An evaluation and correction method for the shear stress transport model based on symbolic regression in three-dimensional flow

The Menter shear stress transport (SST) turbulence model introduces the Bradshaw assumption to establish a local equilibrium condition in most regions of turbulent boundary layers, where the production (Pk) approximately balances the dissipation rate (ε). However, under adverse pressure gradient conditions, this equilibrium may suppress the development of turbulent kinetic energy within the boundary layer, leading to an earlier separation location. To address this limitation, the SST-symbolic regression evolution (SRE) correction model developed based on the SR method has been shown to effectively delay the separation point in two-dimensional flows. To further assess its performance in complex three-dimensional flows, the ONERA M6 wing is selected as a representative test case for validation. Furthermore, based on the original streamwise correction, the same formulation is extended to the spanwise direction to achieve a coupled modification in both the streamwise and spanwise directions, aiming to investigate anisotropic characteristics in three-dimensional flows. The results suggest that the SST-SRE method provides improved predictions over the baseline SST model for the selected ONERA M6 and ARA M100 cases, especially in regions affected by three-dimensional separation. Moreover, the coupled SST-symbolic regression evolution three-dimensional correction model effectively alleviates the upwash phenomenon in corner regions, thereby enhancing the model's accuracy in predicting complex three-dimensional flows.