Modification of Reynolds-stress model with two-component limit for predicting separated flows

Complex vortical flows significantly affect turbomachinery performance, making their accurate prediction critical, especially under off-design conditions. Conventional linear eddy viscosity models struggle to accurately predict these flow features, mainly associated with flow separation. The Reynolds-stress model (RSM), which closes at the second-order moment level, shows potential to improve the prediction of turbulence non-equilibrium and anisotropy. However, the simulation accuracy is sensitive to the modeling of the pressure–strain term. To improve the predictive accuracy in separated flows, a modified RSM is proposed, which incorporates a cubic pressure–strain term derived from the two-component limit (TCL) and a linear pressure–strain term based on the Launder–Reece–Rodi (LRR) model in the near-wall region, and is referred to as the TCL/LRR-ω model. Inspired by Wilocox stress-ω model, the pressure–strain terms related to pressure-echo effects are omitted through incorporating the ω scale determination equation. A new blending function is designed to enhance sensitivity to three-dimensional vortex stretching. This blending could facilitate the transition from the near-wall linear pressure–strain term to the cubic term in the mainstream. Additionally, the Yap correction is employed to mitigate unphysical streamline backbending near reattachment. The proposed TCL/LRR-ω model and Speziale–Sarkar–Gatski/Launder–Reece–Rodi (SSG/LRR-ω) model are implemented in the OpenFOAM and compared with the shear stress transport (SST) model. Validation is conducted across three attached-flow cases and four separated-flow cases under adverse pressure gradients. The results for velocity profiles, Reynolds stresses, skin friction, and pressure coefficients demonstrate that the TCL/LRR-ω model outperforms both the SST and SSG/LRR-ω models in predicting mean flow and turbulence characteristics.