Field inversion machine learning augmented turbulence modeling for time-accurate unsteady flow

Field inversion machine learning (FIML) has the advantages of model consistency and low data dependency and has been used to augment imperfect turbulence models. However, the solver-intrusive field inversion has a high entry bar, and existing FIML studies focused on improving only steady-state or time-averaged periodic flow predictions. To break this limit, this paper develops an open-source FIML framework for time-accurate unsteady flow, where both spatial and temporal variations of flow are of interest. We augment a Reynolds-Averaged Navier–Stokes (RANS) turbulence model's production term with a scalar field. We then integrate a neural network (NN) model into the flow solver to compute the above augmentation scalar field based on local flow features at each time step. Finally, we optimize the weights and biases of the built-in NN model to minimize the regulated spatial-temporal prediction error between the augmented flow solver and reference data. We consider the spatial-temporal evolution of unsteady flow over a 45° ramp and use only the surface pressure as the training data. The unsteady-FIML-trained model accurately predicts the spatial-temporal variations of unsteady flow fields. In addition, the trained model exhibits reasonably good prediction accuracy for various ramp angles, Reynolds numbers, and flow variables (e.g., velocity fields) that are not used in training, highlighting its generalizability. The FIML capability has been integrated into our open-source framework DAFoam. It has the potential to train more accurate RANS turbulence models for other unsteady flow phenomena, such as wind gust response, bubbly flow, and particle dispersion in the atmosphere.