Applications of Explicit Algebraic Reynolds Stress Models to Transonic Turbulence Flow Simulations Based on Discontinuous Galerkin Methods

Two applications of the non-linear eddy-viscosity model EARSM are presented in the simulations of transonic turbulent flow involving shock waves and other related complex features. The simulations are implemented applying an in-house CFD program based on the unstructured discontinuous Galerkin method, an alternative discretization method of the classical finite volume one to precisely capture the flow features. A series of turbulence feature variables in boundary layers are comparatively observed and analyzed. For the first case of transonic flow over a bump, the redistribution effect of Reynolds stress components rooted in the non-linear constitution relation promotes streamwise turbulence fluctuation and suppresses the normal one in boundary layer, comparing with the traditional linear constitution relation, especially when passing the shocks. The production magnitudes of the turbulence shear stress and kinetic energy for the non-linear model show slightly more sensitive to perturbations, such as the occurrence of shock front or compression corner, than the linear one. For the second case of a transonic turbine vane, similar redistribution effect of the non-linear model is also verified on suction surface around the strong shock. The straightforward redistribution effect is absent on pressure surface around middle part of the vane with favorable pressure gradients. There the non-linear model evaluates higher magnitudes of streamwise, normal and shear Reynolds stress components than the linear one, thus resulting locally stronger heat convection and higher surface temperature.