Asymptotic defect boundary-layer theory applied to hypersonic flows

Abstract

For hypersonic re-entry flows, the bow shock wave upstream of the spacecraft is the cause of an inviscid vortical flow in the shock layer. PrandtPs equations are unable to cope with outer flow vorticity, whereas Van Dyke's matched asymptotic expansions approach no longer gives a good matching of the viscous and inviscid solutions when the boundary layer is thick. A new approach, using a defect formulation in the viscous region together with a matched asymptotic expansions technique, has been developed. The so-derived equations are consistent with PrandtPs or Van Dyke's equations. Fair predictions are achieved for incompressible flows with external vorticity only with second-order solutions because displacement effects have to be accounted for, whereas for hypersonic flows where displacement effects are weak, a good agreement with Navier-Stokes solutions is obtained with a first-order approach.