Frequency Transform Method for Transient Analysis of Nuclear Reactors in Monte Carlo

The Frequency Transform method is used for the first time to efficiently model a multiple-second transient problem with Monte Carlo (MC). This is achieved by coupling MC with a time-dependent coarse mesh finite difference (TD-CMFD) diffusion solver. TD-CMFD presents a large advantage over commonly used point kinetics equations since it preserves spatial resolution during the transient and provides equivalence with the high-order method through nonlinear diffusion coefficients. As TD-CMFD computes time-dependent and spatially dependent neutronics information, it also computes frequencies that describe the rate of change of neutron and delayed precursor concentrations. These frequencies are used in MC shape function calculations as an approximation for the time derivatives. As the simulation proceeds, MC calculations update the multigroup cross sections, currents, and diffusion coefficients that are needed in TD-CMFD, and in turn, TD-CMFD updates the frequencies. Our results show the success of the Frequency Transform method in prescribed transient problems on the C5G7 geometry and on a fuel pin geometry. The Frequency Transform method showed significant improvement compared to the Adiabatic approximation, which does not use any frequency information in the MC calculation. The improvements in spatial resolution are shown to be a direct result of frequencies. Additionally, a study of how TD-CMFD’s nonlinear diffusion coefficients behave in time provides a first-of-its-kind study of how equivalence factors are impacted by transients.