Modeling the effect of upstream temperature fluctuations on shock/homogeneous turbulence interaction

Abstract

Reynolds-averaged Navier–Stokes (RANS) equations can yield significant error when applied to the interaction of turbulence with shock waves. This is often due to the fact that RANS turbulence models do not account for the underlying physical phenomena correctly. For example, in the presence of appreciable temperature fluctuations in the upstream flow, turbulence amplification across a shock is significantly affected by the magnitude of the temperature fluctuations and the sign of the upstream velocity-temperature correlation [Mahesh et al., J. Fluid Mech. 334, 353 (1997)]. Standard two-equation models with compressibility correction do not reproduce this effect. We use the interaction of homogeneous isotropic turbulence with a normal shock to suggest improvements to the k-ϵ model. The approach is similar to that presented in an earlier work [Sinha et al., Phys. Fluids 15, 2290 (2003)]. Linear inviscid analysis is used to study the effect of upstream temperature fluctuations on the evolution of turbulent kinetic energy k across the shock. The dominant mechanisms contributing to the k amplification are identified and then modeled in a physically consistent way. The dissipation rate equation is also altered based on linear analysis results. The modifications yield significant improvement over existing two-equation models and the new model predictions are found to match linear theory and direct numerical simulation data well.