Data-Driven RANS closure with Model Derived Turbulence Variables

Abstract

Data-driven turbulence modeling is currently a popular approach in constructing new RANS models with improved performance. Even though data-driven models have generally failed to extrapolate outside training cases well, they harbor potential in design-space exploration. Currently the most popular data-driven models typically employ a corrective approach, where a Reynolds stress correction improves upon an existing precursor RANS simulation without coupling with the RANS solver. Corrective models are trained on data from a RANS simulation and thus are limited in predictive capability and accuracy. On the other hand, the rarely used iterative models utilize DNS data for training and completely couple with the solver, and thus they have the potential to provide more accuracy. In this article, we propose the use of model derived turbulence variables to train iterative data-driven models. The model derived variables are arrived at by freezing the flow variables on the grid and solving turbulent transport equations to convergence. A model form is arrived that is Galilean invariant, frame invariant and unit invariant for a particular design space in consideration. A dense feed-forward neural network is used as a surrogate model for the functional mapping in the model. Numerical results for the popular periodic hills benchmark problem are presented to demonstrate the effectiveness of iterative models for design space exploration.