Todd S. Palmer

Discretizing the diffusion equation on unstructured polygonal meshes in two dimensions

We derive a discretization of the two-dimensional diffusion equation for use with unstructured meshes of polygons. The scheme is presented in r–z geometry, but can easily be applied to x–y geometry. The method is “node”- or “point”-based and is constructed using a finite volume approach. The scheme is designed to have several important properties, including second-order accuracy, convergence to the exact result as the mesh is refined (regardless of the smoothness of the grid), and preservation of the homogeneous linear solution. Its principle disadvantage is that, in general, it generates an asymmetric coefficient matrix, and therefore requires more storage and the use of non-traditional, and sometimes slowly-converging, iterative linear solvers. On an unstructured triangular grid in x–y geometry, the scheme is equivalent to the linear continuous finite element method with “mass-matrix lumping”. We give computational examples that demonstrate the accuracy and convergence properties of the new scheme relative to other schemes.

Steady-State Thermal-Hydraulic Analysis of the Oregon State University TRIGA Reactor Using RELAP5-3D

Abstract Oregon State University has recently conducted a complete core conversion analysis as part of the Reduced Enrichment for Research and Test Reactors Program. The goals of the thermal-hydraulic steady-state analysis were to calculate natural-circulation flow rates, coolant temperatures, and fuel temperatures as a function of core power, as well as peak values of fuel temperature, cladding temperature, surface heat flux, critical heat flux ratio, and temperature profiles in the hot channel for both the highly enriched uranium and low-enriched uranium cores. RELAP5-3D Version 2.4.2 was used for all computational modeling during the thermal-hydraulic analysis. This is a lumped parameter code forcing engineering assumptions to be made during the analysis. A single-hot-channel model’s results are compared to results produced from more refined two- and eight-channel models in order to identify variations in thermal-hydraulic characteristics as a function of spatial refinement.

An extension of implicit Monte Carlo diffusion: Multigroup and the difference formulation

Implicit Monte Carlo (IMC) and Implicit Monte Carlo Diffusion (IMD) are approaches to the numerical solution of the equations of radiative transfer. IMD was previously derived and numerically tested on grey, or frequency-integrated problems [1]. In this research, we extend Implicit Monte Carlo Diffusion (IMD) to account for frequency dependence, and we implement the difference formulation[2] as a source manipulation variance reduction technique. We derive the relevant probability distributions and present the frequency dependent IMD algorithm, with and without the difference formulation. The IMD code with and without the difference formulation was tested using both grey and frequency dependent benchmark problems. The Su and Olson semi-analytic Marshak wave benchmark was used to demonstrate the validity of the code for grey problems [3]. The Su and Olson semi-analytic picket fence benchmark was used for the frequency dependent problems [4]. The frequency dependent IMD algorithm reproduces the results of both Su and Olson benchmark problems. Frequency group refinement studies indicate that the computational cost of refining the group structure is likely less than that of group refinement in deterministic solutions of the radiation diffusion methods. Our results show that applying the difference formulation to the IMD algorithm can result in an overall increase in the figure of merit for frequency dependent problems. However, the creation of negatively weighted particles from the difference formulation can cause significant numerical instabilities in regions of the problem with sharp spatial gradients in the solution. An adaptive implementation of the difference formulation may be necessary to focus its use in regions that are at or near thermal equilibrium.

Finite element transport using Wachspress rational basis functions on quadrilaterals in diffusive regions

Abstract In 1975, Wachspress developed basis functions that can be constructed upon very general zone shapes, including convex polygons and polyhedra, as well as certain zone shapes with curved sides and faces. Additionally, Adams has recently shown that weight functions with certain properties will produce solutions with full resolution, meaning that they are capable of producing physically meaningful solutions in the diffusive limit. Wachspress rational functions (WRFs) possess these necessary properties. Here, we present methods to construct and integrate WRFs on quadrilaterals. We also present an asymptotic analysis of a discontinuous finite element discretization on quadrilaterals, and we present numerical results.

Neutronic Analysis of the Oregon State TRIGA Reactor in Support of Conversion from HEU Fuel to LEU Fuel

Abstract In support of the conversion of the Oregon State TRIGA Reactor (OSTR) from highly enriched uranium (HEU) fuel to low-enriched uranium (LEU) fuel, a comprehensive neutronic analysis utilizing MCNP5 was performed on the HEU and LEU core configurations. The initial 1974 HEU core provided an opportunity for verification of the MCNP5 baseline model; all fuel elements in the initial core were congruent in geometry and material composition, having no burnup. In addition, a substantial database of core parameters was documented during the initial HEU core start-up. This verification study examined control rod worth, core excess reactivity, burnup, core power, power per element, temperature coefficient of reactivity, void coefficient of reactivity, moderator coefficient of reactivity, axial and radial power profiles, prompt-neutron lifetime, effective delayed-neutron fraction, power defect, and xenon poisoning. Fuel material composition and core loadings are presented. The excellent comparison between the numerical results and the experimental data of the initial HEU core established an objective, credible baseline model and methodology, which were then extended to the LEU core neutronic analysis. Comparison between the numerically calculated core physics values for the new LEU core and data collected during start-up provided a complete verification that the MCNP5 models developed for both the HEU and LEU cores were representative of the OSTR.

Radiolytic microscale power generation based on single chamber fuel cell operation

Proof-of-principle test results are presented for a nuclear-to-electric power generation technique utilizing closed-cycle fuel cell operation. The approach being developed is to first use the decay energy of a radioisotope to generate H2 and O2 from water, and then to utilize these species in a fuel cell to generate electricity. The principle of operation allows the device to regenerate its own reactants and operate continuously as a closed system for as long as the primary source of power, namely the radioisotope, is active. With micro engineering and fabrication techniques available today, a miniaturized integrated package of 1 cm3 in size and producing power in the 10 mW range appears feasible in a mature design. Smaller devices producing less power would also be possible. For this project, a unique fuel cell capable of utilizing mixed reactants at room temperature has been developed. The efficiency of this early fuel cell design falls in the range between 10 and 20%. Measured power output from a radioisotope fueled test cell approached 0.45 mW for several hours with a radiation leakage rate estimated at 490 mrem yr−1.

A Comparison of Pulsing Characteristics of the Oregon State University TRIGA Reactor with FLIP and LEU Fuel

Abstract The Oregon State TRIGA Reactor (OSTR) was converted from highly enriched uranium (HEU) Fuel Life Improvement Program (FLIP) fuel to low-enriched uranium (LEU) fuel in October 2008. This effort was driven by the U.S. Department of Energys Reduced Enrichment for Research and Test Reactor program. The new LEU fuel is 30/20 U-Zr1.6H (30% uranium in the fuel matrix, 19.75 wt% enriched) in contrast to the FLIP fuel having U-Zr1.6H (8.5% uranium in the fuel matrix, 70 wt% enriched). This new fuel composition provides the best match in performance of the available mixture ratios when compared to the previous FLIP fuel. To support conversion, a complete assessment and reevaluation of the OSTR Safety Analysis Report was performed. This evaluation included steady-state thermal-hydraulic and neutronics characterizations of the HEU and LEU cores as well as a transient behavior (pulse) analysis of both core types. This paper presents a summary of the methods used and results produced during the pulse analysis identifying power, temperature, and reactivity during pulsed operation for the FLIP and new LEU fuel. This analysis was performed using RELAP5-3D version 2.4.2 and point reactor kinetics simulation software; these two methods are found to agree very well. We discuss the differences between the two fuels and the impact of pulse behavior on the safety limits for the converted reactor.

A Five-Year Core for a Small Modular Light Water Reactor

Abstract To address the energy needs of developing countries and remote communities, Oregon State University has proposed the Multi-Application Small Light Water Reactor (MASLWR) design. This design uses 8% enriched fuel to achieve five years of operation without refueling. The specific operational conditions (lower pressure and temperature of fuel and coolant), increased enrichment of fuel, and extensive use of gadolinium burnable absorbers lead to significantly different neutron physics compared to conventional pressurized water reactors. In particular, spectrum hardening due to increased thermal neutron absorption, changes in kinetic parameters due to the isotopic content of the fresh and irradiated fuel, and fuel and control rod shadowing by burnable absorbers are consequences of the design requirements. Enhanced neutron leakage from the small MASLWR core also adds complexity. Neutron reflectors and a unique fuel-loading pattern compensate the pronounced axial and radial gradients of the neutron flux and power generation. This paper discusses the neutron physics and thermal-hydraulic issues of the core design for a small reactor with increased fuel enrichment and natural circulation of the coolant. The paper describes three evolutionary steps of the MASLWR core design process and discusses core parameters, advantages, disadvantages, and design limitations as they appeared during the core design feasibility study. The paper demonstrates the feasibility of the core design for five effective years of nonrefueled operation with 8.0% enriched UO2 fuel.

A Coupled Diffusion Synthetic Acceleration for Binary Stochastic Mixture Transport Iterations

Abstract The standard model for transport through binary stochastic media involves two coupled transport equations. Previous research has shown that several types of source iterations applied to the solution of these equations can converge arbitrarily slowly when one or both of the materials is optically thick and diffusive. In this work, we derive, analyze, and implement an acceleration scheme for binary stochastic mixture transport iterations. The equations are derived using the modified four-step method and take the form of discretized coupled diffusion equations. A Fourier analysis indicates that for a wide variety of physical problems and spatial mesh sizes, the scheme is rapidly convergent. Spectral radii measured during these accelerated iterations compare very well with Fourier analysis predictions.

Deterministic Phonon Transport Predictions of Thermal Conductivity in Uranium Dioxide With Xenon Impurities

We present a method for solving the Boltzmann transport equation (BTE) for phonons by modifying the neutron transport code Rattlesnake which provides a numerically efficient method for solving the BTE in its Self-Adjoint Angular Flux form. Using this approach, we have computed the reduction in thermal conductivity of uranium dioxide (UO