On the longitudinal heat flux in a Couette flow

The problem of shear motion of a gas (Couette flow) is studied. Two infinite parallel plates with temperatures T₁ and T₂ separated by the distance L each move in their own plane with velocities u₀ and -u₀, respectively. It is assumed that there is a monatomic gas between the plates. In such a formulation, the Couette problem has been considered earlier by many authors. A difference in the present paper is that it investigates the behavior of the heat flux directed along the plates. It has been found that the presence of this heat flux has a strong influence on the direction of energy transfer that is established in a Couette flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 162–166, May–June, 1980.We are grateful to O. S. Ryzhov and A. T. Onufriev for discussions which led to the writing of the present paper.     

Finite element analysis of flow in a gas-filled rotating annulus

Linearized multidimensional flow in a gas centrifuge can be described away from the ends by Onsager's pancake equation. However a rotating annulus results in a slightly different set of boundary conditions from the usual symmetry at the axis of rotation. The problem on an annulus becomes ill-posed and requires some special attention. Herein we treat axially linear inner and outer rotor temperature distributions and velocity slip. An existence condition for a class of non-trivial, one-dimensional solutions is given. New exact solutions in the infinite bowl approximation have been derived containing terms that are important at finite gap width and non-vanishing velocity slip. The usual one-dimensional, axially symmetric solution is obtained as a limit. Our previously reported finite element algorithm has been extended to treat this new class of problems. Effects of gap width, temperature and slip conditions are illustrated. Lastly, we report on the compressible, finite length, circular Couette flow for the first time.     

A lattice Boltzmann model for adsorption breakthrough

A lattice Boltzmann model is developed to simulate the one-dimensional (1D) unsteady state concentration profiles, including breakthrough curves, in a fixed tubular bed of non-porous adsorbent particles. The lattice model solves the 1D time dependent convection–diffusion–reaction equation for an ideal binary gaseous mixture, with solute concentrations at parts per million levels. The model developed in this study is also able to explain the experimental adsortption/desorption data of organic vapours (toluene) on silica gel under varying conditions of temperature, concentrations and flowrates. Additionally, the programming code written for simulating the adsorption breakthrough is modified with minimum changes to successfully simulate a few flow problems, such as Poiseuille flow, Couette flow, and axial dispersion in a tube. The present study provides an alternative numerical approach to solving such types of mass transfer related problems.     

Solution of the temperature jump (Knudsen layer flow) and linear heat-transfer problems for two parallel plates in a rarefied gas

The Monte Carlo method [1, 2] is used to solve the linearized Boltzmann equation for the problem of heat transfer between parallel plates with a wall temperature jump (Knudsen layer flow). The linear Couette problem can be separated into two problems: the problem of pure shear and the problem of heat transfer between two parallel plates. The Knudsen layer problem is also linear [3] and, like the Couette problem, can be separated into the velocity slip and temperature jump problems. The problems of pure shear and velocity slip have been examined in [2].The temperature jump problem was examined in [4] for a model Boltzmann equation. For the linearized Boltzmann equation the problems noted above have been solved either by expanding the distribution function in orthogonal polynomials [5–7], which yields satisfactory results for small Knudsen numbers, or by the method of moments, with an approximation for the distribution function selected from physical considerations in the form of polynomials [8–10]. The solution presented below does not require any assumptions on the form of the distribution function.The concrete calculations were made for a molecular model that we call the Maxwell sphere model. It is assumed that the molecules collide like hard elastic spheres whose sections are inversely proportional to the relative velocity of the colliding molecules. A gas of these molecules is close to Maxwellian or to a gas consisting of pseudo-Maxwell molecules [3].     

Rarefied flow in a channel and a periodic system of channels

the steady two-dimensional isothermal rarefied flow in a channel formed by two parallel flat plates of finite length is studied on the basis of the numerical solution of a linearized kinetic problem. The channel may either be isolated or constitute a cell of a periodic cascade consisting of zero-thickness plates arranged one above the other. As the channel length increases, the flow in it approaches the asymptotic one-dimensional Poiseuille flow. It is shown that the asymptotic dependence of the gas flow rate on the low Knudsen number corresponding to an infinitely long channel is already attained for a channel of length equal to several channel widths, if the flow rate is referred to the pressure gradient at the middle of the channel rather than to the mean pressure difference at the channel ends. The effect of the boundary conditions imposed on the channel entrance is investigated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 166–175, May–June, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 98-01-00443).     

Two-phase couette flow

A study is made of plane laminar Couette flow, in which foreign particles are injected through the upper boundary. The effect of the particles on friction and heat transfer is analyzed on the basis of the equations of two-fluid theory. A two-phase boundary layer on a plate has been considered in [1, 2] with the effect of the particles on the gas flow field neglected. A solution has been obtained in [3] for a laminar boundary layer on a plate with allowance for the dynamic and thermal effects of the particles on the gas parameters. There are also solutions for the case of the impulsive motion of a plate in a two-phase medium [4–6], and local rotation of the particles is taken into account in [5, 6]. The simplest model accounting for the effect of the particles on friction and heat transfer for the general case, when the particles are not in equilibrium with the gas at the outer edge of the boundary layer, is Couette flow. This type of flow with particle injection and a fixed surface has been considered in [7] under the assumptions of constant gas viscosity and the simplest drag and heat-transfer law. A solution for an accelerated Couette flow without particle injection and with a wall has been obtained in [6]. In the present paper fairly general assumptions are used to obtain a numerical solution of the problem of two-phase Couette flow with particle injection, and simple formulas useful for estimating the effect of the particles on friction and heat transfer are also obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–46, May–June, 1976.     

Flopping phenomenon of flow behind two plates placed side-by-side normal to the flow direction

Experiments were made for the flow over two side-by-side normal plates for which the gap ratios are in the range 1.4–2.1 and the Teynolds numbers are at 6.6 × 10³ and 1.8 × 10⁴. At low gap ratios, i.e., 1.4–1.6. the gap flow appears always to be biased and flip-flops to the preferred side non-periodically with respect to time. As the gap ratio becomes larger, the percentage of time occupied by the gap flow in the biased state decreases and the non-biased state of the gap flow becomes prevalent. A comparison of the experimental results obtained under five free stream turbulence conditions further shows that the addition of artificial disturbance into the free stream promotes gap flow flopping at low gap ratios.     

Oscillatory Couette flow of rotating Sisko fluid

The oscillatory Couette flow of a magnetohydrodynamic （MHD） Sisko fluid between two infinite non-conducting parallel plates is explored in a rotating frame. The lower plate is fixed, and the upper plate is oscillating in its own plane. Using MATLAB, a numerical solution to the resulting nonlinear system is presented. The influence of the physical parameters on the velocity components is analyzed. It is found that the effect of rotation on the primary velocity is more significant than that on the secondary velocity. Further, the oscillatory character in the flow is also induced by rotation. The considered flow situation behaves inertialess when the Reynolds number is small.     

Unsteady natural convection Couette flow of heat generating/absorbing fluid between vertical parallel plates filled with porous material

The extended Brinkman Darcy model for momentum equations and an energy equation is used to calculate the unsteady natural convection Couette flow of a viscous incompressible heat generating/absorbing fluid in a vertical channel(formed by two infinite vertical and parallel plates) filled with the fluid-saturated porous medium.The flow is triggered by the asymmetric heating and the accelerated motion of one of the bounding plates.The governing equations are simplified by the reasonable dimensionless parameters and solved analytically by the Laplace transform techniques to obtain the closed form solutions of the velocity and temperature profiles.Then,the skin friction and the rate of heat transfer are consequently derived.It is noticed that,at different sections within the vertical channel,the fluid flow and the temperature profiles increase with time,which are both higher near the moving plate.In particular,increasing the gap between the plates increases the velocity and the temperature of the fluid,however,reduces the skin friction and the rate of heat transfer.     

Unsteady Couette flow of a micropolar fluid with slip

The unsteady Couette flow of an isothermal incompressible micropolar fluid between two infinite parallel plates is investigated. The motion of the fluid is produced by a time-dependent impulsive motion of the lower plate while the upper plate is set at rest. A linear slip, of Basset type, boundary condition on both plates is used. Two particular cases are discussed; in the first case we have assumed that the plate moves with constant speed and in the second case we have supposed that the plate oscillates tangentially. The solution of the problem is obtained in the Laplace transform domain. The inversion of the Laplace transform is carried out numerically using a numerical method based on Fourier series expansion. Numerical results are represented graphically for the velocity, microrotation, and volume flux for various values of the time, slip and micropolar parameters.     

直立码头前船波浪力耦合计算模型

建立了外域用Boussinesq方程、内域用刚体运动方程的直立码头前二维船剖面波浪力的时 域计算耦合模型,内域与外域在交界面的匹配条件是流量连续和压力相等. 进行了相关模型 实验,并把计算结果与实验结果进行了对比. 推导了船体与水底和直立码头之间间隙内流体 运动的自振频率,研究了间隙内流体运动的共振现象.     

Axisymmetric nonstationary flow around an obstable in a cylindrical tube

Questions associated with the interaction between a gas stream and a body in a launching tube, especially the high-speed propulsion of a body by a gas stream [1], have become of great interest in recent years. Partial destruction of the body and the formation of a gap between the body and the launching tube, through which the working gas will flow, inevitably occurs at high velocities. In this case it is possible to consider the ejection of a free body which does not come into contact with the walls of the launching tube as it is accelerated. An analogous problem occurs in the transportation of containers in a tube under the effect of a compressed gas [2], as well as in a gas-dynamic analysis of piston apparatus with different kinds of gas flow through the orifice inmoving or fixed pistons. The interaction between the gas stream and the body or the obstacle in the launching tube must be known for a theoretical investigation of all these problems. The solution is obtained by numerical integration of the nonstationary gas-dynamic equations by means of a through-computation difference scheme [3]. Values of the blockage factors are found for different freestream Mach numbers, for which the reflected shock stands off at infinity upstream. A comparison is given with the one-dimensional approximation obtained under the assumption that the body being streamlined is replaced by two jumps of a strong discontinuity on which the mass, momentum, and energy conservation conditions are satisfied. The results obtained are used in the problem of ejection of a free body from a launching tube under the effect of an unsteady gas flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 81–86, July–August, 1978.     

Plane Couette flow of binary gaseous mixture in the whole range of the Knudsen number

The Couette flow of binary gaseous mixtures is studied on the basis of the McCormack model of the Boltzmann equation, which was solved numerically by the discrete velocity method. The calculations were carried out for three mixtures of noble gases: neon–argon, helium–argon, and helium–xenon. The stress tensor and bulk velocity of both species were calculated for several values of the gas rarefaction in the range from 0.01 to 40 for three values of the molar concentrations: 0.1,0.5 and 0.9. The numerical solution together with an analytical solution based on the slip boundary condition cover the whole range of the gas rarefaction. It was showed that the Couette flow is weakly affected by the intermolecular interaction law.     

Drag on a body placed between two parallel plates in a hele-shaw flow

In [1], the drag was found that acts on a circular gas bubble between two parallel plates in a slow viscous flow. In the present paper, the problem considered in [1] is solved for a body of arbitrary shape under the assumption that the conditions of a Hele-Shaw flow are satisfied. An expression is obtained for the drag containing only one coefficient in the expansion of the complex potential in a Laurent series.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 161–162, September–October, 1979.     

A Kinetic Approach to the Plane Poiseuille Flow Over a Porous Matrix

The Poiseuille–Couette gas flow in a channel and the gas flow through an adjacent porous medium are considered when the governing equations are obtained via a molecular kinetic approach based on the Boltzmann equation. The mass continuity, momentum balance and energy conservation are written for the gas in the contiguous regions, whereas the behavior of the solid matrix obeys to the heat diffusion equation. Two different space scalings lead to different forms of the equations for the steady flow through the fully saturated matrix. The boundary conditions at the interface between the two domains are investigated via a matching procedure.     

Direct numerical simulation of turbulent Taylor–Couette flow

The direct numerical simulation (DNS) of the Taylor–Couette flow in the fully turbulent regime is described. The numerical method extends the work by Quadrio and Luchini [M. Quadrio, P. Luchini, Eur. J. Mech. B/Fluids 21 (2002) 413–427], and is based on a parallel computer code which uses mixed spatial discretization (spectral schemes in the homogeneous directions, and fourth-order, compact explicit finite-difference schemes in the radial direction). A DNS is carried out to simulate for the first time the turbulent Taylor–Couette flow in the turbulent regime. Statistical quantities are computed to complement the existing experimental information, with a view to compare it to planar, pressure-driven turbulent flow at the same value of the Reynolds number. The main source for differences in flow statistics between plane and curved-wall flows is attributed to the presence of large-scale rotating structures generated by curvature effects.     

MHD Couette two-fluid flow and heat transfer in presence of uniform inclined magnetic field

The MHD Couette flow of two immiscible fluids in a parallel plate channel in the presence of an applied electric and inclined magnetic field is investigated in the paper. One of the fluids is assumed to be electrically conducting, while the other fluid and the channel plates are assumed to be electrically insulating. Separate solutions with appropriate boundary conditions for each fluid are obtained and these solutions are matched at the interface using suitable matching conditions. The partial differential equations governing the flow and heat transfer are transformed to ordinary differential equations and closed-form solutions are obtained in both fluid regions of the channel. The results for various values of the Hartmann number, the angle of magnetic field inclination, the loading parameter and the ratio of the heights of the fluids are presented graphically to show their effect on the flow and heat transfer characteristics.     

Nonisothermal Couette flow of a non-Newtonian fluid under the action of a pressure gradient

Nonisothermal Couette flow has been studied in a number of papers [1–11] for various laws of the temperature dependence of viscosity. In [1] the viscosity of the medium was assumed constant; in [2–5] a hyperbolic law of variation of viscosity with temperature was used; in [6–8] the Reynolds relation was assumed; in [9] the investigation was performed for an arbitrary temperature dependence of viscosity. Flows of media with an exponential temperature dependence of viscosity are characterized by large temperature gradients in the flow. This permits the treatment of the temperature variation in the flow of the fluid as a hydrodynamic thermal explosion [8, 10, 11]. The conditions of the formulation of the problem of the articles mentioned were limited by the possibility of obtaining an analytic solution. In the present article we consider nonisothermal Couette flows of a non-Newtonian fluid under the action of a pressure gradient along the plates. The equations for this case do not have an analytic solution. Methods developed in [12–14] for the qualitative study of differential equations in three-dimensional phase spaces were used in the analysis. The calculations were performed by computer.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 26–30, May–June, 1981.     

Measurements of rivulet flow between parallel vertical plates

The research presented considers laminar, fully-developed rivulet flow in the channel formed by two parallel vertical plates for flows intermediate between a lower limit of droplet flow and an upper limit where the rivulets meander. Although this regime is likely the most simple rivulet flow regime, it does not appear to have been previously investigated in detail. In an earlier paper, the authors derived relations to predict the terminal Reynolds number and non-dimensional width of the rivulet under the approximation that the width is large relative to the gap width of the plates (the spacing between the plates). The objective of the present study is to examine the limits of this simple treatment as the relative width becomes small, i.e., as the rivulets become narrow. Experiments were performed measuring rivulet widths and flow rates for gap widths ranging from 0.152 mm to 0.914 mm with water, light mineral oil, ethyl alcohol and water with a wetting agent. Predictions were found to agree well with the measurements for width-to-spacing ratios as low as unity and less. A numerical analysis shows that a plausible explanation of unexpected agreement for narrow rivulets is that the error in this one-dimensional assumption is approximately countered by the error in neglecting flow in the edge region. To account for curvature of the liquid–air interface at the edges, an additional geometric relationship was assumed; this approach also was found to be a good representation.     

Instability analysis of modulated Taylor vortices

This study investigates the instability analysis of modulated Taylor vortices flow by utilising a numerical method. Based on the consideration that the outer cylinder is fixed and the inner cylinder rotates at a non-zero averaged speed under varying modulated amplitudes and frequencies, the flow is converted from one-dimension Couette flow to Taylor vortices. When the modulated amplitude is greater than 1 and the rotation speed of the inner cylinder exceeds the threshold value for one-dimensional flow, the flow will be more stable at intermediate and high frequencies. When the modulated amplitude is sufficiently large and the inner cylinder rotates at medium frequency, subharmonic flow arises.