An efficient method for solving flow field in high temperature gas-cooled reactor

Abstract

In thermal-hydraulic analysis of pebble-bed high temperature gas-cooled reactor (HTR), the flow field calculation is a crucial and time-consuming process. It can be treated as a mathematical problem of solving sparse linear algebraic equations, which can be solved by direct method or iterative method. By analyzing the geometric model and flow field in HTR, it is found that the flow field consists of one-dimensional (1D) and multidimensional regions. Based on the characteristics of fluid flow in pebble-bed HTR, some acceleration methods are presented in this paper, including a new matrix reordering method, symbolic factorization and block matrix solving. The main idea of matrix reordering is to arrange the 1D regions in a specific order in front of the matrix, while the other regions are placed at the back. After reordering, the fill-ins in Gauss elimination can be greatly reduced, so the direct method can be speed up. The reordered matrix is also suitable for using block matrix solvers to enhance the efficiency of matrix solving. In addition, symbolic factorization is also an efficient technique to reduce the time cost in Gauss elimination by recording the fill-ins and the elimination process. These acceleration techniques can be integrated with matrix solvers to form a variety of solving methods, which have been implemented in the DAYU3D code developed in Institute of Nuclear and New Energy Technology (INET) at Tsinghua University. To evaluate the efficiency of these methods, calculations have been performed on a number of typical cases of pebble-bed HTR. It was found that Gauss elimination coupled with matrix reordering and symbolic factorization techniques, has remarkable advantage compared with other solvers. In comparison to Gauss elimination, about 84%–94% reduction in fluid matrix solving time is observed in the test cases of pebble-bed HTR.