Machine learning techniques for accuracy improvement of RANS simulations

Abstract

There is a wide number of applications where the flow is turbulent. Since Direct Numerical Simulation (DNS) and experiments are expensive, the use of Reynolds Average Navier-Stokes (RANS) models is a necessity. However, the obtained models from this approach have low accuracy. This fact justifies the high demand for better models. In this work, a technique that uses machine learning, by means of neural networks, is used to correct the κ- RANS model considering the DNS data as ideal. The methodologies available in the literature employ the Reynolds stress tensor as the main quantity to be corrected. Once this entity is corrected, the velocity field is recalculated by the RANS transport equations. Consequently, the obtained velocity field gets closer to DNS results. However, in the present work, such methodology is criticized due to the existence of uncertainties in the turbulent stress field provided by DNS databases. It is known that the second-order statistical moments (Reynolds stress tensor) are not as well converged as the first order ones (mean velocity and pressure fields) in DNS simulations. These uncertainties are propagated, and contaminate the mean velocity field calculated from it. For this reason, it is proposed, as a new methodology, the correction of the divergent of the Reynolds stress tensor, because it is the only part that is computed in the mean linear momentum balance. This divergence can be calculated from the mean velocity and pressure fields, which are well converged, using the mean linear momentum equation. The results obtained so far have demonstrated that the divergent correction of the RANS turbulent stress field is able to reconstruct mean velocity fields closer to the DNS than the complete tensor correction usually employed in the literature.