Inviscid hypersonic flow over plane power-law bodies

Abstract

Theoretical solutions based on the expansion scheme for large x and large M_∞, as proposed by Freeman (1962), are obtained for the asymptotic inviscid flow over plane bodies of the shape y/d = (x/d)^m in the range $\frac{2}{3}/\gamma < m < \frac{2}{3}$ where blast wave theory applies as a first approximation. In particular, the second-order terms, which are necessary to satisfy the body boundary conditions for the normal velocity are computed. The magnitude of the second-order terms is found to increase from zero at $m=\frac{2}{3}/\gamma $ to infinity at $m = \frac{2}{3}.$

As a comparison with theory, experiments at M_∞ = 8·2 were made with two plane power-law bodies in the range $\frac{2}{3}/\gamma < m < \frac{2}{3} $ and on a plane parabola with a tangent wedge nose. These consisted of the determination of shock-wave shapes, surface pressure distributions and detailed investigations of the distribution of pitot and static pressure across the shock layer.

The experimental results are in good agreement with the theory in the case m =1/2, where the second-order effects are small. At m = 5/8 the region of validity of the theory is limited to much larger distances from the nose of the body and larger Mach numbers. Accordingly, the prediction for the deviation from firstorder theory, although being correct in sign, is too small. Shock-wave shapes on bodies of the same power but of different size are correlated by the similarity theory when scaled with respect to the dimension d.

The experimental results obtained with the wedge-parabola are in very good agreement with a characteristics solution by C. H. Lewis (1965, unpublished).