Field Inversion Machine Learning for Predicting Time-Resolved Unsteady Flows in Dynamic Stall

This study develops an open-source field inversion machine learning (FIML) capability to improve RANS turbulence models' accuracy in predicting time-resolved unsteady flows for airfoil dynamic stall processes. We augment the Spalart-Allmaras (SA) turbulence model's production term with a spatial-temporal scalar field beta. We then solve an inverse problem by optimizing the beta field to minimize the RANS prediction errors for dynamic stall. The error is quantified as the lift time-series difference between the SA and reference k-w SST model. Due to the limitation of gradient-based optimization size, we choose the beta field at a few time instances as design variables and linearly interpolate the beta fields at other time steps. Once the optimal scalar fields are computed, we connect them with local flow features using a neural network (NN) model. The results show that the augmented SA model significantly reduces the time-resolved unsteady flow prediction errors for integral (drag, lift, and moment coefficients), surface (pressure profiles), and field variables (velocity field), although only the lift is used as training data. In addition, the augmented SA model shows reasonable generalizability for unseen flow conditions. The proposed unsteady FIML framework is implemented in the DAFoam framework and is open to the public. It has the potential to augment the RANS turbulence model for accurately predicting other challenging unsteady flow problems.