Modified Crocco-Lees Mixing Theory for Supersonic Separated and Reattaching Flows

Abstract

Re-examination of the Crocco-Lees method has shown that the previous quantitative disagreement between theory and experiment in the region of flow up to separation was caused primarily by the improper C(K) relation assumed. A new C(K) correlation, based on low-speed theoretical and experimental data and on supersonic experimental results, has been developed and found to be satisfactory for accurate calculation of two-dimensional laminar super sonic flows up to separation. A study of separated and reattaching regions of flow has led to a physical model which incorporates the concept of the dividing streamline and the results of experiment. According to this physical model, viscous momentum transport is the essential mechanism in the zone between separation and the beginning of reattachment, while the reattachment process is, on the contrary, an essentially inviscid process. This physical model has been translated into Crocco-Lees language using a semi-empirical approach, and approximate C(K) and F(K) relations have been determined for the separated and reattaching regions. The results of this analysis have been applied to the problem of shock wave-laminar boundary layer interaction, and satisfactory quantitative agreement with experiment has been achieved.