1,721,003 research outputs found
An energy recondensation method using the discrete generalized multigroup energy expansion theory
Full text linkIn this paper, the discrete generalized multigroup (DGM) method was used to recondense the coarse group cross-sections using the core level solution, thus providing a correction for neighboring effect found at the core level. This approach was tested using a discrete ordinates implementation in both 1-D and 2-D. Results indicate that 2 or 3 iterations can substantially improve the flux and fission density errors associated with strong interfacial spectral changes as found in the presence of strong absorbers, reflector of mixed-oxide fuel. The methodology is also proven to be fully consistent with the multigroup methodology as long as a flat-flux approximation is used spatially
The OpenMC Monte Carlo particle transport code
Full text linkA new Monte Carlo code called OpenMC is currently under development at the Massachusetts Institute of Technology as a tool for simulation on high-performance computing platforms. Given that many legacy codes do not scale well on existing and future parallel computer architectures, OpenMC has been developed from scratch with a focus on high performance scalable algorithms as well as modern software design practices. The present work describes the methods used in the OpenMC code and demonstrates the performance and accuracy of the code on a variety of problems.United States. Department of Energy (DE-AC05-00OR22725
Solving eigenvalue response matrix equations with nonlinear techniques
Full text linkThis paper presents new algorithms for use in the eigenvalue response matrix method (ERMM) for reactor eigenvalue problems. ERMM spatially decomposes a domain into independent nodes linked via boundary conditions approximated as truncated orthogonal expansions, the coefficients of which are response functions. In its simplest form, ERMM consists of a two-level eigenproblem: an outer Picard iteration updates the k-eigenvalue via balance, while the inner λ -eigenproblem imposes neutron balance between nodes. Efficient methods are developed for solving the inner λ-eigenvalue problem within the outer Picard iteration. Based on results from several diffusion and transport benchmark models, it was found that the Krylov-Schur method applied to the λ -eigenvalue problem reduces Picard solver times (excluding response generation) by a factor of 2–5. Furthermore, alternative methods, including Picard acceleration schemes, Steffensen’s method, and Newton’s method, are developed in this paper. These approaches often yield faster k-convergence and a need for fewer k-dependent response function evaluations, which is important because response generation is often the primary cost for problems using responses computed online (i.e., not from a precomputed database). Accelerated Picard iteration was found to reduce total computational times by 2–3 compared to the unaccelerated case for problems dominated by response generation. In addition, Newton’s method was found to provide nearly the same performance with improved robustness
Predicting Correlation Coefficients for Monte Carlo Eigenvalue Simulations
Full text linkMonte Carlo methods are most often considered as a reference for neutron transport simulations since very limited approximations are made abount nuclear data and system geometry. To report uncertainty of any tally evaluated as generation averages, the sample variance is divided by the number of active generations, which is based on the assumption that
the neutron generations are independent. Correlation effects between neutrons in multiplying systems, particularly when performing power iteration to evaluate eigenvalues have been observed in previous work. Neglecting the correlation effect results in an underestimate of uncertainty
reported by Monte Carlo calculations. Previous work has also proposed methods to predict the underestimation ratio. Yamamoto et al expanded the fission source distribution with diffusion equation modes, performed numerical simulation of
the AR(autoregressive) process of the expansion coefficients
and used the correlation of the AR process to predict that of the Monte Carlo eigenvalue simulation. Sutton applied the discretized phase space (DPS) approach to predict the underestimation ratio but the method cannot predict the ratio when one neutron generates offspring in different phase space regions or generates a random number of offspring. This paper presents a method to predict the correlation effect with the model of multitype branching processes (MBP). The method requires simulations for one generation of neutrons without knowing the source distribution and
can predict the underestimation ratio for the cases where the traditional DPS approach does not work. The generation-to-generation correlation determines the convergence rate of active generations, the bias of variance estimator for each generation and the underestimation ratio of variance estimator for tallies averaged over active generations. The generation-to-generation correlation is characterized by the Auto-Correlation Coefficients (ACC) between tallies from different generations.United States. Dept. of Energy (Consortium for Advanced Simulation of Light Water Reactors. Contract DE-AC05-00OR22725
Techniques for Stabilizing Coarse-Mesh Finite Difference (CMFD) in Methods of Characteristics (MOC)
Full text linkThe Coarse-Mesh Finite Difference (CMFD) method has been widely used to effectively accelerate neutron transport calculations. It was however found to be at times unstable in the presence of strong heterogeneities. The common practice to improve stability is to employ a damping factor on the nonlinear diffusion coefficient terms, but there is no method to determine the optimal damping factor for a practical reactor problem prior to the calculation. This paper investigates two problem-agnostic
techniques that stabilize reactor calculations that would otherwise diverge with undamped CMFD. The first technique is to perform additional energy sweeps for the upscattering group region during the high-order
MOC calculation to generate more accurate information to pass into the CMFD calculation. The second technique extends the traditional scalar flux prolongation to provide spatial variations inside each acceleration cell. This study uses the 2D C5G7 problem and the Babcock & Wilcox 1810 series critical experiment benchmark to evaluate these methods. Numerical simulations showed that both techniques stabilize CMFD, and that the linear prolongation technique did not incur additional computational cost compared to the optimally damped conventional metho
Analysis of correlations and their impact on convergence rates in Monte Carlo eigenvalue simulations
Full text linkThis paper provides an analysis of the generation-to-generation correlations as observed when solving full core eigenvalue problems on PWR systems. Many studies have in the past looked at the impact of these correlations on reported variance and this paper extends the analysis to the observed convergence rate on the tallies, the effect of tally size and the effect of generation size. Since performing meaningful analysis on such a large problem is inherently difficult, a simple homogeneous reflective cube problem with analytical solution was developed that exhibits similar behavior to the full core PWR benchmark. The data in this problem was selected to match the dimensionality of the reactor problem and preserve the migration length travelled by neutrons. Results demonstrate that the variance will deviate significantly from the 1/N (N being the number of simulated particles) convergence rate associated with truly independent generations, but will eventually asymptote to 1/N after 1000's of generations regardless of the numbers of neutrons per generation. This indicates that optimal run strategies should emphasize lower number of active generations with greater number of neutrons per generation to produce the most accurate tally results. This paper also describes and compares three techniques to evaluate suitable confidence intervals in the presence of correlations, one based on using history statistics, one using generation statistics and one batching generations to reduce batch-to-batch correlation. Keywords: Monte Carlo, Tally Convergence, Autocorrelation, Confidence IntervalsUnited States. Department of Energy (Consortium for Advanced Simulation of Light Water Reactors. Contract DE-AC05-00OR22725
Windowed multipole sensitivity to target accuracy of the optimization procedure
Full text linkThis paper compares the accuracy of the windowed multipole direct Doppler broadening method to that of the ENDF-B/VII.1 libraries that come with MCNP6. Various windowed multipole libraries were generated with different maximum allowed relative errors. Then, the libraries were compared to the MCNP6 data via resonance integral and through single assembly Monte Carlo analysis. Since the windowed multipole uses resonance parameters, resonance integrals are only affected by the number of resonances included in the library and not by the order of the background fitting function. The relative performance of each library with varying maximum allowed error was evaluated. It was found that setting a maximum target relative error of 0.1% in the library provided highly accurate data that closely matches the MCNP6 data for all temperatures of interest, while still having suitable computational performance. Additionally, a library with a maximum relative error of 1% also provided reasonable accuracy on eigenvalue and reaction rates with a noticeable improvement on performance, but with a few statistically significant differences with the MCNP6 data.United States. Department of Energy (Consortium for Advanced Simulation of Light Water Reactors (CASL), contract No. DE-AC05-00OR22725)United States. Department of Energy (Center for Exascale Simulation of Advanced Reactors (CESAR), contract No. DE-AC02-06CH11357))United States. Department of Energy (Nuclear Energy University Programs Graduate Fellowship, contract No. DE-NE-0000102
Progress toward Monte Carlo–thermal hydraulic coupling using low-order nonlinear diffusion acceleration methods
Full text linkA new approach for coupled Monte Carlo (MC) and thermal hydraulics (TH) simulations is proposed using low-order nonlinear diffusion acceleration methods. This approach uses new features such as coarse mesh finite difference diffusion (CMFD), multipole representation for fuel temperature feedback on microscopic cross sections, and support vector machine learning algorithms (SVM) for iterations between CMFD and TH equations. The multipole representation method showed small differences of about 0.3% root mean square (RMS) error in converged assembly source distribution compared to a conventional MC simulation with ACE data at the same temperature. This is within two standard deviations of the real uncertainty. Eigenvalue differences were on the order of 10 pcm. Support vector machine regression was performed on-the-fly during MC simulations. Regression results of macroscopic cross sections parametrized by coolant density and fuel temperature were successful and eliminated the need of partial derivative tables generated from lattice codes. All of these new tools were integrated together to perform MC-CMFD-TH-SVM iterations. Results showed that inner iterations between CMFD-TH-SVM are needed to obtain a stable solution
Simple benchmark for evaluating self-shielding models
Full text linkAccounting for self-shielding effects is paramount to accurate generation of multigroup cross sections for use in deterministic reactor physics neutronics calculations. Historically, equivalence in dilution and subgroup techniques have been the preeminent means of accounting for these effects, but recent work has proposed new solutions, including the Embedded Self-Shielding Method (ESSM). This paper presents a very simple benchmark problem to compare these and future self-shielding methods. The benchmark is perhaps the simplest problem in which both energy and spatial self-shielding effects are important, a two-region problem with a lumped resonant material. A single resonance in a
single energy group is considered. Scattering is approximated using the narrow resonance approximation, decoupling each energy value and allowing an easily-computed reference solution to be obtained.
Equivalence in dilution using two-term rational expansions and the subgroup method were both found to give very accurate solutions on this benchmark, with errors less than 1% in nearly all cases. One-term rational expansions and ESSM showed much larger errors
A Cumulative migration method for computing rigorous transport cross sections and diffusion coefficients for LWR lattices with Monte Carlo
Full text linkA new method for computing homogenized assembly neutron transport cross sections and diffusion coefficients that is both rigorous and computationally efficient is proposed in this paper. In the limit of a homogeneous hydrogen slab, the new method is equivalent to the long-used, and only-recently-published CASMO transport method. The rigorous method is used to demonstrate the sources of inaccuracy in the commonly applied “out-scatter” transport correction. It is also demonstrated that the newly developed method is directly applicable to lattice calculations performed by Monte Carlo and is capable of computing rigorous homogenized transport cross sections for arbitrarily heterogeneous lattices. Comparisons of several common transport cross section approximations are presented for a simple problem of infinite medium hydrogen. The new method has also been applied in computing 2-group diffusion data for an actual PWR lattice from BEAVRS benchmark.Idaho National Laboratory (Contract DE-AC07-05ID14517
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