An interpretable machine learning-based model of turbulent Prandtl number for supercritical CO2 under buoyancy

Existing studies identify the failure of turbulent heat flux modeling—particularly the constant turbulent Prandtl number (Pr_t) assumption—as the primary cause of inaccurate heat transfer deterioration (HTD) predictions in supercritical fluids. To address this, we propose a dynamic Pr_t prediction framework based on interpretable machine learning (ML) to elucidate Pr_t evolution under buoyancy effects. The model comprises a Pr_t distribution framework integrating the thermophysical parameter (Pr) and a comprehensive factor f_sp that captures system parameter influences, and an ML module that nonlinearly maps multi-parameter effects into f_sp, overcoming the limitations of traditional empirical correlations. Results show that the model significantly improves HTD prediction accuracy and reveals that strong buoyancy necessitates a lower Pr_t to compensate for the turbulent diffusion attenuation. SHAP-based interpretability analysis further quantifies parameter influence hierarchies: heat flux and mass flow rate dominate HTD, inlet temperature, and pressure act independently without interfering with the effects of other parameters on heat transfer, and diameter amplifies the negative effects of heat flux and mass flow rate through synergistic interactions. This study establishes a high-accuracy, mechanically interpretable modeling paradigm for optimizing supercritical systems.