Blunt Body Viscous Layer with and without a Magnetic Field

Abstract

The present paper is mainly concerned with the solution for the viscous flow in the shock layer about the stagnation region of a sphere in hypersonic flow. The Reynolds numbers considered are in a range too low to apply usual boundary layer theory within the shock layer, but are large enough that the shock wave may be regarded as a discontinuous surface. This viscous layer problem has been studied previously by Probstein. With the assumption of constant density in the shock layer an analytic solution is applied to this problem both with and without an applied magnetic field. This solution makes use of the fact that the ratio of the density ahead of the shock to that behind the shock (ε) is small. The solution has been found in analytic form to first order in ε. In the nonmagnetic case numerical results for both the shock wave detachment distance and skin friction are presented for a value of ε = 0.1 and they are shown to be in good agreement with the exact numerical calculations of Probstein and Kemp. Numerical results are also presented on the effect of an applied magnetic field on both the shock wave detachment distance and skin friction. It is found that for a fixed value of ε and Reynolds number the skin friction decreases and the detachment distance increases for increasing values of the magnetic field parameter S which is proportional to the magnetic pressure divided by the total pressure.