Modeling shock unsteadiness in shockÕturbulence interaction

The RANS ~Reynolds averaged Navier–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 – e model applied to shock/ turbulence interaction. Mahesh et al. @J. Fluid Mech. 334, 353 ~1997!# and Lee et al. @J. Fluid Mech. 340, 22 ~1997!# 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, pressure-velocity correlation, and up-stream entropy fluctuations play an important role in the interaction. Current RANS models based on the eddy viscosity assumption yield very high amplification of 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 high Mach 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. © 2003 American Institute of Physics. @DOI: 10.1063/1.1588306#