Analysis of Imbedded Transonic Shock Wave Influence on Turbulent Boundary Layer Separation

摘要

A strong viscous-inviscid interaction model has been developed for predicting the detailed properties of the flow in the vicinity of an imbedded transonic shock wave interacting with a turbulent boundary layer in cases where the shock wave is of sufficient strength to result in flow separation. In this interaction model the inviscid flow is analyzed with a compressible stream function analysis specifically developed for mixed subsonic-supersonic flow regions. In the present effort this analysis has been extended to include upstream vorticity effects and the boundary-layer displacement effects. Numerous calculations are presented which demonstrates the capability of this analysis to predict transonic rotational flow. The viscous analysis in this interaction model is a newly developed inverse boundary-layer analysis which accounts for normal pressure gradients and imbedded shock waves. The equations are solved with a coupled implicit finite-difference scheme subject to the condition that the flow at the edge of viscous layer merges asymptotically with the outer inviscid flow. A model problem has been analyzed with this generalized inverse boundary-layer procedure and no stability problems were encountered.