Sparse Macro-track Transport Acceleration Method for 3-D Pebble-bed Geometry

Abstract

The method of characteristics has very strong geometric adaptability and can be used to solve the 3-D whole core problem of high temperature gas-cooled pebble-bed reactor. However, it suffers from the disadvantages of thousands of iterations and slow calculation speed. At present, there have been some attempts to reduce calculation time for method of characteristics, including coarse mesh finite difference (CMFD), general coarse mesh rebalance (GCMR) and general coarse mesh finite difference (GCMFD). The CMFD method is applied to realize the acceleration of regular region like squares. Furthermore, to break through the limitation of macroscopic regular geometry for the numerical acceleration method, researchers successively propose the GCMR method and the GCMFD method, but these methods are very complex to implement in irregular geometries and some approximation factors must be introduced. Based on the analysis of more dense tracks are arranged for the 3-D model, the sparse macro-track transport acceleration method was proposed, which greatly reduces the calculation amount of the acceleration equation and obtains a very good acceleration efficiency without reducing the accuracy. The 2-D method of characteristics divides the angular space into M azimuthal angles and P pole angles. The 3-D method of characteristics generally uses a level symmetric quadrature set. In 2-D geometry, the angle is relatively more dense at the poles. As a result, the 2-D macro-track transport acceleration can select a small number of azimuth angles with reflection symmetry and one pole angle as the solution directions of the acceleration equation. The sparse macro-track transport acceleration method implemented in this paper used the same angles as the method of characteristics. The number of tracks for 3-D problems is an order of magnitude higher than for 2-D problems. That is why reducing the number of 3-D tracks is a promising method for reducing the amount of accelerated equation calculation. This paper applied the macro-track transport acceleration method to 3-D whole core problem of high temperature gas-cooled pebble-bed reactor to solve the problem of irregular geometric numerical acceleration. The sparsity, macro-track length limit, and the maximum iteration step limit of the macro-track method are the main factors that affect the acceleration performance. The selection method of acceleration parameters was studied through two benchmark problems. Excellent speedup ratio can be obtained by setting the sparsity to 3-5, the macro-track length to around 2.0 cm, the acceleration iteration steps limit to 20-60. The results of 3-D small light water reactor benchmark and simplified pebble-bed reactor core model show that about 7 times the time speedup ratio and about corresponding 20 times the iterative step speedup ratio can be achieved.

Keywords

• high temperature gas-cooled pebble-bed reactor
• method of characteristics
• macro-track transport acceleration method
• neutron transport