A data-driven turbulence modeling for the Reynolds stress tensor transport equation

The long lasting demand for better turbulence models and the still prohibitively computational cost of high-fidelity fluid dynamics simulations, like direct numerical simulations and large eddy simulations, have led to a rising interest in coupling available high-fidelity datasets and popular, yet limited, Reynolds averaged Navier-Stokes simulations through machine learning (ML) techniques. Many of the recent advances used the Reynolds stress tensor or, less frequently, the Reynolds force vector as the target for these corrections. In the present work, we considered an unexplored strategy, namely to use the modeled terms of the Reynolds stress transport equation as the target for the ML predictions, employing a neural network approach. After that, we solve the coupled set of governing equations to obtain the mean velocity field. We apply this strategy to solve the flow through a square duct. The obtained results consistently recover the secondary flow, which is not present in the baseline simulations that used the kappa-epsilon$$ \kappa -\epsilon $$ model. The results were compared with other approaches of the literature, showing a path that can be useful in the seek of more universal models in turbulence. A data-driven turbulence model that solves the Reynolds stress transport equation along with the momentum balance is developed, the model is fueled by a source-term that combines the unclosed terms in the Reynolds stress tensor equation. Using neural networks, trained with direct numerical simulations data, we were able to predict this source-term and correct the Reynolds averaged Navier-Stokes flow in the square-duct. This is the first time that machine learning corrections of turbulent flows are driven by a coupled transport equation combined with the momentum equations. image