A Low-Reynolds Number Explicit Algebraic Stress Model

A low-Reynolds number extension of the explicit algebraic stress model, developed by Gatski and Speziale (GS) is proposed. The turbulence anisotropy $Πb$ and production to dissipation ratio $P∕ϵ$ are modeled that recover the established equilibrium values for the homogeneous shear flows. The devised (⁠$Πb$⁠, $P∕ϵ$⁠) combined with the model coefficients prevent the occurrence of nonphysical turbulence intensities in the context of a mild departure from equilibrium, and facilitate an avoidance of numerical instabilities, involved in the original GS model. A new near-wall damping function $fμ$ in the eddy viscosity relation is introduced. To enhance dissipation in near-wall regions, the model constants $Cϵ(1,2)$ are modified and an extra positive source term is included in the dissipation equation. A realizable time scale is incorporated to remove the wall singularity. The turbulent Prandtl numbers $σ(k,ϵ)$ are modeled to provide substantial turbulent diffusion in near-wall regions. The model is validated against a few flow cases, yielding predictions in good agreement with the direct numerical simulation and experimental data.