Data-driven Optimisation of Closure Coefficients of a Turbulence Model

Abstract

The solution of the Reynolds-averaged Navier-Stokes equations employs an appropriate set of equations for the turbulence modelling. The closure coefficients of the turbulence model were calibrated using empiricism and arguments of dimensional analysis. These coefficients are considered universal, but there is no guarantee this property applies to test cases other than those used in the calibration process. This work aims at revisiting the universality of the closure coefficients of the original Spalart-Allmaras turbulence model using machine learning, adaptive design of experiments and accessing a high-performance computing facility. The automated calibration procedure is carried out once for a transonic, wall-bounded flow around the RAE 2822 aerofoil. It was found that: a) an optimal set of closure coefficients exists that minimises numerical deviations from experimental data; b) the improved prediction accuracy of the calibrated turbulence model is consistent across different flow solvers; and c) the calibrated turbulence model outperforms slightly the standard model in analysing complex flow features around the ONERA M6 wing. A by-product of this study is a fully calibrated turbulence model that leverages on current state-of-the-art computational techniques, overcoming inherent limitations of the manual fine-tuning process.