Modeling Feedback Effects of Transient Nuclear Systems Using Monte Carlo

Abstract

Monte Carlo neutron transport is the gold standard for accurate neutronics simulation of nuclear reactors in steady-state because each term of the neutron transport equation can be directly tallied using continuous-energy cross sections rather than needing to make approximations in energy, angle, or geometry. However, the time dependent equation includes time derivatives of flux and delayed neutron precursors which are difficult to tally. While it is straightforward to explicitly model delayed neutron precursors, and thus solve the time dependent problem in Direct Monte Carlo, this is such a costly approach that the practical length of transient calculations is limited to about 1 second. In order to solve longer problems, a high-order/low-order approach was adopted that uses the omega method to approximate the time derivatives as frequencies. These frequencies are spatially distributed and provided by a low-order Time Dependent Coarse Mesh Finite Difference diffusion solver. While this scheme has been previously applied to prescribed transients, thermal feedback is now incorporated to provide a fully self-propagating Monte Carlo transient multiphysics solver which can be applied to transients of several seconds long.

Several recently developed techniques are used in the implementation of the proposed coupling approaches. Firstly, underrelaxed Monte Carlo, which is a steady-state technique that stabilizes the search for temperature distributions, is applied to find initial conditions. Secondly, tally derivatives are a Monte Carlo perturbation technique that can identify how a tally will change with respect to a small change in the system. Test problems of varying complexity are carried out in flow-initiated transients to show the versatility of these methods.

Overall, this multi-level, multiphysics, transient solver provides a bridge between high fidelity Monte Carlo neutronics and the fast multi-group diffusion methods that are currently used in safety analysis.