Toward More General Turbulence Models via Multicase Computational-Fluid-Dynamics-Driven Training

Abstract

The accuracy of machine-learned turbulence models often diminishes when applied to flow cases outside the training data set. In an effort to improve the predictive accuracy of data-driven models for an expanded set of cases, an extension of a computational fluid dynamics (CFD)-driven training framework consisting of three key steps is proposed. Firstly, a list of candidate flow-related parameters is selected to supplement Pope’s general tensor basis hypothesis. Secondly, modeling an additional production term may benefit the overall predictions in certain situations. Finally, the Reynolds-averaged Navier–Stokes (RANS) evaluations of candidate models are performed on several different flows simultaneously during the model training iterations. Five free-shear and five wall-bounded flow cases are chosen to train or test data-driven turbulence models. It is shown that the machine-learned models from the present multicase CFD-driven framework can significantly improve the predictive accuracy for the test cases where the baseline RANS results showed significant error from the ground truth. Meanwhile, for cases in which the baseline produced good results, the new models do not perform worse. Further analysis shows that the new models can adapt to opposite trends of turbulent diffusion required for the different cases with a common correction. Moreover, the trained models can be simplified and still achieve similar improvement as the whole expressions.

Data-Driven Turbulence Modelling of Transient Unsteady Flow in Stratified Water Storage Tanks

“…The resultant turbulent time and length scales are then used to calculate the target non-dimensional second-moment and the flow features by Eq. ( 7)− (9). Finally, around two millions data points for all the quantities are sampled over the whole domain with refinement in the inlet jet penetration region.…”

“…Researchers developed machine learnt scalar flux models for flows with different Prandtl numbers [5], different Reynolds numbers [32] in a channel, and for various Rayleigh numbers in natural, forced and mixed convection [39,40]. At the same time, several studies have also tried to explore physicsconstrained data-driven modelling via feature-space engineering [33], interpretable tree-based modelling [12], and by attempting to increase the generalizability of the models through multi-case CFD-driven training [9]. Amongst the different training approaches, the symbolic regression has the advantage of generating interpretable closed-form mathematical models, which are easier to implement and interpret.…”

Robust Optimisation of Ultrasonic Flow Meters by Computational Fluid Dynamics and Enhanced Turbulence Modelling

“…As a solution to this issue, Fang et al [139] suggested including more cases in the training process of CFD-driven optimisation which means that in each evaluation of the optimisation algorithm, more CFD simulations have to be completed to include more a posteriori results in the training process. Fang et al [139] investigated this solution with a multi-case CFD-driven optimisation including different turbulent phenomena. They reported that this solution helped with the generalisability of the new model, however, their new models still have to be separated into either wall-free or wall-bounded flows.…”

“…One of the most important topics in data-driven RANS modelling is the generalisability of the new models for unseen cases [138]. It has been suggested that using a multi-case CFDdriven approach to consider different turbulent phenomena during the optimisation process can help with the generalisability of the new model [139]. However, even these new models are still specific to either wall-free or wall-bounded flows; therefore, the generalisability problem requires further investigation.…”