Interaction of shock waves with turbulent flow has significant effect in high-speed flows. The shock wave amplifies the turbulent fluctuations and the amplification can be highly anisotropic. We study these aspects in the interaction of homogeneous isotropic turbulence with a normal shock wave. Existing Reynolds stress models are applied to this model problem and their accuracy is evaluated against available DNS data (Larsson & Lele, 2009). The model predictions match data for weak shocks, but significantly overpredict Reynolds stresses for high Mach numbers. We then propose an improvement to include the damping effect of unsteady shock oscillations. It is based on linear interaction analysis applied to canonical shock-turbulence problem.
(Sinha et al., 2003). The turbulent fluctuations make the shock unsteady, resulting in a coupling between the instantaneous shock speed and the turbulent velocity fluctuations. This leads to a damping effect on the amplification of shock-normal Reynolds stress. We apply the shock-unsteady correction proposed by Sinha et al. (2003) to the Gerolymos et al. (2004) Reynolds stress model, where the model closure coefficient is based on linear theory results. It brings down the amplification of both streamwise and transverse Reynolds stresses significantly to match DNS data over the entire range of Mach numbers. Additional changes in the turbulent dissipation rate equation and anisotropy effects in the dissipation rate are proposed. The new Reynolds stress model is a significant improvement over existing models, especially for high Mach numbers, and it compares well with DNS data of canonical shock-turbulence interaction.
The publications in 2015 do not have abstract in it. Pl add the following abstract to the Russel's paper and Jagadish's paper is to be reloaded with details provided above. Also by moving the cursor to the abstract link, the abstract should get displayed automatically without clicking. If possible, pl do this change and to other abstracts too.