On the Numerical Calculation of Detached Bow Shock Waves in Hypersonic Flow

Abstract

A method is described for calculating examples of hypersonic flow with a detached bow shock wave past a bluff axially symmetric body. The form of the shock wave is assumed, and the analysis is based on a Cauchy problem for the stream function in the subsonic region, where the motion is governed by a partial differential equation of elliptic type. Through analytic continuation into the complex domain, the Cauchy problem is reformulated in such a manner that it becomes properly set in the subsonic region. This leads to a stable scheme for computation of the flow by finite differences. Numerical examples at freestream Mach Number 5.8 are presented in which the flow is determined throughout the subsonic region, and, in particular, the detachment distance, the location of the sonic line, and the pressure distribution along the body are calculated. These results are in excellent agreement with experimental data obtained at the California Institute of Technology.