Inviscid Stability of Hypersonic Strong Interaction Flow Over a Flat Plate

Abstract

For the region near the leading edge in the viscous flow over a hypersonic flat plate, limit process asymptotic expansions have been studied for the Navier-Stokes equations that give two primary decks for the flow structure. The limit used for each is equivalent to keeping the Viscous Interaction Parameter χ fixed as the reciprocal of the Reynolds number ∈ → 0. The main focus is to incorporate the simultaneous effects of the finite vertical domain, strong curved shock induced by the effective 3/4 power body corresponding to the boundary layer thickness δ(x) and the stratification of the flow into the stability calculation, where x is the streamwise coordinate. The appropriate equations for the perturbations are obtained with a secondary limit of the amplitude parameter ε → 0. Parallel flow approximations and modal factorization of the x dependent part of the disturbances are naturally suppressed in this formulation. The initial-boundary value problem for these quantities is solved numerically by a marching technique. Results indicate that the disturbances generally decay for the specific heat ratio γ = 1.4 for typical initial distributions at the upstream station. On the other hand, amplification occurs with reduced shock layer thickness associated with lower values of γ.