Tally derivative based surrogate models for faster Monte Carlo multiphysics

Abstract

Existing neutron transport methods used in the nuclear power industry rely on a complex toolchain of modeling and simulation software. Each link in this chain applies various approximations to the spatial, angular, and energy distributions of the problem variables; and these approximations can limit solver predictive capabilities. Monte Carlo (MC) neutron transport is a high-fidelity method that can relax many of these approximations and possibly replace much of the existing toolchain. However, MC neutron transport is also very slow, particularly when coupled into a multiphysics solver. Some researchers have published runtime costs of over 100 000 cpuhours to converge a quarter-core multiphysics problem with MC --

an expense which makes MC-based tools prohibitive for regular use. In response to this issue, some researchers have developed acceleration techniques using the diffusion-based CMFD (coarse mesh finite difference) method. This thesis extends that work by coupling the CMFD solver directly to the thermalhydraulics solvers in a multiphysics simulation. To enable this coupling, MC differential tallies are used to compute the feedback dependence of CMFD parameters. Novel methods based on the windowed multipole cross section representation are used to compute fuel temperature derivatives along with coolant density derivatives. This differential tally approach proves to be flexible; the same procedure is applied to each coarse mesh cell regardless of the presence of control rods, burnable poisons, spacer grids, 135Xe, or other details of the MC model.

With the inclusion of a simple pin power reconstruction scheme, these methods create a surrogate neutronics solver capable of bi-directional coupling with thermal-hydraulics. This surrogate can then accelerate multiphysics convergence by reducing the reliance on costly MC simulations. Furthermore, a novel source-weight clipping procedure is introduced to damp MCCMFD instabilities. Because this clipping procedure does not require multiple MC generations, CMFD and multiphysics coupling can be performed after each MC generation --

even the first generation. This allows simulations to be run with very few MC generations, a feature which alleviates the cost of using many neutrons per MC generation to reduce the impact of fission source distribution undersampling. This methodology is tested on a quarter-core model of the BEAVRS benchmark, a large pressurized water reactor. Simplified subchannel fluid dynamics, fuel pin heat transfer, and equilibrium xenon solvers are included to form a multiphysics system. Without the presented acceleration methods, these quarter-core multiphysics simulations using 200 million neutrons per generation are projected to require 3 300 cpu core-hours to reach stationarity. With the presented methods, this cost falls to 270 core-hours. Further results are shown to demonstrate the runtime costs needed to tightly resolve fine-mesh power distributions with projected runtime savings of 6� over prior work.