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
It is important to be able to accurately predict the neutron flux outside the immediate reactor core for a variety of safety and material analyses. Monte Carlo radiation transport calculations are required to produce these high-fidelity ex-core responses. The Virtual Environment for Reactor Applications (VERA) provides the automated capability to launch independent Shift [1] fixed-source and eigenvalue Monte Carlo (MC) calculations for user-specified state points during a standard Virtual Environment for Reactor Applications (VERA) calculation. VERA couples MPACT with COBRA-TF (CTF) to Shift to perform ex-core tallies for multiple state points concurrently, with each component capable of parallel execution on independent processor domains. In these ex-core calculations, MPACT is coupled to CTF and performs the in-core depletion and heat transfer calculation, followed by a fixed-source Shift transport calculation including ex-core regions to produce ex-core responses. The fission source, fuel pin temperatures, moderator temperature and density, boron concentration, and fuel pin depleted isotopic compositions can be transferred to Shift from the MPACT calculation. Specifically, VERA performs fluence calculations in the core barrel outward to the end of the pressure vessel and detector response calculations in ex-core detectors. It also performs the requested tallies in any user-defined ex-core regions. VERA takes advantage of the General Geometry (GG) package in Shift. This gives VERA the flexibility to explicitly model features outside the core barrel, including detailed vessel models, detectors, and power plant details. A very limited set of experimental and numerical benchmarks is available for ex-core simulation comparison. The Consortium for Advanced Simulation of Light Water Reactors has developed a set of ex-core benchmark problems to include as part of the VERA verification and validation set of problems. The ex-core capability in VERA has been tested on small representative assembly problems, multi-assembly problems, as well as quarter-core and full-core problems. VERAView has also been extended to visualize these vessel fluence results from VERA. This manual serves to present a guide to VERA users about the methodology behind ex-core calculations and the details of input, output, and analysis of results from these calculations. Details in this version of the manual are based on features in VERA 4.0.1. Consortium for Advanced Simulation of LWRs iv CASL-U-2018-1556-002 Ex-core Modeling with VERA User Manual DEVELOPER TEAM The following people are contributors to the development of the specific parts of VERA relevant for ex-core calculations.
The MPACT code, being developed collaboratively by the University of Michigan and Oak Ridge National Laboratory, is the primary deterministic neutron transport solver being deployed within the Virtual Environment for Reactor Applications (VERA) as part of the Consortium for Advanced Simulation of Light Water Reactors (CASL). In many applications of the MPACT code, transport-corrected scattering has proven to be an obstacle in terms of stability, and considerable effort has been made to try to resolve the convergence issues that arise from it. Most of the convergence problems seem related to the transport-corrected cross sections, particularly when used in the 2D method of characteristics (MOC) solver, which is the focus of this work. In this paper, the stability and performance of the 2-D MOC solver in MPACT is evaluated for two iteration schemes: Gauss-Seidel and Jacobi. With the Gauss-Seidel approach, as the MOC solver loops over groups, it uses the flux solution from the previous group to construct the inscatter source for the next group. Alternatively, the Jacobi approach uses only the fluxes from the previous outer iteration to determine the inscatter source for each group. Consequently for the Jacobi iteration, the loop over groups can be moved from the outermost loop-as is the case with the Gauss-Seidel sweeper-to the innermost loop, allowing for a substantial increase in efficiency by minimizing the overhead of retrieving segment, region, and surface index information from the ray tracing data. Several test problems are assessed: (1) Babcock & Wilcox 1810 Core I, (2) Dimple S01A-Sq, (3) VERA Progression Problem 5a, and (4) VERA Problem 2a. The Jacobi iteration exhibits better stability than Gauss-Seidel, allowing for converged solutions to be obtained over a much wider range of iteration control parameters. Additionally, the MOC solve time with the Jacobi approach is roughly 2.0-2.5× faster per sweep. While the performance and stability of the Jacobi iteration are substantially improved compared to the Gauss-Seidel iteration, it does yield a roughly 8-10% increase in the overall memory requirement.
CASL members TVA, Westinghouse, and Oak Ridge National Laboratory have successfully completed a detailed simulation of the initial startup of Watts Bar Nuclear Unit 2 (WBN2) using the advanced reactor simulation tools known as VERA. WBN2 is the first commercial power reactor to join the nation's electrical grid in over two decades, and the modern core design and availability of data make it an excellent benchmark for CASL. Calculations were performed three months prior to the startup, and in the first blind application of VERA to a new reactor, predicted criticality and physics parameters very close to those later measured by TVA. Subsequent calculations with the latest version of VERA and using exact measurement conditions improved the results even further. The escalation to full power required approximately five months, including several intermediate testing power plateaus. The entire power, temperature, and control rod history was simulated with VERA by the hour, requiring 4,130 time steps, and included isotopic depletion and decay through ten additional shutdown intervals. TVA provided the startup data, as well as measured boron concentrations, reactor temperatures, ex-core axial flux difference (AFD), and twelve measured incore neutron flux distributions. The entire simulation required 892,837 core-hours, or 13.5 days on 2,784 cores. This included 16,605 neutronics/thermal-hydraulic iterations.
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