Linearized theory of axisymmetric hypersonic source flow past bodies of revolution

Abstract

The linearized theory of axisymmetric hypersonic source flow past a slender pointed body is treated by using linearized potential theory, assuming that the hypersonic parameter is less than unity. The governing equation in the transformed co-ordinates with the ratio of specific heats γ = 1.5 shows a modified form relative to the equation for parallel flow, whereas that with γ = 2 shows essentially the same form. Some numerical calculations for a cone and a cone-cylinder are presented, and the surface pressure distributions obtained for both γ = 1.5 and 2 show that there is a considerable pressure-distribution difference between source flow and parallel flow. The pressure on a cone in hypersonic source flow approaches zero downstream, while, if the cone has a cylindrical afterbody, the pressure recovers to the free-stream value quickly. This suggests that the static pressure probe for supersonic parallel flow is useful also in source flow.

Supersonic radial flow past sharp-nosed cones

“…At the same time, for -y=2 the ratio remains constant along the whole cone generator . Note that this was predicted earlier within the framework of the linear theory [7] .…”

“…In theoretical derivations it is more convenient to use r, as an independent variable, in view of the existence of the relationships (1 .3) . However, in practice determining the quantity r, is somewhat difficult, whereas there is no difficulty in determining the Mach number M E. From this point of view, using the Mach number ME as a governing parameter (as, for instance, in [4][5][6][7][8]) is preferable . In what follows the values of both parameters will be given when presenting the results .…”

“…If a conical body is immersed in a nonuniform gas flow, for instance in a radial flow, a scale length appears in the flow past the cone, so that it ceases to be self-similar . In that case conical flow exists only in a small vicinity of the sharp nose ; farther on the flow rearranges itself into a new limiting state which stabilizes at large distances from the body vertex .Supersonic source flows past sharp-nosed bodies were studied in [4][5][6][7] by means of approximate methods . These studies were restricted to the case of slender bodies in a hypersonic stream, so that the solutions obtained are valid only at small distances from the sharp nose .…”