Simplified Reynolds-stress model based detached eddy simulations in fixed coordinate system

The hybrid Reynolds-Averaged Navier-Stokes (RANS) / Large Eddy Simulation (LES) method has gained prominent attention in simulating aeronautical separation flows. Improved Delayed Detached Eddy Simulation (IDDES) model is one of the hybrid RANS/LES methods that has received positive evaluations, but its performance heavily depends on the RANS model used. In this paper, a new IDDES under the Semi-differential Reynolds-Stress Model (Semi-RSM) framework is proposed, which inherently accounts for the modeled stress anisotropy like the traditional RSM-based IDDES but requires less cost. The enhanced efficiency benefits from the algebraic treatment of the Reynolds shear stress equations in the traditional RSM, namely, the original seven transport equations are reduced to four. Four test cases are simulated to assess the performance of the proposed Semi-RSM IDDES. The first case is decay of isotropic turbulence, which helps calibrate the detached eddy simulation coefficients in the new model. The next two cases are separated flows over straight wing and delta wing, showing that Semi-RSM IDDES outperforms the traditional linear eddy viscosity based IDDES in high angles of attack flows. The final case is three-element airfoil, where modeling the Reynolds stress anisotropy in separated shear layer is crucial to predict the slat flow statistics.