Density effects on post-shock turbulence structure and dynamics

Abstract

Turbulence structure resulting from multi-fluid or multi-species, variable-density isotropic turbulence interaction with a Mach 2 shock is studied using turbulence-resolving shock-capturing simulations and Eulerian (grid) and Lagrangian (particle) methods. The complex roles that density plays in the modification of turbulence by the shock wave are identified. Statistical analyses of the velocity gradient tensor (VGT) show that density variations significantly change the turbulence structure and flow topology. Specifically, a stronger symmetrization of the joint probability density function (PDF) of second and third invariants of the anisotropic VGT, PDF$(Q^{\ast },R^{\ast })$, as well as the PDF of the vortex stretching contribution to the enstrophy equation, are observed in the multi-species case. Furthermore, subsequent to the interaction with the shock, turbulent statistics also acquire a differential distribution in regions having different densities. This results in a nearly symmetric PDF$(Q^{\ast },R^{\ast })$ in heavy-fluid regions, while the light-fluid regions retain the characteristic tear-drop shape. To understand this behaviour and the return to ‘standard’ turbulence structure as the flow evolves away from the shock, Lagrangian dynamics of the VGT and its invariants is studied by considering particle residence times and conditional particle variables in different flow regions. The pressure Hessian contributions to the VGT invariants transport equations are shown to be not only affected by the shock wave, but also by the density in the multi-fluid case, making them critically important to the flow dynamics and turbulence structure.