Modal analysis with proper orthogonal decomposition of hypersonic separated flows over a double wedge

The unsteady behavior of an Edney type-IV shock-dominated hypersonic separated flows over a double-wedge geometry for different gas compositions are studied using the time-accurate direct-simulation Monte Carlo (DSMC) and window proper orthogonal decomposition (WPOD) methods. Near steady state, we find that the POD modes can be correlated with the global modes predicted by linear stability theory. The WPOD analyses show that the first mode for each flow quantity outlines the corresponding steady-state solution and that higher spatial POD modes are pronounced in the bow shock, separation, and transmitted shocks and shear layers, thereby coupling these regions. The temporal modes corresponding to each macroscopic flow quantities are observed to have the same decay rates. The effects of three types of gas compositions - molecular nitrogen, nonreacting air consisting of molecular nitrogen and oxygen, and reacting air with oxygen dissociation and the N2 + O exchange reactions - on flow stability are considered. Nonequilibrium thermochemical effects are found to change the shock structures, the size of the separation region, and the time required to reach steady state. The decay rate of the least damped eigenmode for the chemically reacting air case is found to be smaller in comparison to the nonreacting air case since the translational temperatures downstream of the bow shock are lower due to endothermic chemical reactions. The simulated heat fluxes and shock standoff distance are found to be in qualitative agreement with recent experiments where the freestream density is eight times higher than the current DSMC computations.