IMPROVEMENT OF SST TURBULENCE MODEL IN ADVERSE PRESSURE GRADIENT FLOW

Accurate prediction of adverse pressure gradients and flow separation is critically important in numerous high-performance engineering industries such as aircraft design, engine design, and mechanical engineering. However, widely used Reynolds-averaged Navier-Stokes (RANS) models within the engineering community, such as the Spalart-Allmaras (SA) turbulence model, often exhibit unsatisfactory performance in predicting adverse pressure gradients. Although the Shear stress transport (SST) k-ω turbulence model incorporates the Bradshaw’s assumption which improves the sensitivity of the model to adverse pressure gradient influence, its predictions under adverse pressure gradients still exhibit deviations, manifesting in practical applications as premature separation prediction and delayed reattachment. This paper investigates the underlying causes of the SST model's inaccuracy in predicting separation under adverse pressure gradients by analyzing its construction mechanism and governing equations, integrated with a wall friction decomposition formula. The analysis of this paper identifies the Bradshaw’s assumption as a key contributor to the inaccuracy. Specifically, the assumption imposes a forced equilibrium between the turbulent kinetic energy production terms and dissipation terms. This constraint artificially limits the generation of Reynolds stress and turbulent kinetic energy, consequently diminishing the flow's ability to resist separation. To address this limitation, an improved SST turbulence model is proposed, namely SST-m turbulence model. The modification involves dynamically scaling the structural parameter a_1 based on the local ratio of turbulent kinetic energy production to dissipation terms within critical flow regions. The enhanced model was rigorously validated using benchmark cases including flow over a Gaussian bump, a two-dimensional turbulence separation bubble, and a two-dimensional hump. The results demonstrate that, for flow separation induced by adverse pressure gradients, the modified model achieves superior predictive capabilities for both separation onset and reattachment locations compared to the original SST model. Furthermore, calculations of Reynolds stress and turbulent kinetic energy distributions show varying degrees of enhancement, confirming the model's improved physical fidelity.