Dynamics of isoconcentration surfaces in weak shock turbulent mixing interaction

Abstract

When developing closures for nonpremixed turbulent combustion ocuuring in supersonic regime, the probability density function is an attractive approach. It is required, however, to find an appropriate strategy to close the diffusive (mixing) part of the problem. Within supersonic turbulent combustion devices, mixing layers interact with shock waves and compression zones. Hence, it is crucial to seek out basic effects related to pressure jumps needing to be accounted for in modeling mixing. Direct numerical simulations are performed to investigate properties of mixing in weakly nonisentropic flows. The simulations correspond to the interaction between a weak shock and a mixing zone. Different conditions for injecting the mixing zone upstream from the weak shock are considered in the simulations. First, it is observed that the appearance of secondary pressure waves attached to the weak shock can be justified in the light of previous studies devoted to shock vortex interactions. Results suggest that the hypothesis of a linear relationship between the frequency of mixing and the inverse of an eddy breakup time fails within the interaction zone. Then, a statistical formalism, suitable to describe isoconcentration surfaces, is chosen to study increase in mixing rate induced by compressions. It is observed that the details of properties of shock turbulent mixing interaction strongly depend on the degree of mixing upstream from the compression. In particular, for a low mixing rate upstream of the pressure jump, the total stretch of surfaces is more controlled by curvature than by in-plane strain rate, whereas blob type injection leads to modifications of stretch induced by strain rate. Moreover, the strain rate becomes negative within the compression zone, and it rapidly relaxes to positive values downstream from the pressure jump, whereas the impact of weak shocks on the curvature of the field is sustained far downstream from the compression zone. Conclusions are drawn for further developments in modeling mixing.