Data-augmented turbulence modeling by reconstructing Reynolds stress discrepancies for adverse-pressure-gradient flows

Turbulence modeling based on the Reynolds-averaged Navier-Stokes (RANS) method has been widely applied in industry, but its performance in some complex flows is far from satisfactory. The improvement of turbulence models based on the traditional framework has not made breakthrough progress for decades. In this study, a data-driven turbulence modeling framework based on the reconstruction of Reynolds stress discrepancies is used to aid in the improvement of turbulence models, with the Reynolds stresses of the shear-stress transport model being modified in the eigenspace. The large eddy simulation (LES) dataset of a set of bump cases is used to provide high-fidelity information on adverse-pressure-gradient flows for the modeling framework. First, the Reynolds stress tensors of RANS and LES are compared in terms of amplitude, shape, and orientation. Then, the random forest (RF) algorithm is employed to map the mean flow features to the Reynolds stress discrepancies. The well-trained RF model greatly improves the predictions of Reynolds stresses and other flow variables for the attachment and separation states and enables the numerical simulations to have predictive accuracy close to LES and computation time of the same order of magnitude as RANS.