Accurate numerical simulations of shock–turbulence interaction (STI) are conducted with a hybrid monotonicity-preserving–compact-finite-difference scheme for a detailed study of STI in variable density flows. Theoretical and numerical assessments of data confirm that all turbulence scales as well as the STI are well captured by the computational method. Linear interaction approximation (LIA) convergence tests conducted with the shock-capturing simulations exhibit a similar trend of converging to LIA predictions to shock-resolving direct numerical simulations (DNS). The effects of density variations on STI are studied by comparing the results corresponding to an upstream multi-fluid mixture with the single-fluid case. The results show that for the current parameter ranges, the turbulence amplification by the normal shock wave is much higher and the reduction in turbulence length scales is more significant when strong density variations exist. Turbulent mixing enhancement by the shock is also increased and stronger mixing asymmetry in the postshock region is observed when there is significant density variation. The turbulence structure is strongly modified by the shock wave, with a differential distribution of turbulent statistics in regions having different densities. The dominant mechanisms behind the variable density STI are identified by analysing the transport equations for the Reynolds stresses, vorticity, normalized mass flux and density specific volume covariance.
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 density play in the modification of turbulence by the shock wave are identified. Statistical analyses of the velocity gradient tensor (VGT) show that the 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 velocity gradient tensor, PDF(Q * , R * ), 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 symmetrical PDF(Q * , R * ) in heavy fluid regions, while the light fluid regions retain the characteristic tear-drop shape. To understand this behavior and the return to "standard" turbulence structure as the flow evolves away from the shock, Lagrangian dynamics of the VGT and its invariants are 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. arXiv:1908.05327v1 [physics.flu-dyn]
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