A symbolic regression-based modification to the Bradshaw's assumption in the Menter shear-stress transport turbulence model under adverse pressure gradient

This paper proposes an enhanced turbulence model (SST-sr) to improve the predictive accuracy of the Menter shear-stress transport (SST) model in adverse pressure gradient (APG) flows. The original Menter SST model incorporates the Bradshaw's assumption to introduce the transport effects of Reynolds stress. While this assumption enhances model's sensitivity to APG, it enforces an equilibrium condition between the production P k and dissipation ϵ of turbulent kinetic energy (TKE) (namely P k ≈ ϵ ) across most turbulent boundary layer regions. This means the persistent application of Bradshaw's assumption under APG conditions ( P k > ϵ ) will artificially suppress the magnitudes of Reynolds stress and TKE, causing premature flow separation. To improve this limitation while retaining the Bradshaw's assumption, we propose a modification to its parameter a 1 . Based on eddy viscosity principles, a relationship is hypothesized between a 1 and the local turbulence parameter P k / ϵ . Given discrepancies in SST-modeled P k / ϵ distributions, we employ the symbolic regression (SR) approach to derive an approximation function of P k / ϵ from Direct Numerical Simulation (DNS) data by using local turbulence parameters k S / ϵ and l o g 10 ( y + ) . The function is modified into SST model in the form of a series of auxiliary functions, establishing the SST-sr model on this basis. The performance of the SST-sr model is verified across one zero pressure gradient (ZPG) and four APG test cases, with systematic comparisons against baseline SST predictions. The results demonstrate that the SST-sr model can effectively mitigate the premature separation issue of the SST mode, while enhancing the prediction accuracy for Reynolds stress, TKE, and average velocity profiles.