Improvement of the SST model for streamline curvature effect based on field inversion and symbolic regression

Due to the coordinate-invariant nature of traditional eddy viscosity models, it is challenging to accurately predict flows with specific directional influences without modification. The rotation of reference frames or curved wall flows significantly increases the complexity of turbulence, making the accurate prediction of directional turbulent flows crucial, especially for aircrafts which have curved walls and wings. This paper improves the eddy viscosity coefficient by considering the mathematical principles of directional flow effects during model correction, using a data-driven framework of field inversion and symbolic regression. The development is oriented towards an SST-SC model suitable for flows with streamline curvature. The iterative Kalman filter algorithm is used to solve the inversion problem, and the inversion results serve as training data for the correction model, which is trained through symbolic regression. A series of representative cases are employed for model verification and validation. The findings indicate that the inversion process produces favorable results, and the enhanced model developed using the inversion data exhibits good generalizability.