Direct numerical simulation of supersonic turbulent expansion corner with shock impingement

Abstract

This study conducted a direct numerical simulation of an incident shock wave impinging at an angle of 33.2° on a 12° supersonic turbulent expansion corner at Mach 2.25 to determine the influence of expansion on the physics of interaction. The point of nominal impingement was located at the tip of the expansion corner. This scenario was compared in detail with interactions in the case of a flat plate under the same inflow conditions. The expansion led to a significant reduction in the wall pressure and the size of the separation bubble. The pre-multiplied spectra of the fluctuating wall pressure indicated that the motion induced by the low-frequency shock was strongly inhibited by the presence of an expansion corner. The root mean-squared wall pressure declined rapidly downstream of the corner, and relaxed at a nearly constant level very close to its upstream value. The evolution of the reattached boundary layer was analyzed in terms of its velocity profile, map of anisotropic invariance, and turbulent kinetic energy, and a quick recovery process was clearly identified. Moreover, the analysis of decomposition of the mean skin friction revealed the dominant contribution of the turbulent kinetic energy regardless of the effect of expansion. Unlike in the case of flat-plate interaction, the component of negative spatial growth became positive owing to large positive streamwise heterogeneity, and could be neglected. Bidimensional empirical-mode decomposition was used to decompose the fluctuations into four modes with specific spanwise length scales, and the primary mechanism for the generation of skin friction was linked to small-scale structures in the near-wall region.