Conference Agenda

For safety studies of nuclear reactor cores, a Finite Volume thermal-hydraulic code with pourous media approach named THYC was developed by EDF to simulate steady-state flows of a two-phase mixture within the core of a nuclear reactor. The steady-state solution is obtained through a fictitious transient. Despite a relatively low individual computational time, many statepoints are considered in the safety studies, which can represent significant CPU time.

To speed up the computation, one possible objective is to reduce the number of iterations (i.e., the number of time steps) required to reach convergence. In the present work, the idea is to train a neural network to predict steady-state solutions and use this prediction to initialize the transient computation. This method allows to combine the advantages of neural network prediction, in terms of rapidity, with that of the THYC model, in terms of the physical validation of the solution.

To evaluate the potential of this method, a simplified 1D code was designed. It simulates a two-phase water-vapor flow in a heated channel. A neural network was trained to predict the solution fields from imposed boundary conditions. In this paper, we give a presentation of the methodology, the database selection process, the structure of the neural network and the optimization of the network's hyperparameters. The highlight of this work is that, by introducing spatial frequencies in the error for the optimization of the neural network, we significantly reduce the number of iterations by 50% to 80%.

To establish an efficient and high-precision model calibration method for enabling virtual entities (e.g., digital twins) to synchronously track performance variations of physical counterparts, this study focuses on the feedwater heater model. A weighted method and the artificial bee colony (ABC) optimization algorithm are integrated to develop an intelligent calibration method, along with a prediction-correction-based acceleration technique. The proposed methods are tested on feedwater heater models from typical Gen II, Gen III, and Gen IV reactors. Results demonstrate that the acceleration technique improves calibration efficiency by 60- fold. The intelligent calibration method outperforms traditional manual approaches in both efficiency and accuracy: for single-load-case calibration, it achieves 99% accuracy within 0.5 seconds; for multi-load-case calibration, 98% accuracy is attained within 1 second, and 99% accuracy within 10 minutes. Thus, the calibration method and acceleration technique developed in this study meet the requirements of high efficiency and precision for virtual entities such as digital twins.

Printed Circuit Heat Exchangers (PCHEs) are one of the promising heat exchanger candidates for advanced nuclear reactors and high-temperature applications. This study focuses on developing machine learning models to predict the friction factor (f_D) and Nusselt number (Nu) for semi-circular zigzag channels in PCHEs. A number of data samples were collected from published literature including the channel geometric characteristics and operating conditions. Various machine learning techniques were employed, involving the linear regression with non-linear transformations, kernel methods (Kernel Ridge Regression and Support Vector Regression), and Artificial Neural Networks (ANNs). The Kernel Ridge Regression (KRR) model with a polynomial kernel of degree 6 achieved good performance for Nu prediction, with an R² score above 0.99 and low percentage errors (MAPE < 4%, MPE < 20%). This developed model can contribute to optimize the heat transfer performance of PCHEs, but its application is limited to helium as the working fluid. However, the ANN model for fD prediction, while showing promising results (R² > 0.97, MAPE < 10%), exhibited high maximum percentage errors (MPE > 100%), indicating challenges in predicting the friction factors (fD) less than 0.1. This study highlights the potential of utilizing machine learning models to improve the PCHE design. However, the expanded datasets covering a wider range of geometric configurations, working fluids, and operating conditions, and a detailed analysis of the input feature distribution would be useful to improve model accuracy.

The main drawback of empirical correlations in thermal-hydraulics system codes is that the prediction capability heavily relies on the quality of the data and vastness of the experimental data employed in the study. Therefore, in a long-term research program to improve the accuracy and reliability of the safety analysis methods of nuclear reactors at Hanoi University of Science and Technology, we have developed a method of integrating data-driven and machine learning models with a computing program on the basis of the following two basic modules: (1) experimental data analysis and predictive model development based on experimental data; (2) code develoment module based on conservation equations using the finite volume element method. In this paper, we introduce preliminary results with some case studies.

Thermal stratification in large enclosures is an integral phenomenon to nuclear reactor system safety. Currently, the effective model for thermal stratification utilizes a multi-scale method that integrates 1-D system-level and 3-D CFD code, which offers thermal stratification details while supplying system-level data across various domains. Nonetheless, harmonizing two codes that operate on different spatial and temporal scales presents a significant challenge, with high-resolution CFD simulations requiring substantial computational resources. This study introduced a data-driven coarse-grid turbulence model based on local flow characteristics at a significantly coarser scale targeting improved efficiency and accuracy in reactor safety analysis concerning thermal stratification. A machine learning framework has been introduced to expedite the RANS-solving process by coupling of OpenFOAM and TensorFlow, which entails training a deep neural network with fine-grid CFD-generated data to predict turbulent eddy viscosity. The feasibility of the developed data-driven turbulence model was proven through the SUPERCAVNA experimental facility problem validation.