Physics-informed data-driven unsteady Reynolds-averaged Navier–Stokes turbulence modeling for particle-laden jet flows

With the assistance of deep learning (DL), we present a framework for predicting the turbulent eddy viscosity in unsteady Reynolds-averaged Navier–Stokes (URANS) simulations for particle-laden jet flows. We report a complete workflow from identifying the input flow and particle quantities in the training phase to predicting the flow and particle fields in the testing phase. The framework incorporates a deep neural network model, also known as multi-layer perceptrons, into the momentum equations of the Euler–Lagrangian gas–solid flow system. A data-driven, physics-informed DL approach was employed to predict the modeled turbulent eddy viscosity field, formulated as a function of the instantaneous flow and particle quantities. In the training phase, these regression functions were trained with an existing high-fidelity direct numerical simulation database. In the testing phase, the trained model was then used to predict the instantaneous local eddy viscosity to update the closure term and to solve the URANS equations iteratively. A series of round, turbulent particle-laden jets in a co-flow with various Stokes numbers were assessed, including those beyond the range of conditions employed for training. The proposed DL–URANS model was found to provide enhanced accuracy for predicting both flow and particle quantities when compared with the baseline URANS simulation.