Effect of vibrational excitation on vorticity amplification and transportation in shock/isotropic turbulence interaction : a numerical investigation

Abstract

The canonical shock/isotropic turbulence interaction (SITI) at high shock Mach numbers (Ms) is studied by conducting direct numerical simulation (DNS) for thermally perfect gas (TPG) and calorically perfect gas (CPG). Combining DNS with linear interaction analysis (LIA), the amplification of vorticity variance across the shock wave is studied. It is found that the changes in vortical velocity fluctuation amplitude and turbulent length scales under vibrational excitation have a competitive effect on vorticity amplification. The latter is dominant and leads to the transverse vorticity amplification increasing by 32.2% at Ms = 6.0. Based on the LIA theory, a vorticity amplification model for SITI considering vibrational excitation is established. Furthermore, the impact of vibrational excitation on the downstream vorticity transportation is examined through an analysis of the transport equation. The vibrational excitation strengthens both the vortex stretching and viscous dissipation of streamwise vorticity but only alters the viscous dissipation of transverse vorticity. Then, the vorticity transportations of different turbulent structures for CPG and TPG are compared. The comparison indicates that the increment of vortex stretching for streamwise vorticity variance is sustained by the enhanced turbulent structures corresponding to the stable-node/saddle/saddle, and the rapid decay of transverse vorticity variance for TPG is associated with the enhanced viscous dissipation of the nonfocal turbulent structure.