placed in the CSF system. The infusion test is used to assess CSF system dynamics and to aid in the selection of patients that will benefit from shunt surgery. The infusion test can be divided into three parts: a mathematical model, an infusion protocol and a parameter estimation method. A non-linear differential equation is used...
DEFF Research Database (Denmark)
Rasmussen, Anders Rønne; Sørensen, Mads Peter; Gaididei, Yuri Borisovich
2010-01-01
A wave equation, that governs finite amplitude acoustic disturbances in a thermoviscous Newtonian fluid, and includes nonlinear terms up to second order, is proposed. The equation preserves the Hamiltonian structure of the fundamental fluid dynamical equations in the non dissipative limit. An exact...... thermoviscous shock solution is derived. This solution is, in an overall sense, equivalent to the Taylor shock solution of the Burgers equation. However, in contrast to the Burgers equation, the model equation considered here is capable to describe waves propagating in opposite directions. Studies of head...
Oscillation theory for second order dynamic equations
Agarwal, Ravi P; O''Regan, Donal
2003-01-01
The qualitative theory of dynamic equations is a rapidly developing area of research. In the last 50 years, the Oscillation Theory of ordinary, functional, neutral, partial and impulsive differential equations, and their discrete versions, has inspired many scholars. Hundreds of research papers have been published in every major mathematical journal. Many books deal exclusively with the oscillation of solutions of differential equations, but most of these books appeal only to researchers who already know the subject. In an effort to bring Oscillation Theory to a new and broader audience, the authors present a compact, but thorough, understanding of Oscillation Theory for second order differential equations. They include several examples throughout the text not only to illustrate the theory, but also to provide new direction.
Optics and Fluid Dynamics Department. Annual progress report for 2001
International Nuclear Information System (INIS)
Bindslev, H.; Hanson, S.G.; Lynov, J.P.; Petersen, P.M.; Skaarup, B.
2002-03-01
The Optics and Fluid Dynamics Department performs basic and applied research within three scientific programmes: 1) laser systems and optical materials, 2) optical diagnostics and information processing and 3) plasma and fluid dynamics. The department has core competence in: optical sensors, optical materials, optical storage, bio-optics, numerical modelling and information processing, non-linear dynamics and fusion plasma physics. The research is supported by several EU programmes, including EURATOM, by Danish research councils and by industry. A summary of the activities in 2001 is presented. (au)
Optics and Fluid Dynamics Department. Annual Progress Report for 2002
International Nuclear Information System (INIS)
Bindslev, H.; Hanson, S.G.; Lynov, J.P.; Petersen, P.M.; Skaarup, B.
2003-05-01
The Optics and Fluid Dynamics Department performs basic and applied research within three scientific programmes: (1 Laser systems and optical materials (2 Optical diagnostics and information processing and (3 Plasma and fluid dynamics. The department has core competences in: optical sensors, optical materials, optical storage, biophotonics, numerical modelling and information processing, non-linear dynamics and fusion plasma physics. The research is supported by several EU programmes, including EURATOM, by Danish research councils and by industry. A summary of the activities in 2002 is presented. (au)
Optics and Fluid Dynamics Department. Annual progress report for 2003
International Nuclear Information System (INIS)
Bindslev, H.; Hanson, S.G.; Lynov, J.P.; Petersen, P.M.; Skaarup, B.
2004-05-01
The Optics and Fluid Dynamics Department performs basic and applied research within three scientific programmes: (1 laser systems and optical materials, (2 optical diagnostics and information processing and (3 plasma and fluid dynamics. The department has core competences in: optical sensors, optical materials, optical storage, biophotonics, numerical modelling and information processing, non-linear dynamics, fusion plasma physics and plasma technology. The research is supported by several EU programmes, including EURATOM, by Danish research councils and by industry. A summary of the activities in 2003 is presented. (au)
Optics and Fluid Dynamics Department. Annual Progress Report for 2002
Energy Technology Data Exchange (ETDEWEB)
Bindslev, H; Hanson, S G; Lynov, J P; Petersen, P M; Skaarup, B
2003-05-01
The Optics and Fluid Dynamics Department performs basic and applied research within three scientific programmes: (1) Laser systems and optical materials (2) Optical diagnostics and information processing and (3) Plasma and fluid dynamics. The department has core competences in: optical sensors, optical materials, optical storage, biophotonics, numerical modelling and information processing, non-linear dynamics and fusion plasma physics. The research is supported by several EU programmes, including EURATOM, by Danish research councils and by industry. A summary of the activities in 2002 is presented. (au)
Reconstruction of dynamical equations for traffic flow
Kriso, S.; Friedrich, R.; Peinke, J.; Wagner, P.
2001-01-01
Traffic flow data collected by an induction loop detector on the highway close to Koeln-Nord are investigated with respect to their dynamics including the stochastic content. In particular we present a new method, with which the flow dynamics can be extracted directly from the measured data. As a result a Langevin equation for the traffic flow is obtained. From the deterministic part of the flow dynamics, stable fixed points are extracted and set into relation with common features of the fund...
FLOWPLOT2, 2-D, 3-D Fluid Dynamic Plots
International Nuclear Information System (INIS)
Cobb, C.K.; Tunstall, J.N.
1989-01-01
1 - Description of program or function: FLOWPLOT2 is a plotting program used with numerical or analytical fluid dynamics codes to create velocity vector plots, contour plots of up to three fluid parameters (e.g. pressure, density, and temperature), two-dimensional profile plots, three-dimensional curve plots, and/or three-dimensional surface plots for either the u or v velocity components. If the fluid dynamics code computes a transient or simulated time related solution, FLOWPLOT2 can also be used to generate these plots for any specified time interval. Multiple cases generating different plots for different time intervals may be run in one execution of the program. In addition, plots can be created for selected two- dimensional planes of three-dimensional steady-state problems. The user has the option of producing plots on CalComp or Versatec plotters or microfiche and of creating a compressed dataset before plotting. 2 - Method of solution: FLOWPLOT2 reads a dataset written by the fluid dynamics code. This dataset must be written in a specified format and must contain parametric data at the nodal points of a uniform or non-uniform rectangular grid formed by the intersection of the grid lines of the model. 3 - Restrictions on the complexity of the problem - Maxima of: 2500 nodes, 40 y-values for 2-D profile plots and 3-D curve plots, 20 contour values, 3 fluid parameters
Advances in nonlinear partial differential equations and stochastics
Kawashima, S
1998-01-01
In the past two decades, there has been great progress in the theory of nonlinear partial differential equations. This book describes the progress, focusing on interesting topics in gas dynamics, fluid dynamics, elastodynamics etc. It contains ten articles, each of which discusses a very recent result obtained by the author. Some of these articles review related results.
Methods of mathematical modelling continuous systems and differential equations
Witelski, Thomas
2015-01-01
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
The incompressible non-relativistic Navier-Stokes equation from gravity
International Nuclear Information System (INIS)
Bhattacharyya, Sayantani; Minwalla, Shiraz; Wadia, Spenta R.
2009-01-01
We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a forcing function identical to the action of a background electromagnetic field on the effectively charged fluid. We demonstrate that special conformal symmetries of the parent relativistic theory descend to 'accelerated boost' symmetries of the Navier-Stokes equations, uncovering a conformal symmetry structure of these equations. Applying our scaling limit to holographically induced fluid dynamics, we find gravity dual descriptions of an arbitrary solution of the forced non-relativistic incompressible Navier-Stokes equations. In the holographic context we also find a simple forced steady state shear solution to the Navier-Stokes equations, and demonstrate that this solution turns unstable at high enough Reynolds numbers, indicating a possible eventual transition to turbulence.
Solutions to three-dimensional Navier-Stokes equations for incompressible fluids
Directory of Open Access Journals (Sweden)
Jorma Jormakka
2010-07-01
Full Text Available This article gives explicit solutions to the space-periodic Navier-Stokes problem with non-periodic pressure. These type of solutions are not unique and by using such solutions one can construct a periodic, smooth, divergence-free initial vector field allowing a space-periodic and time-bounded external force such that there exists a smooth solution to the 3-dimensional Navier-Stokes equations for incompressible fluid with those initial conditions, but the solution cannot be continued to the whole space.
Transport equations, Level Set and Eulerian mechanics. Application to fluid-structure coupling
International Nuclear Information System (INIS)
Maitre, E.
2008-11-01
My works were devoted to numerical analysis of non-linear elliptic-parabolic equations, to neutron transport equation and to the simulation of fabrics draping. More recently I developed an Eulerian method based on a level set formulation of the immersed boundary method to deal with fluid-structure coupling problems arising in bio-mechanics. Some of the more efficient algorithms to solve the neutron transport equation make use of the splitting of the transport operator taking into account its characteristics. In the present work we introduced a new algorithm based on this splitting and an adaptation of minimal residual methods to infinite dimensional case. We present the case where the velocity space is of dimension 1 (slab geometry) and 2 (plane geometry) because the splitting is simpler in the former
Chaotic dynamics and diffusion in a piecewise linear equation
International Nuclear Information System (INIS)
Shahrear, Pabel; Glass, Leon; Edwards, Rod
2015-01-01
Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems
Chaotic dynamics and diffusion in a piecewise linear equation
Shahrear, Pabel; Glass, Leon; Edwards, Rod
2015-03-01
Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.
Engineering applications of computational fluid dynamics
Awang, Mokhtar
2015-01-01
This volume presents the results of Computational Fluid Dynamics (CFD) analysis that can be used for conceptual studies of product design, detail product development, process troubleshooting. It demonstrates the benefit of CFD modeling as a cost saving, timely, safe and easy to scale-up methodology.
Dynamical symmetries of semi-linear Schrodinger and diffusion equations
International Nuclear Information System (INIS)
Stoimenov, Stoimen; Henkel, Malte
2005-01-01
Conditional and Lie symmetries of semi-linear 1D Schrodinger and diffusion equations are studied if the mass (or the diffusion constant) is considered as an additional variable. In this way, dynamical symmetries of semi-linear Schrodinger equations become related to the parabolic and almost-parabolic subalgebras of a three-dimensional conformal Lie algebra (conf 3 ) C . We consider non-hermitian representations and also include a dimensionful coupling constant of the non-linearity. The corresponding representations of the parabolic and almost-parabolic subalgebras of (conf 3 ) C are classified and the complete list of conditionally invariant semi-linear Schrodinger equations is obtained. Possible applications to the dynamical scaling behaviour of phase-ordering kinetics are discussed
Feasibility of Applying Controllable Lubrication to Dynamically Loaded Journal Bearings
DEFF Research Database (Denmark)
Estupinan, Edgar Alberto; Santos, Ilmar
2009-01-01
A multibody dynamic model of the main mechanical components of a hermetic reciprocating compressor is presented in this work. Considering that some of the mechanical elements are interconnected via thin fluid films, the multibody dynamic model is coupled to the equations from the dynamics...... of the fluid films, based on fluid film theory. For a dynamically loaded journal bearing, the fluid film pressure distribution can be computed by numerically solving the Reynolds equation, by means of finite-difference method. Particularly, in this study the main focus is on the lubrication behavior...... and reaction forces in a reciprocating compressor have a cyclic behavior, periodic oil pressure injection rules based on the instantaneous crank angle and load bearing condition can be established. In this paper, several bearing configurations working under different oil pressure injection rules conditions...
Equilibrium and nonequilibrium dynamics of soft sphere fluids.
Ding, Yajun; Mittal, Jeetain
2015-07-14
We use computer simulations to test the freezing-point scaling relationship between equilibrium transport coefficients (self-diffusivity, viscosity) and thermodynamic parameters for soft sphere fluids. The fluid particles interact via the inverse-power potential (IPP), and the particle softness is changed by modifying the exponent of the distance-dependent potential term. In the case of IPP fluids, density and temperature are not independent variables and can be combined to obtain a coupling parameter to define the thermodynamic state of the system. We find that the rescaled coupling parameter, based on its value at the freezing point, can approximately collapse the diffusivity and viscosity data for IPP fluids over a wide range of particle softness. Even though the collapse is far from perfect, the freezing-point scaling relationship provides a convenient and effective way to compare the structure and dynamics of fluid systems with different particle softness. We further show that an alternate scaling relationship based on two-body excess entropy can provide an almost perfect collapse of the diffusivity and viscosity data below the freezing transition. Next, we perform nonequilibrium molecular dynamics simulations to calculate the shear-dependent viscosity and to identify the distinct role of particle softness in underlying structural changes associated with rheological properties. Qualitatively, we find a similar shear-thinning behavior for IPP fluids with different particle softness, though softer particles exhibit stronger shear-thinning tendency. By investigating the distance and angle-dependent pair correlation functions in these systems, we find different structural features in the case of IPP fluids with hard-sphere like and softer particle interactions. Interestingly, shear-thinning in hard-sphere like fluids is accompanied by enhanced translational order, whereas softer fluids exhibit loss of order with shear. Our results provide a systematic evaluation
The Mathlet Toolkit: Creating Dynamic Applets for Differential Equations and Dynamical Systems
Decker, Robert
2011-01-01
Dynamic/interactive graphing applets can be used to supplement standard computer algebra systems such as Maple, Mathematica, Derive, or TI calculators, in courses such as Calculus, Differential Equations, and Dynamical Systems. The addition of this type of software can lead to discovery learning, with students developing their own conjectures, and…
International Nuclear Information System (INIS)
Kraenkel, R.A.; Pereira, J.G.; Manna, M.A.
1991-01-01
The (2+1)-dimensional Burgers equation is obtained as the equation of motion governing the surface perturbations of a shallow viscous fluid heated from below, provided the Rayleigh number of the system satisfy the condition R ≠ 30. A solution to this equation is explicity exhibited and it is argued that it describes the nonlinear evolution of a nearly one-dimensional kink. (author)
International Nuclear Information System (INIS)
Angelo, G.; Andrade, D.A.; Angelo, E.; Carluccio, T.; Rossi, P.C.R.; Talamo, A.
2011-01-01
Highlights: → A thermal fluid dynamics numerical model was created for a gas cooled subcritical fast reactor. → Standard k-ε model, Eddy Viscosity Transport Equation model underestimates the fuel temperature. → For a conservative assumption, SSG Reynolds stress model was chosen. → Creep strength is the most important parameter in fuel design. - Abstract: The entire nuclear fuel cycle involves partitioning classification and transmutation recycling. The usage of a tokamak as neutron sources to burn spent fuel in a gas cooled subcritical fast reactor (GCSFR) reduces the amount of long-lived radionuclide, thus increasing the repository capacity. This paper presents numerical thermal and fluid dynamics analysis for a gas cooled subcritical fast reactor. The analysis aim to determine the operational flow condition for this reactor, and to compare three distinct turbulence models (Eddy Viscosity Transport Equation, standard k-ε and SSG Reynolds stress) for this application. The model results are presented and discussed. The methodology used in this paper was developed to predict the coolant mass flow rate. It can be applied to any other gas cooled reactor.
Moving interface problems and applications in fluid dynamics
Khoo, Boo Cheong; Lin, Ping
2008-01-01
This volume is a collection of research papers presented at the program on Moving Interface Problems and Applications in Fluid Dynamics, which was held between January 8 and March 31, 2007 at the Institute for Mathematical Sciences (IMS) of the National University of Singapore. The topics discussed include modeling and simulations of biological flow coupled to deformable tissue/elastic structure, shock wave and bubble dynamics and various applications including biological treatments with experimental verification, multi-medium flow or multi-phase flow and various applications including cavitation/supercavitation, detonation problems, Newtonian and non-Newtonian fluid, and many other areas. Readers can benefit from some recent research results in these areas.
Generalized master equations for non-Poisson dynamics on networks.
Hoffmann, Till; Porter, Mason A; Lambiotte, Renaud
2012-10-01
The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Accordingly, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that this equation reduces to the standard rate equations when the underlying process is Poissonian and that its stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We conduct numerical simulations and also derive analytical results for the stationary solution under the assumption that all edges have the same waiting-time distribution. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature.
International Nuclear Information System (INIS)
Chang, J.; Sandler, S.I.
1995-01-01
The correlation functions of homonuclear hard-sphere chain fluids are studied using the Wertheim integral equation theory for associating fluids and the Monte Carlo simulation method. The molecular model used in the simulations is the freely jointed hard-sphere chain with spheres that are tangentially connected. In the Wertheim theory, such a chain molecule is described by sticky hard spheres with two independent attraction sites on the surface of each sphere. The OZ-like equation for this associating fluid is analytically solved using the polymer-PY closure and by imposing a single bonding condition. By equating the mean chain length of this associating hard sphere fluid to the fixed length of the hard-sphere chains used in simulation, we find that the correlation functions for the chain fluids are accurately predicted. From the Wertheim theory we also obtain predictions for the overall correlation functions that include intramolecular correlations. In addition, the results for the average intermolecular correlation functions from the Wertheim theory and from the Chiew theory are compared with simulation results, and the differences between these theories are discussed
Structure, thermodynamics, and dynamical properties of supercooled liquids
International Nuclear Information System (INIS)
Kambayashi, Shaw
1992-12-01
The equilibrium properties of supercooled liquids with repulsive soft-sphere potentials, u(r) = ε(σ/r) n , have been obtained by solving the integral equation of the theory of liquids and by performing constant-temperature molecular dynamics (MD) simulations. A thermodynamically consistent approximation, proposed recently by Rogers and Young (RY), has been examined for the supercooled soft-sphere fluids. Then, a new approximation for the integral equation, called MHNCS (modified hypernetted-chain integral equation for highly supercooled soft-sphere fluids) approximation, is proposed. The solution of the MHNCS integral equation for highly supercooled liquid states agrees well with the results of computer simulations. The MHNCS integral equation has also been applied for binary soft-sphere mixtures. Dynamical properties of soft-sphere fluids have been investigated by molecular dynamics (MD) simulations. The reduced diffusion constant is found to be insensitive to the choice of the softness of the potential. On the other hand, the spectrum of the velocity autocorrelation function shows a pronounced dependence on the softness of the potential. These significant dynamical properties dependent on the softness parameter (n) are consistent to dynamical behavior observed in liquid alkali metals and liquefied inert gases. The self-part of the density-density autocorrelation function obtained shows a clear nonexponential decay in intermediate time, as the liquid-glass transition is approached. (J.P.N.) 105 refs
Physical dynamics of quasi-particles in nonlinear wave equations
International Nuclear Information System (INIS)
Christov, Ivan; Christov, C.I.
2008-01-01
By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field equations. In particular, we show that a linear superposition of the non-interacting shapes of two solitons offers a qualitative (and to a good approximation quantitative) description of the true two-soliton solution, provided that the trajectories of the centers of the superimposed solitons are considered unknown. Via variational calculus, we establish that the dynamics of the quasi-particles obey a pseudo-Newtonian law, which includes cross-mass terms. The successful identification of the governing equations of the (discrete) quasi-particles from the (continuous) field equation shows that the proposed approach provides a basis for the passage from the continuous to a discrete description of the field
Physical dynamics of quasi-particles in nonlinear wave equations
Energy Technology Data Exchange (ETDEWEB)
Christov, Ivan [Department of Mathematics, Texas A and M University, College Station, TX 77843-3368 (United States)], E-mail: christov@alum.mit.edu; Christov, C.I. [Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010 (United States)], E-mail: christov@louisiana.edu
2008-02-04
By treating the centers of solitons as point particles and studying their discrete dynamics, we demonstrate a new approach to the quantization of the soliton solutions of the sine-Gordon equation, one of the first model nonlinear field equations. In particular, we show that a linear superposition of the non-interacting shapes of two solitons offers a qualitative (and to a good approximation quantitative) description of the true two-soliton solution, provided that the trajectories of the centers of the superimposed solitons are considered unknown. Via variational calculus, we establish that the dynamics of the quasi-particles obey a pseudo-Newtonian law, which includes cross-mass terms. The successful identification of the governing equations of the (discrete) quasi-particles from the (continuous) field equation shows that the proposed approach provides a basis for the passage from the continuous to a discrete description of the field.
International Nuclear Information System (INIS)
Sandoval, Miguel A.; Fuentes, Rosalba; Walsh, Frank C.; Nava, José L.; Ponce de León, Carlos
2016-01-01
Highlights: • Computational fluid dynamic simulations in a filter-press stack of three cells. • The fluid velocity was different in each cell due to local turbulence. • The upper cell link pipe of the filter press cell acts as a fluid mixer. • The fluid behaviour tends towards a continuous mixing flow pattern. • Close agreement between simulations and experimental data was achieved. - Abstract: Computational fluid dynamics (CFD) simulations were carried out for single-phase flow in a pre-pilot filter press flow reactor with a stack of three cells. Velocity profiles and streamlines were obtained by solving the Reynolds-Averaged Navier-Stokes (RANS) equations with a standard k − ε turbulence model. The flow behaviour shows the appearance of jet flow at the entrance to each cell. At lengths from 12 to 15 cm along the cells channels, a plug flow pattern is developed at all mean linear flow rates studied here, 1.2 ≤ u ≤ 2.1 cm s −1 . The magnitude of the velocity profiles in each cell was different, due to the turbulence generated by the change of flow direction in the last fluid manifold. Residence time distribution (RTD) simulations indicated that the fluid behaviour tends towards a continuous mixing flow pattern, owing to flow at the output of each cell across the upper cell link pipe, which acts as a mixer. Close agreement between simulations and experimental RTD was obtained.
Energy Technology Data Exchange (ETDEWEB)
Bowers, Geoffrey [Alfred Univ., NY (United States)
2017-04-05
United States Department of Energy grant DE-FG02-10ER16128, “Computational and Spectroscopic Investigations of the Molecular Scale Structure and Dynamics of Geologically Important Fluids and Mineral-Fluid Interfaces” (Geoffrey M. Bowers, P.I.) focused on developing a molecular-scale understanding of processes that occur in fluids and at solid-fluid interfaces using the combination of spectroscopic, microscopic, and diffraction studies with molecular dynamics computer modeling. The work is intimately tied to the twin proposal at Michigan State University (DOE DE-FG02-08ER15929; same title: R. James Kirkpatrick, P.I. and A. Ozgur Yazaydin, co-P.I.).
Some fluid dynamical problems in astrophysics
International Nuclear Information System (INIS)
Drury, L.O.
1979-06-01
Certain aspects of the cosmic turbulence theory of galaxy formation are considered. Using a generalized form of a transformation due to Kurskov and Ozernoi I exhibit a formal equivalence between the problem of turbulence in an expanding universe containing a coupled matter-radiation fluid and in a non-expanding fluid with a time-dependent viscosity. This enables me to extend the Olson-Sachs formula for vorticity generation in cosmic turbulence to a matter-radiation fluid and to show that, the turbulence can not have an inertial subrange at the epoch of recombination. The linear inviscid stability of axisymmetric flows is considered. Using the projective form of the perturbation equations I obtain a simple proof of a generalised Richardson criterion which holds for all boundary conditions which do not actively feed energy to the perturbation. Further analysis shows the uniform density and pressure discs with self-similar rotation laws, are stable to perturbations which are incompressible in character, but that instability is a generic feature of differentially rotating compressible systems. The problem of numerically solving boundary value problems of the Orr-Sommerfeld type by shooting methods is considered, and a unifying geometrical interpretation of the principal methods is described. (author)
Directory of Open Access Journals (Sweden)
Mustapha Lahmar
2015-04-01
Full Text Available On the basis of the V. K. Stokes micro-continuum theory, the effects of couple stresses on the nonlinear dynamic response of the unbalanced Jeffcott’s flexible rotor supported by layered hydrodynamic journal bearings is presented in this paper. A nonlinear transient modified Reynolds’ equation is derived and discretized by the finite element method to obtain the fluid-film pressure field as well as the film thickness by means of the implicit Euler method. The nonlinear orbits of the rotor center are determined by solving the nonlinear differential equations of motion with the explicit Euler’s scheme taking into account the flexibility of rotor. According to the obtained results, the combined effects of couple stresses due to the presence of polymer additives in lubricant and the pressure dependent viscosity on the nonlinear dynamic response of the rotor-bearing system are significant and cannot be ignored or overlooked. As expected, these effects are more noticeable for polymers characterized by higher length molecular chains.
Schwinger Dyson equations: Dynamical chiral symmetry breaking and confinement
International Nuclear Information System (INIS)
Roberts, C.D.
1992-01-01
A representative but not exhaustive review of the Schwinger-Dyson equation (SDE) approach to the nonperturbative study of QCD is presented. The main focus is the SDE for the quark self energy but studies of the gluon propagator and quark-gluon vertex are also discussed insofar as they are important to the quark SDE. The scope of this article is the application of these equations to the study of dynamical chiral symmetry breaking, quark confinement and the phenomenology of the spectrum and dynamics of QCD
Some aspects of fluid-structure coupling
International Nuclear Information System (INIS)
Kulak, R.F.
1982-01-01
The numerical simulation of nonlinear, transient fluid-structure interactions (FSI) is a current area of concern by researchers in various fields, including the field of nuclear reactor safety. This paper primarily discusses the formulation used in an algorithm that couples three-dimensional hydrodynamic and structural domains. The fluid domain is governed by the Navier-Stokes equations, and the structural domain is governed by the equations of nonlinear structural dynamics. Here, both the fluid and structure are discretized using finite elements. The fluid is discretized with eight-noded quasi-Eulerian hexahedrons and the structural components are represented by Lagrangian triangular plate elements. The semi-discretized equations of motion are solved using an explicit temporal integrator. The coupling is accomplished by satisfying interface mechanics. The structure imposes kinematic constraints to the moving fluid boundary, and the fluid in turn provides an external loading on the structure. At each interface node, normals are computed from the nodal basis functions of only the hydrodynamic nodes. By defining the interface normal in this manner, it becomes independent of the type of structural boundary (i.e. shell, plate, continuum etc.) and thus makes this aspect of the coupling independent of the structure type. Results for several problems are presented and these include a comparison between analytical results for a FSI problem and numerical predictions
Dynamics of vortex structures in a stratified rotating fluid
Sokolovskiy, Mikhail A
2013-01-01
This book presents an extensive analysis of the dynamics of discrete and distributed baroclinic vortices in a multi-layer fluid that characterizes the main features of the large and mesoscales dynamics of the atmosphere and the ocean.
Equation-free dynamic renormalization in a glassy compaction model
International Nuclear Information System (INIS)
Chen, L.; Kevrekidis, I. G.; Kevrekidis, P. G.
2006-01-01
Combining dynamic renormalization with equation-free computational tools, we study the apparently asymptotically self-similar evolution of void distribution dynamics in the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev. Lett. 88, 125701 (2002)]. We illustrate fixed point and dynamic approaches, forward as well as backward in time; these can be used to accelerate simulators of glassy dynamic phenomena
Equation-free dynamic renormalization in a glassy compaction model
Chen, L.; Kevrekidis, I. G.; Kevrekidis, P. G.
2006-07-01
Combining dynamic renormalization with equation-free computational tools, we study the apparently asymptotically self-similar evolution of void distribution dynamics in the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev. Lett. 88, 125701 (2002)]. We illustrate fixed point and dynamic approaches, forward as well as backward in time; these can be used to accelerate simulators of glassy dynamic phenomena.
Colour in visualisation for computational fluid dynamics
Kinnear, D; Atherton, MA; Collins, MW; Dokhan, J; Karayiannis, TG
2006-01-01
Colour is used in computational fluid dynamic (CFD) simulations in two key ways. First it is used to visualise the geometry and allow the engineers to be confident that the model constructed is a good representation of the engineering situation. Once an analysis has been completed, colour is used in post-processing the data from the simulations to illustrate the complex fluid mechanic phenomena under investigation. This paper describes these two uses of colour and provides some examples to il...
International Nuclear Information System (INIS)
Bleyer, U.; Muecket, J.P.
1980-01-01
In general the Birkhoff theorem is violated in non-Einsteinian theories of gravitation. We show for theories in which the dynamical equations do not follow from the field equations that time-dependent vacuum solutions are needed in order to join nonstatic spherically symmetric incoherent matter distributions. It is shown for Treder's tetrad theories that such vacuum solutions exist and a continuous and unique junction is possible. In generalization of these results we consider the problem in what theories of gravitation the dynamical equations do not follow from the field equations. This consideration leads to non-Einsteinian theories like bimetric theories or Treder's tetrad theories containing supplementary geometrical quantities which are not dynamical variables of the theory. (author)
Computational electrochemo-fluid dynamics modeling in a uranium electrowinning cell
International Nuclear Information System (INIS)
Kim, K.R.; Choi, S.Y.; Kim, S.H.; Shim, J.B.; Paek, S.; Kim, I.T.
2014-01-01
A computational electrochemo-fluid dynamics model has been developed to describe the electrowinning behavior in an electrolyte stream through a planar electrode cell system. Electrode reaction of the uranium electrowinning process from a molten-salt electrolyte stream was modeled to illustrate the details of the flow-assisted mass transport of ions to the cathode. This modeling approach makes it possible to represent variations of the convective diffusion limited current density by taking into account the concentration profile at the electrode surface as a function of the flow characteristics and applied current density in a commercially available computational fluid dynamics platform. It was possible to predict the conventional current-voltage relation in addition to details of electrolyte fluid dynamics and electrochemical variables, such as the flow field, species concentrations, potential, and current distributions throughout the galvanostatic electrolysis cell. (author)
Cellular-automata supercomputers for fluid-dynamics modeling
International Nuclear Information System (INIS)
Margolus, N.; Toffoli, T.; Vichniac, G.
1986-01-01
We report recent developments in the modeling of fluid dynamics, and give experimental results (including dynamical exponents) obtained using cellular automata machines. Because of their locality and uniformity, cellular automata lend themselves to an extremely efficient physical realization; with a suitable architecture, an amount of hardware resources comparable to that of a home computer can achieve (in the simulation of cellular automata) the performance of a conventional supercomputer
A Computational Fluid Dynamics Algorithm on a Massively Parallel Computer
Jespersen, Dennis C.; Levit, Creon
1989-01-01
The discipline of computational fluid dynamics is demanding ever-increasing computational power to deal with complex fluid flow problems. We investigate the performance of a finite-difference computational fluid dynamics algorithm on a massively parallel computer, the Connection Machine. Of special interest is an implicit time-stepping algorithm; to obtain maximum performance from the Connection Machine, it is necessary to use a nonstandard algorithm to solve the linear systems that arise in the implicit algorithm. We find that the Connection Machine ran achieve very high computation rates on both explicit and implicit algorithms. The performance of the Connection Machine puts it in the same class as today's most powerful conventional supercomputers.
A new hybrid code (CHIEF) implementing the inertial electron fluid equation without approximation
Muñoz, P. A.; Jain, N.; Kilian, P.; Büchner, J.
2018-03-01
We present a new hybrid algorithm implemented in the code CHIEF (Code Hybrid with Inertial Electron Fluid) for simulations of electron-ion plasmas. The algorithm treats the ions kinetically, modeled by the Particle-in-Cell (PiC) method, and electrons as an inertial fluid, modeled by electron fluid equations without any of the approximations used in most of the other hybrid codes with an inertial electron fluid. This kind of code is appropriate to model a large variety of quasineutral plasma phenomena where the electron inertia and/or ion kinetic effects are relevant. We present here the governing equations of the model, how these are discretized and implemented numerically, as well as six test problems to validate our numerical approach. Our chosen test problems, where the electron inertia and ion kinetic effects play the essential role, are: 0) Excitation of parallel eigenmodes to check numerical convergence and stability, 1) parallel (to a background magnetic field) propagating electromagnetic waves, 2) perpendicular propagating electrostatic waves (ion Bernstein modes), 3) ion beam right-hand instability (resonant and non-resonant), 4) ion Landau damping, 5) ion firehose instability, and 6) 2D oblique ion firehose instability. Our results reproduce successfully the predictions of linear and non-linear theory for all these problems, validating our code. All properties of this hybrid code make it ideal to study multi-scale phenomena between electron and ion scales such as collisionless shocks, magnetic reconnection and kinetic plasma turbulence in the dissipation range above the electron scales.
Yu, Alex; Jackson, Trachette; Tsume, Yasuhiro; Koenigsknecht, Mark; Wysocki, Jeffrey; Marciani, Luca; Amidon, Gordon L; Frances, Ann; Baker, Jason R; Hasler, William; Wen, Bo; Pai, Amit; Sun, Duxin
2017-11-01
Gastrointestinal (GI) fluid volume and its dynamic change are integral to study drug disintegration, dissolution, transit, and absorption. However, key questions regarding the local volume and its absorption, secretion, and transit remain unanswered. The dynamic fluid compartment absorption and transit (DFCAT) model is proposed to estimate in vivo GI volume and GI fluid transport based on magnetic resonance imaging (MRI) quantified fluid volume. The model was validated using GI local concentration of phenol red in human GI tract, which was directly measured by human GI intubation study after oral dosing of non-absorbable phenol red. The measured local GI concentration of phenol red ranged from 0.05 to 168 μg/mL (stomach), to 563 μg/mL (duodenum), to 202 μg/mL (proximal jejunum), and to 478 μg/mL (distal jejunum). The DFCAT model characterized observed MRI fluid volume and its dynamic changes from 275 to 46.5 mL in stomach (from 0 to 30 min) with mucus layer volume of 40 mL. The volumes of the 30 small intestine compartments were characterized by a max of 14.98 mL to a min of 0.26 mL (0-120 min) and a mucus layer volume of 5 mL per compartment. Regional fluid volumes over 0 to 120 min ranged from 5.6 to 20.38 mL in the proximal small intestine, 36.4 to 44.08 mL in distal small intestine, and from 42 to 64.46 mL in total small intestine. The DFCAT model can be applied to predict drug dissolution and absorption in the human GI tract with future improvements.
Duncan, Comer; Jones, Jim
1993-01-01
A key ingredient in the simulation of self-gravitating astrophysical fluid dynamical systems is the gravitational potential and its gradient. This paper focuses on the development of a mixed method multigrid solver of the Poisson equation formulated so that both the potential and the Cartesian components of its gradient are self-consistently and accurately generated. The method achieves this goal by formulating the problem as a system of four equations for the gravitational potential and the three Cartesian components of the gradient and solves them using a distributed relaxation technique combined with conventional full multigrid V-cycles. The method is described, some tests are presented, and the accuracy of the method is assessed. We also describe how the method has been incorporated into our three-dimensional hydrodynamics code and give an example of an application to the collision of two stars. We end with some remarks about the future developments of the method and some of the applications in which it will be used in astrophysics.
Fluid dynamics computer programs for NERVA turbopump
Brunner, J. J.
1972-01-01
During the design of the NERVA turbopump, numerous computer programs were developed for the analyses of fluid dynamic problems within the machine. Program descriptions, example cases, users instructions, and listings for the majority of these programs are presented.
Dynamical stability in fluid-structure interaction
International Nuclear Information System (INIS)
Planchard, J.; Thomas, B.
1991-01-01
The aim of the paper is to investigate the dynamical stability of a group of elastic tubes placed in a cross-flow which obeys to the Navier-Stokes equations. The stability of this coupled system is deduced from the study of a quadratic eigenvalue problem arising in the linearized equations. The instability occurs when the real part of one of the eigenvalues becomes positive; the steady state is then replaced by a time-periodic state which is stable (Hopf bifurcation phenomenon). Some numerical methods for solving the quadratic eigenvalue problem are described [fr
A review on rising bubble dynamics in viscosity-stratified fluids
Indian Academy of Sciences (India)
Kirti Chandra Sahu
Multiphase flow; non-Newtonian; immiscible fluids; bubbles; numerical simulations. 1. Introduction. The fluid dynamics of a gas bubble rising due to buoyancy in a surrounding .... Figure 2. Behaviour of a single bubble rising in quiescent liquid.
A generalized Clebsch transformation leading to a first integral of Navier–Stokes equations
Energy Technology Data Exchange (ETDEWEB)
Scholle, M., E-mail: markus.scholle@hs-heilbronn.de; Marner, F., E-mail: florian.marner@hs-heilbronn.de
2016-09-23
In fluid dynamics, the Clebsch transformation allows for the construction of a first integral of the equations of motion leading to a self-adjoint form of the equations. A remarkable feature is the description of the vorticity by means of only two potential fields fulfilling simple transport equations. Despite useful applications in fluid dynamics and other physical disciplines as well, the classical Clebsch transformation has ever been restricted to inviscid flow. In the present paper a novel, generalized Clebsch transformation is developed which also covers the case of incompressible viscous flow. The resulting field equations are discussed briefly and solved for a flow example. Perspectives for a further extension of the method as well as perspectives towards the development of new solution strategies are presented. - Highlights: • A generalized Clebsch transformation is established applying to viscous flow. • The resulting 5 equations are a first integral of Navier–Stokes-equations. • An axisymmetric stagnation flow against a solid wall is considered as flow example. • Perspectives of the method for other problems, e.g. in solid mechanics are discussed.
A generalized Clebsch transformation leading to a first integral of Navier–Stokes equations
International Nuclear Information System (INIS)
Scholle, M.; Marner, F.
2016-01-01
In fluid dynamics, the Clebsch transformation allows for the construction of a first integral of the equations of motion leading to a self-adjoint form of the equations. A remarkable feature is the description of the vorticity by means of only two potential fields fulfilling simple transport equations. Despite useful applications in fluid dynamics and other physical disciplines as well, the classical Clebsch transformation has ever been restricted to inviscid flow. In the present paper a novel, generalized Clebsch transformation is developed which also covers the case of incompressible viscous flow. The resulting field equations are discussed briefly and solved for a flow example. Perspectives for a further extension of the method as well as perspectives towards the development of new solution strategies are presented. - Highlights: • A generalized Clebsch transformation is established applying to viscous flow. • The resulting 5 equations are a first integral of Navier–Stokes-equations. • An axisymmetric stagnation flow against a solid wall is considered as flow example. • Perspectives of the method for other problems, e.g. in solid mechanics are discussed.
A Gas-Kinetic Method for Hyperbolic-Elliptic Equations and Its Application in Two-Phase Fluid Flow
Xu, Kun
1999-01-01
A gas-kinetic method for the hyperbolic-elliptic equations is presented in this paper. In the mixed type system, the co-existence and the phase transition between liquid and gas are described by the van der Waals-type equation of state (EOS). Due to the unstable mechanism for a fluid in the elliptic region, interface between the liquid and gas can be kept sharp through the condensation and evaporation process to remove the "averaged" numerical fluid away from the elliptic region, and the interface thickness depends on the numerical diffusion and stiffness of the phase change. A few examples are presented in this paper for both phase transition and multifluid interface problems.
Eu, Byung Chan
2008-09-07
In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel.
Effect of centrifugation on dynamic susceptibility of magnetic fluids
Pshenichnikov, Alexander; Lebedev, Alexander; Lakhtina, Ekaterina; Kuznetsov, Andrey
2017-06-01
The dispersive composition, dynamic susceptibility and spectrum of times of magnetization relaxation for six samples of magnetic fluid obtained by centrifuging two base colloidal solutions of the magnetite in kerosene was investigated experimentally. The base solutions differed by the concentration of the magnetic phase and the width of the particle size distribution. The procedure of cluster analysis allowing one to estimate the characteristic sizes of aggregates with uncompensated magnetic moments was described. The results of the magnetogranulometric and cluster analyses were discussed. It was shown that centrifugation has a strong effect on the physical properties of the separated fractions, which is related to the spatial redistribution of particles and multi-particle aggregates. The presence of aggregates in magnetic fluids is interpreted as the main reason of low-frequency (0.1-10 kHz) dispersion of the dynamic susceptibility. The obtained results count in favor of using centrifugation as an effective means of changing the dynamic susceptibility over wide limits and obtaining fluids with the specified type of susceptibility dispersion.
Lie Group Classifications and Non-differentiable Solutions for Time-Fractional Burgers Equation
International Nuclear Information System (INIS)
Wu Guocheng
2011-01-01
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Waichman, Karol; Barmashenko, Boris D.; Rosenwaks, Salman
2017-10-01
Analysis of beam propagation, kinetic and fluid dynamic processes in Cs diode pumped alkali lasers (DPALs), using wave optics model and gasdynamic code, is reported. The analysis is based on a three-dimensional, time-dependent computational fluid dynamics (3D CFD) model. The Navier-Stokes equations for momentum, heat and mass transfer are solved by a commercial Ansys FLUENT solver based on the finite volume discretization technique. The CFD code which solves the gas conservation equations includes effects of natural convection and temperature diffusion of the species in the DPAL mixture. The DPAL kinetic processes in the Cs/He/C2H6 gas mixture dealt with in this paper involve the three lowest energy levels of Cs, (1) 62S1/2, (2) 62P1/2 and (3) 62P3/2. The kinetic processes include absorption due to the 1->3 D2 transition followed by relaxation the 3 to 2 fine structure levels and stimulated emission due to the 2->1 D1 transition. Collisional quenching of levels 2 and 3 and spontaneous emission from these levels are also considered. The gas flow conservation equations are coupled to fast-Fourier-transform algorithm for transverse mode propagation to obtain a solution of the scalar paraxial propagation equation for the laser beam. The wave propagation equation is solved by the split-step beam propagation method where the gain and refractive index in the DPAL medium affect the wave amplitude and phase. Using the CFD and beam propagation models, the gas flow pattern and spatial distributions of the pump and laser intensities in the resonator were calculated for end-pumped Cs DPAL. The laser power, DPAL medium temperature and the laser beam quality were calculated as a function of pump power. The results of the theoretical model for laser power were compared to experimental results of Cs DPAL.
Fluid dynamics via examples and solutions
Nazarenko, Sergey
2014-01-01
"This is an excellent book for fluid dynamics students. It gives a good overview of the theory through a large set of worthy example problems. After many classical textbooks on the subject, there is finally one with solved exercises. I fully appreciate the selection of topics."-Professor Miguel Onorato, Physics Department, University of Torino.
Modern Fluid Dynamics Intermediate Theory and Applications
Kleinstreuer, Clement
2010-01-01
Features pedagogical elements that include consistent 50/50 physics-mathematics approach when introducing material, illustrating concepts, showing flow visualizations, and solving problems. This title intends to help serious undergraduate student solve basic fluid dynamics problems independently, and suggest system design improvements
Directory of Open Access Journals (Sweden)
A. A. Hemeda
2013-01-01
Full Text Available An extension of the so-called new iterative method (NIM has been used to handle linear and nonlinear fractional partial differential equations. The main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently. Therefore, a general framework of the NIM is presented for analytical treatment of fractional partial differential equations in fluid mechanics. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include the fractional wave equation, fractional Burgers equation, fractional KdV equation, fractional Klein-Gordon equation, and fractional Boussinesq-like equation are investigated to show the pertinent features of the technique. Comparison of the results obtained by the NIM with those obtained by both Adomian decomposition method (ADM and the variational iteration method (VIM reveals that the NIM is very effective and convenient. The basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus.
Effect of Fluid Dynamic Viscosity on the Strength of Chalk
DEFF Research Database (Denmark)
Hedegaard, K.; Fabricius, Ida Lykke
The mechanical strength of high porosity and weakly cemented chalk is affected by the fluid in the pores. In this study, the effect of the dynamic viscosity of non-polar fluids has been measured on outcrop chalk from Sigerslev Quarry, Stevns, Denmark. The outcome is that the measured strength...... of the chalk decreases with increasing dynamic viscosity. The proposed qualitative explanation is that pressure difference supports and enhances the generation of microscopic shear and tensile failures....
NASA-VOF3D, 3-D Transient, Free Surface, Incompressible Fluid Dynamic
International Nuclear Information System (INIS)
Torrey, M.D.
1992-01-01
1 - Description of program or function: NASA-VOF3D is a three- dimensional, transient, free surface, incompressible fluid dynamics program. It is specifically designed to calculate confined flows in a low gravity environment in which surface physics must be accurately treated. It allows multiple free surfaces with surface tension and wall adhesion and includes a partial cell treatment that allows curved boundaries and internal obstacles. Variable mesh spacing is permitted in all three coordinate directions. Boundary conditions available are rigid free-slip wall, rigid no-slip, wall, continuative, periodic, and specified pressure outflow boundary. 2 - Method of solution: NASA-VOF3D simulates incompressible flows with free surfaces using the volume-of-fluid (VOF) algorithm. This technique is based on the use of donor-acceptor differencing to track the free surface across an Eulerian grid. The free surfaces are treated by introducing a function defined to be unity at any point occupied by the fluid and zero elsewhere. The complete Navier- Stokes equations for an incompressible fluid are solved by finite differences with surface tension effects included. Wall adhesion may be included or neglected as a user option. The pressures (and velocities) are advanced in time throughout the computing mesh by either a conjugate residual method or the successive over-relaxation (SOR) method. The conjugate residual method is vectorized for the Cray and uses a scaled coefficient matrix. 3 - Restrictions on the complexity of the problem: NASA-VOF3D is restricted to cylindrical coordinate representation of the geometry. A three-dimensional wall-adhesion procedure is available only for straight-walled containers
Finite approximations in fluid mechanics
International Nuclear Information System (INIS)
Hirschel, E.H.
1986-01-01
This book contains twenty papers on work which was conducted between 1983 and 1985 in the Priority Research Program ''Finite Approximations in Fluid Mechanics'' of the German Research Society (Deutsche Forschungsgemeinschaft). Scientists from numerical mathematics, fluid mechanics, and aerodynamics present their research on boundary-element methods, factorization methods, higher-order panel methods, multigrid methods for elliptical and parabolic problems, two-step schemes for the Euler equations, etc. Applications are made to channel flows, gas dynamical problems, large eddy simulation of turbulence, non-Newtonian flow, turbomachine flow, zonal solutions for viscous flow problems, etc. The contents include: multigrid methods for problems from fluid dynamics, development of a 2D-Transonic Potential Flow Solver; a boundary element spectral method for nonstationary viscous flows in 3 dimensions; navier-stokes computations of two-dimensional laminar flows in a channel with a backward facing step; calculations and experimental investigations of the laminar unsteady flow in a pipe expansion; calculation of the flow-field caused by shock wave and deflagration interaction; a multi-level discretization and solution method for potential flow problems in three dimensions; solutions of the conservation equations with the approximate factorization method; inviscid and viscous flow through rotating meridional contours; zonal solutions for viscous flow problems
Ill-posedness of Dynamic Equations of Compressible Granular Flow
Shearer, Michael; Gray, Nico
2017-11-01
We introduce models for 2-dimensional time-dependent compressible flow of granular materials and suspensions, based on the rheology of Pouliquen and Forterre. The models include density dependence through a constitutive equation in which the density or volume fraction of solid particles with material density ρ* is taken as a function of an inertial number I: ρ = ρ * Φ(I), in which Φ(I) is a decreasing function of I. This modelling has different implications from models relying on critical state soil mechanics, in which ρ is treated as a variable in the equations, contributing to a flow rule. The analysis of the system of equations builds on recent work of Barker et al in the incompressible case. The main result is the identification of a criterion for well-posedness of the equations. We additionally analyze a modification that applies to suspensions, for which the rheology takes a different form and the inertial number reflects the role of the fluid viscosity.
Approximate Riemann solver for the two-fluid plasma model
International Nuclear Information System (INIS)
Shumlak, U.; Loverich, J.
2003-01-01
An algorithm is presented for the simulation of plasma dynamics using the two-fluid plasma model. The two-fluid plasma model is more general than the magnetohydrodynamic (MHD) model often used for plasma dynamic simulations. The two-fluid equations are derived in divergence form and an approximate Riemann solver is developed to compute the fluxes of the electron and ion fluids at the computational cell interfaces and an upwind characteristic-based solver to compute the electromagnetic fields. The source terms that couple the fluids and fields are treated implicitly to relax the stiffness. The algorithm is validated with the coplanar Riemann problem, Langmuir plasma oscillations, and the electromagnetic shock problem that has been simulated with the MHD plasma model. A numerical dispersion relation is also presented that demonstrates agreement with analytical plasma waves
Green Algae as Model Organisms for Biological Fluid Dynamics
Goldstein, Raymond E.
2015-01-01
In the past decade, the volvocine green algae, spanning from the unicellular Chlamydomonas to multicellular Volvox, have emerged as model organisms for a number of problems in biological fluid dynamics. These include flagellar propulsion, nutrient uptake by swimming organisms, hydrodynamic interactions mediated by walls, collective dynamics and transport within suspensions of microswimmers, the mechanism of phototaxis, and the stochastic dynamics of flagellar synchronization. Green algae are well suited to the study of such problems because of their range of sizes (from 10 μm to several millimeters), their geometric regularity, the ease with which they can be cultured, and the availability of many mutants that allow for connections between molecular details and organism-level behavior. This review summarizes these recent developments and highlights promising future directions in the study of biological fluid dynamics, especially in the context of evolutionary biology, that can take advantage of these remarkable organisms.
Directory of Open Access Journals (Sweden)
Jiazhou Wu
2018-06-01
Full Text Available A three-dimensional multiphysical transient model was developed to investigate keyhole formation, weld pool dynamics, and mass transfer in laser welding of dissimilar materials. The coupling of heat transfer, fluid flow, keyhole free surface evolution, and solute diffusion between dissimilar metals was simulated. The adaptive heat source model was used to trace the change of keyhole shape, and the Rayleigh scattering of the laser beam was considered. The keyhole wall was calculated using the fluid volume equation, primarily considering the recoil pressure induced by metal evaporation, surface tension, and hydrostatic pressure. Fluid flow, diffusion, and keyhole formation were considered simultaneously in mass transport processes. Welding experiments of 304L stainless steel and industrial pure titanium TA2 were performed to verify the simulation results. It is shown that spatters are shaped during the welding process. The thickness of the intermetallic reaction layer between the two metals and the diffusion of elements in the weld are calculated, which are important criteria for welding quality. The simulation results correspond well with the experimental results.
International Nuclear Information System (INIS)
Kataoka, Isao; Tomiyama, Akio
2004-01-01
The simplified and physically reasonable basic equations for the gas-liquid dispersed flow were developed based on some appropriate assumptions and the treatment of dispersed phase as isothermal rigid particles. Based on the local instant formulation of mass, momentum and energy conservation of the dispersed flow, time-averaged equations were obtained assuming that physical quantities in the dispersed phase are uniform. These assumptions are approximately valid when phase change rate and/or chemical reaction rate are not so large at gas-liquid interface and there is no heat generation in within the dispersed phase. Detailed discussions were made on the characteristics of obtained basic equations and physical meanings of terms consisting the basic equations. It is shown that, in the derived averaged momentum equation, the terms of pressure gradient and viscous momentum diffusion do not appear and, in the energy equation, the term of molecular thermal diffusion heat flux does not appear. These characteristics of the derived equations were shown to be very consistent concerning the physical interpretation of the gas-liquid dispersed flow. Furthermore, the obtained basic equations are consistent with experiments for the dispersed flow where most of averaged physical quantities are obtained assuming that the distributions of those are uniform within the dispersed phase. Investigation was made on the problem whether the obtained basic equations are well-posed or ill-posed for the initial value problem. The eigenvalues of the simplified mass and momentum equations are calculated for basic equations obtained here and previous two-fluid basic equations with one pressure model. Well-posedness and ill-posedness are judged whether the eigenvalues are real or imaginary. The result indicated the newly developed basic equations always constitute the well-posed initial value problem while the previous two-fluid basic equations based on one pressure model constitutes ill
Differential equations, dynamical systems, and an introduction to chaos
Smale, Stephen; Devaney, Robert L
2003-01-01
Thirty years in the making, this revised text by three of the world''s leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra.The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of the Field''s Medal for his work in dynamical systems.* Developed by award-winning researchers and authors* Provides a rigorous yet accessible introduction to differential equations and dynamical systems* Includes bifurcation theory throughout* Contains numerous explorations for students to embark uponNEW IN THIS EDITION* New contemporary material and updated applications* Revisions throughout the text, including simplification...
Review of computational fluid dynamics (CFD) researches on nano fluid flow through micro channel
Dewangan, Satish Kumar
2018-05-01
Nanofluid is becoming a promising heat transfer fluids due to its improved thermo-physical properties and heat transfer performance. Micro channel heat transfer has potential application in the cooling high power density microchips in CPU system, micro power systems and many such miniature thermal systems which need advanced cooling capacity. Use of nanofluids enhances the effectiveness of t=scu systems. Computational Fluid Dynamics (CFD) is a very powerful tool in computational analysis of the various physical processes. It application to the situations of flow and heat transfer analysis of the nano fluids is catching up very fast. Present research paper gives a brief account of the methodology of the CFD and also summarizes its application on nano fluid and heat transfer for microchannel cases.
Syringe irrigation: blending endodontics and fluid dynamics
Boutsioukis, C.; van der Sluis, L.W.M.; Basrani, B.
2015-01-01
Syringe irrigation remains a widely used irrigant delivery method during root canal treatment. An interdisciplinary approach involving well-established methods from the field of fluid dynamics can provide new insights into the mechanisms involved in cleaning and disinfection of the root canal system
Directory of Open Access Journals (Sweden)
Klaudia Oleschko
2017-04-01
Full Text Available Recently p-adic (and, more generally, ultrametric spaces representing tree-like networks of percolation, and as a special case of capillary patterns in porous media, started to be used to model the propagation of fluids (e.g., oil, water, oil-in-water, and water-in-oil emulsion. The aim of this note is to derive p-adic dynamics described by fractional differential operators (Vladimirov operators starting with discrete dynamics based on hierarchically-structured interactions between the fluids’ volumes concentrated at different levels of the percolation tree and coming to the multiscale universal topology of the percolating nets. Similar systems of discrete hierarchic equations were widely applied to modeling of turbulence. However, in the present work this similarity is only formal since, in our model, the trees are real physical patterns with a tree-like topology of capillaries (or fractures in random porous media (not cascade trees, as in the case of turbulence, which we will be discussed elsewhere for the spinner flowmeter commonly used in the petroleum industry. By going to the “continuous limit” (with respect to the p-adic topology we represent the dynamics on the tree-like configuration space as an evolutionary nonlinear p-adic fractional (pseudo- differential equation, the tree-like analog of the Navier–Stokes equation. We hope that our work helps to come closer to a nonlinear equation solution, taking into account the scaling, hierarchies, and formal derivations, imprinted from the similar properties of the real physical world. Once this coupling is resolved, the more problematic question of information scaling in industrial applications will be achieved.
McKenzie, J. F.; Dubinin, E.; Sauer, K.; Doyle, T. B.
2004-08-01
Perturbation reductive procedures, as used to analyse various weakly nonlinear plasma waves (solitons and periodic waves), normally lead to the dynamical system being described by KdV, Burgers' or a nonlinear Schrödinger-type equation, with properties that can be deduced from an array of mathematical techniques. Here we develop a fully nonlinear theory of one-dimensional stationary plasma waves, which elucidates the common nature of various diverse wave phenomena. This is accomplished by adopting an essentially fluid dynamic viewpoint. In this unified treatment the constants of the motion (for mass, momentum and energy) lead naturally to the construction of the wave structure equations. It is shown, for example, that electrostatic, Hall magnetohydrodynamic and ion cyclotron acoustic nonlinear waves all obey first-order differential equations of the same generic type for the longitudinal flow field of the wave. The equilibrium points, which define the soliton amplitude, are given by the compressive and/or rarefactive roots of a total plasma ‘energy’ or ‘momentum’ function characterizing the wave type. This energy function, which is an algebraic combination of the Bernoulli momentum and energy functions for the longitudinal flow field, is the fluid dynamic counterpart of the pseudo-potentials, which are characteristic of system structure equations formulated in other than fluid variables. Another general feature of the structure equation is the phenomenon of choked flow, which occurs when the flow speed becomes sonic. It is this trans-sonic property that limits the soliton amplitudes and defines the critical collective Mach numbers of the waves. These features are also obtained in multi-component plasmas where, for example, in a bi-ion plasma, momentum exchanges between protons and heavier ions are mediated by the Maxwell magnetic stresses. With a suitable generalization of the concept of a sonic point in a bi-ion system and the corresponding choked flow
Modeling of Dynamic Fluid Forces in Fast Switching Valves
DEFF Research Database (Denmark)
Roemer, Daniel Beck; Johansen, Per; Pedersen, Henrik Clemmensen
2015-01-01
Switching valves experience opposing fluid forces due to movement of the moving member itself, as the surrounding fluid volume must move to accommodate the movement. This movement-induced fluid force may be divided into three main components; the added mass term, the viscous term and the socalled...... history term. For general valve geometries there are no simple solution to either of these terms. During development and design of such switching valves, it is therefore, common practice to use simple models to describe the opposing fluid forces, neglecting all but the viscous term which is determined...... based on shearing areas and venting channels. For fast acting valves the opposing fluid force may retard the valve performance significantly, if appropriate measures are not taken during the valve design. Unsteady Computational Fluid Dynamics (CFD) simulations are available to simulate the total fluid...
Fluid dynamics of acoustic and hydrodynamic cavitation in hydraulic power systems
Ferrari, A.
2017-03-01
Cavitation is the transition from a liquid to a vapour phase, due to a drop in pressure to the level of the vapour tension of the fluid. Two kinds of cavitation have been reviewed here: acoustic cavitation and hydrodynamic cavitation. As acoustic cavitation in engineering systems is related to the propagation of waves through a region subjected to liquid vaporization, the available expressions of the sound speed are discussed. One of the main effects of hydrodynamic cavitation in the nozzles and orifices of hydraulic power systems is a reduction in flow permeability. Different discharge coefficient formulae are analysed in this paper: the Reynolds number and the cavitation number result to be the key fluid dynamical parameters for liquid and cavitating flows, respectively. The latest advances in the characterization of different cavitation regimes in a nozzle, as the cavitation number reduces, are presented. The physical cause of choked flows is explained, and an analogy between cavitation and supersonic aerodynamic flows is proposed. The main approaches to cavitation modelling in hydraulic power systems are also reviewed: these are divided into homogeneous-mixture and two-phase models. The homogeneous-mixture models are further subdivided into barotropic and baroclinic models. The advantages and disadvantages of an implementation of the complete Rayleigh-Plesset equation are examined.
Schrödinger–Langevin equation with quantum trajectories for photodissociation dynamics
Energy Technology Data Exchange (ETDEWEB)
Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw
2017-02-15
The Schrödinger–Langevin equation is integrated to study the wave packet dynamics of quantum systems subject to frictional effects by propagating an ensemble of quantum trajectories. The equations of motion for the complex action and quantum trajectories are derived from the Schrödinger–Langevin equation. The moving least squares approach is used to evaluate the spatial derivatives of the complex action required for the integration of the equations of motion. Computational results are presented and analyzed for the evolution of a free Gaussian wave packet, a two-dimensional barrier model, and the photodissociation dynamics of NOCl. The absorption spectrum of NOCl obtained from the Schrödinger–Langevin equation displays a redshift when frictional effects increase. This computational result agrees qualitatively with the experimental results in the solution-phase photochemistry of NOCl.
Sparse learning of stochastic dynamical equations
Boninsegna, Lorenzo; Nüske, Feliks; Clementi, Cecilia
2018-06-01
With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems from simulation data. In this study, we extend SINDy to stochastic dynamical systems which are frequently used to model biophysical processes. We prove the asymptotic correctness of stochastic SINDy in the infinite data limit, both in the original and projected variables. We discuss algorithms to solve the sparse regression problem arising from the practical implementation of SINDy and show that cross validation is an essential tool to determine the right level of sparsity. We demonstrate the proposed methodology on two test systems, namely, the diffusion in a one-dimensional potential and the projected dynamics of a two-dimensional diffusion process.
Essential Computational Fluid Dynamics
Zikanov, Oleg
2011-01-01
This book serves as a complete and self-contained introduction to the principles of Computational Fluid Dynamic (CFD) analysis. It is deliberately short (at approximately 300 pages) and can be used as a text for the first part of the course of applied CFD followed by a software tutorial. The main objectives of this non-traditional format are: 1) To introduce and explain, using simple examples where possible, the principles and methods of CFD analysis and to demystify the `black box’ of a CFD software tool, and 2) To provide a basic understanding of how CFD problems are set and
On the characteristics of a numerical fluid dynamics simulator
International Nuclear Information System (INIS)
Winkler, K.H.A.; Norman, M.L.; Norton, J.L.
1986-01-01
John von Neumann envisioned scientists and mathematicians analyzing and controlling their numerical experiments on nonlinear dynamic systems interactively. The authors describe their concept of a real-time Numerical Fluid Dynamics Simulator NFDS. The authors envision the NFDS to be composed of simulation processors, data storage devices, and image processing devices of extremely high power and capacity, interconnected by very high throughput communication channels. They present individual component performance requirements for both real-time and playback operating modes of the NFDS, using problems of current interest in fluid dynamics as examples. Scaling relations are derived showing the dependence of system requirements on the dimensionality and complexity of the numerical model. The authors conclude by extending their analysis to the system requirements posed in modeling the more involved physics of radiation hydrodynamics
International Nuclear Information System (INIS)
Sieniutycz, S.; Berry, R.S.
1993-01-01
A Lagrangian with dissipative (e.g., Onsager's) potentials is constructed for the field description of irreversible heat-conducting fluids, off local equilibrium. Extremum conditions of action yield Clebsch representations of temperature, chemical potential, velocities, and generalized momenta, including a thermal momentum introduced recently [R. L. Selinger and F. R. S. Whitham, Proc. R. Soc. London, Ser. A 302, 1 (1968); S. Sieniutycz and R. S. Berry, Phys. Rev. A 40, 348 (1989)]. The basic question asked is ''To what extent may irreversibility, represented by a given form of the entropy source, influence the analytical form of the conservation laws for the energy and momentum?'' Noether's energy for a fluid with heat flow is obtained, which leads to a fundamental equation and extended Hamiltonian dynamics obeying the second law of thermodynamics. While in the case of the Onsager potentials this energy coincides numerically with the classical energy E, it contains an extra term (vanishing along the path) still contributing to an irreversible evolution. Components of the energy-momentum tensor preserve all terms regarded standardly as ''irreversible'' (heat, tangential stresses, etc.) generalized to the case when thermodynamics includes the state gradients and the so-called thermal phase, which we introduce here. This variable, the Lagrange multiplier of the entropy generation balance, is crucial for consistent treatment of irreversible processes via an action formalism. We conclude with the hypothesis that embedding the first and second laws in the context of the extremal behavior of action under irreversible conditions may imply accretion of an additional term to the classical energy
Kobayashi, Y.; Kitamura, N.; Ieda, A.; Yoshizumi, M.; Imada, S.; Tsugawa, Y.; Burch, J. L.; Russell, C. T.; Moore, T. E.; Giles, B. L.; Paterson, W.; Torbert, R. B.; Ergun, R.; Saito, Y.; Yokota, S.; Machida, S.
2017-12-01
Magnetic reconnection is a basic physical process by which energy of magnetic field is converted into the kinetic energy of plasmas. In recent years, MMS missionconsisting of four spacecraft has been conducted aiming at elucidating the physical mechanism of merging themagnetic fields in the vicinity of the magnetic neutral linethat exists in the central part of the structure. In this paper, we examine the magnetic field frozen-in relation near the magnetic neutral line as well as the causal relationship between electron and ion dynamics in the frame of two fluid equations.Theoretically, it is shown that electrons are frozen-in to the magnetic fields while ion's frozen-in relation is broken in the ion dissipation region. However, when we examined the observational data around 1307 UT on October 16, 2015 when MMS spacecraft passed through the vicinity of the magnetic neutral line [Burch et al., Science 2016] , it was confirmed that the frozen-ion relation was not established for electrons in the ion dissipation region. In addition, we found that intense wave electric fields in this region. From the spectral analysis of the waves, it turned out that their characteristic frequencies are the lower-hybrid and electron cyclotron frequencies.In the framework of the two-fluid equation, we can evaluate the values of each term of the equations of motion for both ions and electrons except for the collision term from MMS spacecraft data. Therefore, it is possible to obtain collision terms for both species. Since magnetospheric plasma is basically collisionless, it is considered that the collision term is due to anomalous resistivity associated with the excited waves . On the other hand, in the two-fluid equation system, the two vectors corresponding to the collision terms of ions and electrons have the same absolute value. Because the force exerted between the two is the internal force, they should face in the opposite direction. However, the vectors corresponding to the
Possible fluid dynamical interpretation of some reported features in the Jovian atmosphere
Maxworthy, T.; Redekopp, L. G.
1980-01-01
A fluid dynamical interpretation is presented of the two major types of disturbance found in the southern hemisphere of Jupiter by the Voyager 1 imaging data. The observed features always occur together, and consist of a compact elliptically shaped formation having an anticyclonic flow which is poleward of a pair of more elongated cyclonic structures, as in the Great Red Spot and the white ovals. It is noted that the anticyclonic features at 41 deg S may be described by the cnoidal wave solutions to the appropriate nonlinear evolution equation, and that flow patterns derived in the vicinity of the Great Red Spot and white ovals are strikingly similar to those obtained for the flow around a solitary wave of the type than can exist in a zonal flow such as that found in the Jupiter atmosphere. Results of computations in terms of solitary wave theory of flow fields in the atmospheric structure and zonal velocity profiles determined from Voyager infrared spectroscopy and radiometry data are then presented which show that the pattern must be a singular solitary wave mode, the east-west structure of which is best described by the Korteweg-de-Vries equation
A Multiscale Model for Virus Capsid Dynamics
Directory of Open Access Journals (Sweden)
Changjun Chen
2010-01-01
Full Text Available Viruses are infectious agents that can cause epidemics and pandemics. The understanding of virus formation, evolution, stability, and interaction with host cells is of great importance to the scientific community and public health. Typically, a virus complex in association with its aquatic environment poses a fabulous challenge to theoretical description and prediction. In this work, we propose a differential geometry-based multiscale paradigm to model complex biomolecule systems. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum domain of the fluid mechanical description of the aquatic environment from the microscopic discrete domain of the atomistic description of the biomolecule. A multiscale action functional is constructed as a unified framework to derive the governing equations for the dynamics of different scales. We show that the classical Navier-Stokes equation for the fluid dynamics and Newton's equation for the molecular dynamics can be derived from the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows.
A multiscale model for virus capsid dynamics.
Chen, Changjun; Saxena, Rishu; Wei, Guo-Wei
2010-01-01
Viruses are infectious agents that can cause epidemics and pandemics. The understanding of virus formation, evolution, stability, and interaction with host cells is of great importance to the scientific community and public health. Typically, a virus complex in association with its aquatic environment poses a fabulous challenge to theoretical description and prediction. In this work, we propose a differential geometry-based multiscale paradigm to model complex biomolecule systems. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum domain of the fluid mechanical description of the aquatic environment from the microscopic discrete domain of the atomistic description of the biomolecule. A multiscale action functional is constructed as a unified framework to derive the governing equations for the dynamics of different scales. We show that the classical Navier-Stokes equation for the fluid dynamics and Newton's equation for the molecular dynamics can be derived from the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows.
International Nuclear Information System (INIS)
Fraser, D.G.; Refson, K.
1992-01-01
The molecular dynamics calculations reported above give calculated P-V-T properties for H 2 O up to 1500 K and 100 GPa, which agree remarkably well with the available experimental data. We also observe the phase transition to a crystalline, orientationally disordered cubic ice structure. No account was taken of molecular flexibility in these calculations nor of potential dissociation at high pressures as suggested by Hamman (1981). However, we note that the closest next-nearest-neighbour O-H approach remains significantly greater than the TIP4P fixed O-H bond length within the water molecule for all pressures studied. The equation of state proposed here should be useful for estimating the properties of H 2 O at up to 1500 K and 100 G Pa (1 Mbar) and is much easier to use in practice than modified Redlich Kwong equations. Extension of these methods to the studies of other fluids and of fluid mixtures at high temperatures and pressures will require good potential models for the species involved, and this is likely to involve a combination of good ab initio work and semiempirical modelling. Once developed, these models should allow robust predictions of thermodynamic properties beyond the range of the experimental data on the basis of fundamental molecular information
Inverse solutions for a second-grade fluid for porous medium ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
to the free spiraling of electrons and ions about the magnetic lines of force before ... An understanding of the dynamics of fluids in porous media has practical ... viscous term in order to account for the vorticity diffusion caused by the boundary resis- ... The governing equations that describe the flow of a Newtonian fluid is the ...
Blocken, B.J.E.; Gualtieri, C.
2012-01-01
Computational Fluid Dynamics (CFD) is increasingly used to study a wide variety of complex Environmental Fluid Mechanics (EFM) processes, such as water flow and turbulent mixing of contaminants in rivers and estuaries and wind flow and air pollution dispersion in urban areas. However, the accuracy
Groves, Curtis Edward
2014-01-01
Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This paper describes an approach to quantify the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft without the use of test data. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional "validation by test only" mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions. Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computational Fluid Dynamics can be used to verify these requirements; however, the model must be validated by test data. This research includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available and open source solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT, STARCCM+, and OPENFOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid Dynamics model using the methodology found in "Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations". This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics
Groves, Curtis Edward
2014-01-01
Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This paper describes an approach to quantify the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft without the use of test data. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional validation by test only mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions.Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computational Fluid Dynamics can be used to verify these requirements; however, the model must be validated by test data. This research includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available and open source solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT, STARCCM+, and OPENFOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid Dynamics model using the methodology found in Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations. This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions
LSZ asymptotic condition and dynamic equations in quantum field theory
International Nuclear Information System (INIS)
Arkhipov, A.A.; Savrin, V.I.
1983-01-01
Some techniques that may be appropriate for the derivation of dynamic equations in quantum field theory are considered. A new method of deriving equations based on the use of LSZ asymptotic condition is described. It is proved that with the help of this method it becomes possible to obtain equations for wave functions both of scattering and bound states. Work is described in several papers under the dame title. The first paper is devoted to the Bethe-Salpeter equation
Existence of the passage to the limit of an inviscid fluid.
Goldobin, Denis S
2017-11-24
In the dynamics of a viscous fluid, the case of vanishing kinematic viscosity is actually equivalent to the Reynolds number tending to infinity. Hence, in the limit of vanishing viscosity the fluid flow is essentially turbulent. On the other hand, the Euler equation, which is conventionally adopted for the description of the flow of an inviscid fluid, does not possess proper turbulent behaviour. This raises the question of the existence of the passage to the limit of an inviscid fluid for real low-viscosity fluids. To address this question, one should employ the theory of turbulent boundary layer near an inflexible boundary (e.g., rigid wall). On the basis of this theory, one can see how the solutions to the Euler equation become relevant for the description of the flow of low-viscosity fluids, and obtain the small parameter quantifying accuracy of this description for real fluids.
Atomistic Modeling of the Fluid-Solid Interface in Simple Fluids
Hadjiconstantinou, Nicolas; Wang, Gerald
2017-11-01
Fluids can exhibit pronounced structuring effects near a solid boundary, typically manifested in a layered structure that has been extensively shown to directly affect transport across the interface. We present and discuss several results from molecular-mechanical modeling and molecular-dynamics (MD) simulations aimed at characterizing the structure of the first fluid layer directly adjacent to the solid. We identify a new dimensionless group - termed the Wall number - which characterizes the degree of fluid layering, by comparing the competing effects of wall-fluid interaction and thermal energy. We find that in the layering regime, several key features of the first layer layer - including its distance from the solid, its width, and its areal density - can be described using mean-field-energy arguments, as well as asymptotic analysis of the Nernst-Planck equation. For dense fluids, the areal density and the width of the first layer can be related to the bulk fluid density using a simple scaling relation. MD simulations show that these results are broadly applicable and robust to the presence of a second confining solid boundary, different choices of wall structure and thermalization, strengths of fluid-solid interaction, and wall geometries.
Annual review of fluid mechanics. Volume 23
International Nuclear Information System (INIS)
Lumley, J.L.; Van Dyke, M.; Reed, H.L.
1991-01-01
Recent advances in theoretical, experimental, and computational fluid mechanics are discussed in a collection of annual review essays. Topics addressed include Lagrangian ocean studies, drag reduction in nature, the hydraulics of rotating strait and sill flow, analytical methods for the development of Reynolds-stress closures in turbulence, and exact solutions of the Navier-Stokes equations. Consideration is given to the theory of hurricanes, flow phenomena in CVD of thin films, particle-imaging techniques for experimental fluid mechanics, symmetry and symmetry-breaking bifurcations in fluid dynamics, turbulent mixing in stratified fluids, numerical simulation of transition in wall-bounded shear flows, fractals and multifractals in fluid turbulence, and coherent motions in the turbulent boundary layer
Mechanics of couple-stress fluid coatings
Waxman, A. M.
1982-01-01
The formal development of a theory of viscoelastic surface fluids with bending resistance - their kinematics, dynamics, and rheology are discussed. It is relevant to the mechanics of fluid drops and jets coated by a thin layer of immiscible fluid with rather general rheology. This approach unifies the hydrodynamics of two-dimensional fluids with the mechanics of an elastic shell in the spirit of a Cosserat continuum. There are three distinct facets to the formulation of surface continuum mechanics. Outlined are the important ideas and results associated with each: the kinematics of evolving surface geometries, the conservation laws governing the mechanics of surface continua, and the rheological equations of state governing the surface stress and moment tensors.
Fluid dynamics of out of equilibrium boost invariant plasmas
Blaizot, Jean-Paul; Yan, Li
2018-05-01
By solving a simple kinetic equation, in the relaxation time approximation, and for a particular set of moments of the distribution function, we establish a set of equations which, on the one hand, capture exactly the dynamics of the kinetic equation, and, on the other hand, coincide with the hierarchy of equations of viscous hydrodynamics, to arbitrary order in the viscous corrections. This correspondence sheds light on the underlying mechanism responsible for the apparent success of hydrodynamics in regimes that are far from local equilibrium.
Terzic, Jenny; Nagarajah, Romesh; Alamgir, Muhammad
2013-01-01
Accurate fluid level measurement in dynamic environments can be assessed using a Support Vector Machine (SVM) approach. SVM is a supervised learning model that analyzes and recognizes patterns. It is a signal classification technique which has far greater accuracy than conventional signal averaging methods. Ultrasonic Fluid Quantity Measurement in Dynamic Vehicular Applications: A Support Vector Machine Approach describes the research and development of a fluid level measurement system for dynamic environments. The measurement system is based on a single ultrasonic sensor. A Support Vector Machines (SVM) based signal characterization and processing system has been developed to compensate for the effects of slosh and temperature variation in fluid level measurement systems used in dynamic environments including automotive applications. It has been demonstrated that a simple ν-SVM model with Radial Basis Function (RBF) Kernel with the inclusion of a Moving Median filter could be used to achieve the high levels...
Modified dynamical equation for dye doped nematic liquid crystals
Energy Technology Data Exchange (ETDEWEB)
Manohar, Rajiv, E-mail: rajlu1@rediffmail.co [Liquid Crystal Research Lab, Physics Department, University of Lucknow, Lucknow 226007 (India); Misra, Abhishek Kumar; Srivastava, Abhishek Kumar [Liquid Crystal Research Lab, Physics Department, University of Lucknow, Lucknow 226007 (India)
2010-04-15
Dye doped liquid crystals show changed dielectric properties in comparison to pure liquid crystals. These changes are strongly dependent on the concentration of dye. In the present work we have measured dielectric properties of standard nematic liquid crystals E-24 and its two guest host mixtures of different concentrations with Anthraquinone dye D5. The experimental results are fitted using linear response and in the light of this we have proposed some modifications in the dynamical equation for the nematic liquid crystals by introducing two new variables as dye concentration coefficients. The limitations of the proposed equation in high temperature range have also been discussed. With the help of the proposed dynamical equation for the guest-host liquid crystals (GHLCs) it is possible to predict the various parameters like rotational viscosity, dielectric anisotropy and relaxation time for GHLCs at other concentrations of dye in liquid crystals theoretically.
Zang, Thomas A.; Green, Lawrence L.
1999-01-01
A challenge for the fluid dynamics community is to adapt to and exploit the trend towards greater multidisciplinary focus in research and technology. The past decade has witnessed substantial growth in the research field of Multidisciplinary Design Optimization (MDO). MDO is a methodology for the design of complex engineering systems and subsystems that coherently exploits the synergism of mutually interacting phenomena. As evidenced by the papers, which appear in the biannual AIAA/USAF/NASA/ISSMO Symposia on Multidisciplinary Analysis and Optimization, the MDO technical community focuses on vehicle and system design issues. This paper provides an overview of the MDO technology field from a fluid dynamics perspective, giving emphasis to suggestions of specific applications of recent MDO technologies that can enhance fluid dynamics research itself across the spectrum, from basic flow physics to full configuration aerodynamics.
Computational Fluid Dynamics in Ventilation Design
DEFF Research Database (Denmark)
Nielsen, Peter V.
2008-01-01
This paper is based on the new REHVA Guidebook Computational Fluid Dynamics in Ventilation Design (Nielsen et al. 2007) written by Peter V. Nielsen, Francis(Nielsen 2007) written by Peter V. Nielsen, Francis Allard, Hazim B. Awbi, Lars Davidson and Alois Schälin. The guidebook is made for people....... The guidebook introduces rules for good quality prediction work, and it is the purpose of the guidebook to improve the technical level of CFD work in ventilation.......This paper is based on the new REHVA Guidebook Computational Fluid Dynamics in Ventilation Design (Nielsen et al. 2007) written by Peter V. Nielsen, Francis(Nielsen 2007) written by Peter V. Nielsen, Francis Allard, Hazim B. Awbi, Lars Davidson and Alois Schälin. The guidebook is made for people...... who need to use and discuss results based on CFD predictions, and it gives insight into the subject for those who are not used to work with CFD. The guidebook is also written for people working with CFD who have to be more aware of how this numerical method is applied in the area of ventilation...
Dynamic simulation of an electrorheological fluid
International Nuclear Information System (INIS)
Bonnecaze, R.T.; Brady, J.F.
1992-01-01
A molecular-dynamics-like method is presented for the simulation of a suspension of dielectric particles in a nonconductive solvent forming an electrorheological fluid. The method accurately accounts for both hydrodynamic and electrostatic interparticle interactions from dilute volume fractions to closest packing for simultaneous shear and electric fields. The hydrodynamic interactions and rheology are determined with the Stokesian dynamics methodology, while the electrostatic interactions, in particular, the conservative electrostatic interparticle forces, are determined from the electrostatic energy of the suspension. The energy of the suspension is computed from the induced particle dipoles by a method previously developed [R. T. Bonnecaze and J. F. Brady, Proc. R. Soc. London, Ser. A 430, 285 (1990)]. Using the simulation, the dynamics can be directly correlated to the observed macroscopic rheology of the suspension for a range of the so-called Mason number, Ma, the ratio of viscous to electrostatic forces. The simulation is specifically applied to a monolayer of spherical particles of areal fraction 0.4 with a particle-to-fluid dielectric constant ratio of 4 for Ma=10 -4 to ∞. The effective viscosity of the suspension increases as Ma -1 or with the square of the electric field for small Ma and has a plateau value at large Ma, as is observed experimentally. This rheological behavior can be interpreted as Bingham plastic-like with a dynamic yield stress. The first normal stress difference is negative, and its magnitude increases as Ma -1 at small Ma with a large Ma plateau value of zero. In addition to the time averages of the rheology, the time traces of the viscosities are presented along with selected ''snapshots'' of the suspension microstructure
Dynamic analysis of multibody system immersed in a fluid medium
International Nuclear Information System (INIS)
Wu, R.W.; Liu, L.K.; Levy, S.
1977-01-01
This paper is concerned primarily with the development and evaluation of an analysis method for the reponse prediction of immersed systems to seismic and other dynamic excitations. For immersed multibody systems, the hydrodynamic interaction causes coupled motion among the solid bodies. Also, under intense external excitations, impact between bodies may occur. The complex character of such systems inhibit the use of conventional analytical solutions in closed form. Therefore, approximate numerical schemes have been devised. For an incompressible, inviscid fluid, the hydrodynamic forces exerted by the fluid on solid bodies are determined to be linearly proportional to the acceleration of the vibrating solid bodies; i.e., the presence of the fluid only affects the inertia of the solid body system. A finite element computer program has been developed for computing this hydrodynamic (or added) mass effect. This program can be used to determine the hydrodynamic mass of a two-dimensional fluid field with solid bodies of arbitrary geometry. Triangular elements and linear pressure interpolation function are used to discretize the fluid region. The component element method is used to determine the dynamic response of the multibody system to externally applied mechanical loading or support excitation. The present analysis method for predicting the dynamic response of submerged multibody system is quite general and pertains to any number of solid bodies. However in this paper, its application is demonstrated only for 4 and 25 body systems. (Auth.)
Global dynamics of a nonlocal delayed reaction-diffusion equation on a half plane
Hu, Wenjie; Duan, Yueliang
2018-04-01
We consider a delayed reaction-diffusion equation with spatial nonlocality on a half plane that describes population dynamics of a two-stage species living in a semi-infinite environment. A Neumann boundary condition is imposed accounting for an isolated domain. To describe the global dynamics, we first establish some a priori estimate for nontrivial solutions after investigating asymptotic properties of the nonlocal delayed effect and the diffusion operator, which enables us to show the permanence of the equation with respect to the compact open topology. We then employ standard dynamical system arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated by the diffusive Nicholson's blowfly equation and the diffusive Mackey-Glass equation.
Woodcock, T E; Woodcock, T M
2012-03-01
I.V. fluid therapy does not result in the extracellular volume distribution expected from Starling's original model of semi-permeable capillaries subject to hydrostatic and oncotic pressure gradients within the extracellular fluid. Fluid therapy to support the circulation relies on applying a physiological paradigm that better explains clinical and research observations. The revised Starling equation based on recent research considers the contributions of the endothelial glycocalyx layer (EGL), the endothelial basement membrane, and the extracellular matrix. The characteristics of capillaries in various tissues are reviewed and some clinical corollaries considered. The oncotic pressure difference across the EGL opposes, but does not reverse, the filtration rate (the 'no absorption' rule) and is an important feature of the revised paradigm and highlights the limitations of attempting to prevent or treat oedema by transfusing colloids. Filtered fluid returns to the circulation as lymph. The EGL excludes larger molecules and occupies a substantial volume of the intravascular space and therefore requires a new interpretation of dilution studies of blood volume and the speculation that protection or restoration of the EGL might be an important therapeutic goal. An explanation for the phenomenon of context sensitivity of fluid volume kinetics is offered, and the proposal that crystalloid resuscitation from low capillary pressures is rational. Any potential advantage of plasma or plasma substitutes over crystalloids for volume expansion only manifests itself at higher capillary pressures.
Dynamical symmetries of the Klein-Gordon equation
International Nuclear Information System (INIS)
Zhang Fulin; Chen Jingling
2009-01-01
The dynamical symmetries of the two-dimensional Klein-Gordon equations with equal scalar and vector potentials (ESVPs) are studied. The dynamical symmetries are considered in the plane and the sphere, respectively. The generators of the SO(3) group corresponding to the Coulomb potential and the SU(2) group corresponding to the harmonic oscillator potential are derived. Moreover, the generators in the sphere construct the Higgs algebra. With the help of the Casimir operators, the energy levels of the Klein-Gordon systems are yielded naturally
Exact solution of an electroosmotic flow for generalized Burgers fluid in cylindrical domain
Directory of Open Access Journals (Sweden)
Masood Khan
Full Text Available The present paper reports a theoretical study of the dynamics of an electroosmotic flow (EOF in cylindrical domain. The Cauchy momentum equation is first simplified by incorporating the electrostatic body force in the electric double layer and the generalized Burgers fluid constitutive model. The electric potential distribution is given by the linearized Poisson–Boltzmann equation. After solving the linearized Poisson–Boltzmann equation, the Cauchy momentum equation with electrostatic body force is solved analytically by using the temporal Fourier and finite Hankel transforms. The effects of important involved parameters are examined and presented graphically. The results obtained reveal that the magnitude of velocity increases with increase of the Debye–Huckel and electrokinetic parameters. Further, it is shown that the results presented for generalized Burgers fluid are quite general so that results for the Burgers, Oldroyd-B, Maxwell and Newtonian fluids can be obtained as limiting cases. Keywords: Generalized Burgers fluid, Electroosmotic flow, Fourier and Hankel transform
Magnetoviscosity in magnetic fluids: Testing different models of the magnetization equation
Directory of Open Access Journals (Sweden)
Huei Chu Weng
2013-09-01
Full Text Available Despite a long research history, theoretical predictions for the material properties as well as the flow fields and characteristics of magnetic fluids were not well consistent with the experimental data. The lack of a universally accepted magnetization equation for accurately modeling hydrodynamics of magnetic fluids/nanofluids is particularly a major issue. In this paper, we give an overview on the continuum theory and test the six well-known models via comparisons with magnetoviscosity measurements to make clear the magnetization relaxation due to the rotation of magnetic particles and see how well they make predictions on the basis of numerical calculations. Results reveal that the ML model leads to unexplainable behavior. Moreover, the WC model with a ‘relaxation rate’ modification is found to reproduce the predictions of the MRSh model, which agree well with experimental data. The revised WC model (WCC should therefore be preferred.