The range of applicability of some similitude laws for heat transfer, friction and drag coefficients is discussed on the basis of numerical solutions of the complete viscous shock layer equations describing hypersonic flow past blunt bodies .The method of matched asymptotic expansions [1] is used widely in the theory of hypersonic flow past bodies ; this method enables one to solve simplified gasdynamic equations in the first terms of the expansion of the unknown functions in asymptotic series in terms of a small parameter [2][3][4] . Similitude relations for the shock wave stand-off distance, the drag and friction coefficients, the convective and radiative heat transfer to impermeable bodies, which are of practical importance, have been obtained in the last few years on the basis of these solutions [2][3][4][5] . In the case of the intense subsonic injection of a foreign gas from the body surface, another small parameter appears, namely, the momentum ratio for the injected and oncoming gases [6,7] . In this case it is also possible to construct an asymptotic solution and to obtain, for example, the shape of the contact surface separating two flows [7] .The results of asymptotic and numerical studies of supersonic viscous nonuniform wake-type flows past blunt bodies with and without gas injection from the body surface were reviewed in [8] .Since the convergence of asymptotic solutions in the general case of nonlinear gasdynamic equations has not been proved strictly from the mathematical standpoint, the problem of the accuracy and the applicability range of the approximate similitude relations thus obtained arises . In order to arrive at an answer to this problem, it would be well to carry out a systematic comparison with the results of either specifically designed aerodynamical experiments or numerical solutions of the more accurate (non-simplified) gasdynamic equations .In recent years a numerical method of solving the complete viscous layer equations has been developed [9] . This makes it possible to calculate the distributions of all the gasdynamic parameters in the shock layer adjacent to a blunt cone with or without gas injection from the body surface, in uniform and nonuniform oncoming streams [10][11][12] . Comparison of the numerical solutions for flow past a sphere and a blunt cone obtained by this method with the experimental data and other numerical and asymptotic solutions [10][11][12] shows that the method possesses high accuracy and requires less computation time than time-dependent methods for the Navier-Stokes equations . On the basis of the approximate asymptotic solutions, a general similarity law was derived in [13] for convective heat transfer to the side surface of a slender blunt body in laminar hypersonic flow, as well as for other gasdynamic parameters . The similitude laws for inviscid flow past blunt slender bodies and viscous flow past sharp slender bodies follow from this law as special cases .

532.526.2The study of flow field and heat exchange about blunt bodies when the oncoming supersonic stream is substantially nonuniform has been of much practical interest lately. In [1] we considered the results of experimental and theoretical study of the resistance, heat exchange, and the gasdynamic picture of the flow past a pair of bodies, one of which is behind the other in a supersonic stream. The experimental results in [1] were obtained for a relatively small separation between the bodies (no more than 20 calibers). The study is carried out by theoretical methods when the bodies are separated by a large distance (several hundred calibers) [2][3][4][5][6]. In [2, 3] we obtained asymptotic solutions for the problem of the flow of a nonuniform wake-type stream past a blunt body for moderate (Re** < 103) and high (Re** > 105) Reynolds numbers. In [1,[4][5][6] as a result of numerical solution of the equations of a thin viscous shock layer (on the assumption that the shock wave is equidistant from the surface of the body) we obtained relations for the heat exchange, friction, and the criterion of flow without separation as functions of the parameters of the problem.For a uniform mainstream the method of a thin viscous shock layer (TVSL) gives results that are in satisfactory agreement with calculations with more exact methods [7, 8]. The applicability of the TVSL method [4-6] and asymptotic formulas [2, 3] to the case of a nonuniform supersonic stream of the far wake type flowing past a blunt body has not been examined sufficiently.It is a particularly complicated matter to prove that the asymptotic expansions converge to an exact solution of the problem when there are several small parameters in which the expansions are made (t = P**/Ps, Re** -lcz, M** -2, etc., where p** and Ps are the density in the mainstream and behind the step, Re** and M** are the Reynolds and Mach numbers). The answer to these questions can be obtained either from systematic comparisons of the calculated gasdynamic parameters over a wide range with the results of specially designed aerodynamic experiments (which are often complex or impossible) or from a comparison with numerical solutions of more exact (unsimplified) equations of gasdynamics.This study of a nonuniform supersonic flow past blunt bodies is based on the equations of a complete viscous shock layer (CVSL), which are solved numerically by using the effective method of global iterations [7][8][9][10][11]. The high accuracy and speed of this method as applied to CSVL equations have been confirmed by a comparison with experiment and the results of numerical solution of the Navier-Stokes equations by the method of fixing [7, 9, 10].As shown here, in the case of low Reynolds numbers (Re** = 50-100) the asymptotic formulas for a heat flux from [2] give practically the same results as does the numerical solution of TVSL equations. A comparison of the numerical solution of TVSL and CVSL equations showed that for a wake-type nonuniform mainstream the TVSL method leads to substantia...