Stability analysis of supersonic entropy layers including shock effects

Abstract

The prediction of the laminar/turbulent transition location in supersonic boundary layers plays an important role to accurately compute aerodynamic forces and heating rates for the aerodynamic design and control of hypersonic vehicles. The stability characteristics of supersonic boundary layers depend e.g. on nose bluntness, transverse curvature, wall temperature, shock waves, etc. Most parameters can be theoretically investigated by performing conventional stability calculations with vanishing or asymptotic perturbation conditions at the far field. In this approach the formation of a shock in front of the leading edge of a blunt body is ignored. However, to improve the understanding of the interaction between instability waves originating inside supersonic boundary layer with those coming from the inviscid entropy layer, the presence of the shock has to be taken into account.This paper presents a method, how shock effects can be physically consistently included in stability calculations. The outer free-stream boundary conditions are replaced by appropriate shock conditions. The required perturbation equations can be derived from the linearized unsteady Rankine-Hugoniot equations, accounting for the effect of shock oscillations due to perturbated waves which originate from the flow field windward of the shock.