Effect of a Thin Longitudinal Inviscid Vortex on a Two-Dimensional Pre-Separation Boundary Layer

For large Reynolds numbers, an asymptotic solution of the Navier-Stokes equations describing the effect of a thin longitudinal vortex with a constant circulation on the development of an incompressible steady two-dimensional laminar boundary layer on a flat plate is obtained. It is established that, in a narrow wall region extending along the vortex filament, the viscous flow is described by the 3-D boundary layer equations. A solution of these equations for small values of the vortex circulation is studied. It is found that the solution of the two-dimensional pre-separation boundary layer equations collapses. This is attributable to the singular behavior of the 3-D disturbances near the zero-longitudinal-friction points.     

Free convection boundary-layer flow above a nearly horizontal surface in a porous medium with newtonian heating

In this paper the steady free convection boundary-layer along a semi-infinite, slightly inclined (both positive and negative) to the horizontal plate embedded in a porous medium with the flow generated by Newtonian heating has been investigated. The asymptotic solution near the leading edge and the full numerical solution along the whole plate domain have been obtained numerically, whilst the asymptotic solution far downstream along the plate has been obtained analytically. For a positive inclination the full numerical solution is in agreement with the asymptotic solutions. However, for a negatively inclined plate, only the small asymptotic solution near the leading edge of the plate can be predicted giving an insight that the model for a negatively inclined plate, whilst mathematically interesting, is not physically realistic.     

Influence of the flow in the neighborhood of a stagnation point on the characteristics of an electrostatic probe

The transverse flow around an electrically conductive plate by a weakly ionized gas stream is investigated in this paper. A formulation of the problem and an algorithm of the solution are given. For certain values of the parameters the equations for the shielding and viscous layers are integrated numerically to permit estimation of the influence of the free stream velocity on the voltampere characteristic of a flat probe.     

The Flow and Heat Transfer at Start-Up of an Arbitrarily Shaped Body in a Viscous Heat-Conducting Gas

The flow corresponding to the start-up of an arbitrarily shaped body in a viscous heat-conducting gas is analyzed. The established fact of fluid incompressibility at short times is used. In the first approximation, in the neighborhood of each point on the body surface the flow and heat transfer are proved to be the same as for an infinite plate coinciding with the tangential plane at this point. The corrections for the curvature of the body surface are found. For determining the flows near a cylinder of arbitrary shape and near a spherical bluntness, the start-up problems for a circular cylinder and a sphere are considered. The possibility of extending the results to the case of reacting gases is discussed.     

Hall effects on hydromagnetic flow on an oscillating porous plate

In this paper, an analysis is made on the unsteady flow of an incompressible electrically conducting viscous fluid bounded by an infinite porous flat plate. The plate executes harmonic oscillations at a frequency n in its own plane. A uniform magnetic field Ho is imposed perpendicular to the direction of the flow. It is found that the solution also exists for blowing at the plate. The temperature distribution is also obtained by taking viscous and Joule dissipation into account. The mean wall temperature θo（O） decreases with the increase in the Hall parameter m. It is found that no temperature distribution exists for the blowing at the plate.     

Natural convection near a vertical plate with ramped wall temperature

The unsteady natural convective flow of an incompressible viscous fluid near a vertical plate has been considered. It is assumed that the bounding plate has a ramped temperature profile. The exact solutions of the energy and momentum equations, under the usual Boussinesq approximation, have been obtained in closed form. There are two different solutions for the fluid velocity—one valid for the fluids of Prandtl numbers different from unity, and the other for which the Prandtl number is unity. The variations of the fluid temperature, velocity as well as the Nusselt number and wall skin friction have been presented graphically. The natural convection near a ramped temperature plate has also been compared with the flow near a plate with constant temperature.     

Biharmonic Problem in a Rectangle

This paper addresses the fascinating long history of the classical two-dimensional biharmonic problem for a rectangular domain. Among various mathematical and engineering approaches, the method of superposition is effective for solving mechanical problems concerning creeping flow of viscous fluid set up in a rectangular cavity by tangential velocities applied along its walls, an equilibrium of an elastic rectangle, and bending of a clamped thin rectangular elastic plate by a normal load. The object of this paper is both to clarify some purely mathematical questions connected with the solution of the infinite systems of linear algebraic equations and to provide a considerable simplification of the numerical algorithm. The method is illustrated by several examples of steady Stokes flow in a square cavity.     

A simple numerical technique for transient creep flows with free surfaces

A simple, but powerful iterative technique is presented for the numerical solution of the time-dependent flow of an incompressible viscous fluid with or without a free surface. The usual numerical stability restrictions related to the viscous acceleration terms are avoided using standard implicit differencing techniques. The properties and accuracy of the method are illustrated by several calculational examples.     

The Opposing Effect of Viscous Dissipation Allows for a Parallel Free Convection Boundary-Layer Flow Along a Cold Vertical Flat Plate

External free convection boundary-layer flows are usually treated by neglecting the effect of viscous dissipation. This assumption always results in a non-parallel flow, besides a strong parallel component also a weak transversal component of the (steady) velocity field occurs. The present paper shows, however, that the weak opposing effect of the buoyancy forces due to heat release by viscous dissipation, can give rise along a cold vertical plate adjacent to a fluid saturated porous medium to a strictly parallel steady free convection flow. This boundary-layer flow is described by an algebraically decaying exact analytical solution of the basic balance equations.     

The hydromagnetic flow over an oscillating flat plate with arbitrary periodic oscillation

In this paper, the hydromagnetic flow over a flat plate with arbitrary periodic oscillation is solved exactly. The solution is also applicable for common incompressible viscous flow over a flat plate with arbitrary oscillation. It is found that the penetration of hydromagnetic flow will decrease with increasing non-dimensional magnetic parameter M. The transient part will die away after a certain time for a specific M. The solution will collapse into the steady-state case after a long time. However, for non-hydromagnetic flow, there will be no steady-state solution if the coefficient of the zero-frequency component is not zero.     

Analytical Investigation of the Effect of Viscous Dissipation on Couette Flow in a Channel Partially Filled with a Porous Medium

An analytical study of viscous dissipation effect on the fully developed forced convection Couette flow through a parallel plate channel partially filled with porous medium is presented. A uniform heat flux is imposed at the moving plate while the fixed plate is insulated. In the fluid-only region the flow field is governed by Navier–Stokes equation while the Brinkman-extended Darcy law relationship is considered in the fully saturated porous medium. The interface conditions are formulated with an empirical constant β due to the stress jump boundary condition. Fluid properties are assumed to be constant and the longitudinal heat conduction is neglected. A closed-form solution for the velocity and temperature distributions and also the Nusselt number in the channel are obtained and the viscous dissipation effect on these profiles is briefly investigated.     

非结构网格二阶有限体积法中黏性通量离散格式精度分析与改进

非结构网格二阶有限体积离散方法广泛应用于计算流体力学工程实践中,研究非结构网格二阶精度有限体积离散方法的计算精度具有现实意义. 计算精度主要受到网格和计算方法的影响,本文从单元梯度重构方法、黏性通量中的界面梯度计算方法两个方面考察黏性流动模拟精度的影响因素. 首先从理论上分析了黏性通量离散中的“奇偶失联”问题,并通过基于标量扩散方程的制造解方法验证了“奇偶失联”导致的精度下降现象,进一步通过引入差分修正项消除了“奇偶失联”并提高了扩散方程计算精度;其次,在不同类型、不同质量的网格上进行基于扩散方程的制造解精度测试,考察单元梯度重构方法、界面梯度计算方法对扩散方程计算精度的影响,结果显示,单元梯度重构精度和界面梯度计算方法均对扩散方程计算精度起重要作用;最后对三个黏性流动算例(二维层流平板、二维湍流平板和二维翼型近尾迹流动)进行网格收敛性研究,初步验证了本文的结论,得到了计算精度和网格收敛性均较好的黏性通量计算格式.      

Slow Viscous Flow through Arbitrary Triangular Tubes and Its Application in Modelling Porous Media Flows

In this article we extend the analytical solution for viscous flow in an equilateral triangular tube to irregular triangular tubes. The validity of the solution is examined and proved by comparison with the numerical simulation results. With the new extension of the equations, the average velocity of viscous flow through an arbitrary triangular tube can be readily calculated as a function of inscribed radius of the triangular cross-section of the tube, and the volumetric flow rate is computed as a function of inscribed radius and the cross- sectional area. To illustrate the advantages in using an arbitrary triangular tube for modelling a porous medium, we present examples of tube bundle models, which give a wide range of variation in porosity and permeability with a fixed pore size distribution, by using various combinations of three types of triangular tubes.     

Formation of a region of interaction and of a wake with the instantaneous start of a plate in an incompressible liquid

The flow arising in an incompressible liquid if, at the initial moment of time, a plate of finite length starts to move with a constant velocity in its plane, is discussed. For the case of an infinite plate, there is a simple exact solution of the Navier—Stokes equations, obtained by Rayleigh. The case of the motion of a semiinfinite plate has also been discussed by a number of authors. Approximate solutions have been obtained in a number of statements; for the complete unsteadystate equations of the boundary layer the statement was investigated by Stewartson (for example, [1–3]); a numerical solution of the problem by an unsteady-state method is given in [4]. The main stress in the present work is laid on investigation of the region of the interaction between a nonviscous flow and the boundary layer near the end of a plate. In passing, a solution of the problem is obtained for a wake, and a new numerical solution is also given for the boundary layer at the plate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 3–8, March–April, 1977.     

The effects of the side walls on the flow of a second grade fluid in ducts with suction and injection

The effects of the side walls on the flow in ducts with suction and injection are examined. Three illustrative examples are given. The first example considers the effect of the side walls on the flow over a porous plate. The second example considers the flow between two parallel porous plates and the third example is devoted to the investigation of the flow in a rectangular duct with two porous walls. Exact solution of the governing equation using the no-slip boundary condition and an additional condition are obtained. The expression of the velocity, the volume flux and the vorticity are given. It is found that for large values of the cross-Reynolds number near the suction region the flow for a Newtonian fluid does not satisfy the boundary condition, but it does not behave in the same way for a second grade fluid. Three examples considered show that there are pronounced effects of the side walls on the flows of a second grade fluid in ducts with suction and injection.     

Flow around the afterbody of a plate in a longitudinal gas stream with transverse injection from the lateral surface

The flow around the afterbody of a plate of finite thickness in a supersonic gas stream is investigated on the basis of a numerical solution of the time-dependent Navier-Stokes equations for a compressible viscous heat-conducting gas. The change in the flow pattern with the onset of transverse slot injection from the body surface in the vicinity of the base section is studied. For constant supersonic injection, both steady and unsteady flow regimes could be obtained depending on the values of certain relevant parameters.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 157–163, March–April, 1996.     

Flow of a vortical stream in the neighborhood of the critical point

A study was made of the axisymmetric flow of a viscous incompressible fluid in the neighborhood of the critical point of an obstacle when steady-state vortices oriented in the direction of the angular coordinate are introduced into the oncoming flow. A solution is presented of the equation for the transfer of a vortex in the case of an external flow containing a single largesize vortex in the low-frequency part of the spectrum. Using a finite integral Hankel transform, the problem is reduced to the solution of a system of ordinary differential equations. It is shown that a sufficiently large-size vortex can have a considerable effect on the structure of viscous flow near an obstacle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 85–89, November–December, 1970.     

Determining unsteady aerodynamic forces for three-dimensional plate cascade in subsonic gas flow

The general solution for the problem of three-dimensional gas flow through a cascade of plates was obtained in [1], It is shown below that in the considered direct and inverse aerodynamic problems there may exist nontrivial solutions for uniform boundary conditions. The flow regimes for which such solutions exist may be treated as aerodynamic resonance.The examples presented of the calculation for a plate cascade illustrate the behavior of the unsteady aerodynamic forces near the aerodynamic resonance regimes and make it possible to evaluate the limits of applicability of the hypothesis of plane sections. In addition, the calculation results show the possibility of self-induced vibrations of plate cascades with a single degree of freedom in a subsonic gas stream.     

水泵叶片表面三维边界层计算

本文用有限差分法计算混流式可逆水力机械水泵工况叶片表面的三维边界层。水泵叶轮中主流区的三维势流由直接边界元法计算。对于叶片面附近的粘性流动。用三维半正交坐标系中的边界层方程表示。为了提高计算精度采用贴体坐标技术生成边界层区域的计算网格。并利用Cebeci等变换函数及Keller差分格式离散方程。用分块解法求解。计算叶轮叶片表面的压力分布与相应试验结果进行了对比。