William A. Wieselquist

PSI Methodologies for Nuclear Data Uncertainty Propagation with CASMO-5M and MCNPX: Results for OECD/NEA UAM Benchmark Phase I

Capabilities for uncertainty quantification (UQ) with respect to nuclear data have been developed at PSI in the recent years and applied to the UAM benchmark. The guiding principle for the PSI UQ development has been to implement nonintrusive “black box” UQ techniques in state-of-the-art, production-quality codes used already for routine analyses. Two complimentary UQ techniques have been developed thus far: (i) direct perturbation (DP) and (ii) stochastic sampling (SS). The DP technique is, first and foremost, a robust and versatile sensitivity coefficient calculation, applicable to all types of input and output. Using standard uncertainty propagation, the sensitivity coefficients are folded with variance/covariance matrices (VCMs) leading to a local first-order UQ method. The complementary SS technique samples uncertain inputs according to their joint probability distributions and provides a global, all-order UQ method. This paper describes both DP and SS implemented in the lattice physics code CASMO-5MX (a special PSI-modified version of CASMO-5M) and a preliminary SS technique implemented in MCNPX, routinely used in criticality safety and fluence analyses. Results are presented for the UAM benchmark exercises I-1 (cell) and I-2 (assembly).

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 cell-local finite difference discretization of the low-order quasidiffusion equations for neutral particle transport on unstructured quadrilateral meshes

We present a quasidiffusion (QD) method for solving neutral particle transport problems in Cartesian XY geometry on unstructured quadrilateral meshes, including local refinement capability. Neutral particle transport problems are central to many applications including nuclear reactor design, radiation safety, astrophysics, medical imaging, radiotherapy, nuclear fuel transport/storage, shielding design, and oil well-logging. The primary development is a new discretization of the low-order QD (LOQD) equations based on cell-local finite differences. The accuracy of the LOQD equations depends on proper calculation of special non-linear QD (Eddington) factors from a transport solution. In order to completely define the new QD method, a proper discretization of the transport problem is also presented. The transport equation is discretized by a conservative method of short characteristics with a novel linear approximation of the scattering source term and monotonic, parabolic representation of the angular flux on incoming faces. Analytic and numerical tests are used to test the accuracy and spatial convergence of the non-linear method. All tests exhibit O(h^2) convergence of the scalar flux on orthogonal, random, and multi-level meshes.

Validating and Verifying a New Thermal-Hydraulic Analysis Tool

The Idaho National Engineering and Environmental Laboratory (INEEL) has developed a new analysis tool by coupling the Fluent computational fluid dynamics (CFD) code to the RELAP5-3D{sup C}/ATHENA advanced thermal-hydraulic analysis code. This tool enables researchers to perform detailed, three-dimensional analyses using Fluents CFD capability while the boundary conditions required by the Fluent calculation are provided by the balance-of-system model created using RELAP5-3D{sup C}/ATHENA. Both steady-state and transient calculations can be performed, using many working fluids and point to three-dimensional neutronics. A general description of the techniques used to couple the codes is given. The validation and verification (V and V) matrix is outlined. V and V is presently ongoing. (authors)

Rod Internal Pressure Distribution and Uncertainty Analysis Using FRAPCON

The discharge rod internal pressure (RIP) and cladding hoop stress (CHS) distributions are quantified for Watts Bar Nuclear Unit 1 (WBN1) fuel rods by modeling core cycle design data, operation data, and as-built fuel enrichments and densities of each fuel rod in FRAPCON-3.5. A methodology is developed that tracks intercycle assembly movements and assembly batch fabrication information to build individual FRAPCON inputs for each evaluated WBN1 fuel rod. An alternate model for the amount of helium released from the zirconium diboride (ZrB2) integral fuel burnable absorber (IFBA) layer is derived and applied to FRAPCON output data to quantify the RIP and CHS for these types of fuel rods. SCALE/Polaris is used to quantify fuel rod–specific spectral quantities and the amount of gaseous fission products produced in the fuel for use in FRAPCON inputs. Fuel rods with ZrB2 IFBA layers (i.e., IFBA rods) are determined to have RIP predictions that are elevated when compared to fuel rods without IFBA layers (i.e., standard rods) despite the fact that IFBA rods often have reduced fill pressures and annular fuel pellets. The primary contributor to elevated RIP predictions at burnups less than and greater than 30 GWd/tonne U is determined to be the total fuel rod void volume and the amount of released fission gas in the fuel rod, respectively. Cumulative distribution functions (CDFs) are prepared from the distribution of RIP and CHS predictions for all standard and IFBA rods. The provided CDFs allow for the determination of the portion of WBN1 fuel rods that exceeds a specified RIP or CHS limit. Results are separated into IFBA and standard rods so that the two groups may be analyzed individually. FRAPCON results are provided in sufficient detail to enable the recalculation of the RIP while considering any desired plenum gas temperature, total void volume, or total amount of gas present in the void volume. A method to predict the CHS from a determined or assumed RIP is also proposed that is based on the approximately linear relationship between the CHS and the RIP. Finally, improvements to the computational methodology of FRAPCON are proposed.

Status Report on NEAMS PROTEUS/ORIGEN Integration

The US Department of Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) Program has contributed significantly to the development of the PROTEUS neutron transport code at Argonne National Laboratory and to the Oak Ridge Isotope Generation and Depletion Code (ORIGEN) depletion/decay code at Oak Ridge National Laboratory. PROTEUS’s key capability is the efficient and scalable (up to hundreds of thousands of cores) neutron transport solver on general, unstructured, three-dimensional finite-element-type meshes. The scalability and mesh generality enable the transfer of neutron and power distributions to other codes in the NEAMS toolkit for advanced multiphysics analysis. Recently, ORIGEN has received considerable modernization to provide the high-performance depletion/decay capability within the NEAMS toolkit. This work presents a description of the initial integration of ORIGEN in PROTEUS, mainly performed during FY 2015, with minor updates in FY 2016.

Nonlinear Projective-Iteration Methods for Solving Transport Problems on Regular and Unstructured Grids

This is a project in the field of fundamental research on numerical methods for solving the particle transport equation. Numerous practical problems require to use unstructured meshes, for example, detailed nuclear reactor assembly-level calculations, large-scale reactor core calculations, radiative hydrodynamics problems, where the mesh is determined by hydrodynamic processes, and well-logging problems in which the media structure has very complicated geometry. Currently this is an area of very active research in numerical transport theory. main issues in developing numerical methods for solving the transport equation are the accuracy of the numerical solution and effectiveness of iteration procedure. The problem in case of unstructured grids is that it is very difficult to derive an iteration algorithm that will be unconditionally stable.

One Validation Case of the CFD Software Fluent: Part of the Development Effort of a New Reactor Analysis Tool

To model Generation IV reactor systems in detail, INEEL is currently developing a new thermal hydraulic analysis tool coupling RELAP5-3D / ATHENA© and the computational fluid dynamics (CFD) software, Fluent. One of the first steps in this endeavor is extensive validation and verification (V&V) of Fluent for various situations of interest, such as the abrupt expansion of a gas entering a gas-cooled reactor core. Fluent results were compared to validation data provided by Baughn, et al. on turbulent air flow through an axisymmetric pipe expansion with constant wall heat flux [1] and uniform wall temperature [2]. Fluent peak Nusselt numbers varied 25% from validation data—well outside experimental uncertainties of 5%. However, non-peak Nusselt numbers varied only 10% from validation data and fully-developed Nusselt numbers were in good agreement with widely-accepted empirical relations such as the Dittus-Boelter Correlation.Copyright