Prediction of Critical Heat Flux in Vertical Tubes by Physics-informed Neural Networks

The safety of thermohydraulic systems with two-phase flow is directly related to the Critical Heat Flux (CHF), which characterizes the transition from nucleate boiling to film boiling with a significant reduction of heat transfer efficiency. CHF prediction is crucial in nuclear power plants (NPPs), where thermohydraulic margins are critical for safe operation. Recent efforts to improve CHF prediction in vertical tubes have increasingly relied on data-driven approaches using Artificial Intelligence (AI) and Machine Learning (ML) techniques. Nevertheless, purely data-driven models often lack intrinsic physical information, limiting their broader acceptance for practical applications in safety-critical systems like NPPs. In this work, we explore the use of physics-informed neural networks (PINNs) for CHF prediction in vertical tubes. The Westinghouse (W-3) empirical correlation, an empirical CHF correlation developed by Westinghouse Electric Company for water-cooled reactors, is employed as the physical model integrated into the learning process of the PINN. Specifically, two different forms of physical loss function for PINN are formulated. The first form is based on simple differences (SD) between the predicted CHF from the model and the CHF calculated using W-3 correlation; the second form is based on partial derivatives (PD) of the W-3 correlation computed with respect to the input parameters. The developed PINN models are validated using experimental CHF data from the US Nuclear Regulatory commission (NRC), provided by the Working Party on Scientific Issues and Uncertainty Analysis of Reactor Systems (WPRS) Expert Group on Reactor Systems Multi-Physics (EGMUP) task force on AI/ML for Scientific Computing in Nuclear Engineering projects, promoted by the OECD/NEA. The results indicate that the predictive performance of the proposed PINN models exceeds those of the Look-Up Table (LUT) and purely data-driven deep neural networks, confirming the benefit of integrating physical knowledge into the learning process for enhancing accuracy and reliability of the prediction model.

Keywords: Nuclear reactor safety, Thermohydraulic systems, Critical heat flux, Artificial intelligence, Physics-informed neural networks.