Modeling shock unsteadiness in shock/turbulence interaction

The RANS (Reynolds averagedNavier-Stokes) equations can yield significant error when applied to practical flows involving shock waves. We use the interaction of homogeneous isotropic turbulence with a normal shock to suggest improvements in the k-ε model applied to shock/turbulence interaction. Mahesh et al.¹ and Lee et al.² present direct numerical simulation (DNS) and linear analysis of the flow of isotropic turbulence through a normal shock, where it is found that mean compression, shock unsteadiness, pressurevelocity correlation and upstream entropy fluctuations play an important role in the interaction. Current RANS models based on the eddy viscosity assumption yield very high amplification in the turbulent kinetic energy, k, across the shock. Suppressing the eddy viscosity in a shock improves the model predictions, but is inadequate to match theoretical results at highMach numbers. We modify the k-equation to include a term due to shock unsteadiness, and model it using linear analysis. The dissipation rate equation is similarly altered based on linear analysis results. These modifications improve the model predictions considerably, and the new model is found to match the linear theory and DNS data well.