Direct numerical simulation of supersonic bump flow with shock impingement

Abstract

Direct numerical simulations are carried out to identify the effects of shock impingement on the behavior of bump flow at free-stream Mach number of 2.25. Two cosine-shaped bump cases, with and without an impinging oblique shock at an angle of 33.2{degree sign}, are compared. The shock impingement exhibits a remarkable influence on the pattern of the shock system and on the size of the separation region. Spectral analysis finds that low-frequency unsteadiness is significantly enhanced by the impingement interaction, and the proper orthogonal decomposition highlights the low-frequency breathing motion of the separation bubble, which is accurately reconstructed using only the first ten low-order modes. Downstream of the bump, the Reynolds stress components and the turbulence kinetic energy both exhibit a general amplification, with the peaks reoccurring at outer wall-normal locations. Turbulent kinetic energy budget analysis shows the greatly increased production in the outer layer which is balanced by turbulent transport and dissipation. Anisotropy-invariant map analysis identifies enhanced isotropic turbulence in the vicinity of the bump, which is qualitatively modified into a two-component axisymmetric state around the reattachment point. In addition, the mean skin friction decomposition suggests that the shock impingement has little influence on the predominant contribution of turbulence kinetic energy production, apart from the spatial growth dominance at the bump summit in the absence of the impinging shock. Interestingly, a scale-decomposed analysis quantitatively demonstrates that the contributions of small-scale structures are attenuated, but those of large-scale ones are relatively increased, with a contribution of more than 80% with shock impingement.