Cross section modeling using Monte Carlo tally derivatives for transient multiphysics prediction

Abstract

Monte Carlo neutron transport is often seen as the standard for accurate neutronics simulation of nuclear reactors in steady-state. However, the time dependent equation includes time derivatives of flux and delayed neutron precursors which are difficult to model and tally. In this work, a high-order/low-order approach is adopted that uses the omega method to approximate the time derivatives as frequencies. 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. Such multiphysics problems are less straight-forward than prescribed transients that can be forced to be axially symmetric or otherwise artificially constrained. This work leverages tally derivatives, which are a Monte Carlo perturbation technique that can identify how a tally will change with respect to a small change in the system, to successfully predict thermal feedback and greatly improve accuracy in an axially non-symmetric, flow-initiated transient. Results show good agreement with a reference solution where very fine outer time steps are used for Monte Carlo calculations.