Laminar boundary layer in an equilibrium dissociated gas for arbitrary external velocity distribution

The development of machine computing technology permits calculating the boundary layer by direct numerical integration of the corresponding system of partial differential equations [1, 2]. In order to derive general conclusions concerning the boundary layer with a pressure gradient we must perform the integration for each concrete form of velocity specification at the outer edge of the boundary layer. The method of calculating the boundary layer used in the present study [3], based on the solution of a universal (independent of the specification of the velocity at the outer edge of the boundary layer) system of equations, permits the clarification of several general relationships.     

Laminar boundary layer on swept-back wings of infinite span at an angle of attack

A study is made of the flow of a compressible gas in a laminar boundary layer on swept-back wings of infinite span in a supersonic gas flow at different angles of attack. The surface is assumed to be either impermeable or that gas is blown or sucked through it. For this flow and an axisymmetric flow an analytic solution to the problem is obtained in the first approximation of an integral method of successive approximation. For large values of the blowing or suction parameters, asymptotic solutions are found for the boundary layer equations. Some results of numerical solution of the problem obtained by the finite-difference method are given for wings of various shapes in a wide range of angles characterizing the amount by which the wings are swept back and also the blowing or suction parameters. A numerical solution is obtained for the equations of the three-dimensional mixing layer formed in the case of strong blowing of gas from the surface of the body. The analytic and numerical solutions are compared and the regions of applicability of the analytic expressions are estimated. On the basis of the solutions obtained in the present paper and studies of other authors a formula is proposed for the calculation of the heat fluxes to a perfectly catalytic surface of swept-back wings in a supersonic flow of dissociated and ionized air at different angles of attack. Flow over swept-back wings at zero angle of attack has been considered earlier (see, for example, [1–4]) in the theory of a laminar boundary layer. In [5], a study was made of flow over swept-back wings at nonzero angle of attack at small and moderate Reynolds numbers in the framework of the theory of a hypersonic viscous shock layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 27–39, May–June, 1980.We thank G. A. Tirskii for a helpful discussion of the results.     

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.     

Nonlinear Knudsen boundary layer on an infinitely thin permeable membrane

The state of a gas in the neighborhood of an infinitely thin permeable membrane whose sides have different temperatures is investigated. The dimensions of orifices in the membrane are much less than the mean molecular free path. The gas temperatures and pressures on both sides of the membrane outside the nonlinear Knudsen layers adjacent to the membrane and variations in these parameters in the Knudsen layers are determined. The investigation is carried out by solving the Boltzmann kinetic equation by means of the direct simulation Monte-Carlo method. The semiempirical Maxwell method is also used for consideration of the molecular flows on both sides of the membrane when analyzing the temperatures and the pressures. The solution to the nonlinear problem is compared with the solution to the linear problem of a jump temperature near a nonisothermal porous body obtained earlier.     

Laminar boundary layer in a swirling flow

The spatial non-self-similar boundary layer in a compressible gas in a swirling flow is studied. Boundary-layer equations are written in variables ensuring constancy of the coefficients of first derivatives and are solved by the finite-difference method. Boundary-layer peculiarities in the presence of a return circulation region in the channel are clarified.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 43–49, January–February, 1976.     

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 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).     

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 stability on membrane type deformable surfaces

In connection with the successful experiments of Kramer [l, 2] on models sheathed by flexible coverings, attempts have been made to explain theoretically the effect of boundary deformation on the position of the point of stability loss in the boundary layer. Korotkin [3] examined the stability of a plane laminar boundary layer on an elastic surface under the assumption of a linear connection between the pressure perturbation and the normal deformation of the surface. Benjamin [4] and Landahl [5] investigated the stability of the laminar boundary layer on a membrane type surface under the assumption that the physical characteristics of the surface depend on the perturbing flow wavelength. In the following we examine stability of Blasius flow on a membrane type surface whose physical characteristics are constant along the length.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, vol. 10, no. 6, pp. 52–56, November–December, 1969.     

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.     

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.