Showing papers on "Hele-Shaw flow published in 1998"
TL;DR: In this paper, the Lagrange approach is used to define reduced bases and the basis functions in this approach are obtained from the numerical solutions, and the feasibility of this method for flow control is demonstrated on boundary control problems in closed cavity and wall-bounded channel flows.
306 citations
TL;DR: In this paper, three-dimensional steady states in plane Couette flow and traveling-wave solutions in plane Poiseuille flow were calculated for stress boundary conditions, and the results suggest that the underlying process is generic and fundamental to both transitional and developed turbulence.
Abstract: Three-dimensional steady states in plane Couette flow and traveling-wave solutions in plane Poiseuille flow are calculated for stress boundary conditions. The procedure is tied to a self-sustaining mechanism associated with the coherent structures that have been observed in turbulent shear flows. The exact states in both types of flow are remarkably similar to each other and to the coherent structures. They survive down to Reynolds numbers below the critical value for turbulence onset. These results suggest that the underlying process is generic and fundamental to both transitional and developed turbulence.
294 citations
TL;DR: In this paper, the authors used the lattice Boltzmann method (LBM) to simulate viscous fluid flow through a column of glass beads and found that the normalized velocity distribution is sensitive to the spatial resolution but not the details of the packing.
Abstract: The lattice Boltzmann method (LBM) is used to simulate viscous fluid flow through a column of glass beads. The results suggest that the normalized velocity distribution is sensitive to the spatial resolution but not the details of the packing. With increasing spatial resolution, simulation results converge to a velocity distribution with a sharp peak near zero. A simple argument is presented to explain this result. Changes in the shape of the distribution as a function of flow rate are determined for low Reynolds numbers, and the large-velocity tail of the distribution is shown to depend on the packing geometry. The effect of a finite Reynolds number on the apparent permeability is demonstrated and discussed in relation to previous results in the literature. Comparison with velocity distributions from NMR (nuclear magnetic resonance) spectroscopy finds qualitative agreement after adjusting for diffusion effects in the NMR distributions.
227 citations
TL;DR: In this paper, a simulation of turbulent flow over a sinusoidal solid wavy surface was investigated by a direct numerical simulation using a spectral element technique and the results showed that the train of waves has an amplitude to wavelength ratio of 0.05.
Abstract: Turbulent flow over a sinusoidal solid wavy surface was investigated by a direct numerical simulation using a spectral element technique. The train of waves has an amplitude to wavelength ratio of 0.05. For the flow conditions (Re=hUb/2ν= 3460) considered, adverse pressure gradients were large enough to cause flow separation. Numerical results compare favorably with those of Hudson's (1993) measurements. Instantaneous flow fields show a large variation of the flow pattern in the spanwise direction in the separated bubble at a given time. A surprising result is the discovery of occasional velocity bursts which originate in the separated region and extend over large distances away from the wavy wall. Turbulence in this region is very different from that near a flat wall in that it is associated with a shear layer which is formed by flow separation.
168 citations
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28 Aug 1998TL;DR: In this article, the theoretical streamline pattern, given by the classical solution of the inviscid flow theory, is demonstrated in Figure 1 where the difference between an attached flow and its separated counterpart is demonstrated.
Abstract: Separation is a fluid dynamic phenomenon that influences the behaviour of a wide variety of liquid and gas flows. The difference between an attached flow and its separated counterpart is demonstrated in Figure 1 where the theoretical streamline pattern, given by the classical solution of the inviscid flow theory1
164 citations
TL;DR: In this article, it is shown that the elastic instability is determined by the elastic Deborah number, De, and the polymer concentration only, while the Reynolds number becomes completely irrelevant, and experimentally it is found that the flow instability leads to a strongly nonlinear flow transition.
Abstract: Experiments on flow stability and pattern formation in Couette flow between two cylinders with highly elastic polymer solutions are reported. It is found that the flow instabilities are determined by the elastic Deborah number, De, and the polymer concentration only, while the Reynolds number becomes completely irrelevant. A mechanism of such “purely elastic” instability was suggested a few years ago by Larson, Shaqfeh, and Muller [J. Fluid Mech. 218, 573 (1990)], referred to as LMS. It is based on the Oldroyd-B rheological model and implies a certain functional relation between De at the instability threshold and the polymer contribution to the solution viscosity, ηp/η, that depends on the polymer concentration. The elastic force driving the instability arises when perturbative elongational flow in radial direction is coupled to the strong primary azimuthal shear. This force is provided by the “hoop stress” that develops due to stretching of the polymer molecules along the curved streamlines. It is found experimentally that the elastic instability leads to a strongly nonlinear flow transition. Therefore, the linear consideration by LMS is expanded to include finite amplitude velocity perturbations. It is shown that the nature of the elastic force implies major asymmetry between inflow and outflow in finite amplitude secondary flows. This special feature is indeed exhibited by the experimentally observed flow patterns. For one of the flow patterns it is also shown that the suggested elastic force should be quite efficient in driving it, which is important evidence for the validity of the mechanism proposed by LMS. Further, the predicted relation between De and ηp/η is tested. At fixed ηp/η the elastic instability is found to occur at constant Deborah number in a broad range of the solution relaxation times in full agreement with the theoretical prediction. The experimentally found dependence of the Deborah number on ηp/η also agrees with the theoretical prediction rather well if a proper correction for the shear thinning is made. This provides further support to the proposed instability mechanism.
151 citations
TL;DR: Several models have been developed to describe the standard experiment, of flow along a finite length of elastic tube mounted at its ends on rigid tubes and contained in a chamber whose pressure can be independently varied as mentioned in this paper.
Abstract: Laboratory experiments designed to shed light on fluid flow through collapsible tubes, a problem with several physiological applications, invariably give rise to a wide variety of self-excited oscillations. The object of modelling is to provide scientific understanding of the complex dynamical system in question. This paper outlines some of the models that have been developed to describe the standard experiment, of flow along a finite length of elastic tube mounted at its ends on rigid tubes and contained in a chamber whose pressure can be independently varied. Lumped and one-dimensional models have been developed for the study of steady flow and its instability, and a variety of oscillation types are indeed predicted. However, such models cannot be rationally derived from the full governing equations, relying as they do on several crude, ad hoc assumptions such as that concerning the energy loss associated with flow separation at the time-dependent constriction during large-amplitude oscillations. A complete scientific description can be given, however, for a related two-dimensional configuration, of flow in a parallel-sided channel with a segment of one wall replaced by a membrane under longitudinal tension T. The flow and membrane displacement have been calculated successively by lubrication theory, Stokes-flow computation, steady Navier–Stokes computation and unsteady Navier–Stokes computation. For a given Reynolds number, Re, steady flow becomes unstable when T falls below a critical value (equivalently, when Re exceeds a critical value for fixed T), and the consequent oscillations reveal at least one period-doubling bifurcation as T is further reduced. The effect of wall inertia has also been investigated: it is negligible if the flowing fluid is water, but leads to an independent, high frequency flutter when it is air. The computations require very large computer resources, and a simpler model would be desirable. Investigation of the streamlines of the flow and the distribution of viscous energy dissipation reveals how the one-dimensional model might be improved; but such improvement is as yet incomplete.
146 citations
TL;DR: In this paper, a coarse-grained description of the evolution of the microstructure of a viscous ferroliquid is presented, based on the discovery that strongly overdamped flow problems can be considered as a gradient flux of the relevant energy functional.
Abstract: A viscous ferroliquid is trapped between two narrowly spaced parallel sheets of glass, the Hele‐Shaw cell. The ferroliquid fills a cylindrical domain with cross section Ω and the rest of the cell is filled with a fluid of negligible viscosity. In the absence of any other forces, the effect of surface tension at the interface between the fluids is such that the liquid is at rest if Ω is circular. Starting from time t=0 a strong magnetic field perpendicular to the cell is applied, so that the ferroliquid is instantaneously uniformly magnetized in this direction. For t>0, two competing forces act on the liquid: surface tension and magnetostatic repulsion. The liquid reacts to these forces by undergoing a strongly overdamped flow, preserving its volume and its uniform magnetization. In the regime of strong magnetization, it is observed that an initially disk‐like phase configuration undergoes a fingering instability, that these fingers grow and form a labyrinth and that the domain covered by this microstructure spreads. We start from a model for the evolution of $\Omega$ proposed by Jackson, Goldstein & Cebers. Conventional analysis does not bridge the gap between the early stages (captured by the linearization) and the late stages of the evolution (described by a variational problem). Numerical analysis only captures the early stages. We present a new type of analysis for the intermediate stage. It allows us to introduce a coarse-grain description of this evolution of microstructure in a rational way: We derive an evolution equation for the local volume fraction of the gap filled by the ferroliquid. Our analysis is based on the discovery that this type of strongly overdamped flow problems can be considered as a gradient flux of the relevant energy functional.
136 citations
TL;DR: The law of the wall and related correlations underpin much of current computational fluid dynamics (CFD) software, either directly through use of so-called wall functions or indirectly in near-wall turbulence models as discussed by the authors.
Abstract: The law of the wall and related correlations underpin much of current computational fluid dynamics (CFD) software, either directly through use of so-called wall functions or indirectly in near-wall turbulence models. The correlations for near-wall flow become crucial in solution of two problems of great practical importance, namely, in prediction of flow at high Reynolds numbers and in modeling the effects of surface roughness. Although the two problems may appear vastly different from a physical point of view, they share common numerical features. Some results from the 'super-pipe' experiment at Princeton University are analyzed along with those of previous experiments on the boundary layer on an axisymmetric body to identify features of near-wall flow at high Reynolds numbers that are useful in modeling. The study is complemented by a review of some computations in simple and complex flows to reveal the strengths and weaknesses of turbulence models used in modern CFD methods. Similarly, principal results of classical experiments on the effects of sand-grain roughness are reviewed, along with various models proposed to account for these effects in numerical solutions
130 citations
TL;DR: In this paper, a weakly nonlinear analysis of the Saffman-Taylor viscous fingering instability is presented, in which a less viscous fluid displaces a more viscous one between narrowly spaced parallel plates in a Hele-Shaw cell.
126 citations
TL;DR: In this paper, the authors studied numerically gas flaw in microchannels and found that the working fluids art nitrogen and helium, and their Knudsen numbers at the channel outlet are 0.055 and 0.165, respectively.
Abstract: The present work studies numerically gas flaw in microchannels. The working fluids art nitrogen and helium, and their Knudsen numbers at the channel outlet are 0.055 and 0.165, respectively. The proposed model assumes the fluid is a continuum but employs a slip boundary condition on the channel wall. The results of the present study reveal some interesting features of microchannel flows. First, because of the extraordinarily small dimensions, a large pressure gradient is required to drive the flow. Although the pressure gradient is large, the velocity remains very small in the cases studied owing to the high shear stress at the wall. In the nitrogen flows studied, the maximum u velocity is only 1,16 m /s for a pressure ratio of 2.701. Second, since the Reynolds numbers are small, of the order of 10-310-2 for the flows simulated, they can be safely assumed to be laminar. Third, gas flow in microchannels is typically classified into one of four flow regions: continuum flow, slip flow, transition flow, and f...
TL;DR: In this article, the instability characteristics of laterally sheared flow types have been studied by means of a modified depth-averaged Orr-Sommerfeld equation that describes spatial and temporal growth of disturbances in the nominally parallel flow.
Abstract: Free turbulent shear flows, such as mixing layers or jets, can exist in a shallow fluid layer. Flows of these types have many hydraulic, environmental or geophysical applications. The instability characteristics of these laterally sheared flow types have been studied by means of a modified depth-averaged Orr-Sommerfeld equation that describes spatial and temporal growth of disturbances in the nominally parallel flow. Two major parameters, a bed-friction parameter and a Reynolds number control the flow behavior. In addition, the width of the flow domain relative to the sheared zone width can have secondary influences. Results are presented as stability diagrams for the separate and joint effects of viscosity and bed-friction, respectively. Comparisons with available experimental evidence are given.
TL;DR: In this paper, the authors investigated secondary flow patterns, pressure drop and heat transfer in rib-roughened rectangular channels, where ribs are attached to the wide channel walls in order to set up swirling motions.
TL;DR: In this paper, the authors studied the effect of electrical conductivity and viscosity on the Reynolds number of the conical meniscus of a Taylor cone and found that it is highly dependent on both the electrical conductivities and the viscosities of the liquid.
Abstract: Liquid motions inside Taylor cones exhibit interesting features which are not well understood yet. In addition to the flow rate injected through the electrified needle to which the conical meniscus is anchored, the action of the tangential electrical stress on the cone surface induces a recirculating meridional motion, towards the apex along the generatrix and away from it along the axis. Sometimes, a vigorous swirl is observed. The characteristic value of the liquid velocity is found to be highly dependent on both the electrical conductivity and the viscosity of the liquid, so that the Reynolds number of the liquid flow varies from very small values ~creeping flow! for the case of highly conducting and viscous liquids to relatively large values for liquids with sufficiently low values of the liquid conductivity and viscosity. Theoretical conical flows for low and high values of the Reynolds number show qualitatively good agreement with photographs of real flows inside Taylor cones. In particular, the existence of a vigorous swirl which is observed in the electrospraying of paraffins and other poorly conducting and low viscosity liquids can be explained as bifurcation of a primarily nonswirling meridional flow when the Reynolds number reaches a critical value. @S1063-651X~98!01512-8#
TL;DR: In this article, a new, fast, accurate, and roundoff-error robust numerical technique for integrating unsteady incompressible Navier?Stokes equations in cylindrical coordinates is presented.
TL;DR: In this paper, a numerical study of fluid flow and heat transfer around periodic cylinder arrays under laminar cross flow conditions is presented, and the validity of the Forchheimer and Ergun correlations is shown to be suspect for flow in this highly porous media.
TL;DR: In this paper, a semi-implicit Stokes solver is used to compute the formation of fingers for relatively small initial amplitudes as well as larger amplitudes in two and three dimensions as initial value problems.
Abstract: The flow of two viscous liquids is investigated numerically with a volume of fluid scheme. The scheme incorporates a semi-implicit Stokes solver to enable computations at low Reynolds numbers, and a second-order velocity interpolation. The code is validated against linear theory for the stability of two-layer Couette flow, and weakly nonlinear theory for a Hopf bifurcation. Examples of long-time wave saturation are shown. The formation of fingers for relatively small initial amplitudes as well as larger amplitudes are presented in two and three dimensions as initial-value problems. Fluids of different viscosity and density are considered, with an emphasis on the effect of the viscosity difference. Results at low Reynolds numbers show elongated fingers in two dimensions that break in three dimensions to form drops, while different topological changes take place at higher Reynolds numbers.
TL;DR: In this article, a mechanism by which smooth initial conditions evolve towards a topological reconfiguration of fluid interfaces is studied in the context of Darcy's law in the case of thin fluid layers, where nonlinear PDEs for the local thickness are derived from an asymptotic limit of the vortex sheet representation.
Abstract: A mechanism by which smooth initial conditions evolve towards a topological reconfiguration of fluid interfaces is studied in the context of Darcy’s law. In the case of thin fluid layers, nonlinear PDEs for the local thickness are derived from an asymptotic limit of the vortex sheet representation. A particular example considered is the Rayleigh–Taylor instability of stratified fluid layers, where the instability of the system is controlled by a Bond number B. It is proved that, for a range of B and initial data “subharmonic” to it, interface pinching must occur in at least infinite time. Numerical simulations suggest that “pinching” singularities occur generically when the system is unstable, and in particular immediately above a bifurcation point to instability. Near this bifurcation point an approximate analytical method describing the approach to a finite-time singularity is developed. The method exploits the separation of time scales that exists close to the first instability in a system of finite ex...
TL;DR: In this paper, the motion of triaxial ellipsoids embedded in a three-dimensional flow, i.e., which cannot be reduced to a local plane Couette flow, is calculated.
Abstract: The aim of the paper is to get insight into flow patterns visualized by suspended anisotropic reflective particles. The motion of triaxial ellipsoids embedded in a three-dimensional flow, i.e., which cannot be reduced to a local plane Couette flow, is calculated. Both the asymptotic trajectory and the transient time to reach it are discussed. These results are used to simulate laser sheet visualizations of two classical three-dimensional flows (Taylor–Couette vortices and flow between rotating disks) where the particle history is shown to be negligible. The simulated visualizations are well compared to experimental ones but the paper addresses the fact that the legitimate question of what shows the visualization does not have a simple answer. Nevertheless, these results open the way for quantitative comparisons between computational fluid dynamics and experimental visualizations.
TL;DR: A detailed analysis of experimental and numerical results for flow and heat transfer in similar offset strip-fin geometries is presented in this paper, where surface-average heat transfer and pressure drop, local Nusselt numbers and skin friction coefficients on the fin surface, instantaneous flow structures, and local time-averaged velocity profiles are contrasted for a range of Reynolds numbers using both prior and new experimental results.
Abstract: A detailed analysis of experimental and numerical results for flow and heat transfer in similar offset strip-fin geometries is presented Surface-average heat transfer and pressure drop, local Nusselt numbers and skin friction coefficients on the fin surface, instantaneous flow structures, and local time-averaged velocity profiles are contrasted for a range of Reynolds numbers using both prior and new experimental and numerical results This contrast verifies that a two-dimensional unsteady numerical simulation captures the important features of the flow and heat transfer for a range of conditions However, flow three-dimensionality appears to become important for Reynolds numbers greater than about 1300, and thermal boundary conditions are important for Reynolds numbers below 1000 The results indicate that boundary layer development, flow separation and reattachment, wake formation, and vortex shedding are all important in this complex geometry
TL;DR: In this article, the fluid flow through a cascade of bifurcations was investigated by direct simulation of the 2D Navier-Stokes equations, and it was shown that flow distribution becomes significantly heterogeneous at an increased Reynolds number.
Abstract: We investigate the fluid flow through a cascade of bifurcations by direct simulation of the 2D Navier-Stokes equations. We show that, for a fully symmetric tree with n generations (n $ 3d, the flow distribution becomes significantly heterogeneous at an increased Reynolds number. We develop a binary tree model and find that the distribution of flow at the outlet branches can be described by a self-affine landscape, with a self-affine exponent a › 0.9 for the human lung. We suggest that the asymmetric flow occurring in symmetric branched structures may be important both for the morphogenesis of the bronchial tree, and for its functioning during inspiration. [S00319007(98)06724-6]
TL;DR: In this article, a purely elastic flow instability occurring in the lid-driven cavity flow of two semi-dilute polymer solutions is reported and the effect of cavity aspect ratio on the dynamical structure of the unstable flow is quantitatively investigated.
Abstract: Experimental observations of a purely elastic flow instability occurring in the lid-driven cavity flow of two semi-dilute polymer solutions are reported and the effect of cavity aspect ratio on the dynamical structure of the unstable flow is quantitatively investigated. The spatial and temporal characteristics of the secondary flow are measured using flow visualization, laser Doppler velocimetry, and digital particle image velocimetry. At the onset conditions the disturbances appear in the form of spatially periodic flow cells which propagate along the neutral direction of the cavity. The secondary flow structure is analogous to the Taylor–Gortler vortices observed in inertially driven hydrodynamic instabilities. The critical onset conditions for two elastic test fluids and five different aspect ratios correlate with a recently proposed dimensionless stability criterion which incorporates measures of the local streamline radius of curvature and the non-Newtonian normal stresses in the flow domain.
TL;DR: In this article, the existence and uniqueness of a solution to the N-dimensional Hele-Shaw flow problem with surface tension as the driving mechanism were proved and global existence in time and exponential decay of the solution near equilibrium were also proved.
Abstract: This paper addresses short-time existence and uniqueness of a solution to the N-dimensional Hele–Shaw flow problem with surface tension as driving mechanism. Global existence in time and exponential decay of the solution near equilibrium are also proved. The results are obtained in Sobolev spaces Hs with sufficiently large s. The main tools are perturbations of a fixed reference domain, linearization with respect to these perturbations, a quasilinearization argument based on a geometric invariance property, and a priori energy estimates.
TL;DR: In this article, the authors considered the control of wake instabilities in the flow of an electrically conducting fluid around a circular cylinder by means of external magnetic fields and presented curves of neutral 2-D stability in the (Re, N )-parameter plane separating steady and periodic flow regimes.
TL;DR: In this article, a simple fluid displacing a shear thinning fluid confined in a Hele-Shaw cell is studied, and it is shown that the finger width decreases towards zero for small values of the surface tension parameter.
Abstract: We make a theoretical study of the behavior of a simple fluid displacing a shear thinning fluid confined in a Hele-Shaw cell. To study the Saffman-Taylor instability when the displaced fluid is non-Newtonian we face the problem of having a field which is non-Laplacian. By means of a hodographic transformation we are able to solve the problem in the case of weak shear thinning while taking into account the non-Laplacian character of the equation. Our results predict that the finger width decreases towards zero for small values of the surface tension parameter which is inversely proportional to the finger velocity.
TL;DR: In this paper, the authors used a fractional-step finite-difference:spectral-element method to calculate the 3D wake of a circular cylinder exposed to a steady-approach flow.
Abstract: SUMMARY The three-dimensional (3D) unsteady viscous wake of a circular cylinder exposed to a steady approach flow is calculated using a fractional-step finite-difference:spectral-element method. The calculated flow fields at Reynolds numbers of 100 (2D) and 200 (3D) are examined in detail. The flow field at Re 100 is 2D as expected, while the flow field at Re200 has distinct 3D features, with spanwise wavelengths of about 3.75 cylinder diameters. The calculated results produce drag and lift coefficients and Strouhal numbers that agree extremely well with the experimental values. These 3D values at Re 200 are in better agreement with experimental values than the results of a 2D calculation at Re 200, which is expected. © 1998 John Wiley & Sons, Ltd. The flow in the wake of a circular cylinder is three-dimensional (3D), even before it becomes turbulent. The present study concerns the combined finite difference:spectral method calculation of the steady approach flow past a fixed circular cylinder at Reynolds numbers large enough for the wake to be three-dimensional, but not turbulent. The onset of the 3D wake will be discussed and it will be shown that the proper representation of the wake has a noticeable effect on the Strouhal number and the drag and lift coefficients. Specifically, the flow will be represented in terms of the primitive-variables form of the time-dependent Navier‐Stokes equations for an incompressible fluid. A fractional-step method, which is a combination of the methods of Karniadakis et al. [1] and Kim and Moin [2], is used to advance the solution in time. For a circular cylinder in a steady approach flow, the 2D vortex structures are unstable to 3D disturbances at a Reynolds number of about 170. A synopsis of the steady approach flow situation follows. When the Reynolds number, Re UD:n, where U, D, and n are, respectively, the freestream velocity, diameter of the cylinder, and kinematic viscosity of the fluid, is smaller than 40, the flow is steady with two symmetrical vortices attached to the downstream side of the cylinder. When the Reynolds number is slightly larger, ReB 60, the trailing vortex sheet becomes unstable and develops an unsteady wavy pattern. Vortex shedding occurs for 60B ReB170; the attached vortices become asymmetric and are shed alternately at a
TL;DR: In this article, the Saffman-Taylor instability (STI) was studied in a linear channel for a magnetic fluid subjected to an external magnetic field, where the competition between the hydrodynamic effects and the capillary effects leads to the formation of an interface between the air and the fluid which has a finger shape.
Abstract: Viscous fingering phenomenon in a linear channel is studied for a magnetic fluid subjected to an external magnetic field. The competition between the hydrodynamic effects and the capillary effects leads to the formation of an interface between the air and the fluid which has a finger shape. It is the so-called Saffman–Taylor instability (STI). The influence of the magnetic effects depends on the direction of the applied field: it is possible either to enhance or to reduce the destabilizing phenomena. We study the onset of the STI and compare the experimental results with the linear analysis including the magnetic contribution. In the nonlinear regime, the measurement of the width of the finger as a function of the direction and the amplitude of the magnetic field is understood using a phenomenological approach.
TL;DR: In this paper, a Taylor-Couette flow with the outer cylinder is stationary and the inner cylinder is accelerated linearly from rest to a desired speed was investigated. And the results showed that when the acceleration (dRe/dt) is higher than a critical value of about 2.2
Abstract: In this Brief Communication, we report a new finding on a Taylor–Couette flow in which the outer cylinder is stationary and the inner cylinder is accelerated linearly from rest to a desired speed. The results show that when the acceleration (dRe/dt) is higher than a critical value of about 2.2 s−1, there exists a new flow regime in which the flow pattern shows remarkable resemblance to regular Taylor vortex flow but is of shorter wavelength. However, when the acceleration is lower than 2.2 s−1, a wavy flow is found to occur for the same Reynolds number range. To our knowledge, this is probably the first time that such a phenomenon has been observed. For completeness, the case of a decelerating cylinder is also investigated, and the results are found to be almost the same.
TL;DR: In this article, a steady flow of a rarefied gas induced by a temperature field is investigated, on the basis of kinetic theory, for the case where the temperature of each boundary is uniform (i.e., where the flow caused by the nonuniformity of the boundary temperature, such as the thermal transpiration flow, vanishes).
Abstract: A steady flow of a rarefied gas induced by a temperature field is investigated, on the basis of kinetic theory, for the case where the temperature of each boundary is uniform (i.e., where the flow caused by the nonuniformity of the boundary temperature, such as the thermal transpiration flow, vanishes). More specifically, a rarefied gas confined in the gap between two coaxial elliptic cylinders at rest with different uniform temperatures is considered, and the steady gas flow induced in the gap is analyzed numerically by the direct simulation Monte Carlo method for a wide range of the Knudsen number. The flow patterns, together with the density and temperature fields, are obtained, and the features of the flow are clarified.
TL;DR: In this article, the authors consider flow in a cylindrical container of circular section filled with a viscous fluid driven by the motion of flat belts across the partially open end walls of the container.
Abstract: Consider a cylindrical container of circular section filled with a viscous fluid. We consider flow in such a cylinder driven by the motion of flat belts across the partially open end walls of the container. The flow field is determined by the use of a vector eigenfunction expansion. The critical points that are exhibited in the plane of symmetry include elliptic points, foci, and saddles. As the parameters are varied one can have bifurcations in which one type of critical point bifurcates to a collection of others. An example of a limiting surface is also demonstrated. Since the flow fields considered have little symmetry, the three-dimensional streamlines are for the most part not closed. As a consequence the flow fields tend to globalize structures that would otherwise have been isolated. This feature can have important consequences for mixing.