Engineering topics

Ganapol, Barry

Publications and source records attributed to Ganapol, Barry.

4 records

DOE OSTI2021

An Analytic Benchmark for Neutron Boltzmann Transport with Downscattering—Part I: Flux and Eigenvalue Solutions

Computing in the energy dimension is one of the greatest challenges confronting present-day deterministic neutron transport solvers. Accurately resolving the neutron flux as neutrons downscatter across resonances in the nuclear cross sections currently requires considerable computing power and suffers from approximation errors. Flux uncertainty resulting from the uncertainty of the resonance structure is the single-largest cause of reactivity uncertainty. Any additional reference solution for the critical neutron downscattering problem with resonance phenomena would be a boon to verification and validation of neutronics codes. This paper establishes a benchmark to verify the accuracy of neutron transport criticality solvers along the energy dimension. For the first time, the analytic solution of the flux amplitude is derived in the particular case of an infinite homogeneous medium with isotropic scattering in the center of mass and an arbitrary number of no-threshold, neutral particle reaction resonances (e.g., radiative capture, fission, and resonance scattering). Furthermore, original analytic expressions are established to quantify the discrepancy between the ψ k (E) and ψ α (E) flux amplitudes, respective solutions of the multiplication factor k, or the exponential time-evolution frequency α eigenproblems. The physical study of these relations led to analysis of their first-order relative difference near the criticality condition α=0. Finally, numerical solutions are provided to a benchmark problem constituted of the first resonance of 239 Pu, the 6.67-eV resonance of 238 U, and a scattering isotope with a flat cross section, allowing for the computational verification of the energy resolution of current neutron transport criticality codes. Through these novel results, this analytic benchmark can serve as a reference to verify the energy resolution and sensitivity analysis of neutron transport criticality calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Global error analysis of the Chebyshev rational approximation method

The Chebyshev rational approximation method (CRAM) has become a widely adopted method for solving nuclear depletion problems. Therefore, understanding CRAM’s accuracy is important for the safe operation of nuclear power plants. This article performs a global error analysis of CRAM and finds that, as the length of the time step approaches zero, the relative error measured between the exact and CRAM solutions at a fixed end time approaches one and infinity for even and odd orders, respectively; for intermediate time step sizes, a minimum in relative error is observed. Finally, we show that the reason for CRAM’s behavior is that the method is inconsistent. Two best practices for using CRAM, derived from these results, are: (1) use CRAM order 16 or higher, (2) if necessary, increase the CRAM order when multiphysics coupling requires smaller time steps.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2002

Clues to Coral Reef Health: Integrating Radiative Transfer Modeling and Hyperspectral Data

An important contribution to coral reef research is to improve spectral distinction between various health states of coral species in areas subject to harmful anthropogenic activity and climate change. New insights into radiative transfer properties of corals under healthy and stressed conditions can advance understandings of ecological processes on reefs and allow better assessments of the impacts of large-scale bleaching and disease events, Our objective was to examine the spectral and spatial properties of hyperspectral sensors that may be used to remotely sense changes in reef community health. We compare in situ reef environment spectra (healthy coral, stressed coral, dead coral, algae, and sand) with airborne hyperspectral data to identify important spectral characteristics and indices. Additionally, spectral measurements over a range of water depths, relief, and bottom types are compared to help quantify bottom-water column influences. In situ spectra were collected in July and August 2002 at the Long Rock site in the Andros Island, Bahamas coastal zone coral reef. Our primary emphasis was on Acropora palmata (or elkhorn coral), a major reef building coral, which is prevalent in the study area, but is suffering from white band disease. A. palmata is currently being, proposed as an endangered species because its populations have severely declined in many areas of the Caribbean. In addition to the A. palmata biotope, we have collected spectra of at least seven other coral biotopes that exist within the study area, each with different coral community composition, density of corals, relief, and size of corals. Coral spectral reflectance was then input into a radiative transfer model, CORALMOD (CM1), which is based on a leaf radiative transfer model. In CM1, input coral reflectance measurements produce modeled reflectance through an inversion at each visible wavelength to provide the absorption spectrum. Initially, we imposed a scattering baseline that is the same regardless of the coral condition and that coral is optically thick and no light is transmitted through coral. Here we will focus on methodology, experimental design, and initial findings of the in situ spectral measurements and preliminary output from the radiative transfer model.

Guild, Liane↗

NASA NTRS1993

Development of deterministic transport methods for low energy neutrons for shielding in space

Transport of low energy neutrons associated with the galactic cosmic ray cascade is analyzed in this dissertation. A benchmark quality analytical algorithm is demonstrated for use with BRYNTRN, a computer program written by the High Energy Physics Division of NASA Langley Research Center, which is used to design and analyze shielding against the radiation created by the cascade. BRYNTRN uses numerical methods to solve the integral transport equations for baryons with the straight-ahead approximation, and numerical and empirical methods to generate the interaction probabilities. The straight-ahead approximation is adequate for charged particles, but not for neutrons. As NASA Langley improves BRYNTRN to include low energy neutrons, a benchmark quality solution is needed for comparison. The neutron transport algorithm demonstrated in this dissertation uses the closed-form Green's function solution to the galactic cosmic ray cascade transport equations to generate a source of neutrons. A basis function expansion for finite heterogeneous and semi-infinite homogeneous slabs with multiple energy groups and isotropic scattering is used to generate neutron fluxes resulting from the cascade. This method, called the FN method, is used to solve the neutral particle linear Boltzmann transport equation. As a demonstration of the algorithm coded in the programs MGSLAB and MGSEMI, neutron and ion fluxes are shown for a beam of fluorine ions at 1000 MeV per nucleon incident on semi-infinite and finite aluminum slabs. Also, to demonstrate that the shielding effectiveness against the radiation from the galactic cosmic ray cascade is not directly proportional to shield thickness, a graph of transmitted total neutron scalar flux versus slab thickness is shown. A simple model based on the nuclear liquid drop assumption is used to generate cross sections for the galactic cosmic ray cascade. The ENDF/B V database is used to generate the total and scattering cross sections for neutrons in aluminum. As an external verification, the results from MGSLAB and MGSEMI were compared to ANISN/PC, a routinely used neutron transport code, showing excellent agreement. In an application to an aluminum shield, the FN method seems to generate reasonable results.

Ganapol, Barry↗