A gPC-based approach to uncertain interaction of oblique shocks and supersonic mixing layers

The present paper focuses on the stochastic response of a two-dimensional shock wave impingement on a spatially evolving mixing layer to parametric uncertainties. Both the oblique shock angle and the convective Mach number are considered as random parameters and the generalized Polynomial Chaos (gPC) theory is coupled with standard deterministic numerical simulations through a spectral collocation projection methodology. In this framework, the two input parameters investigated are considered as random variables with a given probability distribution over the range of investigation prescribed. The uncertainty is then propagated through the computational model to statistically quantify their effect on the results. This study allows for a better understanding of the flow sensitivity to such uncertainties and underlines the coupling process between the stochastic parameters. Some results of direct numerical simulations of the multicomponent, compressible, reactive Navier-Stokes equations are reported here for the particular case of a two-dimensional mixing layer. Special emphasis is placed on the effects associated with heat release.