Thomas J. Downar

Optimization of Pressurized Water Reactor Shuffling by Simulated Annealing with Heuristics

Simulated-annealing optimization of reactor core loading patterns is implemented with support for design heuristics during candidate pattern generation. The SIMAN optimization module uses the advan...

Modified distorted Born iterative method with an approximate Fréchet derivative for optical diffusion tomography

In frequency-domain optical diffusion imaging, the magnitude and the phase of modulated light propagated through a highly scattering medium are used to reconstruct an image of the scattering and absorption coefficients in the medium. Although current reconstruction algorithms have been applied with some success, there are opportunities for improving both the accuracy of the reconstructions and the speed of convergence. In particular, conventional integral equation approaches such as the Born iterative method and the distorted Born iterative method can suffer from slow convergence, especially for large spatial variations in the constitutive parameters. We show that slow convergence of conventional algorithms is due to the linearized integral equations’ not being the correct Frechet derivative with respect to the absorption and scattering coefficients. The correct Frechet derivative operator is derived here. However, the Frechet derivative suffers from numerical instability because it involves gradients of both the Green’s function and the optical flux near singularities, a result of the use of near-field imaging data. To ameliorate these effects we derive an approximation to the Frechet derivative and implement it in an inversion algorithm. Simulation results show that this inversion algorithm outperforms conventional iterative methods.

OPTIMIZATION OF CORE RELOAD DESIGN FOR LOW-LEAKAGE FUEL MANAGEMENT IN PRESSURIZED WATER REACTORS

A method was developed to optimize pressurized water reactor low-leakage core reload designs that features the decoupling and sequential optimization of the fuel arrangement and control problems. The two-stage optimization process provides the maximum cycle length for a given fresh fuel loading subject to power peaking constraints. In the first stage, a best fuel arrangement is determined at the end of cycle (EOC) in the absence of all control poisons by employing a direct search method. The constant power, Haling depletion is used to provide the cycle length and EOC power peaking for each candidate core fuel arrangement. In the second stage, the core control poison requirements to meet the core peaking constraints throughout the cycle are determined using an approximate nonlinear programming technique.

An incomplete domain decomposition preconditioning method for nonlinear nodal kinetics calculations

Methods are proposed for the efficient parallel solution of nonlinear nodal kinetics equations. Because the two-node calculation in the nonlinear nodal method is naturally parallelizable, the majority of the effort is devoted to the development of parallel methods for solving the coarse-mesh finite difference (CMFD) problem. A preconditioned Krylov subspace method (biconjugate gradient stabilized) is chosen as the iterative algorithm for the CMFD problem, and an efficient parallel preconditioning scheme is developed based on domain decomposition techniques. An incomplete lowerupper triangular factorization method is first formulated for the coefficient matrices representing each three-dimensional subdomain, and coupling between subdomains is then approximated by incorporating only the effect of the nonleakage terms of neighboring subdomains. The methods are applied to fixed-source problems created from the International Atomic Energy Agency three-dimensional benchmark problem. The effectiveness of the incomplete domain decomposition preconditioning on a multiprocessor is evidenced by the small increase in the number of iterations as the number of subdomains increases. Through the application to both CMFD-only and nodal calculations, it is demonstrated that speedups as large as 49 with 96 processors are attainable in the nonlinear nodal kinetics calculations.

Thorium fuel performance in a tight-pitch light water reactor lattice

Abstract Research on the utilization of thorium-based fuels in the intermediate neutron spectrum of a tight-pitch light water reactor (LWR) lattice is reported. The analysis was performed using the Studsvik/Scandpower lattice physics code HELIOS. The results show that thorium-based fuels in the intermediate spectrum of tight-pitch LWRs have considerable advantages in terms of conversion ratio, reactivity control, nonproliferation characteristics, and a reduced production of long-lived radiotoxic wastes. Because of the high conversion ratio of thorium-based fuels in intermediate spectrum reactors, the total fissile inventory required to achieve a given fuel burnup is only 11 to 17% higher than that of 238U fertile fuels. However, unlike 238U fertile fuels, the void reactivity coefficient with thorium-based fuels is negative in an intermediate spectrum reactor. This provides motivation for replacing 238U with 232Th in advanced high-conversion intermediate spectrum LWRs, such as the reduced-moderator reactor or the supercritical reactor.

Use of Thorium in Light Water Reactors

Abstract Thorium-based fuels can be used to reduce concerns related to the proliferation potential and waste disposal of the conventional light water reactor (LWR) uranium fuel cycle. The main sources of proliferation potential and radiotoxicity are the plutonium and higher actinides generated during the burnup of standard LWR fuel. A significant reduction in the quantity and quality of the generated Pu can be achieved by replacing the 238U fertile component of conventional low-enriched uranium fuel by 232Th. Thorium can also be used as a way to manage the growth of plutonium stockpiles by burning plutonium, or achieving a net-zero transuranic production, sustainable recycle scenario. This paper summarizes some of the results of recent studies of the performance of thorium-based fuels. It is concluded that the use of heterogeneous U-Th fuel provides higher neutronic potential than a homogeneous fuel. However, in the former case, the uranium portion of the fuel operates at a higher power density, and care is needed to meet the thermal margins and address the higher-burnup implications. In macroheterogeneous designs, the U-Th fuel can yield reduced spent-fuel volume, toxicity, and decay heat. The main advantage of Pu-Th oxide over mixed oxide is better void reactivity behavior even for undermoderated designs, and increased burnup of Pu.

Generalized Perturbation Theory for Constant Power Core Depletion

The generalized perturbation theory was developed to accommodate constant power core depletion. The resulting adjoint equations are distinguished from the corresponding constant flux depletion system by the coupling of adjacent time intervals in the source of the generalized adjoint flux equation. The method is demonstrated first with an analytic solution to an infinite medium problem. A system of numerical equations is then formulated to be consistent with the number density iteration scheme used to simulate constant power depletion in the code REBUS at Argonne National Laboratory. A two-dimensional (R-Z) fast reactor example similar to that used by previous authors for constant flux depletion is solved here to provide a consistent basis for evaluating the present work. The sensitivity coefficients predicted by constant power depletion perturbation theory are consistently within a few percent of the exact calculation.

High-fidelity light water reactor analysis with the numerical nuclear reactor

Abstract The Numerical Nuclear Reactor (NNR) was developed to provide a high-fidelity tool for light water reactor analysis based on first-principles models. High fidelity is accomplished by integrating full physics, highly refined solution modules for the coupled neutronic and thermal-hydraulic phenomena. Each solution module employs methods and models that are formulated faithfully to the first principles governing the physics, real geometry, and constituents. Specifically, the critical analysis elements that are incorporated in the coupled code capability are a direct whole-core neutron transport solution and an ultra-fine-mesh computational fluid dynamics/heat transfer solution, each obtained with explicit (sub-fuel-pin-cell level) heterogeneous representations of the components of the core. The considerable computational resources required for such highly refined modeling are addressed by using massively parallel computers, which together with the coupled codes constitute the NNR. To establish confidence in the NNR methodology, verification and validation of the solution modules have been performed and are continuing for both the neutronic module and the thermal-hydraulic module for single-phase and two-phase boiling conditions under prototypical pressurized water reactor and boiling water reactor conditions. This paper describes the features of the NNR and validation of each module and provides the results of several coupled code calculations.

Convergence Analysis of the Nonlinear Coarse-Mesh Finite Difference Method for One-Dimensional Fixed-Source Neutron Diffusion Problem

Abstract The convergence rates of the nonlinear coarse-mesh finite difference (CMFD) method and the coarse-mesh rebalance (CMR) method are derived analytically for one-dimensional, one-group solutions of the fixed-source diffusion problem in a nonmultiplying infinite homogeneous medium. The derivation was performed by linearizing the nonlinear algorithm and by applying Fourier error analysis to the linearized algorithm. The mesh size measured in units of the diffusion length is shown to be a dominant parameter for the convergence rate and for the stability of the iterative algorithms. For a small mesh size problem, the nonlinear CMFD is shown to be a more effective acceleration method than CMR. Both CMR and two-node CMFD algorithms are shown to be unconditionally stable. However, the one-node CMFD becomes unstable for large mesh sizes. To remedy this instability, an underrelaxation of the current correction factor for the one-node CMFD method is successfully introduced, and the domain of stability is significantly expanded. Furthermore, the optimum underrelaxation parameter is analytically derived, and the one-node CMFD with the optimum relaxation is shown to be unconditionally stable.

Measurement of Neutron Yields From

We have performed measurements of neutron production from UF4 samples using liquid scintillator as the detector material. Neutrons and gamma rays were separated by a multichannel digital pulse shape discriminator, and the neutron pulse-height spectra were unfolded using sequential least-squares optimization with an active set strategy. The unfolded spectra were compared to estimates calculated with the SOURCES 4C code.