An innovative modification to the Menter shear-stress transport turbulence model employing the symbolic regression approach

Drawing from the non-equilibrium link between the production P_k and dissipation ϵ of turbulent kinetic energy (TKE), we advocate for the introduction of a limiter to modulate the TKE production term within the Menter shear-stress transport (SST) model. The original SST model is made more sensitive to the adverse pressure gradient (APG) by Bradshaw's assumption. Bradshaw's assumption introduces the equilibrium condition P k / ϵ = 1 in most regions of the turbulent boundary layer. In the APG flows with P k ≫ ϵ , the equilibrium condition suppresses the magnitude of TKE (k) within the boundary layer, resulting in an early separation problem. To address this issue, we employ the symbolic regression (SR) to scrutinize the physical correlation between P k / ϵ and local turbulence parameters, obtaining an approximate function F_SR that encapsulates the relationship between P k / ϵ , S k / ϵ , and y⁺ in the APG flow. Following its incorporation into the original SST model in the form of a limiter, the F_SR evolves into the SST-Symbolic Regression Evolution model. The SST-SRE is then applied to four cases with APGs. The modification leads to an increase in the skin-friction coefficient C_f in the APGs region and causes a downstream shift in the separation location, improving the consistency with high-accuracy data and experimental results. It is demonstrated that this correction can improve the early separation problem in the Menter SST turbulence model.