Improvement of transition prediction model in hypersonic boundary layer based on field inversion and machine learning framework

TLDR

The classical four‑equation γ–Reθ transition model is accurate for low‑speed flows but fails at hypersonic speeds due to compressibility effects and multiple instability modes, prompting interest in data‑driven approaches. This study develops a data‑driven framework that extends the γ–Reθ model’s predictive capability for hypersonic boundary‑layer transition through field inversion and machine learning. An iterative regularized ensemble Kalman filter first retrieves the spatial distribution of the perturbation correction term β for the switching function Fonset1, and a random‑forest model then maps average flow features to β, with validation on flat‑plate and blunt‑cone cases across varied Reynolds numbers, temperatures, and bluntness. The enhanced model accurately predicts transition onset location and transition‑zone length, and the machine‑learning analysis shows that the effective length scale is a key input feature for hypersonic transition simulation.

Abstract

The classical four-equation γ−Reθ transition model has presented excellent accuracy in low-speed boundary layer transition prediction. However, once the incoming flow reaches hypersonic speed, the original model is no longer applicable due to the compressibility problem and the appearance of multiple instability modes. Recently, there has been widespread interest in data-driven modeling for quantifying uncertainty or improving model prediction accuracy. In this paper, a data-driven framework based on field inversion and machine learning is performed to extend the prediction capability of the original γ−Reθ transition model for the hypersonic boundary layer transition. First, the iterative regularized ensemble Kalman filter method is applied to obtain the spatial distribution of the perturbation correction term β for the switching function Fonset1, and the effectiveness of this method is initially verified in the hypersonic flat plate case. Then, the random forest algorithm is adopted to construct a mapping from the average flow features to β. The generalizability of the well-trained learning model is fully validated in the blunt cone cases with different unit Reynolds numbers, free-stream flow temperature, and bluntness. The simulation results indicate that the performance of the original γ−Reθ transition model in the hypersonic boundary layer transition prediction is significantly improved, and the boundary layer transition onset location and the length of transition zone can be correctly obtained. In addition, the machine learning model investigates the importance of the input features and confirms that the effective length scale plays a significant role in the numerical simulation of the hypersonic boundary layer transition.