Theory-based prediction of separation angle and peak pressure for laminar separated hypersonic compression corner flows

Abstract

Interactions between shock waves and the boundary layer will cause high pressure loads and severe heating locally on the material surface in hypersonic separation–reattachment flows. In this paper, theoretical modeling is employed to study the separation angle and peak pressure of hypersonic compression corner flows with separated regions at low-to-medium Reynolds number. According to the characteristics of wall pressure distribution and flow field structures, an equivalent double shocks inviscid flow model for peak pressure is introduced. Based on this model, combining the “free-interaction theory,” formulas for the separation angle and peak pressure with freestream parameters (Mach number and Reynolds number) and the geometry corner angle are derived, and the reasonability and effectiveness are also shown by the numerical data provided by the direct simulation Monte Carlo method. It is revealed that the separation angle is almost independent of the freestream Mach number, and the ratio of peak pressure to freestream pressure is approximately proportional to the square of the freestream Mach number under strong viscous interaction conditions. Moreover, it is indicated that present theoretical results can be extended to axisymmetric flows through the discussion of hypersonic separated flows generated by a hollow cylinder-flare geometry.