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

This paper addresses the issue of predicting separated flows with Reynolds-averaged Navier-Stokes (RANS) turbulence models, which are essential for many engineering tasks. Traditional RANS models usually struggle with this task, so recent efforts have focused on data-driven methods such as field inversion and machine learning (FIML) to correct this issue by adjusting the baseline equations. However, these FIML methods often reduce accuracy in attached boundary layers. To address this issue, we developed a "conditioned field inversion" technique. This method adjusts the corrective factor beta (used by FIML) in the shear-stress transport (SST) model. It multiplies beta with a shield function fd that is off in the boundary layer and on elsewhere. This maintains the accuracy of the baseline model for the attached flows. We applied both conditioned and classic field inversion to the NASA hump and a curved backward-facing step, creating two datasets. These datasets were used to train two models: SR-CND (symbolic regression-conditioned, from our new method) and SR-CLS (symbolic regression-classic, from the traditional method). The SR-CND model matches the SR-CLS model in predicting separated flows in various scenarios, such as periodic hills, the NLR7301 airfoil, the 3D SAE (Society of Automotive Engineers) car model, and the 3D Ahmed body, and outperforms the baseline SST model in the cases presented in the paper. Importantly, the SR-CND model maintains accuracy in the attached boundary layers, whereas the SR-CLS model does not. Therefore, the proposed method improves separated flow predictions while maintaining the accuracy of the original model for attached flows, offering a better way to create data-driven turbulence models.