Cfd-driven symbolic regression improves rans transition models in turbomachinery
CFD-driven symbolic regression of RANS transition models
Machine Learning
Summary
Predicting when smooth air or fluids start to become turbulent affects how machines like turbines perform. Existing computer models use fixed formulas that don’t always capture the true transition from smooth to turbulent flow. The authors developed a method that combines computer simulations and symbolic math to find better formulas that adjust these models. Their new approach makes predictions more accurate for different flow conditions, improving heat transfer forecasts in turbine simulations without losing stability.
What this means in practice
- •For turbomachinery engineers: Enhance turbulence transition models to predict heat transfer more accurately in turbine blade designs under various operating conditions.
- •For aircraft engine designers: Improve aerodynamic loss estimations by applying refined transition models for better performance analysis of engine components.
Authors
Louenas Zemmour, Xavier Gloerfelt, Paola Cinnella
Abstract
Laminar-turbulent transition governs skin friction, heat transfer and losses in turbomachinery, yet Reynolds-averaged Navier-Stokes (RANS) transition models rely on empirical correlations and hand-calibrated activation functions whose structural deficiencies cannot be resolved by recalibration. We propose a CFD-driven sparse symbolic regression framework to learn interpretable, closed-form corrections to the production and destruction activation functions in the intermittency equation of the local, Galilean-invariant $k$-$ω$-$γ$ model of Ge et al. Each correction combines a polynomial of a local pressure-gradient parameter, controlling amplitude and sign, with a bounded exponential of local flow features, controlling spatial support. This construction bounds the corrections without ad hoc limiters. Coefficients are identified by gradient-free optimization with the RANS solver in the loop, accelerated by POD-Kriging field surrogates, using mean-velocity data from wall-resolved large-eddy simulations (LES) of the ERCOFTAC T3 flat-plate cases. Elastic-net hyperparameters are selected automatically through bi-level optimization with leave-one-case-out cross-validation. The resulting model retains 11 of 21 candidate terms, compared with 20 under conventional grid-search tuning, while achieving comparable or slightly better accuracy on training and unseen cases. Both approaches recover the same leading-order correction. Applied without retraining to the transonic LS89 turbine cascade, far beyond the training envelope, the augmented model remains numerically robust and improves heat-transfer predictions at all four operating points, reducing errors by up to 70% where the baseline predicts premature transition under high freestream turbulence. Residual errors in transition onset and length highlight the limits of training on flat-plate data alone.