Improving the k–ω–γ–Ar transition model by the field inversion and machine learning framework

Abstract

Accurate simulation of transition from the laminar to the turbulent flow is of great importance in industrial applications. In the present work, the framework of field inversion and machine learning has been applied to improve the four-equation k–ω–γ–Ar transition model. The low-speed transitional flows past two airfoils were numerically simulated. Based on the experimental transition locations, the regularizing ensemble Kalman filtering (EnKF) was performed to obtain the distributions of space-varied correction terms for the first mode time scale in the transitional flows over a natural-laminar-flow (NLF) airfoil, NLF(1)-0416. Then, two machine learning methods, random forest (RF) and artificial neutral network (NN), were adopted to construct the mapping from the mean flow variables to the correction terms. Finally, the learned models were embedded into the original solver. The results show that the regularizing EnKF can efficiently obtain the posterior distribution of the correction terms only by the transition locations. Meanwhile, both the RF- and NN-augmented transition models can predict more accurate transition locations past NLF(1)-0416 at both interpolated and extrapolated angles of attack. Moreover, the RF-augmented model can predict more accurate transitional flows on both the windward and leeward sides of NACA0012 at the same angle of attack. It indicates that the discrepancies within the model are learned and reduced. The modified model has good applicability and generalization ability. Furthermore, by analyzing the relative importance of the features in the RF model, it is found that the streamwise pressure gradient plays the most important role in the physical information and interpretation of the learned model.