A field inversion and symbolic regression enhanced Spalart–Allmaras model for airfoil stall prediction

Abstract

A data-driven turbulence modeling method based on symbolic regression (SR) is proposed in this paper to enhance the prediction accuracy of the Spalart–Allmaras (SA) model for airfoil stall. Unlike traditional methods that rely on neural networks and lack physical interpretability, this paper utilizes SR to establish an analytic expression mapping local flow field variables to the SA model correction factor β. The training data are obtained through field inversion with the discrete adjoint method in the flow field of the S809 airfoil. Additionally, a relearning approach proposed in this paper is applied to the SR process to address the issue arising from the multi-solution nature of field inversion. The SA model embedded with β, referred to as the SA-SR model, can be integrated into computational fluid dynamics solvers with negligible computational cost. The generalization performance of the SA-SR model is tested under various conditions and airfoil types. The results indicate that the new model improves the predictive capability for airfoil stall without compromising the performance of the baseline SA model for attached flows.