Neural network-based eddy-viscosity correction for RANS simulations of flows over bi-dimensional bumps

Abstract

The improvement of Reynolds-Averaged Navier–Stokes (RANS) models has become one major issue in the field of computational fluid dynamics (CFD). Despite being largely used in industry, eddy-viscosity models still lack accuracy even for simple flow configurations. In this scenario, we investigate new data-driven approaches for the development of machine-learning augmented turbulence models. The main contribution of this work is providing a machine-learning oriented turbulence model that estimates directly the eddy-viscosity correction, and that does not require the use of additional transport equations. The configuration studied is a turbulent flow over a parametric set of bumps characterized by different levels of curvature, pressure gradient and flow separation. An artificial neural network (ANN) model is trained, cross-validated and tested to construct a mapping between the input features and the two quantities of interest : the eddy viscosity discrepancy and the true eddy viscosity estimated from the numerical database. We showed that the ANN predicts the eddy viscosity discrepancy with good accuracy but when coupled to a RANS solver, the improved solution is very noisy. On the other hand, when predicting the eddy viscosity directly, the ANN-based model successfully reproduce the general flow-field behavior, in terms of pressure and skin-friction distributions. The present methodology was proved to be robust even in predicting extrapolated flows. The methods and results of this work provide useful guidance for turbulence model developers.