On the applicability of some approximate similitude laws in hypersonic aerodynamics

Abstract

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 .