Development of a Generalizable Data-Driven Turbulence Model: Conditioned Field Inversion and Symbolic Regression

This seminar presents a series of interpretable and generalizable data-driven methods for turbulence modeling. The Reynolds-averaged Navier-Stokes (RANS) equations are widely used in engineering, but their turbulence models often struggle with separated flows. While recent advances in data-driven techniques have improved model accuracy in complex separated flows, these models frequently lack interpretability and generalizability, sometimes even reducing accuracy in simple wall-attached flows. Our first approach integrates symbolic regression (SR) with the field inversion and machine learning (FIML) framework to derive an interpretable analytical expression for the correction term β using field inversion data. This expression demonstrates generalizability across diverse cases, including 3D separated flows not included in the training set. However, it occasionally fails to consistently maintain the baseline model's accuracy in wall-attached flows. To address this limitation, we introduce a conditioned field inversion approach that confines corrections to regions outside the attached boundary layer. The resulting SR-CND model retains the capability of correcting separated flows comparably to classical field inversion, while preserving accuracy in attached boundary layers - a feature lacking in the classical method. This model has been validated through several 2D and 3D cases, including configurations from the high-lift prediction workshops (HPWs). Results demonstrate that the flow separation prediction accuracy is superior to that of the baseline model. Finally, we propose a non-local modeling approach to further enhance generalizability. By constructing a transport equation for the correction term β and calibrating its parameters for separated flows using data-driven methods, this model shows improved accuracy in various separated flows compared to the SR-CND model.