Data-Augmented Turbulence Modeling with Physics-Driven Corrections for Separated Compressible Flow

Accurate prediction of compressible separated flows remains a challenge for typical Reynolds-averaged Navier-Stokes (RANS) turbulence models. The field inversion and machine learning (FIML) method is employed to enhance the performance of a RANS model for separated compressible flow. This study introduces novel input features that incorporate compressibility and rotational effects into the FIML framework. The novel input features are based on physically derived RANS corrections, consistent with practices recommended for modeling turbulent flows. A data-augmented RANS model is trained using compressible separated flow over a two-dimensional axisymmetric body. The trained model is evaluated under different flow conditions and geometries, including a three-dimensional axisymmetric body at non-zero angles of attack. The trained model successfully captures separated flows in a wide range of Mach numbers, from subsonic to supersonic. The improved predictive performance of the trained RANS model is attributed to reduced eddy viscosity in the separated region. The contribution of each input feature to eddy viscosity reduction is further quantified using the Shapley additive explanation method.