The Theory of Viscous Hypersonic Flow

Abstract

The flow of gas at hypersonic speed near a solid surface leads to the forma­ tion of a boundary layer whose thickness significantly exceeds (at the same Reynolds number) the thickness of the boundary layer formed at moderate supersonic speeds. The reason for this is the high temperature level and the consequent low density and high coefficient of viscosity in the hypersonic boundary layer. As a result, the effect of viscosity at high supersonic speeds is not confined to the interior of the boundary layer, and leads to substantial changes in the entire flow field. In the first place this is associated with the displacement effect of the boundary layer, which changes the effective shape of the body. Furthermore, thickening of the boundary layer can pro­ duce changes in the character of the flow in the boundary layer itself, as a result of the effect of the vorticity of the outer stream, the increased role of the transverse curvature of the surface, etc. All these effects are usually studied on the basis of the theory of inter­ action of the boundary layer with the outer stream, that is, on the basis of simultaneous consideration of the flow field in the boundary layer and the outer inviscid stream. In cases when the boundary-layer thickness is of an order of magnitude significantly smaller than the thickness of the body, the situation in the first approximation does not differ from the classical one, that is, the outer stream may, in the first approximation, be regarded as independent of the boundary layer. In this case of so-called weak interaction, the problem of studying the influence of the boundary layer upon the outer flow field and secondary effects in the boundary layer itself reduces to the investigation of higher approximations in boundary-layer theory. However if the body is so slender that the boundary layer has comparable or greater thickness, the effects of interaction may determine all functions of the flow field in their leading terms. The study of such cases constitutes the theory of moderate or strong interaction of the boundary layer with the outer stream. This last development has a central place in the present survey, because the theory of higher approximations for a boundary layer is treated in detail in the article by Van Dyke in the first volume of Annual Review of Fluid Mechanics ( 1969). We devote attention primarily to investigations carried out within the last decade, since the earlier period of development of the theory of viscous hypersonic flow is described in detail in the book of Hayes & Probstein (1959a).