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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 811 records · Page 45
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

The Iterated Fission Matrix Method

The fission matrix (FM) method has been successfully demonstrated for different applications. One of the interesting features of this method, which is not possible via standard criticality source Monte Carlo calculations, is the capability to calculate higher forward and adjoint Eigenmodes; however, the accuracy of the estimates for higher eigenvalues strongly depends on the spatial discretization adopted for the fission matrix. A fine mesh ensures accurate results but requires matrices of large size. This is considered a limitation to the applicability of the FM method due to the memory requirements for storage of large full matrices. The adoption of sparse matrix storage (e.g., in MCNP) partially overcomes this problem; nonetheless, the sparse matrix indexing increases the complexity of the implementation of the FM algorithm and introduces the additional task of sparsifying the fission matrix. This summary presents a new method, named the iterated fission matrix (IFM), that allows to estimate higher eigenvalues of multiplying systems on much smaller meshes, but with the same level of accuracy in terms of spatial discretization errors, as compared to the FM method. The following Sections describe this new approach and provide a demonstration using two case studies: a PWR fuel assembly, and a 2D PWR core. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

Multilevel Convergence Analysis of Multigrid-Reduction-in-Time

This study presents a multilevel convergence framework for multigrid-reduction-in-time (MGRIT) as a generalization of previous two-grid estimates. The framework provides a priori upper bounds on the convergence of MGRIT V- and F-cycles, with different relaxation schemes, by deriving the respective residual and error propagation operators. The residual and error operators are functions of the time-stepping operator, analyzed directly and bounded in the norm, both numerically and analytically. We present various upper bounds of different computational cost and varying sharpness. These upper bounds are complemented by proposing analytic formulae for the approximate convergence factor of V-cycle algorithms that take the number of fine grid time points, the temporal coarsening factors, and the eigenvalues of the time-stepping operator as parameters. The paper concludes with supporting numerical investigations of parabolic (anisotropic diffusion) and hyperbolic (wave equation) model problems. We assess the sharpness of the bounds and the quality of the approximate convergence factors. Observations from these numerical investigations demonstrate the value of the proposed multilevel convergence framework for estimating MGRIT convergence a priori and for the design of a convergent algorithm. We further highlight that observations in the literature are captured by the theory, including that two-level Parareal and multilevel MGRIT with F-relaxation do not yield scalable algorithms and the benefit of a stronger relaxation scheme. An important observation is that with increasing numbers of levels MGRIT convergence deteriorates for the hyperbolic model problem, while constant convergence factors can be achieved for the diffusion equation. The theory also indicates that L-stable Runge--Kutta schemes are more amendable to multilevel parallel-in-time integration with MGRIT than A-stable Runge--Kutta schemes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Gas-Cooled High-Temperature Pebble-Bed Reactor Reference Plant Model

This report details a fully coupled neutronics thermal hydraulics reference plant model for a gas-cooled high-temperature pebble-bed reactor. The multiphysics model is developed on the Nuclear Regulatory Commission's Comprehensive Reactor Analysis Bundle (BlueCRAB) available on the Idaho National Laboratory high performance computer, which natively and seamlessly couples Griffin, Pronghorn, and the BISON MOOSE-based applications. Griffin provides the reactor physics capabilities including depletion to the equilibrium core, k-eigenvalue, adjoint, and transient solutions. Pronghorn solves the porous medium equations for the fluid regions and conduction in the solid regions. BISON solves thermal conduction problems for the average pebble and TRISO in the pebble-bed core thus providing the fuel and moderator spatial fields for each pebble burnup group. The neutronics feedback relies primarily on fuel and moderator temperatures. We present results for the coupled steady state equilibrium core and a protected loss of flow event. Although this model is to be considered prototypical with regard to the capabilities in BlueCRAB, its results are consistent with published work by the Institute of Nuclear and New Energy Technology (INET) in China and other research entities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1995

Minimization of the Vibration Energy of Thin-Plate Structures and the Application to the Reduction of Gearbox Vibration

While the vibration analysis of gear systems has been developed, a systematic approach to the reduction of gearbox vibration has been lacking. The technique of reducing vibration by shifting natural frequencies is proposed here for gearboxes and other thin-plate structures using the theories of finite elements, modal analysis, and optimization. A triangular shell element with 18 degrees of freedom is developed for structural and dynamic analysis. To optimize, the overall vibration energy is adopted as the objective function to be minimized at the excitation frequency by varying the design variable (element thickness) under the constraint of overall constant weight. Modal analysis is used to determine the sensitivity of the vibration energy as a function of the eigenvalues and eigenvectors. The optimum design is found by the gradient projection method and a unidimensional search procedure. By applying the computer code to design problems for beams and plates, it was verified that the proposed method is effective in reducing vibration energy. The computer code is also applied to redesign the NASA Lewis gear noise rig test gearbox housing. As one example, only the shape of the top plate is varied, and the vibration energy levels of all the surfaces are reduced, yielding an overall reduction of 1/5 compared to the initial design. As a second example, the shapes of the top and two side plates are varied to yield an overall reduction in vibration energy of 1/30.

Inoue, Katsumi↗
NASA NTRS1996

Classical Trajectories and Quantum Spectra

A classical model of the Schrodinger's wave packet is considered. The problem of finding the energy levels corresponds to a classical manipulation game. It leads to an approximate but non-perturbative method of finding the eigenvalues, exploring the bifurcations of classical trajectories. The role of squeezing turns out decisive in the generation of the discrete spectra.

Mielnik, Bogdan↗
DOE OSTI2016

Fast Multilevel Solvers for a Class of Discrete Fourth Order Parabolic Problems

In this paper, we study fast iterative solvers for the solution of fourth order parabolic equations discretized by mixed finite element methods. We propose to use consistent mass matrix in the discretization and use lumped mass matrix to construct efficient preconditioners. We provide eigenvalue analysis for the preconditioned system and estimate the convergence rate of the preconditioned GMRes method. Furthermore, we show that these preconditioners only need to be solved inexactly by optimal multigrid algorithms. Our numerical examples indicate that the proposed preconditioners are very efficient and robust with respect to both discretization parameters and diffusion coefficients. We also investigate the performance of multigrid algorithms with either collective smoothers or distributive smoothers when solving the preconditioner systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Augmenting the one-shot framework by additional constraints

The (multistep) one-shot method for design optimization problems has been successfully implemented for various applications. To this end, a slowly convergent primal fixed-point iteration of the state equation is augmented by an adjoint iteration and a corresponding preconditioned design update. In this paper we present a modification of the method that allows for additional equality constraints besides the usual state equation. Finally, a retardation analysis and the local convergence of the method in terms of necessary and sufficient conditions are given, which depend on key characteristics of the underlying problem and the quality of the utilized preconditioner.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Symmetry and separability of the neutron diffusion equation

Separation of variables is one of the oldest techniques for solving certain classes of partial differential equations (PDEs). As is the case with many other solution techniques for differential equations, separation of variables may be codified within the broader framework of symmetry analysis. Though the separation of variables technique is frequently used in the nuclear engineering context with various equations describing neutron transport, its connection to the symmetries of those equations has not yet been thoroughly established. It is thus the purpose of this work to establish that connection using neutron diffusion as both an initial step toward analysis of more generally applicable equations, and as a connection to previous results in related problems. Using Lie group analysis, it is found that the traditional space-time separable solution of the neutron diffusion equation (featuring a single α-eigenvalue) corresponds to time translation and flux scaling symmetries. Additional solutions of this equation are also constructed using its broader symmetry set.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

A numerical approach for detecting switch-like bistability in mass action chemical reaction networks with conservation laws

Theoretical analysis of signaling pathways can provide a substantial amount of insight into their function. One particular area of research considers signaling pathways capable of assuming two or more stable states given the same amount of signaling ligand. This phenomenon of bistability can give rise to switch-like behavior, a mechanism that governs cellular decision making. Investigation of whether or not a signaling pathway can confer bistability and switch-like behavior, without knowledge of specific kinetic rate constant values, is a mathematically challenging problem. Recently a technique based on optimization has been introduced, which is capable of finding example parameter values that confer switch-like behavior for a given pathway. Although this approach has made it possible to analyze moderately sized pathways, it is limited to reaction networks that presume a uniterminal structure. It is this limited structure we address by developing a general technique that applies to any mass action reaction network with conservation laws. In this paper we developed a generalized method for detecting switch-like bistable behavior in any mass action reaction network with conservation laws. The method involves (1) construction of a constrained optimization problem using the determinant of the Jacobian of the underlying rate equations, (2) minimization of the objective function to search for conditions resulting in a zero eigenvalue, (3) computation of a confidence level that describes if the global minimum has been found and (4) evaluation of optimization values, using either numerical continuation or directly simulating the ODE system, to verify that a bistability region exists. The generalized method has been tested on three motifs known to be capable of bistability. We have developed a variation of an optimization-based method for the discovery of bistability, which is not limited to uniterminal chemical reaction networks. Successful completion of the method provides an S-shaped bifurcation diagram, which indicates that the network acts as a bistable switch for the given optimization parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1986

Symmetry and stability in Taylor-Couette flow

The flow of a fluid between concentric rotating cylinders (the Taylor problem) is studied by exploiting the symmetries of the system. The Navier-Stokes equations, linearized about Couette flow, possess two zero and four purely imaginary eigenvalues at a suitable value of the speed of rotation of the outer cylinder. There is thus a reduced bifurcation equation on a six-dimensonal space which can be shown to commute with an action of the symmetry group 0(2) x S0(2). The group structure is used to analyze this bifurcation equation in the simplest (nondegenerate) case, and to compute the stabilities of solutions. In particular, when the outer cylinder is counterrotated, transitions which seem to agree with recent experiments of Andereck, Liu, and Swinney (1984) are obtained. It is also possible to obtain the 'main sequence' in this model. This sequence is normally observed in experiments when the outer cylinder is held fixed.

Golubitsky, M.↗
NASA NTRS1992

Viscous and inviscid instabilities of a trailing vortex

The linear stability of the trailing line vortex model of Batchelor (1964) is studied using a spectral collocation and matrix eigenvalue method. The entire unstable region in the swirl/axial wavenumber parameter space is mapped out for various azimuthal wavenumbers for both the inviscid and viscous stability problem. The results of the study provide a direct numerical validation of the large-azimuthal-wavenumber asymptotic analysis of Leibovich and Stewartson (1983). It is shown that accurate results are obtained up to azimuthal wavenumbers of 10,000 and greater, and the agreement with the asymptotic theory is excellent.

Mayer, Ernst W.↗
DOE OSTI2018

Complex Langevin simulation of a random matrix model at nonzero chemical potential

In this study we test the complex Langevin algorithm for numerical simulations of a random matrix model of QCD with a first order phase transition to a phase of finite baryon density. We observe that a naive implementation of the algorithm leads to phase quenched results, which were also derived analytically in this article. We test several fixes for the convergence issues of the algorithm, in particular the method of gauge cooling, the shifted representation, the deformation technique and reweighted complex Langevin, but only the latter method reproduces the correct analytical results in the region where the quark mass is inside the domain of the eigenvalues. In order to shed more light on the issues of the methods we also apply them to a similar random matrix model with a milder sign problem and no phase transition, and in that case gauge cooling solves the convergence problems as was shown before in the literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

MiniApp for Density Matrix Renormalization Group Hamiltonian Application Kernel

We present two miniapps that implement the core computational kernel of the DMRG++ application, a generic C++ code that implements the Density Matrix Renormalization Group (DMRG) algorithm. The DMRG++ core Kronecker multiplication kernel is formulated using a batched BLAS approach, with implementation that targets both multi-core CPUs using OpenMP and GPGPU using the MAGMA library. The kernel evaluates the matrix-vector multiplication of the target Hamiltonian matrix used in Lanczos algorithm for computing the lowest eigenvalue and eigenvector. The Hamiltonian matrix is expressed compactly as sums of Kronecker products of small dense matrices. We demonstrate improved performance of the miniapp on synthetic problem, and show the performance of the DMRG++ application using a plugin based on the miniapp. We also present an OpenMP miniapp that explores the use of nested parallel constructs to implement the Kronecker multiplication kernel, exploring the use of nested OpenMP worksharing and tasking abstractions to implement the multi-level parallel multiplication algorithm. The miniapp has been used as a co-design vehicle for evaluating features in the OpenMP-4.5 and upcoming OpenMP-5.0 standards.

Elwasif, Wael↗
DOE OSTI2016

Criticality calculation of non-ordinary systems

The specific features of calculation of the effective multiplication factor using the Monte Carlo method for weakly coupled and non-asymptotic multiplying systems are discussed. Particular examples are considered and practical recommendations on detection and Monte Carlo calculation of systems typical in numerical substantiation of nuclear safety for VVER fuel management problems are given. In particular, the problems of the choice of parameters for the batch mode and the method for normalization of the neutron batch, as well as finding and interpretation of the eigenvalue spectrum for the integral fission matrix, are discussed.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS1989

Wentzel-Kramers-Brillouin method in the Bargmann representation

It is demonstrated that the Bargmann representation of quantum mechanics is ideally suited for semiclassical analysis, using as an example the WKB method applied to the bound-state problem in a single well of one degree of freedom. For the harmonic oscillator, this WKB method trivially gives the exact eigenfunctions in addition to the exact eigenvalues. For an anharmonic well, a self-consistent variational choice of the representation greatly improves the accuracy of the semiclassical ground state. Also, a simple change of scale illuminates the relationship of semiclassical versus linear perturbative expansions, allowing a variety of multidimensional extensions.

Voros, A.↗
NASA NTRS2005

Introduction to Quantum Simulation

This viewgraph presentation addresses the problem of efficiently simulating the evolution of a quantum system. The contents include: 1) Quantum Simulation; 2) Extracting Answers from Quantum Simulations; 3) Quantum Fourier Transform; 4) Eigenvalue Estimation; 5) Fermionic Simulations.

quantum simulation↗
DOE OSTI2017

Improvement of the 2D/1D Method in MPACT Using the Sub-Plane Scheme

Oak Ridge National Laboratory and the University of Michigan are jointly developing the MPACTcode to be the primary neutron transport code for the Virtual Environment for Reactor Applications (VERA). To solve the transport equation, MPACT uses the 2D/1D method, which decomposes the problem into a stack of 2D planes that are then coupled with a 1D axial calculation. MPACT uses the Method of Characteristics for the 2D transport calculations and P3 for the 1D axial calculations, then accelerates the solution using the 3D Coarse mesh Finite Dierence (CMFD) method. Increasing the number of 2D MOC planes will increase the accuracy of the alculation, but will increase the computational burden of the calculations and can cause slow convergence or instability. To prevent these problems while maintaining accuracy, the sub-plane scheme has been implemented in MPACT. This method sub-divides the MOC planes into sub-planes, refining the 1D P3 and 3D CMFD calculations without increasing the number of 2D MOC planes. To test the sub-plane scheme, three of the VERA Progression Problems were selected: Problem 3, a single assembly problem; Problem 4, a 3x3 assembly problem with control rods and pyrex burnable poisons; and Problem 5, a quarter core problem. These three problems demonstrated that the sub-plane scheme can accurately produce intra-plane axial flux profiles that preserve the accuracy of the fine mesh solution. The eigenvalue dierences are negligibly small, and dierences in 3D power distributions are less than 0.1% for realistic axial meshes. Furthermore, the convergence behavior with the sub-plane scheme compares favorably with the conventional 2D/1D method, and the computational expense is decreased for all calculations due to the reduction in expensive MOC calculations.

Graham, Aaron M↗
DOE OSTI2022

Fast Reactor Physics Model Verification Studies using ARC and PyARC Workflows

PyARC was recently developed at Argonne National Laboratory to automate many of the tasks required in the ARC (Argonne Reactor Computation) fast reactor simulation workflow, from input file generation, code execution, data transfer between ARC codes, and output postprocessing. PyARC will likely be the path forward to train new users of the ARC codes with the goal of wide adoption by the national laboratories, academia, and industry. In particular, for the ANL-JAEA collaboration under the Civil Nuclear Working Group (CNWG) project agreement NE-01, PyARC will be used to model the Joyo and EBR-II reactors for comparisons with measured data and calculated results from JAEA (Task 3: Fast Reactor Fuel and Core). As an additional avenue for verification and validation, this report investigates the use of PyARC towards a variety of existing ARC-based reactor models, in order to understand its efficacy in replicating the behavior of base ARC codes and better understand any limitations within modeling realistic fast reactor problems. To this end, PyARC was used to model the Joyo MKI, RBEC Benchmark-M, PRISM Mod-B, and EBR-II Run 138B cores, and its results were compared to those from existing ARC-based models. It was found that for hexagonal-based geometries PyARC was able to replicate the behavior of ARC codes to within 10 pcm for small reactor cores, and ~150pcm difference in eigenvalue for larger cores. These discrepancies are attributed primarily to differences in local mesh refinement options between ARC and PyARC, which currently cannot be resolved with PyARC’s latest version (1.6.0). In some of these cases, PyARC was used to model steady-state problems with initial core compositions originating from a prior REBUS depletion calculation. While PyARC was not designed to support such steady-state calculations, workarounds were applied to replicate the behavior of ARC-based calculations as closely as possible. Thus, these results demonstrate the wide extent to which they can be applied to fast reactor problems while still providing immense benefit to the user in terms of automating and standardizing common routines within the fast reactor analysis workflow. This study concluded that PyARC will be suitable for modeling the steady-state conditions of the EBR-II and Joyo fast reactors as part of the CNWG project agreement.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗