Research on SCO₂ Critical Flow Prediction Model Based on PINN-HEM Hybrid Framework

The accurate prediction of critical flow in supercritical carbon dioxide (SCO₂) reactor systems is a crucial aspect of pressure drop accident safety analysis. However, the availability of current experimental data is limited and primarily focused on low-temperature and low-pressure regions. This limitation leads to a lack of high-precision, wide-parameter-range models for SCO₂ critical flow. Traditional theoretical models and purely data-driven approaches are characterized by an inherent trade-off between computational efficiency and generalization capability. In contrast, physics-informed neural networks (PINN) integrate physical laws into the neural network framework, which improves both the interpretability and generalization of the model. Within this study, the PINN algorithm was adopted, and the conservation equations of the homogeneous equilibrium model (HEM) were embedded into the loss function to construct the PINN-HEM framework. The HEM framework was chosen for its physical completeness, broad applicability across single-phase, two-phase, short-tube, and long-tube flow regimes, and its foundation in fundamental physical principles rather than numerous simplifying assumptions typical of empirical correlations. By leveraging an extended high-temperature and high-pressure experimental dataset (130-500 ℃, 12-15 MPa), the network parameters of the PINN-HEM model were initialized using a purely data-driven model. Furthermore, the hyperparameters of this purely data-driven model (including the number of hidden layers, the number of nodes per layer, and the L2 regularization coefficient) have been rigorously optimized. This optimized initialization results in a significant reduction in the number of training epochs required for convergence. Consequently, a high-precision PINN-HEM SCO₂ critical flow model applicable across a wide range of parameters was developed. Results demonstrate that, when evaluated across diverse test sets (including long-tube experimental data D1, high-parameter experimental data D2, and numerically generated broad-parameter data D3), a substantial reduction in average relative error is achieved by the PINN-HEM model. Specifically, compared to the PINN-EF model, the average relative error is reduced by 62.65%, 81.00%, and 62.65% on datasets D1, D2 and D3, respectively, by the PINN-HEM model. Furthermore, the contribution of input features within the PINN-HEM model is found to be in closer alignment with fundamental physical principles, resulting in enhanced model interpretability. The potential of PINN in solving complex thermodynamic problems is demonstrated by this research, providing a more accurate and efficient tool for predicting SCO₂ critical flow in reactor systems. The integration of physical constraints ensures that the model not only fits the data but also adheres to the governing physical laws. Consequently, robustness and generalization performance across a broader parameter space are enhanced. For enhanced understanding of PINN model characteristics, subsequent research could explore the influence of individual feature values on the PINN-HEM model’s predictive contributions through SHAP value analysis. Based on SHAP analysis, network hyperparameters could be optimized to improve physical interpretability and generalization capability.