A production term correction for Menter shear-stress transport turbulence model for adverse pressure gradient flows before separation

To address the early separation problem in the Menter Shear-Stress Transport (SST) turbulence model, a correction for the Turbulent Kinetic Energy (TKE) production term, P_k, is introduced to account for the effect of the Adverse Pressure Gradient (APG). The correction is determined based on the distribution of P_k in the APG region before separation. When the friction coefficient C_f is decomposed, its direct dependence on P_k is clearly observed. However, with the introduction of Bradshaw’s assumption, P_k in the SST turbulence model is over-suppressed, resulting in a lower inner peak or no significant inner peak distribution at all. To address this problem, this paper proposes a Gaussian function, H_Gauss, which corrects the numerical values of P_k involved in the calculation of the Menter SST model by focusing on the inner peak region of P_k. The modified SST model is then applied to four cases with APGs. The modification leads to an increase in the wall friction coefficient C_f in the APG region and causes a downstream shift in the separation location, improving the model’s 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.