Data-Driven Calibration of Transition Models for Natural Convection Flows

Abstract This study investigates the physical mechanism of laminar-to-turbulent transition in natural convection by developing algebraic Local-Correlation-based Transition Models (LCTMs) through a physics-based, data-driven framework combining Bayesian optimisation and Symbolic Regression. Accurate transition prediction is critical for high-Rayleigh-number natural convection applications, where standard RANS models and existing transition correlations, calibrated for flows without buoyancy effects, fail to capture the transition onset and boundary layer development. We employ DNS data from differentially heated rectangular cavities (Rayleigh number (Ra) = $$10^{10}$$ to $$10^{11}$$ ) to calibrate model parameters by Bayesian optimisation, then use Symbolic Regression with buoyancy and transition-specific invariants to discover explicit algebraic expressions that generalise across flow conditions. Two models are developed: ML-1, optimised for high Rayleigh-number accuracy, and ML-2, designed for broader generalisation across laminar and turbulent regimes. Validation against a natural convection vertical boundary layer, tall rectangular cavities, and a square cavity demonstrates substantial improvements over baseline RANS models, with the data-driven LCTMs accurately predicting transition location, Nusselt number, and velocity and temperature profiles, showing promising capability for enhancing natural convection predictions while maintaining RANS efficiency.