Overshoot-resolved transition modeling based on field inversion and symbolic regression

TL;DR

This paper introduces a novel approach combining field inversion and symbolic regression to enhance RANS transition models, accurately capturing overshoot phenomena in high-speed flows with improved interpretability and robustness.

Contribution

It develops an interpretable augmentation for RANS models using symbolic regression, effectively resolving overshoot issues in high-speed transitional flows.

Findings

Successfully reproduces overshoot phenomena across test cases

Maintains accurate transition location and length

Demonstrates robustness in low-speed flows

Abstract

Overshoot of high-speed transitional skin-friction and heat-transfer values over their fully turbulent levels is well documented by numerous direct numerical simulations (DNS) and experimental studies. However, this high-speed-specific overshoot phenomenon remains a longstanding challenge in Reynolds-averaged Navier-Stokes (RANS) transition models. In this paper, field inversion and symbolic regression (FISR) methodologies are adopted to explore a generalizable and interpretable augmentation for resolving the missing overshoot characteristic. Specifically, field inversion is implemented on our previous high-speed-improved $k$-$\omega$-$\gamma$-$\widetilde{Re}_{\theta \rm{t}}$ transition-turbulence model. Then symbolic regression is employed to derive an analytical map from RANS mean flow variables to the pre-defined and inferred corrective field $\beta(\mathbf{x})$. Results manifest that the excavated expression faithfully reproduces the overshoot phenomena of transition region over various test cases while does not corrupt model behavior in transition location and length. Based on its transparent functional form, mechanistic investigations are conducted to illustrate the underlying logic for accurate capture of overshoot phenomenon. In addition, importance of protect function in $\beta(\mathbf{x})$, feasibility of a more concise expression for $\beta(\mathbf{x})$, and reliable performance of $\beta(\mathbf{x})$ in low-speed transitional flows are emphasized.