The NILO-CMFD Method for Iteratively Solving Coupled Neutron Transport-Thermal Hydraulics Problems

Abstract

The interactions between neutron radiation and matter are nonlinear. Specifically, certain neutron nuclear reactions (e.g., fission events) generate heat, which modifies the temperature and density of the surrounding material, which in turn modify the neutron interaction probabilities (through the macroscopic cross sections). This nonlinear process is referred to as neutron transport with thermal hydraulics feedback.

Linear transport problems (without feedback) are accurately described by the Neutron Transport Equation (NTE). Discretized forms of the NTE are routinely solved using iterative transport acceleration schemes, for example, the standard Coarse Mesh Finite Difference (CMFD) method. CMFD and related acceleration schemes for linear transport problems are reliable and well-understood. However, when these same iterative methods are applied to nonlinear (i.e. multiphysics) problems, significant performance and stability issues often occur.

In this thesis, we propose modifications to the CMFD procedure, so that it can more robustly and efficiently solve loosely-coupled neutron transport -- thermal hydraulics multiphysics problems. We refer to the new method as Nonlinearly Implicit Low-Order CMFD (NILO-CMFD). In this method, the transport-corrected diffusion equation -- a foundational component of the CMFD method -- is modifed to include approximate thermal hydraulics and nuclear data update physics.

To begin, we provide a general derivation of the 3-D NILO-CMFD method. Then, to initially analyze and test the method, we develop an approximate 1-D multiphysics model of a 3-D nuclear reactor fuel pin. The 1-D model consists of: (i) a 1-D neutron transport equation describing neutron transport, (ii) a 1-D advection-diffusion equation describing fluid temperature variation, (iii) a fuel temperature that depends on the 1-D fission heat source, and (iv) model equations that define the neutron cross sections and related nuclear data in terms of the fluid and fuel temperatures. The implementation of this model in a 1-D test code shows that the NILO-CMFD method overcomes the instabilities that occur in the standard Relaxed-CMFD (R-CMFD) method.

To test the new NILO-CMFD method on realistic 3-D problems, we implemented an incomplete version of the method, NILO-A, in the 3-D neutron transport code MPACT. For multiphysics problems, MPACT is loosely coupled to the 3-D COBRA-TF (CTF) code, which performs subchannel thermal hydraulics calculations. In every 3-D problem that we ran, NILO-CMFD successfully reduced the number of outer iterations to the low number required by CMFD for single-physics calculations. Unfortunately, due to lack of time, we could not implement the full NILO-CMFD method, which would have significantly reduced the wall clock time of the simulations. Consequently, some of our 3-D simulations required more wall clock time to converge than R-CMFD.

Nonetheless, our results show that the NILO-CMFD method is a legitimate generalization of single-physics CMFD to multiphysics problems. The number of outer iterations required by NILO-CMFD to achieve convergence is the same as that of single-physics CMFD, and when the NILO-CMFD nonlinear diffusion solve is well-optimized, we expect the cost of each NILO-CMFD outer iteration to be minimal -- slightly greater than the cost of a single R-CMFD outer iteration.

Overall, our results indicate that the new NILO-CMFD method should be a robust, efficient, and easy-to-implement iteration scheme for solving loosely-coupled neutron transport -- thermal hydraulics multiphysics problems.