Improvement of turbulence model for predicting shock-wave–boundary-layer interaction flows by reconstructing Reynolds stress discrepancies based on field inversion and machine learning

Reynolds-averaged Navier–Stokes (RANS) models have been the mainstay of engineering applications in recent years, and this trend will likely persist in the coming decades. However, the ability of RANS methods to predict complex flows, such as shock-wave/boundary-layer interaction (SWBLI) flows, is inadequate. In the absence of a breakthrough in traditional turbulence modeling, data-driven modeling has emerged as a new paradigm in turbulence research. In this study, a field-inversion and machine-learning framework based on the regularized ensemble Kalman filter (REnKF) was implemented to enhance the predictive ability of the Menter shear-stress transport (SST) model for SWBLI flows. This approach directly modifies the norm and eigenvalues of the Reynolds stress tensor obtained by RANS methods to overcome the limitations of the Boussinesq hypothesis. The spatial distributions of Reynolds stress discrepancies are initially obtained from experimental data using the REnKF method and a parameterization method based on geometric transformation for improved prediction of the training case. Then, a mapping function from local flow variables to discrepancy fields is constructed by selecting appropriate input features and combining them with a random forest algorithm. Our results verify the effectiveness of the framework for SWBLI flows of varying strengths and types. The results also demonstrate that the SST model's simulation ability for SWBLI flows has been significantly improved, providing more accurate predictions of separation and reattachment, considerably lowering the prediction errors for relevant flow variables, and verifying the generalization ability of the proposed framework.