Shane Stimpson

Stability and accuracy of 3D neutron transport simulations using the 2D/1D method in MPACT ☆

A consistent “2D/1D” neutron transport method is derived from the 3D Boltzmann transport equation, to calculate fuel-pin-resolved neutron fluxes for realistic full-core Pressurized Water Reactor (PWR) problems. The 2D/1D method employs the Method of Characteristics to discretize the radial variables and a lower order transport solution to discretize the axial variable. This paper describes the theory of the 2D/1D method and its implementation in the MPACT code, which has become the whole-core deterministic neutron transport solver for the Consortium for Advanced Simulations of Light Water Reactors (CASL) core simulator VERA-CS. Several applications have been performed on both leadership-class and industry-class computing clusters. Results are presented for whole-core solutions of the Watts Bar Nuclear Power Station Unit 1 and compared to both continuous-energy Monte Carlo results and plant data.

VERA Core Simulator methodology for pressurized water reactor cycle depletion

This paper describes the methodology developed and implemented in the Virtual Environment for Reactor Applications Core Simulator (VERA-CS) to perform high-fidelity, pressurized water reactor (PWR), multicycle, core physics calculations. Depletion of the core with pin-resolved power and nuclide detail is a significant advance in the state of the art for reactor analysis, providing the level of detail necessary to address the problems of the U.S. Department of Energy Nuclear Reactor Simulation Hub, the Consortium for Advanced Simulation of Light Water Reactors (CASL). VERA-CS has three main components: the neutronics solver MPACT, the thermal-hydraulic (T-H) solver COBRA-TF (CTF), and the nuclide transmutation solver ORIGEN. This paper focuses on MPACT and provides an overview of the resonance self-shielding methods, macroscopic-cross-section calculation, two-dimensional/one-dimensional (2-D/1-D) transport, nuclide depletion, T-H feedback, and other supporting methods representing a minimal set of the capabilities needed to simulate high-fidelity models of a commercial nuclear reactor. Results are presented from the simulation of a model of the first cycle of Watts Bar Unit 1. The simulation is within 16 parts per million boron (ppmB) reactivity for all state points compared to cycle measurements, with an average reactivity bias of <5 ppmB for the entire cycle. Comparisons to cycle 1 flux map data are also provided, and the average 2-D root-mean-square (rms) error during cycle 1 is 1.07%. To demonstrate the multicycle capability, a state point at beginning of cycle (BOC) 2 was also simulated and compared to plant data. The comparison of the cycle 2 BOC state has a reactivity difference of +3 ppmB from measurement, and the 2-D rms of the comparison in the flux maps is 1.77%. These results provide confidence in VERA-CSs capability to perform high-fidelity calculations for practical PWR reactor problems.

A 2-D/1-D Transverse Leakage Approximation Based on Azimuthal, Fourier Moments

The MPACT code being developed collaboratively by Oak Ridge National Laboratory and the University of Michigan is the primary deterministic neutron transport solver within the Virtual Environment for Reactor Applications Core Simulator (VERA-CS). In MPACT, the two-dimensional (2-D)/one-dimensional (1-D) scheme is the most commonly used method for solving neutron transport–based three-dimensional nuclear reactor core physics problems. Several axial solvers in this scheme assume isotropic transverse leakages, but work with the axial SN solver has extended these leakages to include both polar and azimuthal dependence. However, explicit angular representation can be burdensome for run-time and memory requirements. The work here alleviates this burden by assuming that the azimuthal dependence of the angular flux and transverse leakages are represented by a Fourier series expansion. At the heart of this is a new axial SN solver that takes in a Fourier expanded radial transverse leakage and generates the angular fluxes used to construct the axial transverse leakages used in the 2-D–Method of Characteristics calculations. These new capabilities are demonstrated for the rodded Takeda light water reactor benchmark problem and the extended C5G7 benchmark suite. Results with heterogeneous pins, as in the C5G7 benchmark, indicate that cancelation of error between the angular and spatial representation of the transverse leakages may be a factor in the results obtained. To test this, an alternative C5G7 problem has been formulated using homogenized pin cells to reduce the errors introduced by assuming that the axial transverse leakage is spatially flat. In both the Takeda and C5G7 problems with homogeneous pins, excellent agreement is observed at a fraction of the run time and with notable reductions in memory footprint.