Showing papers on "Incompressible flow published in 1995"
01 Jun 1995
TL;DR: In this article, a level set method for capturing the interface between two fluids is combined with a variable density projection method to allow for computation of two-phase flow where the interface can merge/break and the flow can have a high Reynolds number.
Abstract: A level set method for capturing the interface between two fluids is combined with a variable density projection method to allow for computation of two-phase flow where the interface can merge/break and the flow can have a high Reynolds number. A distance function formulation of the level set method enables one to compute flows with large density ratios (1000/1) and flows that are surface tension driven; with no emotional involvement. Recent work has improved the accuracy of the distance function formulation and the accuracy of the advection scheme. We compute flows involving air bubbles and water drops, to name a few. We validate our code against experiments and theory.
3,556 citations
TL;DR: In this article, the RNG κ-e turbulence model derived by Yakhot and Orszag (1986) based on the Renormalization Group theory has been modified and applied to variable-density engine flows in the present study.
Abstract: The RNG κ-e turbulence model derived by Yakhot and Orszag (1986) based on the Renormalization Group theory has been modified and applied to variable-density engine flows in the present study. The original RNG-based turbulence transport approximations were developed formally for an incompressible flow. In order to account for flow compressibility the RNG e-equation is modified and closed through an isotropic rapid distortion analysis. Computations were made of engine compressing/expanding flows and the results were compared with available experimental observations in a production diesel engine geometry. The modified RNG κ-e model was also applied to diesel spray combustion computations. It is shown that the use of the RNG model is warranted for spray combustion modeling since the ratio of the turbulent to mean-strain time scales is appreciable due to spray-generated mean flow gradients, and the model introduces a term to account for these effects. Large scale flow structures are predicted which ar...
1,200 citations
TL;DR: A time-derivative preconditioning of the Navier-Stokes equations, suitable for both variable and constant density fluids, is developed and is shown to provide accurate steady-state solutions for transonic and low-speed flow of variable density fluids.
Abstract: A time-derivative preconditioning of the Navier-Stokes equations, suitable for both variable and constant density fluids, is developed. The ideas of low-Mach-number preconditioning and artificial compressibility are combined into a unified approach designed to enhance convergence rates of density-based, time-marching schemes for solving flows of incompressible and variable density fluids at all speeds. The preconditioning is coupled with a dual time-stepping scheme implemented within an explicit, multistage algorithm for solving time-accurate flows. The resultant time integration scheme is used in conjunction with a finite volume discretization designed for unstructured, solution-adaptive mesh topologies. This method is shown to provide accurate steady-state solutions for transonic and low-speed flow of variable density fluids. The time-accurate solution of unsteady, incompressible flow is also demonstrated.
925 citations
TL;DR: In this paper, the effects of mesoscale eddies on tracer transports can be parameterized in a large-scale model by additional advection and diffusion of tracers.
Abstract: It is shown that the effects of mesoscale eddies on tracer transports can be parameterized in a large-scale model by additional advection and diffusion of tracers. Thus, tracers are advected by the effective transport velocity, which is the sum of the large-scale velocity and the eddy-induced transport velocity. The density and continuity equations are the familiar equations for adiabatic, Boussinesq, and incompressible flow with the effective transport velocity replacing the large-scale velocity. One of the main points of this paper is to show how simple the parameterization of Gent and McWilliams appears when interpreted in terms of the effective transport velocity. This was not done in their original 1990 paper. It is also shown that, with the Gent and McWilliams parameterization, potential vorticity in the planetary geostrophic model satisfies an equation close to that for tracers. The analogy of this parameterization with vertical mixing of momentum is then described. The effect of the Gent ...
834 citations
01 Jan 1995
424 citations
TL;DR: A novel algorithm is outlined which can be used for the solution of both compressible and incompressible Navier-Stokes or Euler equations and introduces a rational form of balancing dissipation.
Abstract: We outline the formulation of a novel algorithm which can be used for the solution of both compressible and incompressible Navier-Stokes or Euler equations. Full incompressibility can be dealt with if the algorithm is used in its semi-explicit corm and its structure permits arbitrary interpolation cunctions to be used avoiding the Babuska-Brezzi restriction. In a fully explicit version it introduces a rational form of balancing dissipation avoiding the use of arbitrary parameters and forms for this
395 citations
Book•
01 Oct 1995
TL;DR: In this article, the authors describe several computational techniques that can be applied to a variety of problems in thermo-fluid physics, multi-phase flow, and applied mechanics involving moving flow boundaries.
Abstract: This advanced-leveltext describes several computational techniques that can be applied to a variety of problems in thermo-fluid physics, multi-phase flow, and applied mechanics involving moving flow boundaries. Step-by-step discussions of numerical procedures include examples that employ algorithms to solve problems. 1990 edition.
359 citations
TL;DR: In this paper, a hydrodynamic boundary condition is developed to replace the heuristic bounce-back boundary condition used in the majority of lattice Boltzmann simulations, which is applied to the two-dimensional, steady flow of an incompressible fluid between two parallel plates.
Abstract: A hydrodynamic boundary condition is developed to replace the heuristic bounce‐back boundary condition used in the majority of lattice Boltzmann simulations. This boundary condition is applied to the two‐dimensional, steady flow of an incompressible fluid between two parallel plates. Poiseuille flow with stationary plates, and a constant pressure gradient is simulated to machine accuracy over the full range of relaxation times and pressure gradients. A second problem involves a moving upper plate and the injection of fluid normal to the plates. The bounce‐back boundary condition is shown to be an inferior approach for simulating stationary walls, because it actually mimics boundaries that move with a speed that depends on the relaxation time. When using accurate hydrodynamic boundary conditions, the lattice Boltzmann method is shown to exhibit second‐order accuracy.
345 citations
TL;DR: In this article, a mathematical model for the high pressures and sudden velocity changes which may occur in the impact between a region of incompressible liquid and either a solid surface or a second liquid region is presented.
Abstract: A mathematical model is presented for the high pressures and sudden velocity changes which may occur in the impact between a region of incompressible liquid and either a solid surface or a second liquid region. The theory rests upon the well-known idea of pressure impulse, for the sudden initiation of fluid motion in incompressible fluids. We consider the impulsive pressure field which occurs when a moving fluid region collides with a fixed target, such as when an ocean wave strikes a sea wall. The boundary conditions are given for modelling liquid-solid and liquid-liquid impact problems. For a given fluid domain, and a given velocity field just before impact, the theory gives information on the peak pressure distribution, and the velocity after impact. Solutions for problems in simple domains are presented, which give insight into the peak pressures exerted by a wave breaking against a sea wall, and a wave impacting in a confined space. An example of liquid-liquid impact is also examined. Results of particular interest include a relative insensitivity to the shape of the incident wave, and an increased pressure impulse when impact occurs in a confined space. The theory predicts that energy is lost from the bulk fluid motion and we suggest that this energy can be transferred to a thin jet of liquid which is projected away from the impact region.
216 citations
TL;DR: In this article, a numerical simulation of forced convective incompressible flow through porous beds was performed in terms of non-dimensional parameters that successfully cast together all the pertinent influencing effects.
Abstract: The present work centers around the numerical simulation of forced convective incompressible flow through porous beds. Inertial as well as viscous effects are considered in the momentum equation. The mathematical model for energy transport was based on the two-phase equation model, which does not employ local thermal equilibrium assumption between the fluid and the solid phases. The transport processes for two different types of boundary conditions are studied. The analysis was performed in terms of nondimensional parameters that successfully cast together all the pertinent influencing effects. Comparisons were made between our numerical findings and experimental results. Overall, the comparisons that were made for the constant wall heat flux boundary condition display good agreement.
193 citations
TL;DR: In this paper, the authors used the lattice-Boltzmann discretization scheme for solving the time-dependent Navier-Stokes equations in an incompressible flow regime.
TL;DR: In this article, the behavior of a Godunov-projection method for the incompressible Navier-Stokes equations as a function of the resolution of the computational mesh is presented.
TL;DR: This work numerically demonstrates convergence of the BGK schemes to the incompressible Navier-Stokes equations and quantifies the errors associated with compressibility and discretization effects.
TL;DR: In this article, the influence of the location of the lateral boundaries on 2D computation of unsteady incompressible flow past a circular cylinder is investigated, and the minimum distance at which this influence vanishes has been found to be larger than what is commonly assumed.
01 Jan 1995
TL;DR: In this paper, an algorithm is applied in its explicit form to a variety of problems in order to demonstrate its wide range of applicability and excellent performance, such as nearly incompressible, viscous, flows through transonic applications to high speed flows with shocks.
Abstract: An algorithm is applied in its explicit form to a variety of problems in order to demonstrate its wide range of applicability and excellent performance. Examples range from nearly incompressible, viscous, flows through transonic applications to high speed flows with shocks. In most examples linear triangular elements are used in the finite element approximation, but some use of quadratic approximation, again in triangles, indicates satisfactory performance even in the case of severe shocks
TL;DR: In this article, a phase field model of capillarity that accounts for the structure of an interfacial layer formed by two immiscible incompressible liquids is addressed, and a rheological expression for the reversible component of capillary stresses is obtained in terms of the free energy of a binary fluid, which depends on the absolute temperature, composition, and gradient of composition.
Abstract: The phenomenological derivation of a phase field model of capillarity that accounts for the structure of an interfacial layer formed by two immiscible incompressible liquids is addressed. A rheological expression for the reversible component of capillary stresses is obtained in terms of the free energy of a binary fluid, which depends on the absolute temperature, composition, and gradient of composition. This model can be applied to those flows that involve change of topology of a capillary interface, such as coalescence and breakup of drops. As an illustration, an equilibrium of a binary fluid with either a flat or spherical interfacial layer is analyzed, and a thermocapillary flow in an infinite gap is considered.
TL;DR: In this paper, the inviscid limit for two-dimensional incompressible fluids in the plane was investigated and it was shown that if the initial data are vortex patches with smooth boundaries, then the Eulerian dynamics is approached at a rate that is slower than the rate for smooth initial data.
Abstract: We investigate the inviscid limit for two dimensional incompressible fluids in the plane. We prove that, if the initial data are vortex patches with smooth boundaries, then the inviscid Eulerian dynamics is approached at a rate that is slower than the rate for smooth initial data. The circular patches provide lower bounds.
TL;DR: In this article, the authors investigated the anomalous transport in incompressible flow using multiscale techniques and derived an upper bound to eddy diffusivities, valid for both static and time-dependent flow.
Abstract: Standard and anomalous transport in incompressible flow is investigated using multiscale techniques. Eddy diffusivities emerge from the multiscale analysis through the solution of an auxiliary equation. From the latter it is derived an upper bound to eddy diffusivities, valid for both static and time‐dependent flow. The auxiliary problem is solved by a perturbative expansion in powers of the Peclet number resummed by Pade approximants and a conjugate gradient method. The results are compared to numerical simulations of tracers dispersion for three flows having different properties of Lagrangian chaos. It is shown on a concrete example how the presence of anomalous diffusion in deterministic flows can be revealed from the singular behavior of the eddy diffusivity at very small molecular diffusivities.
TL;DR: A variational principle for lower bounds on the time-averaged mass flux for Newtonian fluids driven by a pressure gradient in a channel is derived from the incompressible Navier-Stokes equations and compared with the predictions of conventional turbulence theory.
Abstract: A variational principle for lower bounds on the time-averaged mass flux for Newtonian fluids driven by a pressure gradient in a channel is derived from the incompressible Navier-Stokes equations. When supplied with appropriate test background flow fields, the variational formulation produces explicit estimates for the friction coefficient. These rigorous bounds are compared with the predictions of conventional turbulence theory.
Book•
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01 Jan 1995
TL;DR: In this article, the authors consider the problem of quantifying the flow properties of a mixture of fluids in terms of the velocity and the energy of the mixture. But they do not consider the physical properties of the fluid.
Abstract: 1 Properties of Fluids.- 1.1. Physical Properties of Fluids.- 1.1.1. Liquids.- 1.1.2. Gases.- 1.1.3. Thermodynamic Notions.- 1.2. Transfer Properties.- 1.2.1. Viscosity.- 1.2.2. Thermal Conductivity.- 1.2.3. Fluid Mixtures. Mass Transfer.- 1.2.4. Non-Newtonian Media.- 2 Fundamental Equations of Viscous Flow.- 2.1. Kinematics of Fluid Flow.- 2.1.1. Lagrangian and Eulerian Descriptions.- 2.1.2. Strain Rates.- 2.1.3. Circulation. Stokes' Theorem.- 2.2. Equations of Motion.- 2.2.1. Continuity Equation.- 2.2.2. The Equations of Motion in Stresses.- 2.2.3. The Constitutive Relation for a Newtonian Fluid.- 2.2.4. Remarks on the Second Coefficient of Viscosity.- 2.2.5. Navier-Stokes Equations.- 2.2.6. Noninertial Coordinate System.- 2.3. The Energy Equation.- 2.3.1. Energy Balance for a Fluid Particle.- 2.3.2. Energy Equation for Incompressible Fluids.- 2.3.3. Energy Equation for Compressible Fluids.- 2.4 Orthogonal Curvilinear Coordinate Systems.- 2.4.1. Cylindrical Coordinates.- 2.4.2. Spherical Coordinates.- 3 Basic Equations and Flow Pattern.- 3.1. Posing the Problem of Fluid Flow.- 3.1.1. Assumptions Involved and Mathematical Character of the Basic Equations.- 3.1.2. Initial and Boundary Conditions.- 3.2. Dimensionless Parameters in Viscous Fluid Flow.- 3.2.1. Dimensionless Parameters in Navier-Stokes Equations.- 3.2.2. Dimensionless Parameters in the Energy Equation.- 3.3. Viscous Flow Pattern.- 3.3.1. Pure Viscous Flow.- 3.3.2. Visco-inertial Flow.- 3.3.3. The Boundary'1 Properties of Fluids.- 1.1. Physical Properties of Fluids.- 1.1.1. Liquids.- 1.1.2. Gases.- 1.1.3. Thermodynamic Notions.- 1.2. Transfer Properties.- 1.2.1. Viscosity.- 1.2.2. Thermal Conductivity.- 1.2.3. Fluid Mixtures. Mass Transfer.- 1.2.4. Non-Newtonian Media.- 2 Fundamental Equations of Viscous Flow.- 2.1. Kinematics of Fluid Flow.- 2.1.1. Lagrangian and Eulerian Descriptions.- 2.1.2. Strain Rates.- 2.1.3. Circulation. Stokes' Theorem.- 2.2. Equations of Motion.- 2.2.1. Continuity Equation.- 2.2.2. The Equations of Motion in Stresses.- 2.2.3. The Constitutive Relation for a Newtonian Fluid.- 2.2.4. Remarks on the Second Coefficient of Viscosity.- 2.2.5. Navier-Stokes Equations.- 2.2.6. Noninertial Coordinate System.- 2.3. The Energy Equation.- 2.3.1. Energy Balance for a Fluid Particle.- 2.3.2. Energy Equation for Incompressible Fluids.- 2.3.3. Energy Equation for Compressible Fluids.- 2.4 Orthogonal Curvilinear Coordinate Systems.- 2.4.1. Cylindrical Coordinates.- 2.4.2. Spherical Coordinates.- 3 Basic Equations and Flow Pattern.- 3.1. Posing the Problem of Fluid Flow.- 3.1.1. Assumptions Involved and Mathematical Character of the Basic Equations.- 3.1.2. Initial and Boundary Conditions.- 3.2. Dimensionless Parameters in Viscous Fluid Flow.- 3.2.1. Dimensionless Parameters in Navier-Stokes Equations.- 3.2.2. Dimensionless Parameters in the Energy Equation.- 3.3. Viscous Flow Pattern.- 3.3.1. Pure Viscous Flow.- 3.3.2. Visco-inertial Flow.- 3.3.3. The Boundary'Layer Concept.- 3.4. Other Forms of the Basic Equations.- 3.4.1. The Conservative (Eulerian) Form of the Basic Equations.- 3.4.2. The Equation for Vorticity.- 3.4.3. Two-Dimensional Row.- 3.4.4. Integral Relations (Control Volume Formulation).- 4 Steady Parallel Flow of Incompressible Fluids.- 4.1. Plane Parallel Flow.- 4.1.1. Couette Flow.- 4.1.2. Channel (Poiseuille) Flow.- 4.1.3. Open Channel Flow.- 4.1.4. Combined Couette-Poiseuille Flow.- 4.2. General Couette Flow.- 4.2.1 Two Circular Cylinders.- 4.2.2. Translation of a Semiplane in a Channel.- 4.3. Duct Flow.- 4.3.1. Circular Pipe.- 4.3.2. Ducts of Various Cross Sections.- 4.3.3. Hydraulic Radius.- 4.3.4. Analysis of a System of Ducts.- 4.4. Steady Parallel Flow of Viscoplastic Media.- 4.4.1. Plane Parallel Flow.- 4.4.2. Circular Duct.- 4.5. Influence of Porous Surfaces.- 4.5.1. Quasi-Parallel Flow.- 4.5.2. Channel and Duct Flow.- 5 Other Solutions of Navier-Stokes Equations (Steady Incompressible Flow).- 5.1. Flow upon Concentric Circles.- 5.1.1. Coaxial Rotating Cylinders.- 5.1.2. Particular Cases (Vortex).- 5.2. Motions upon Concurrent Lines.- 5.2.1. Motion between Two Nonparallel Walls.- 5.2.2. Approximate Solutions.- 5.3. Self-Similar Solutions.- 5.3.1. Flow Near a Stagnation Point.- 5.3.2. Flow Near a Rotating Disk.- 5.3.3. Fluid Rotation Near a Plane.- 5.4. Other Solutions.- 5.4.1. Solutions for the Stream Function.- 5.4.2. Pseudo-Plane Motions (Noninertial Coordinates).- 6 Unsteady Viscous Incompressible Flow.- 6.1. Parallel Unsteady Flow.- 6.1.1. General Remarks.- 6.1.2. Plane Unsteady Parallel Flow.- 6.1.3. Examples of Unsteady Parallel Flows.- 6.1.4. Parallel Axisymmetric Row in Ducts.- 6.2. Other Unsteady Motions.- 6.2.1. Unsteady Flow upon Concentric Circles.- 6.2.2. Plane Unsteady Flow.- 6.2.3. Three-Dimensional Unsteady Row.- 7 Thermal Effects in Incompressible Flow.- 7.1. Thermal Effects in Plane Couette Flow.- 7.1.1. Constant Wall Temperature.- 7.1.2. Adiabatic Wall.- 7.1.3. Variable Viscosity.- 7.1.4. Forced Heat Transfer in Slow Motion.- 7.2. Temperature Field in Flow Near Walls.- 7.2.1. Poiseuille Flow with Constant Viscosity.- 7.2.2. Couette-Poiseuille Flow.- 7.2.3. Free Convection between Parallel Walls.- 7.2.4. Temperature Field in Flow between Nonparallel Walls.- 7.2.5. Temperature Field in Flow between Coaxial Rotating Cylinders.- 7.2.6. Temperature Field Near a Stagnation Point.- 7.3. Temperature Field in Duct Flow.- 7.3.1. Influence of Dissipation.- 7.3.2. Circular Pipes.- 7.3.3. Thermal Entrance.- 7.3.4. Extensions.- 8. Compressible Viscous Fluid Flow.- 8.1. Flow between Parallel Plates.- 8.1.1. Couette Flow.- 8.1.2. Isothermal Flow between Parallel Walls.- 8.1.3. Effect of a Transversal Heat Transfer.- 8.2. Shock Wave Structure.- 8.2.1. Shock Structure without Consideration of the Second Coefficient of Viscosity.- 8.2.2. Influence of the Second Coefficient of Viscosity.- 8.2.3. Weak Shock Wave.- 8.3. Viscosity Effccts in Unsteady Flow.- 8.3.1. Impulsive Motion of a Wall.- 8.3.2. Sound Attenuation.- 9 Slow Viscous Flow in Thin Layers (Hydrodynamic Lubrication).- 9.1. Equations of Motion.- 9.1.1. Simplifications of the Equations of Motion.- 9.1.2. The Pressure Equation.- 9.1.3. Mechanisms of Lubrication.- 9.1.4. Boundary Conditions.- 9.2. Liquid Film Lubrication.- 9.2.1. Self-Acting Films.- 9.2.2. Hydrostatic Films.- 9.2.3. Grease Films.- 9.3. Gas Film Lubrication.- 9.3.1. Self-Acting Gas Films.- 9.3.2. Externally Pressurized Gas Films.- 9.4. Elasto-hydrodynamic Lubrication.- 9.4.1. Hydrodynamic Lubrication of Concentrated Contacts.- 9.4.2. Influence of Surface Deformation.- 10 Slow Viscous Flow.- 10.1. General Remarks.- 10.1.1. The Use of Biharmonic Functions.- 10.1.2. Plane Motions.- 10.1.3. Axisymmetric Flow.- 10.1.4. Hele Shaw Flow.- 10.1.5. Extensions of the Hele Shaw Analogy.- 10.2. Slow Rotation of a Viscous Fluid.- 10.2.1. Coordinate Systems.- 10.2.2. Steady Rotation of a Body.- 10.2.3. Unsteady Rotation of a Body.- 10.3. Flow Around Bodies of Revolution.- 10.3.1. Flow Around a Sphere.- 10.3.2. Extensions.- 10.4. Slow Plane Flow.- 10.4.1. General Considerations.- 10.4.2. Direct Methods.- 10.4.3. The Circle Theorem for Slow Viscous Flow.- 11 Visco-inertial Flow in Thin Layers.- 11.1. Incompressible Flow in Thin Layers.- 11.1.1. Approximate Methods.- 11.1.2. Motions between Surfaces at Rest.- 11.1.3. Two-Dimensional Flow between Moving Surfaces.- 11.1.4. Three-Dimensional Flow in Thin Layers.- 11.2. Compressible Flow in Thin Layers.- 11.2.1. General Equations.- 11.2.2. Motions between Surfaces at Rest.- 11.2.3. High-Speed Sliding Motions.- 12 Visco-inertial Flow Around Bodies.- 12.1. Small Perturbation Slow Flow (Oseen Flow).- 12.1.1. General Equations.- 12.1.2. Flow Around a Sphere.- 12.1.3. Plane Flow Past a Circle.- 12.2. Other Approximations for Visco-inertial Flow.- 12.2.1. Small Perturbations from Irrotational Flow.- 12.2.2. Second Direct Approximation for a Slow Flow Around a Sphere. Whitehead's Paradox.- 12.2.3. The Use of the Singular Perturbation Method.- References.
TL;DR: Explonential decay of the spatial Fourier power spectrum for solutions of the incompressible Navier–Stokes equations is established and explicit rigorous lower bounds on a small length scale defined by the exponential decay rate are obtained.
Abstract: Using a method developed by Foias and Temam [J. Funct. Anal. 87, 359 (1989)], exponential decay of the spatial Fourier power spectrum for solutions of the incompressible Navier–Stokes equations is established and explicit rigorous lower bounds on a small length scale defined by the exponential decay rate are obtained.
TL;DR: In this paper, the cavity flowfield is observed to oscillate quite regularly at the Strouhal number of 0.58, which produces an acoustic source of the same frequency.
Abstract: Sound generated by flow over a cavity at a Mach number of 0.1 and a Reynolds number based on cavity length of 5000 is calculated. The computation utilizes a two part technique where the time-dependent incompressible flow is first obtained and then a second calculation is performed for the compressible aspects of the flow. This second calculation utilizes a grid and numerical scheme designed for resolution of acoustic waves. The cavity flowfield is observed to oscillate quite regularly at the Strouhal number of 0.58 which produces an acoustic source of the same frequency. Time histories, spectra, and directivity of the sound radiation are computed.
09 Jan 1995
TL;DR: In this paper, a number of advances in modeling multiphase incompressible flow are described, including high-order Godunov projection methods, piecewise linear interface reconstruction and tracking and the continuum surface force model.
Abstract: A number of advances in modeling multiphase incompressible flow are described. These advances include high-order Godunov projection methods, piecewise linear interface reconstruction and tracking and the continuum surface force model. Examples are given.
TL;DR: In this paper, the authors present numerical simulations of the transition scenario of a rotating fluid flow in a closed cylinder, where the motion is created by a rotating lid and the vortex dynamics appears as stretching, folding and squeezing of flow structures which wave along the contour of a central vortex core.
Abstract: Present numerical simulations of the transition scenario of a rotating fluid flow in a closed cylinder are presented, where the motion is created by a rotating lid. The numerical algorithm, which is based on a finite‐difference discretization of the axisymmetric Navier‐Stokes equations, is validated against experimental visualizations of both transient and stable periodic flows. The complexity of the flow problem is illuminated numerically by injecting flow tracers into the flow domain and following their evolution in time. The vortex dynamics appears as stretching, folding and squeezing of flow structures which wave along the contour of a central vortex core. The main purpose of the study is to clarify the mechanisms of the transition scenario and relate these to experiences known from other dynamical systems and bifurcation theory. The dynamical system was observed to exhibit up to three multiple solutions for the same Reynolds number, and to contain four discernible branches. The transition to strange attractor behavior was identified as a nontrivial Ruelle‐Takens transition through a transient torus. The various solution branches of the rotating flow problem are illustrated by phase portraits and summarized on a frequency diagram.
31 Dec 1995
TL;DR: A particle method for simulating the fragmentation of incompressible viscous fluid is presented in this paper, where pressure gradient, diffusion, incompressibility and free surfaces are modeled by particle interactions.
Abstract: A particle method for simulating the fragmentation of incompressible viscous fluid is presented. Pressure gradient, diffusion, incompressibility and free surfaces are modeled by particle interactions. Since the present method never uses the grid for the calculation, fragmentation of fluids can be analyzed. In addition, the method is free from the numerical diffusion because of fully Lagrangian treatment of particles. Accuracy of each interaction model is assessed with a simple test problem. All models are based on deterministic processes to reduce the computational cost. The collapse of a water column is calculated. The fluid splashing and fragmentation from a free surface are successfully simulated by the present method.
TL;DR: In this paper, the interaction of a two-dimensional flexible membrane wing and laminar, high-Reynolds-number fluid flow is modeled by combining a spatial-coordinate-based finite difference formulation of the equilibrium statement for an elastic membrane with a pressure-based control volume formulation of a Navier-Stokes equations written in general curvilinear body-fitted coordinates.
Abstract: A computational procedure is presented that models the interaction of a two-dimensional flexible membrane wing and laminar, high-Reynolds-number fluid flow. The membrane wing model is derived by combining a spatial-coordinate-based finite difference formulation of the equilibrium statement for an elastic membrane with a pressure-based control volume formulation of the incompressible Navier-Stokes equations written in general curvilinear body-fitted coordinates. The model is applied to initially flat membrane wings of both vanishing and finite material stiffness as well as to flexible inextensible wings with excess length. Computational results are presented for Reynolds numbers between 2 x 10 3 and 10 4 . The results from the viscous-flow-based membrane wing model are compared with predictions using a potential-flow-based model as well as with experimental data for membrane wings in turbulent flow. Although the assumption of laminar flow precludes a quantitative comparison with the available experimental data, the solutions obtained capture many of the significant features of the aeroelastic interaction that are unaccounted for with a potential flow description of the fluid dynamics.
TL;DR: In this article, a numerical investigation of the multiple stable solutions found in confined swirling flows is presented, and the observed toroidal recirculation zones attached to the free surface are described in terms of secondary motions induced by the bending of vortex lines.
Abstract: A numerical investigation of the multiple stable solutions found in confined swirling flows is presented. The flows consist of fluid in a completely filled cylinder driven by the constant corotation of the two end walls. When reflectional symmetry at the cylinder half‐plane is imposed, the flow corresponds to that in a cylinder of half the height driven by the bottom end wall, with the top surface being flat and stress‐free. Comparisons with available experiments in this case are made and the observed toroidal recirculation zones attached to the free surface are described in terms of secondary motions induced by the bending of vortex lines. Calculations are also presented where the reflectional symmetry is not imposed and the possibility of the flow breaking this symmetry is discussed.
TL;DR: In this article, numerical simulations of the deformation behavior of a liquid droplet impinging on a flat solid surface, as well as the flow field inside the droplet were performed using the MAC-type solution method.
Abstract: We are concerned with numerical simulations of the deformation behavior of a liquid droplet impinging on a flat solid surface, as well as the flow field inside the droplet. In the present situation, the case where a droplet impinges on the surface at room temperature with a speed in the order of a few [m/s], is treated. These simulations were performed using the MAC-type solution method to solve a finite-differencing approximation of the Navier-Stokes equations governing an axisymmetric and incompressible fluid flow. For the first case where the liquid is water, the liquid film formed by the droplet impinging on the solid surface flows radially along it and expands in a fairly thin discoid-like shape. Thereafter, the liquid flow shows a tendency to stagnate at the periphery of the circular film, with the result that water is concentrated there is a doughnut-like shape. Subsequently, the water begins to flow backwards toward the center where it accumulates in the central region. For the second case where a n-heptane droplet impinges the surface, the film continues to spread monotonically up to a maximum diameter and there is no recoiling process to cause a backwards flow towards the central region.
TL;DR: A number of different implicit schemes are compared for several two-dimensional flow problems and the generalized minimum residual method preconditioned with the incomplete lower-upper factorization outperforms all other methods by at least a factor of 2.
Abstract: For a computational flow simulation tool to be useful in a design environment, it must be very robust and efficient. To develop such a tool for incompressible flow applications, a number of different implicit schemes are compared for several two-dimensional flow problems in the current study. The schemes include Point-Jacobi relaxation, Gauss-Seidel line relaxation, incomplete lower-upper decomposition, and the generalized minimum residual method preconditioned with each of the three other schemes. The efficiency of the schemes is measured in terms of the computing time required to obtain a steady-state solution for the laminar flow over a backward-facing step, the flow over a NACA 4412 airfoil, and the flow over a three-element airfoil using overset grids. The flow solver used in the study is the INS2D code that solves the incompressible Navier-Stokes equations using the method of artificial compressibility and upwind differencing of the convective terms. The results show that the generalized minimum residual method preconditioned with the incomplete lower-upper factorization outperforms all other methods by at least a factor of 2.