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Validation of MPACT BWR capabilities against critical experiments

Over the years, significant validation work for the neutronics code MPACT has been performed against zero-power critical benchmarks and measured data from operating nuclear power plants. As a part of the Modeling and Analysis of Exelon BWRs for Eigenvalue and Thermal Limits Predictability project, new validation efforts relevant to boiling water reactor (BWR) core applications have been performed. This paper presents the results of the critical experiment portion of the BWR validation efforts for MPACT. The Kritz-4 experiments and IPEN/MB-01 BWR-relevant configurations are modeled with MPACT. The Kritz-4 BWR critical experiments were performed at both cold and hot conditions, which is a unique feature among other critical experiment facilities. The MPACT results with linear source (LS) Method of Characteristics (MOC) have very good agreement with the measured criticality. When using the 60-group BWR library with LS and P2 scattering, the maximum k{sub eff} error is 109 pcm, and the average cold-hot bias is only -0.11 pcm/K. The fission rate distributions of MPACT are also verified with Serpent calculations. For the IPEN facility, two configurations are considered: one with a large central void, and one with a cruciform control rod. The MPACT k{sub eff} errors are less than 50 pcm for all IPEN problems. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Dancoff-based Wigner-Seitz approximation for the subgroup resonance self-shielding in the VERA neutronic simulator MPACT

The MPACT neutronics module of the Virtual Environment for Reactor Analysis (VERA) has used the subgroup method for resonance self-shielding calculation, for which two-dimensional (2D) fixed-source transport calculations are performed using the method of characteristics for resonance energy groups. When considering thermal feedbacks, the subgroup calculation must be performed at each outer iteration. Therefore, the computing time for cross section processing is a significant burden for computational efficiency. The Dancoff-based Wigner-Seitz approximation (DWA) capability has been implemented into MPACT in conjunction with the subgroup method, which has been used in SCALE/XSProc since SCALE version 6.0 and has recently been called an equivalent Dancoff-factor cell (EDC) method. The issue of relatively large reactivity bias in DWA for the gadolinia rods was resolved by introducing multiple Dancoff factors. Benchmark results for the VERA pressurized and boiling water reactor benchmark suites show that the DWA capability would significantly enhance computational efficiency with comparable accuracy. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

MPACT Verification With Magnox Reactor Neutronics Progression Problems

MPACT is a state-of-the-art core simulator designed to perform high-fidelity analysis using whole-core, three-dimensional, pin-resolved neutron transport calculations on modern parallel computing hardware. MPACT was originally developed to model light water reactors, and its capabilities are being extended to simulate gas-cooled, graphite-moderated cores such as Magnox reactors. To verify MPACT’s performance in this new application, the code is being formally benchmarked using representative problems. Progression problems are a series of example models that increase in complexity designed to test a code’s performance. The progression problems include both beginning-of-cycle and depletion calculations. Reference solutions for each progression problem have been generated using Serpent 2, a continuous-energy Monte Carlo reactor physics burnup calculation code.Using the neutron multiplication eigenvalue ke as a metric, MPACT’s performance is assessed on each of the progression problems. Initial results showed that MPACT’s multi-group cross section libraries, originally developed for pressurized water reactor problems, were not sufficient to accurately solve Magnox problems. MPACT’s improved performance on the progression problems is demonstrated using this new optimized cross section library.

Luciano, Nicholas↗

Hexagonal Geometries in MPACT

The MPACT code is a high-fidelity light-water reactor analysis code using whole-core pin-resolved neutron transport calculations on modern parallel-computing hardware. MPACT uses the 2D/1D method to solve 3D neutron transport problems by decomposing the problem into a stack of 2D slices, each of which is solved independently using the method of characteristics (MOC). The slices are then coupled axially using the P3 nodal expansion method (NEM-P3) for the 1D axial calculations. MPACT also employs the coarse mesh finite difference (CMFD) method to accelerate calculations. This manuscript details work supporting advanced reactor designs using hexagonal pins and hexagonal assemblies such as the VVER-1000. If performed correctly, MOC is geometry agnostic. However, MPACT previously had optimizations in place for Cartesian geometries, specifically in the modularization and current calculations. Sections 2 and 3 detail the changes made to MPACT to support MOC and CMFD calculations on hexagonal geometries. Section 4 reports results demonstrating solution consistency for problems run with and without CMFD acceleration, results demonstrating solution consistency when run in serial and parallel, and pincell results using the Monte Carlo code, McCard’s benchmark results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

MPACT Verification and Validation Manual (V.4.3)

As the VERA SQA plan requires, it is the responsibility of the University of Michigan (UM) and Oak Ridge National Laboratory (ORNL), as co-owners of MPACT, to ensure that verification and validation activities are performed and documented in a V&V manual with supporting publications and CASL technical reports which can be provided for reference and distribution within VERA. This document provides the current revision of the MPACT verification and validation (V&V) manual and describes the current state of MPACT V&V and updates the plans for future MPACT V&V activities. The following sections provide an overview of the V&V process used in MPACT, as well as a summary of the status of each component of V&V in the code.

97 MATHEMATICS AND COMPUTING↗

MPACT Verification and Validation Manual Version 4.4

As the VERA SQA plan requires, it is the responsibility of the University of Michigan (UM) and Oak Ridge National Laboratory (ORNL), as co-owners of MPACT, to ensure that verification and validation activities are performed and documented in a V&V manual with supporting publications and CASL technical reports which can be provided for reference and distribution within VERA. This document provides the current revision of the MPACT verification and validation (V&V) manual and describes the current state of MPACT V&V and updates the plans for future MPACT V&V activities. The following sections provide an overview of the V&V process used in MPACT, as well as a summary of the status of each component of V&V in the code.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Development of the MPACT 69-group Library for Magnox Reactor Analysis using CASL VERA

The Consortium for Advanced Simulation of Light Water Reactors (CASL) has developed the CASL toolset, Virtual Environment for Reactor Analysis (VERA), for pressurized water reactor (PWR) analysis. Recently the CASL VERA was improved for Magnox reactor analysis, which required the development of a new cross section library and new geometrical and thermal feedback capabilities for graphite-moderated Magnoxreactors. The MPACT neutronics module of the CASL core simulator is a 3D whole core transport code, which requires a new cross section library with a different energy group structure due to the different neutronic characteristics of Magnox compared with PWR. A new 69-group structure was developed based on the MPACT 51-group structure to have more thermal energy groups and to be a subset of the SCALE 252-group structure. The ENDF/B-VII.1 MPACT 69-group library was developed for Magnox reactor analysis using the SCALE/AMPX and VERA-XSTools for which a super-homogenization method was applied, and transport cross sections were generated for graphite using a neutron leakage conservation method. Benchmark results show that new MPACT 69-group library works reasonably well for Magnox reactor analysis.

Kim, Kang Seog↗

MPACT Theory Manual (V.4.3)

This manual presents the theory underlying the three-dimensional (3D) whole-core, pin-resolved neutron transport calculation methodologies employed in the MPACT code. MPACT’s primary goal is to provide accurate sub-pin power distributions in a computationally efficient manner. To accomplish this, MPACT offers several different transport method options. The 2D/1D method, in which 3D problems are decomposed into an axial stack of radial “slices,” is currently the most commonly used. In this option, two-dimensional (2D) planar solutions are provided by the method of characteristics (MOC), and axial solutions are provided via one-dimensional (1D) approximate diffusion, or P3 solutions. The radial and axial solutions are coupled by (i) axial and radial transverse leakages, and (ii) a global 3D coarse mesh finite difference (CMFD) solve, which provides both acceleration and stability to the solution iteration scheme. The subsequent chapters of this manual present a range of topics, including MOC, CMFD, axial nodal transport solvers, 2D/1D, self-shielding, depletion, thermal-hydraulics, and transient methods. Development of the underlying theory of the 2D/1D method is presented, diagrams are included to highlight important algorithmic flow, and important concepts are discussed as appropriate. This manual is intended to be self-sufficient, but references to published articles and other materials are included for further reading. MPACT is a relatively new code, with new capabilities and many computational methods that did not exist until recently. This manual is an even newer document, with chapters written by several different code contributors working under time constraints. For these reasons, the manual is not yet complete and finalized. Future versions of this manual will address current deficiencies.

97 MATHEMATICS AND COMPUTING↗

MPACT Software Management Plan (V.4.3)

The MPACT code solves a discretized form of the Boltzmann transport equation on a wide variety of geometries and is distributed with a multigroup neutron cross section library. MPACT provides an advanced geometrically resolved neutral-particle transport capability to solve the flux distribution throughout the entire problem geometry, and it can model the isotopic depletion, decay, and activation of materials. The flux solution in MPACT is provided using a 2D/1D synthesis method within the framework of the 3D coarse mesh finite difference (CMFD) method for which axial and radial correction factors are obtained from 2D method of characteristics (MOC) and 1D nodal expansion method (NEM), PN, or SN. Other key characteristics of the MPACT code include the subgroup method and the embedded self-shielding method (ESSM) for resonance treatment, depletion capability based on the ORIGEN exponential matrix method, and a simplified thermal-hydraulics method for temperature/fluid feedback. The sole purpose of the simplified feedback model is to provide a mechanism for testing during code development and to provide a limited capability for educational applications. Work performed at the code level supports the VERA-QA-001, quality assurance program plan (QAPP) and VERA-QA-002, VERA Software Quality Assurance Plan.

97 MATHEMATICS AND COMPUTING↗

MPACT 4.4 Theory Manual

MPACT is a three-dimensional (3D) full-core neutron transport code capable of calculating subpin power distributions. Calculations are based on the Boltzmann transport equation for neutron fluxes for problems in which the detailed geometrical configuration of fuel components such as the pellet and cladding are explicitly retained. The cross-section data needed for the neutron transport calculation are obtained directly from a multigroup cross section library, which has traditionally been used by lattice physics codes to generate few-group homogenized cross sections for nodal core simulators. Hence, MPACT assumes neither a priori homogenization nor group condensation for the full core spatial solution. The 3D MPACT transport solution can be obtained using the method of characteristics (MOC), which employs discrete ray tracing within each fuel pin. However, for practical reactor applications, the direct application of MOC to 3D core configurations requires an excessive amount of memory and computing time due to the very large number of rays. For practical 3D full-core calculations, MPACT commonly uses an approximate “2D/1D” method that treats the radial (x and y) variables differently from the axial (z) variable. In particular, the radial dependence of the solution is calculated using transport theory, and the axial dependence is calculated using diffusion or P 3 theory. The 2D/1D method requires the core to be divided into a vertical stack of axial slices with a thickness of Δ z ≈ 5–10 cm. Each axial slice is divided radially into coarse spatial cells with boundaries that usually constitute the pin cell boundaries, for which Δ x = Δ y ≈ 1.5 cm. Then, each coarse radial cell (pin cell) is divided into 50–100 fine radial cells, which resolve the angular flux in the fuel, cladding, and moderator regions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

An Improved Energy Deposition Model in MPACT and Explicit Heat Generation Coupling with CTF

The default energy deposition model in the CASL neutronics code MPACT assumes all fission energy is deposited locally in fuel rods. Furthermore, equilibrium delayed energy release is assumed for both steady-state and transient calculations. These approximations limit the accurate representation of the heat generation distribution in space and its variations over time, which are essential for power distribution and thermal-hydraulic coupling calculations. In this paper, an improved energy deposition model is presented in both the spatial and time domains. Spatially, the energy deposition through fission, neutron capture, and slowing-down reactions are explicitly modeled to account for the heat generation from all regions of a reactor core, and a gamma smearing scheme is developed that utilizes the gamma sources from neutron fission and capture. In the time domain, the delayed energy release is modeled by solving an additional equation of delayed heat emitters, similar to the equation of delayed neutron precursors.To allow the explicit heat generation coupling, the interfaces between MPACT and CTF were updated to transfer separate heat sources for different material regions (fuel, clad, moderator and guide tube). The results show that the distributions of the energy deposition between MPACT and MCNP agree very well for various 2-D assembly and quarter-core problems without TH feedback. The MPACT/CTF coupled calculation for the hot full power quarter-core case exhibited a reduced peak pin power by 2.3% and a reduced peak fuel centerline temperature by 17 K when using the explicit energy deposition and heat transfer. The new model also shows a maximum 100 pcm keff effect on assembly depletion problems and an increased overall energy release by 7% in a PWR reactivity-initiated accident (RIA) problem.

Liu, Yuxuan↗

MPACT Programmer's Manual (V.4.3)

Figure 1 shows a high-level call chart for MPACT. The call chart uses the actual procedure names, starting with the main program name, MPACT. The only exception is the italicized names where the upstream procedure contains a number of subroutines calls. These calls are logically separated into blocks, such as setup basic info/inputs. Brief descriptions of what the procedure accomplishes are provided where needed. More detailed procedure information, including procedure arguments and definitions, can be found directly in the procedure header in the MPACT source code or Doxygen documentation (http://www.doxygen.nl/).

97 MATHEMATICS AND COMPUTING↗

Subplane Decusping for BWRs in MPACT

Control blade cusping can introduce significant error in boiling water reactor (BWR) calculations with MPACT when blade tips fall partway within an axial method of characteristics (MOC) plane, requiring homogenization of controlled and uncontrolled regions. This work implements subplane decusping for BWRs in MPACT by enabling BWR-compatible subplane coarse mesh finite difference (CMFD) and extending the existing decusping framework to represent between-assembly control blades that insert from the bottom of the core. The method resolves axial heterogeneity on a refined subplane mesh in the low-order solve and uses the resulting subplane flux shape to form flux-volume homogenized transport cross sections for the partially rodded MOC plane. The capability is evaluated using a single physics General Electric (GE)-14 assembly and a multiphysics Peach Bottom Unit 2 Type 1 assembly (PB2T1A) with thermal hydraulic feedback. In both cases, coarse axial meshes with and without subplane decusping are compared against fine mesh reference solutions over the full range of blade withdrawal positions. Subplane decusping reduces maximum/average eigenvalue errors from 3,369/220 pcm to 303/36 pcm for GE-14 and from 6,689/585 pcm to 1,582/109 pcm for PB2T1A. Additionally, it reduces pin power root mean square errors from 5.2%/0.8% to 1.8%/0.2% for GE-14 and from 6.9%/0.6% to 2.3%/0.1% for PB2T1A. These results demonstrate an effective, practical correction for BWR blade cusping in VERA-MPACT.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Coupling MOOSE-Wrapped MPACT to BISON

As part of the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, an effort is being made to leverage codes like Virtual Environment for Reactor Analysis (VERA) and Michigan Parallel Characteristics Transport (MPACT) by coupling them with other NEAMS codes. To facilitate coupling with other Multiphysics Objected Oriented Simulation Environment (MOOSE) applications, a MOOSE-wrapped MPACT app is created. The capability of this app, named Trogdor, is demonstrated by coupling it with another MOOSE app, BISON. Several single pin problems were run to test the Trogdor and BISON coupling.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

MPACT User’s Manual (V.4.3)

The MPACT code is designed to perform high-fidelity light-water reactor (LWR) analysis using whole-core pin-resolved neutron transport calculations on modern parallel-computing hardware. The code consists of several libraries which provide the functionality necessary to solve steady-state eigenvalue problems. Several transport capabilities are available within MPACT including both 2-D and 3-D Method of Characteristics (MOC). A three-dimensional whole core solution based on the 2D-1D solution method provides the capability for full core depletion calculations.

97 MATHEMATICS AND COMPUTING↗

The MPACT 2020 Milestone: Safeguards and Security by Design of Future Nuclear Fuel Cycle Facilities.

The Materials Protection, Accounting, and Control Technologies (MPACT) campaign, within the U.S. Department of Energy Office of Nuclear Energy, has developed a Virtual Facility Distributed Test Bed for safeguards and security design for future nuclear fuel cycle facilities. The purpose of the Virtual Test Bed is to bring together experimental and modeling capabilities across the U.S. national laboratory and university complex to provide a one-stop-shop for advanced Safeguards and Security by Design (SSBD). Experimental testing alone of safeguards and security technologies would be cost prohibitive, but testbeds and laboratory processing facilities with safeguards measurement opportunities, coupled with modeling and simulation, provide the ability to generate modern, efficient safeguards and security systems for new facilities. This Virtual Test Bed concept has been demonstrated using a generic electrochemical reprocessing facility as an example, but the concept can be extended to other facilities. While much of the recent work in the MPACT program has focused on electrochemical safeguards and security technologies, the laboratory capabilities have been applied to other facilities in the past (including aqueous reprocessing, fuel fabrication, and molten salt reactors as examples). This paper provides an overview of the Virtual Test Bed concept, a description of the design process, and a baseline safeguards and security design for the example facility. Parallel papers in this issue go into more detail on the various technologies, experimental testing, modeling capabilities, and performance testing.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Development and Performance Simulations of the MPACT-AGREE Code Coupling Interface for MAGNOX Reactors

MPACT is a whole-core 3D neutron transport code jointly developed by Oak Ridge National Laboratory and the University of Michigan to perform high-fidelity light water reactor (LWR) analysis. Its capability was recently extended for gas-cooled reactor analysis by coupling to the thermo-fluids code AGREE for thermal feedback. This paper presents the MPACT-AGREE code coupling for the simulation of MAGNOX-type gas-cooled graphite-moderated reactors. A coupling interface has been developed, along with methods to accurately simulate MAGNOX type reactors. The coupling mechanics were tested using two problems derived from the Calder Hall reactor. Simulations of these models demonstrated that the codes have been successfully coupled and can provide reasonable results in a tractable simulation time.

Gentry, Cole↗

P{sub N} source expansion nodal method in MPACT for boiling water reactors

This paper describes the one-node P{sub N}-Source Expansion Nodal Method (SENM) axial solver for the 2D/1D method recently implemented in MPACT to support Boiling Water Reactors (BWR) analysis. Since the BWR has a more complicated design and strong burnable absorber, the existing PN-Nodal Expansion Method (NEM) axial solver in MPACT may not be sufficient to accurately represent the intranodal flux and source profiles for BWRs. The one-node P{sub N}-SENM has been implemented in this work to reduce the axial spatial discretization error for BWRs. From numerical results, we verify that the P{sub N}-SENM can improve the accuracy of the pin power prediction, and confirm that P{sub N}-SENM can use more than a 1.5 times larger axial mesh size than P{sub N}-NEM to have similar accuracy for the BWR GE14 3D assembly problem. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗