General nodal expansion method for multi-dimensional neutronics/thermal-hydraulic coupled problems in pebble-bed core systems

Motivated by the high efficiency and accuracy of nodal methods on the coarse meshes and the desire to solve the large-scale coupled problems in pebble-bed high temperature gas cooled reactor (HTR), a general nodal expansion method (GNEM) is successfully developed and extended to solve multi-dimensional neutronics/thermal-hydraulic(N/TH) coupled problems in pebble-bed reactor core systems. The developed GNEM combines the respective advantages of traditional nodal expansion methods (NEM) and modified nodal integral methods (MNIM). Specifically, the local analytical solutions of transverse integral equations in MNIM are obtained with the basis function expansion framework and nodal balance equation in NEM. The unified discrete formulation is also developed so that it's convenient for GNEM to solve neutron diffusion equations, convention diffusion equations, pressure poisson equations, heat transfer equations and porous media flow models in the pebble bed core systems. Then all the governing equations of the N/TH coupled problems can be discretized by the GNEM on the coarse meshes so that the computational scale of coupled problems is greatly reduced for the desired precision. To achieve higher accuracy for the coupled problems on the coarse meshes, the high-order information is successfully transferred between the coupled terms by using GNEM. Finally, the coupled GNEM code is formally developed for N/TH coupled problems in pebble-bed reactor core systems. Numerical results show that the coupled GNEM code can track the reference solutions very well on the coarse meshes and show the high-accuracy advantage and the potential of GNEM for complicated multi-dimensional N/TH coupled problems. Further research is needed to add the coupled GNEM to the HTR analysis code-TINTE in order to simultaneously and effectively solve multi-dimensional coupled problems for realistic HTR reactor systems.