A coupled multi-closure data-driven framework for turbulence modeling of axisymmetric ventilated supercavitation

Ventilated supercavitation involves complex physical phenomena, including multiphase interface evolution, re-entrant-jet dynamics, and strongly anisotropic shear turbulence. Traditional Reynolds-Averaged Navier−Stokes (RANS) models, relying on the linear eddy viscosity hypothesis, often struggle to accurately capture the anisotropic turbulence characteristics and the intricate multiphysics coupling mechanisms inherent in these flows. To improve RANS predictions of axisymmetric ventilated supercavitating flows, this study applies a data-driven turbulence-model modification framework based on coupled multi-closure corrections. High-fidelity large-eddy simulation data are used to construct supervised targets for the Reynolds-stress anisotropy tensor and a residual anisotropy tensor relative to the baseline linear eddy-viscosity model. The modified turbulent kinetic-energy production term is formulated through an effective production anisotropy tensor that combines the directly predicted anisotropy and the residual correction, thereby allowing the two closure branches to act consistently on the mean momentum and turbulent kinetic-energy equations. Model training and validation are conducted for ventilated supercavitation conditions with varying Froude numbers (Fr > 9.1). The results show that, compared with the original RANS model, the modified RANS model improves the prediction accuracy under both interpolation and extrapolation conditions, although the improvement is significantly more pronounced for interpolation cases and remains limited for the out-of-distribution extrapolation case. For a representative interpolation case, the proposed model reduces the prediction error of the mean cavity length from 10.9% to 3.1%, whereas the corresponding error for the investigated extrapolation case is 7.2%. Local flow-field analysis further indicates that the modified RANS model better reproduces the velocity-gradient distribution in the near-wall shear layer and the gas-liquid mixing structures near the cavity closure and wake. The weaker extrapolation performance suggests that broader parameter-space coverage, additional physical constraints, and more diverse high-fidelity data are required to improve generalization. These results demonstrate the applicability of coupled data-driven RANS modification to axisymmetric ventilated supercavitating flows and provide a practical route for improving hydrodynamic predictions within the investigated operating range.