Bayesian Optimization of the GEKO Turbulence Model for Predicting Flow Separation Over a Smooth Surface

Abstract: This paper applies Bayesian-optimization-RANS (turbo-RANS) to improve Reynolds-averaged Navier-Stokes (RANS) turbulence models for a converging-diverging channel, a case with adverse pressure gradients and flow separation. Using Bayesian optimization, the Generalized $k$-$\omega$ (GEKO) model was calibrated by tuning $C_\text{SEP}$ and $C_\text{NW}$ with sparse direct numerical simulation (DNS) data at $Re = 12,600$. The calibration followed the Generalized Error Distribution-based Calibration Procedure (GEDCP), optimizing coefficients based on pressure recovery ($C_p$) and skin friction ($C_f$). The optimized model was evaluated beyond training data. Streamwise velocity ($U$) predictions at $Re = 12,600$ were compared to DNS to assess improvements in $C_p$ and $C_f$. To test robustness, comparisons were made against large-eddy simulation (LES) data at $Re = 20,580$ for velocity and skin friction. Results show that optimized GEKO (turbo-RANS) improves wall quantity predictions, particularly reattachment. Improved velocity profiles at both Reynolds numbers suggest Bayesian-optimized coefficients enhance adverse pressure gradient modeling. The model retains accuracy across different $Re$, showing turbo-RANS' potential in turbulence model corrections that generalize across flows. While skin friction predictions showed limited improvement due to constraints of two-equation models, this study highlights the role of machine learning-assisted RANS calibration in improving predictive accuracy for complex flows. The results suggest optimized coefficients from a single dataset can be applied across moderate $Re$ variations, improving turbo-RANS' applicability for turbulence model tuning.