Physics-Informed Machine Learning for Subcooled Boiling Flow Prediction with DEBORA Experiment

Subcooled boiling flows are critical phenomena in energy systems, characterized by complex multiphase interactions that challenge traditional computational fluid dynamics (CFD) modeling approaches due to their computational intensity and limited real-time applicability. This study presents a comprehensive physics-informed machine learning (PIML) framework for predicting key subcooled boiling flow parameters using sparse 18 experimental data points from the DEBORA (DEveloppement de BOiling Refrigerant Applications) facility. Six ML algorithms were systematically evaluated through multi-output predictions of void fraction, liquid/gas superficial velocity, and mean bubble diameter as functions of radial position and operating conditions. The framework incorporated eight comprehensive physics-based features including dimensionless numbers (Reynolds, Weber, Froude), geometric parameters, and derived flow-specific variables (slip velocity, velocity ratio, drift velocity) to enhance predictive capability and physical interpretability while respecting fundamental conservation principles. Ridge Regression emerged as the superior algorithm for velocity and void fraction predictions, achieving exceptional R² scores of 0.978, 0.995, and 0.999 for void fraction, liquid superficial velocity, and gas superficial velocity respectively, while Random Forest excelled in mean bubble diameter prediction (R²=0.860). The PIML framework successfully captured characteristic subcooled boiling phenomena including wall-peaking void fraction distributions (0.01–0.02 core to 0.16 wall), parabolic velocity profiles with center peaks (~ 2.05 m/s), and radial bubble diameter variations (0.62 mm core to 0.40 mm wall). Comparative analysis with CFD simulations demonstrated equivalent or superior accuracy across most flow parameters, with Ridge Regression achieving maximum relative errors of ~ 5% for void fraction compared to CFD's ~ 12% and Random Forest achieving 3.5% error for gas superficial velocity versus CFD's 5.5%, while providing good computational speedups of 2,330× to 4,566× (394.2 ms versus 30 minutes). Feature importance analysis revealed dimensionless numbers as the most impactful contributors, while extrapolation studies confirmed the models' capability to predict flow behavior beyond experimental measurement ranges with tree-based ensemble methods showing superior extrapolation performance for non-linear physics. Robustness analysis across 100 iterations validated exceptional model stability for Ridge Regression (R²>0.99 for velocities and void fraction), though mean bubble diameter prediction remained challenging across all methods with extreme variability, indicating fundamental modeling challenges requiring specialized approaches. This work establishes PIML as a powerful complement to traditional CFD methods for rapid and accurate prediction of subcooled boiling flow parameters, enabling real-time monitoring, interactive design optimization, and democratized access to advanced thermal fluids analysis for energy system applications.