Jiong Guo

The Improvement of Coupling Method in TINTE by Fully Implicit Scheme

Abstract TINTE is a well-established code for the pebble-bed high-temperature gas-cooled reactor (HTR), including the complicated nuclear module and thermal-hydraulic module, which has been validated by experiments and widely used in the transient behavior simulation. However, only an operator splitting scheme is employed in TINTE to couple the neutronics and thermal hydraulics, and some physical quantities are not consistent in time. As a result, the accuracy and stability are limited by the additional error term derived from the unconverged physical term. In this paper, a fully implicit coupling method was investigated in which the coupled nonlinear fields at each time step are converged using Picard iterations. A physics-based preconditioning is proposed in the work here to further improve the computational performance of the fully implicit coupling method. Seven test problems are implemented based on a practical engineering model, rather than a simple model, to evaluate the performance of the Picard method. The numerical results show that the fully implicit Picard iteration method is more accurate and more stable, which permits longer time steps and a reduction of the computational burden for solving the coupled field equations. The computational efficiency is further enhanced when the physics-based preconditioning is utilized.

A New Nodal Expansion Method with High-Order Moments for the Reduction of Numerical Oscillation in Convection-Diffusion Problems

Abstract The nodal integral method (NIM) has been widely used to solve multidimensional steady-state convection-diffusion problems. However, unphysical oscillating behavior arises when NIM is applied to steep-gradient problems and discontinuous problems. In this paper, a new nodal expansion method (NEM) with high-order moments (NEM_HM) is developed to reduce the numerical oscillation drawback of NIM. High-order moments of transverse-integrated variables are introduced. Based on the definition of Legendre moments, all the expansion coefficients of NEM_HM can be defined as shared moments and unshared moments. Then, the calculation framework of the traditional NEM is extended to include the high-order moments. Additional nodal balance equations are introduced to ensure the uniqueness of all the shared variables such as node-average variables. Finally, coupled discrete equations are obtained in terms of various order moments on the surfaces of the nodes. The classical Smith-Hutton problem and a cross-flow problem are chosen to test the effectiveness of NEM_HM. Numerical results show that the accuracy of NEM_HM outperforms NIM for steep-gradient problems and discontinuous cases.

An Assessment of Coupling Algorithms in HTR Simulator TINTE

Abstract This paper evaluates the performance of neutronic and thermal-hydraulic coupling algorithms in transient problems based on the high-temperature gas-cooled reactor simulator TINTE. In particular, the operator splitting semi-implicit (OSSI), Picard iteration, and Jacobian-free Newton-Krylov (JFNK) methods are compared by a practical engineering model. The OSSI method is employed in the original TINTE. The fully implicit algorithms TINTE-Picard and TINTE-JFNK are implemented in this study. Several special numerical technologies are discussed to improve the performance of JFNK. First, a novel JFNK variant is employed to deal with the multiscale coupling between local fuel sphere temperature and global solid porous media temperature. Second, the preconditioning strategy is determined by making a balance between performance and code burden. Finally, the scaling modifications of the Jacobian matrix and perturbation size are investigated to solve the ill-posed problem. What is more, the framework of TINTE-Picard and TINTE-JFNK is presented, and the key points of implementation are discussed. Numerical results indicate that the advanced coupling algorithms Picard and JFNK can achieve higher computational performance than the original semi-implicit coupling algorithm in TINTE due to the accuracy and stability advantage.

Coupling Methods for HTR-PM Multicircuit Problem

Abstract The High-Temperature Gas-Cooled Reactor–Pebble Bed Module (HTR-PM) is a large-scale complex system that includes reactor core, steam generator, helium circulator, and other important components. When integrating these components, coupling problems such as multiphysics problem, multicircuit problem, multiscale problem, and multimodule problem arise in the numerical simulation. The HTR-PM multicircuit system comprises the primary circuit and secondary circuit, which are simulated by two independent codes and coupled by the interface in the once-through steam generator. Although time-consuming, Picard iteration is a feasible and convenient coupling method to integrate two components because oversolving in the early stages of the iteration causes strong fluctuation between circuits. To address this problem, optimization of the maximum subiteration number and convergence precision have been implemented to improve the efficiency and numerical stability of the Picard iteration. The Dynamic Residual Balance method, an improved version of the Residual Balance method, is proposed to prevent oversolving inside the subiterations. It takes into consideration fluctuation between circuits, and this method is robust in a wide range of cases. Moreover, the nonlinear preconditioned Jacobian-Free Newton-Krylov method, which has less fluctuation between circuits than Picard iteration, is a coupling scheme that updates all the solution variables from the primary circuit and the secondary circuit simultaneously. Outstanding convergence and efficiency can be obtained by implementing the proper preconditioner in this HTR-PM multicircuit problem. The downside is that it requires significant modification to the legacy codes.