Particle Population Diagnosis and Euclidean Minimum Spanning Tree in Monte Carlo Calculation of Power Distribution

Abstract

A mesh-input-free method is not yet established for particle population diagnosis in the power distribution calculation by the Monte Carlo source iteration method. To approach this issue, the Euclidean minimum spanning tree (EMST) in the graph theory was applied to the source particles. A characteristic volume that one particle covers was defined to be the cubic power of the average edge length of EMST. Thirty and one hundred times of the characteristic volume were proposed as weak and strong requirements, respectively, for a minimum tally cell volume since ten particle characteristic volumes can be accommodated within the tally cells producing one-third and 10% of average power density. These requirements were examined against a three-dimensional full-core model of a 1,100 MWe pressurized water reactor. The comparison with the population diagnosis with a mesh in Nucl. Sci. Eng., 158, 15 (2008) shows a lot of promise of the EMST-based approach. Further developmental issues are identified concerning computational time and output fitting. In addition, a practically useful result was obtained as follows. If the three-dimensional uniform tally cells have volume larger than the quarter fuel bundle unit, the EMST-based approach yields a less conservative diagnosis than fissile volume per source particle.

Monte Carlo criticality calculation under extreme condition

“…Because of the presence of the reflector, only a portion of total fissions occur in the central sphere. As a result, the MC criticality calculation is biased for population size smaller than 10,000 starter particles per generation [18]. In the Mennerdahl's problem, about 3% of total fissions occur at the critical sphere and 97% in the subcritical slab [2].…”