Laminar boundary layer in a swirling flow on a permeable surface

Numerical and approximate analytic methods are used to investigate the three-dimensional nonself-similar swirling flow of a uniform gas on an axisymmetric permeable surface. For large values of the injection parameter (in the general case the injection velocity vector forms a nonzero angle with the vector of the outward normal to the flow surface) asymptotic expressions are obtained for the velocity and temperature profiles across the injection layer, the components of the friction stress and the heat flux at the surface. Certain results of a numerical solution of the problem obtained on a broad interval of variation of the injection parameter are presented. By comparing the numerical and asymptotic solutions the accuracy and region of applicability of the latter are estimated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 28–37, November–December, 1985.In conclusion, the author wishes to thank É. A. Gershbein (deceased) for useful discussion of his results.     

Laminar boundary layer in axisymmetric swirling ducted gas flow

Several studies have been published [1–3] in which the authors solve the problem of the laminar boundary layer in an incompressible fluid on the walls of an axisymmetric duct in the presence of swirl in the outer flow. In [3], Loitsyanskii's parametric method of [4, 5], generalized to the case of three-dimensional flow, is used to solve this problem.In this article the parametric method for integrating the universal equations is extended to the solution of the problem of the laminar boundary layer on the wall of an axisymmetric channel in the case of swirling gas flow.     

Laminar boundary layer in flow of a nonequilibrium ionized gas

The motion of a hypersonic body is accompanied by an increase in the gas temperature in the boundary layer up to tens of thousands of degrees, which causes the gas to ionize. Under these conditions there are problems in calculating coefficients of viscosity, diffusion, and heat conduction. Investigations have shown that it is invalid to extrapolate the widely used approximations for transport coefficients in the high temperature region [1–3]. This paper considers the laminar boundary layer in the vicinity of the stagnation point of a blunt body in a stream of monatomic nonequilibrium ionized gas. The main thrust is a more accurate calculation of transport coefficients and an investigation of their effect on profiles of the gasdynamic parameters. A specific calculation is performed for argon by way of example.     

Laminar boundary layer separation at a fin-body junction in a hypersonic flow

Planar laser-induced fluorescence (PLIF) imaging was performed to visualize the fin bow shock, separation shock, viscous shear layer and recirculation region of the flowfield at the junction of a blunt fin and a flat plate. Making use of the temperature dependence of the PLIF technique, images were made sensitive to temperature to provide qualitative information on the flowfield. The PLIF technique was also used as the basis for a flow-tagging technique, making it possible to measure a velocity component and to demonstrate the reverse flow of the separated region. Flow visualisation of the plane of symmetry allowed determination of the point of boundary layer separation, the angle of the separation shock and the bow shock standoff distance. These parameters were compared with predictions made by computational fluid dynamic simulations of the flowfield. Good agreement between theory and experiment was achieved. Comparisons between theoretical and experimental velocity measurements showed good agreement. Received 17 October 2000 / Accepted 13 November 2000     

Laminar boundary layer in a flow past an aerofoil with a circular cavity

The paper describes a numerical study of a method of preventing the separation of a laminar boundary layer from the forward section of a symmetric aerofoil, the flow past which does not separate at zero angle of incidence. In order to increase the maximum angle of incidence at which the flow has still not separated, a circular cavity (vortex cell) located almost completely inside the aerofoil is introduced on the segment vulnerable to separation. The asymptotics of the corresponding flow at high Reynolds number are described using the Prandtl-Batchelor model. Krasnodar. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 52–57, March–April, 1998. The work was financially supported by the International Science Foundation (grants M4K000 and M4K300) and by the Russian Foundation for Fundamental Research (project No. 96-01-01290).     

超音速/高超音速三维边界层的层流控制基金项目

根据可压缩黏性稳定性理论研究了壁面冷却和抽吸对超音速、高超音速三维边界层的层流控制作用.数值结果证明壁面冷却对第一模式起稳定作用,对第二模式有不稳定作用;壁面抽吸对第一、二模式都起稳定作用;直到Me＝7,导致绝热壁边界层转捩的始终是第一模式,Me≥6的冷却壁边界层则是第二模式对转捩起主导作用.壁面冷却能够推迟边界层转捩,但是和二维边界层相比壁面冷却对高速三维边界层的层流控制作用是很有限的.     

Non-axisymmetric boundary layer induced by a swirling downdraft

Most mathematical models of conical swirling flows are exact axisymmetrical solutions of the steady and incompressible Navier–Stokes equations. Some of these models take into account the coupling mechanisms (Chaskalovic and Chauvière 1999, Shtern et al. 1998), but very few mathematical studies try to model non-axisymmetrical conical flows. We propose here a generalisation of the formulation used by Aristov (1998) to study a swirling vertical downdraft limited by a nearly horizontal plane. The use of asymptotic analysis for high Reynolds numbers allows to find non-axisymmetrical analytical solutions for the whole flow.     

Application of the Dorodnitsyn finite element method to swirling boundary layer flow

The Dorodnitsyn finite element method for turbulent boundary layer flow with surface mass transfer is extended to include axisymmetric swirling internal boundary layer flow. Turbulence effects are represented by the two-layer eddy viscosity model of Cebeci and Smith¹ with extensions to allow for the effect of swirl. The method is applied to duct entry flow and a 10 degree included-angle conical diffuser, and produces results in close agreement with experimental measurements with only 11 grid points across the boundary layer. The introduction of swirl (w_e/u_e = 0.4) is found to have little effect on the axial skin friction in either a slightly favourable or adverse pressure gradient, but does cause an increase in the displacement area for an adverse pressure gradient. Surface mass transfer (blowing or suction) causes a substantial reduction (blowing) in axial skin friction and an increase in the displacement area. Both suction and the adverse pressure gradient have little influence on the circumferential velocity and shear stress components. Consequently in an adverse pressure gradient the flow direction adjacent to the wall is expected to approach the circumferential direction at some downstream location.     

Laminar boundary layer with uniform suction on flat plate in oscillating flow

We examine unsteady incompressible fluid flow in a laminar boundary layer with uniform suction for longitudinal flow over a flat plate when the external stream is a flow with constant velocity, on which there is superposed a sinusoidal disturbance convected by the stream, analogous to [1]. We study the stability of such flow in the boundary layer.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 3, pp. 66–70, May–June, 1970.     

Laminar boundary layer on a yawed infinite cylinder

Using mixed momentum and energy integral equations, a simple quadrature method is developed to compute incompressible laminar boundary layer on a yawed infinite cylinder. As an illustration, the results — including various boundary layer thicknesses, form parameters and potential and surface streamlines — are obtained for a circular cylinder and compared with a known solution.     

Laminar boundary layer flow of a nanofluid along a wedge in the presence of suction/injection

The behavior of an incompressible laminar boundary layer flow over a wedge in a nanofluid with suction or injection has been investigated. The model used for the nanofluid integrates the effects of the Brownian motion and thermophoresis parameters. The governing partial differential equations of this problem, subjected to their boundary conditions, are solved by the Runge-Kutta-Gill technique with the shooting method for finding the skin friction and the rate of heat and mass transfer. The result are presented in the form of velocity, temperature, and volume fraction profiles for different values of the suction/injection parameter, Brownian motion parameter, thermophoresis parameter, pressure gradient parameter, Prandtl number, and Lewis number. The conclusion is drawn that these parameters significantly affect the temperature and volume fraction profiles, but their influence on the velocity profile is comparatively smaller.     

Supersonic flow past a wedge on a flat plate. Laminar boundary layer separation and reattachment

Supersonic laminar flow past a two-dimensional “flat-plate/wedge“ configuration is numerically investigated. The pressures at the boundary layer separation and reattachment points are calculated over wide Mach and Reynolds number ranges. The minimum angles of the wedge surface inclination at which a return flow occurs are determined. The results are presented in the form of generalized Mach-number-dependences of the theoretical pressure on the wedge surface initiating boundary layer separation and the pressure at the boundary layer reattachment point.     

Laminar boundary layer on an oscillating wedge

A study is made of the nonstationary laminar boundary layer on a sharp wedge over which a compressible perfect gas flows; the wedge executes slow harmonic oscillations about its front point. It is assumed that the perturbations due to the oscillations are small, and the problem is solved in the linear approximation. It is also assumed that the thickness of the boundary layer is small compared with the thickness of the complete perturbed region. Then in a first approximation the influence of the boundary layer on the exterior inviscid flow can be ignored, and the parameters on the outer boundary of the boundary layer can be taken equal to their values on the body for the case of inviscid flow over the wedge. They are determined from the solution to the inviscid problem that is exact in the framework of the linear formulation. The wall is assumed to be isothermal. The dependence of the viscosity on the temperature is linear. Under these assumptions, the problem of calculating the nonstationary perturbations in the boundary layer on the wedge is a self-similar problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 146–151, July–August, 1980.