Hypersonic Flow

摘要

This paper discusses some of the areas in which our understanding of hypersonic flows has progressed in recent years―with special reference to the hypersonic similarity concept and the hypersonic approximations; the interaction between the boundary layer over a slender body and the external inviscid flow; and the flow over blunt bodies, including the heat-transfer problem. When the inviscid pressure distributions predicted by the hypersonic approximations (Newtonian, shock-expansion, tangent-wedge, and cone) are compared with "exact" solutions and experimental data, it becomes evident that this problem is effectively solved for sharp-nosed slender wings and bodies of revolution. The shock-expansion and tangent-wedge (or tangent-cone) method may also be used to construct the flow field. An examination of the equations of motion shows that the simple tangent-wedge (or cone) method, which is thought by some to be largely semiempirical, actually has a sound theoretical basis. At hypersonic speeds the flow over sharp-nosed slender shapes cannot be properly treated without considering boundary-layer-external flow interactions. Since the mass flux through the boundary layer is small, the streamlines entering the boundary layer are very nearly parallel to the outer edge. In other words, the flow inclination there is the sum of the body inclination and the slope of the boundary layer, and the local pressure is related to the boundary-layer growth rate by means of the tangent-wedge (or tangent-cone) approximation. A second relation between these quantities is provided by the Prandtl boundary-layer equations. For both strong and weak interactions over inclined wedges, for example, the governing viscous interaction parameter is (Mach Number)~3/(Reynolds Number)~(1/2). The straightforward approach to this problem seems to be adequate when the Reynolds Number based on leading-edge thickness, Re_t, is a few hundred or less. For larger Re_t the experimentally measured induced pressures on flat surfaces suggest that the strong bow shock decays surprisingly slowly at high Mach Numbers and that the expansion waves reflected from this shock and impinging on the surface may overwhelm the purely viscous effect. For blunt bodies the modified Newtonian approximation in the form C_p/C_(pmax) = sin~2 θ_b is highly accurate for Mach Numbers above 2.0, even for shapes with rapidly varying (convex) curvature. Current treatments of heat transfer over such bodies are limited to small temperature differences between gas and body surface. For this case the agreement between Sibulkin's theoretical result and experiments in the Mach Number range 2 < M < 5 is good. For large temperature differences an expression quite similar to Sibulkin's is derived based on gas properties evaluated at the surface temperature. This problem appears to be a fruitful one for the investigation of the influence of high temperature gas phenomena on hypersonic fluid mechanics.