Explicit algebraic Reynolds stress model (EARSM) for compressible shear flows

We develop an explicit algebraic Reynolds stress model (EARSM) for high-speed compressible shear flows and validate the model with direct numerical simulation (DNS) data of homogeneous shear flow and experimental data of high-speed mixing-layers. Starting from a pressure–strain correlation model that incorporates compressibility effects, the weak-equilibrium assumption is invoked to derive the EARSM closure expression. The resulting closure is fully explicit and physically realizable and is a function of mean flow strain rate, rotation rate, turbulent kinetic energy, dissipation rate, and gradient Mach number. Homogeneous shear flow calculations show that the model captures the asymptotic behavior of DNS quite well. Linear EARSM calculations of a plane supersonic mixing-layer are performed, and comparison with experimental data shows good agreement. Salient results are agreement of streamwise velocity similarity profiles, mixing-layer spreading rates, and capturing the Langley curve trend.