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On the Presence of Shocks in Mixed Subsonic-Supersonic Flow Patterns

1953; Elsevier BV; Linguagem: Inglês

10.1016/s0065-2156(08)70210-2

0065-2156

Gottfried Guderley,

Spacecraft Dynamics and Control

This chapter shows that the nonexistence of solutions of boundary value problems for the transonic potential flow past a body has, in general, no solution. The nonexistence of the potential flow is a mathematical fact that follows without further physical argument from the properties of the boundary value problem. Even slight changes of the contour in an embedded supersonic region make the flow incompatible with a potential flow. Frankl's argument shows the nonexistence of a potential flow for a general contour in a very simple and concise form. The type of boundary value problem arising is studied using suitable examples. The chapter starts with the mathematical discussion and brings the physical considerations afterward. The mathematical basis is a discussion of the sign of the Jacobian for mapping from the physical to the hodograph plane. In a supersonic region, which is embedded in a subsonic flow, these oscillatory solutions can be expected for physical reasons. A flow pattern is described that makes the occurrence of a wavy flow in the supersonic region plausible. The present investigations consider the change of the contour in a steady flow and ask which other steady flow will arise. They predict that at the end of the supersonic region, a difficulty will arise. It must be emphasized that this difficulty does not mean a major change of the flow pattern as a whole; a major deviation from the original flow will be experienced only in the vicinity of the exit corner of the supersonic region.