Variable Dynamic Mode Decomposition for Estimating Time Eigenvalues in Nuclear Systems
Not provided.
Nuclear Science & Technology↗
SEARCH · Engineering Papers
Results for “Neutron transport equation”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Influence of Irradiation-induced Microstructural Defects on Thermal Transport in Single Crystal Thorium Dioxide
Microstructural defects formed as a result of fission fragment damage are known to drastically alter thermal conductivity, a fuel property that governs the efficiency of a nuclear reactor. A fundamental understanding of radiation-induced effects on thermal transport is critical for the development of advanced fuels. Ion-irradiation has widely been used to simulate the effects of neutron-irradiation by seeding atomic-to-nanoscale defects of controllable size and density. In this work, we investigate the influence of microstructural defects, induced by ion-irradiation, on the thermal properties of single crystal thorium dioxide samples grown using the hydrothermal technique. The samples were irradiated using 2 MeV protons at room temperature. A laser-based modulated thermoreflectance technique was used to measure the thermal diffusivity and conductivity within the damaged ThO2 region. The experimentally measured thermal properties were compared with Boltzmann Transport Equation predictions, to determine the impact of various defect types on the thermal properties of ThO2.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Anderson acceleration stability in NDA-accelerated k-eigenvalue problems
Anderson acceleration (AA) has been used to improve the stability and convergence rate of multiphysics iterative methods for reactor analysis. Most applications studied assume a tightly converged solution for the different physics problems, and AA is usually applied to state variables like temperature, density, and heat generation rate. In this paper, we study the theoretical performance of AA in NDA-accelerated k-eigenvalue problems. The problems and algorithms studied are simplified from the coupled iteration scheme adopted by MPACT and many other high-fidelity whole-core reactor codes. Compared to previous analyses of AA for these iteration schemes, we study the case with a partially converged neutronics solution and possibly partially converged nonlinear diffusion acceleration (NDA)/coarse mesh finite difference (CMFD) solutions. We observe that the performance of the iteration scheme with AA is very sensitive to the initial guess and is affected by the partially converged CMFD solutions. When the NDA solution is fully converged, using AA cannot achieve the optimal convergence rate in large-sized problems. Conversely, if the NDA solution is partially converged, the iteration scheme with AA can diverge or converge extremely slowly. It is found that the loss of robustness for AA is due to the fact that it is applied to the iterative subspace of state variables rather than the fundamental unknowns of the governing equations. To improve the robustness, the scalar flux should also be considered in the implementation of AA. After considering the residuals of flux, we observe that the stability is regardless of the partial convergence of NDA solutions. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Dense nuclear matter equation of state from heavy-ion collisions
The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics. With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, endeavors to develop sophisticated and reliable transport simulations to interpret these experiments, and the advent of multi-messenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS, elucidating its dependence on density, temperature, and isospin asymmetry. Among controlled terrestrial experiments, collisions of heavy nuclei at intermediate beam energies (from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixed-target frame) probe the widest ranges of baryon density and temperature, enabling studies of nuclear matter from a few tenths to about 5 times the nuclear saturation density and for temperatures from a few to well above a hundred MeV, respectively. Collisions of neutron-rich isotopes further bring the opportunity to probe effects due to the isospin asymmetry. However, capitalizing on the enormous scientific effort aimed at uncovering the dense nuclear matter EOS, both at RHIC and at FRIB as well as at other international facilities, depends on the continued development of state-of-the-art hadronic transport simulations. Furthermore, this white paper highlights the essential role that heavy-ion collision experiments and hadronic transport simulations play in understanding strong interactions in dense nuclear matter, with an emphasis on how these efforts can be used together with microscopic approaches and neutron star studies to uncover the nuclear EOS.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
OpenMC
OpenMC is an open source, community-developed framework for performing Monte Carlo particle transport calculations.It is capable of simulating neutron and photon transport below ~50 MeV and also includes a model for bremsstrahlung production of photons by electrons/positrons. Fixed source, k-eigenvalue, and subcritical multiplication problems can be solved. Problem geometries can be modeled either using constructive solid geometry or a CAD representation. A flexible and efficient tally system enables a wide variety of physical quantities to be tallied and analyzed. OpenMC can run in parallel using a hybrid MPI and OpenMP programming model and has been extensively tested on leadership class supercomputers. A built-in Bateman equation solver enables the modeling of material composition changes due to irradiation. One of the unique features of OpenMC is its rich, extensible Python and C/C++ programming interfaces that enable programming pre- and post-processing, multigroup cross section generation, workflow automation, multiphysics coupling, and the visualization of geometry and tally results. In addition to the core Monte Carlo transport solver and associated APIs, OpenMC includes a Python-based nuclear data interface that enables power users to inspect, modify,and perform various types of nuclear data processing on ENDF, ACE, and OpenMC¿s native HDF5 files
ROMANO, PaulK.↗
Gravitational Wave Eigenfrequencies from Neutrino-driven Core-collapse Supernovae
Abstract Core-collapse supernovae (CCSNe) are predicted to produce gravitational waves (GWs) that may be detectable by Advanced LIGO/Virgo. These GW signals carry information from the heart of these cataclysmic events, where matter reaches nuclear densities. Recent studies have shown that it may be possible to infer the properties of the proto-neutron star (PNS) via GWs generated by hydrodynamic perturbations of the PNS. However, we lack a comprehensive understanding of how these relationships may change with the properties of CCSNe. In this work, we build a self-consistent suite of over 1000 exploding CCSNe from a grid of progenitor masses and metallicities combined with six different nuclear equations of state (EOS). Performing a linear perturbation analysis on each model, we compute the resonant GW frequencies of the PNS, and we motivate a time-agnostic method for identifying characteristic frequencies of the dominant GW emission. From this, we identify two characteristic frequencies, of the early- and late-time signal, that measure the surface gravity of the cold remnant neutron star, and simultaneously constrain the hot nuclear EOS. However, we find that the details of the CCSN model, such as the treatment of gravity or the neutrino transport, and whether it explodes, noticeably change the magnitude and evolution of the PNS eigenfrequencies.
79 ASTRONOMY AND ASTROPHYSICS↗
Multilevel-in-Space-and-Energy CMFD in VERA
For full-core modeling in the Virtual Environment for Reactor Analysis (VERA), the three-dimensional multigroup eigenvalue neutron transport problem is solved by MPACT. To improve the efficiency of MPACT, advancements have been made in the transport accelerator. Multilevel-in-energy and multilevel-in-space coarse mesh finite difference (CMFD) solvers were developed to improve the efficiency of the CMFD accelerator. In this paper a new multilevel-in-space-and-energy CMFD solver is developed with coarsening in both space and energy on every level. Several different strategies are investigated for coarsening groups in energy. Modified V-cycle and multiple-cycle algorithms are evaluated for solving the multilevel equations. The performance of these solvers is compared for typical full-core reactor physics problems.
42 ENGINEERING↗
Development of a three-dimensional APOLLO3 neutrons deterministic scheme for the CABRI reactor
CABRI is an experimental reactor to study the fuel behavior during reactivity injection transients. These transients being highly multiphysics, the development of suitable modeling and simulation tools to simulate them is important for the optimization of the tests and the control of the experimental conditions. This paper focuses on the development of an APOLLO3 deterministic core calculation tool dedicated to the CABRI transient analysis. It represents the first stage of the incremental process for the implementation of a multiphysics time-dependent modeling of the CABRI transient. The neutron calculation scheme is based on a classical two-step approach. The first step consists of a 281-energy group calculation flux with the TDT-MOC (Method Of Characteristics) solver for cross-section space and energy (23 groups) collapsing for the CABRI different assembly clusters. The bias on a 2D core neutron calculation due to the self-shielding calculation and collapsing on a restricted pattern are investigated thanks to a comparison with a direct full 2D calculation on a quarter of core. The second step relies on a pin-resolved transport 3D transport core calculation with the SN solver MINARET. A progressive numerical validation process is followed to quantify the calculation biases on reactivity and reaction rates at each step using reference calculations with the stochastic code TRIPOLI4. The next development stage toward a multiphysics scheme will be the implementation of the 3D-kinetics equation resolution and the coupling with a core thermal-hydraulics model. (authors)
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
Physical, numerical, and computational challenges of modeling neutrino transport in core-collapse supernovae
The proposal that core collapse supernovae are neutrino driven is still the subject of active investigation more than 50 years after the seminal paper by Colgate and White. The modern version of this paradigm, which we owe to Wilson, proposes that the supernova shock wave is powered by neutrino heating, mediated by the absorption of electron-flavor neutrinos and antineutrinos emanating from the proto-neutron star surface, or neutrinosphere. Neutrino weak interactions with the stellar core fluid, the theory of which is still evolving, are flavor and energy dependent. The associated neutrino mean free paths extend over many orders of magnitude and are never always small relative to the stellar core radius. Thus, neutrinos are never always fluid like. Instead, a kinetic description of them in terms of distribution functions that determine the number density of neutrinos in the six-dimensional phase space of position, direction, and energy, for both neutrinos and antineutrinos of each flavor, or in terms of angular moments of these neutrino distributions that instead provide neutrino number densities in the four-dimensional phase-space subspace of position and energy, is needed. In turn, the computational challenge is twofold: (i) to map the kinetic equations governing the evolution of these distributions or moments onto discrete representations that are stable, accurate, and, perhaps most important, respect physical laws such as conservation of lepton number and energy and the Fermi–Dirac nature of neutrinos and (ii) to develop efficient, supercomputer-architecture-aware solution methods for the resultant nonlinear algebraic equations. In this review, we present the current state of the art in attempts to meet this challenge.
79 ASTRONOMY AND ASTROPHYSICS↗
Neutrino signal from proto-neutron star evolution: Effects of opacities from charged-current–neutrino interactions and inverse neutron decay
In this work, we investigate the impact of charged-current–neutrino processes on the formation and evolution of neutrino spectra during the deleptonization of proto-neutron stars. To this end we develop the full kinematics of these reaction rates consistent with the nuclear equation of state, including weak magnetism contributions. This allows us to systematically study the impact of inelastic contributions and weak magnetism on the $ν_e$ and $\bar{ν}_e$ luminosities and average energies. Furthermore, we explore the role of the inverse neutron decay, also known as the direct Urca process, on the emitted spectra of $\bar{ν}_e$. This process is commonly considered in the cooling scenario of cold neutron stars but has so far been neglected in the evolution of hot proto-neutron stars. We find that the inverse neutron decay becomes the dominating opacity source for low-energy $\bar{ν}_e$. Accurate three-flavor Boltzmann neutrino transport enables us to relate the magnitude of neutrino fluxes and spectra to details of the treatment of weak processes. This allows us to quantify the corresponding impact on the conditions relevant for the nucleosynthesis in the neutrino-driven wind, which is ejected from the proto-neutron star surface during the deleptonization phase.
79 ASTRONOMY AND ASTROPHYSICS↗
Radiation Transport and Shielding for Space Exploration and High Speed Flight Transportation
Transportation of ions and neutrons in matter is of direct interest in several technologically important and scientific areas, including space radiation, cosmic ray propagation studies in galactic medium, nuclear power plants and radiological effects that impact industrial and public health. For the proper assessment of radiation exposure, both reliable transport codes and accurate data are needed. Nuclear cross section data is one of the essential inputs into the transport codes. In order to obtain an accurate parametrization of cross section data, theoretical input is indispensable especially for processes where there is little or no experimental data available. In this grant period work has been done on the studies of the use of relativistic equations and their one-body limits. The results will be useful in choosing appropriate effective one-body equation for reaction calculations. Work has also been done to improve upon the data base needed for the transport codes used in the studies of radiation transport and shielding for space exploration and high speed flight transportation. A phenomenological model was developed for the total absorption cross sections valid for any system of charged and/or uncharged collision pairs for the entire energy range. The success of the model is gratifying. It is being used by other federal agencies, national labs and universities. A list of publications based on the work during the grant period is given below and copies are enclosed with this report.
Maung, Khin Maung↗
Steady detonation propagation in thin channels with strong confinement
We examine asymptotically the dynamics of two-dimensional, steady detonation wave propagation and failure for a strongly confined high explosive (HE), in which the width of the explosive is small relative to the reaction zone length. An energy balance equation is derived, which shows how the longitudinal acceleration of subsonic flow behind the detonation shock is influenced both by chemical reaction and by the effects of HE boundary streamline deflection, specifically via the induced rate of change of mass flux through the detonation wave. The latter serves to either counteract or reinforce the acceleration of longitudinal flow, depending on the sign of the gradient of the boundary streamline deflection at the detonation shock. The analysis is valid for general equations of state and chemical reaction rates in the HE. The asymptotically derived form of the energy equation represents an eigenvalue problem for the determination of the steady detonation propagation speed, solved via a shooting method. We explore specific results for ideal and stiffened equations of state, along with a pressure-dependent reaction rate for which changes in the pressure exponent and reaction order are also studied. We consider the influences of both straight and curved HE boundary streamline shapes. The asymptotic analysis reveals significant physical insights into how detonation propagation and failure are affected by strong confinement.
42 ENGINEERING↗
Dynamical Aspects of the Quark Gluon Plasma
Shortly after the Big Bang the entire universe was filled with a nearly perfect fluid known as the Quark Gluon Plasma. Relativistic heavy ion collisions can now reproduce this fluid in the laboratory where the Quark Gluon Plasma exhibits a rapid but smooth cross-over phase transition into hadrons at vanishing net-baryon densities. Recent experiments plan to explore finite baryon densities where a critical point is expected. If found, this would mark the first discovery of a critical point in a relativistic system described by a fundamental theory of nature, which would have far-reaching consequences for high-energy nuclear physics and nuclear astrophysics (such as in neutron star mergers). Characteristic temperatures of equilibrium (e.g. the inflection point of the entropy density) and transport coefficients (e.g. minimum of the shear viscosity over entropy density) vary widely at a cross-over phase transition but converge at a critical point, and extracting the behavior of these characteristic temperatures is a major focal point of this research. Specifically, the interplay between strange and light hadrons is exploited to study the flavor hierarchy in the cross-over region. To investigate this, a viscous relativistic hydrodynamics framework with two conserved charges is being developed into a new open-source code along with initial conditions that contain baryon number and strangeness. Flow observables sensitive to the equation of state and transport coefficients are calculated across beam energies. New techniques are being developed to study this flavor hierarchy from first principles and to extract the characteristic temperatures from experimental data. Through this new dynamical framework, this project provides essential guidance to the Beam Energy Scan II runs at Relativistic Heavy-Ion Collider and the future Facility for Antiproton and Ion Research facility in the search for the Quantum Chromodynamic critical point and subsequent investigation of the baryon-rich Quark Gluon Plasma.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Numerical investigation of two-dimensional buoyancy-driven eddies in liquid metal magnetohydrodynamic flows in breeding blankets *
Abstract Lead–lithium flows are key features in the design of tokamak breeding blanket concepts such as the dual-coolant lead–lithium (DCLL). Since they flow under magnetic fields, they are affected by magnetohydrodynamic (MHD) effects. The neutron flux originating in the tokamak plasma heats the breeding blanket channels in a non-uniform manner, inducing buoyancy forces in the liquid metal. Buoyancy may become a source of quasi-two-dimensional (Q2D) turbulence, and the appearance of eddies may affect the transport of heat and tritium across the blanket. Blankets characterized by high-speed liquid metal flows (such as DCLL) will need ceramic insulating walls to reduce the MHD-related pressure drop in the channels. In our simulations, we have used the Q2D model proposed by Sommeria and Moreau (SM82) which is especially suitable for modeling electrically insulating channel flows. On top of that, we have modelled buoyancy forces in the momentum equation using the Oberbeck–Boussinesq approximation. In this work, we include a validation of the implemented Q2D model in buoyancy-driven cases and identify a thermohydraulic configuration that promotes the generation of eddies and the accumulation of tritium. We also show the results provided by our post-processing tool based on the bi-dimensional fast Fourier transform for eddy detection and characterization. We complete our investigation by performing an initial assessment of how eddies can accumulate tritium in the breeding blanket. We conclude by discussing the relevance of preventing accumulation of tritium within the blanket and suggest a possible solution.
Suarez, Daniel (ORCID:0000000251740100)↗
The MP{sub N} method: a new angular discretization method based on piecewise polynomial interfaces fluxes
In transport calculations, it is well known how S{sub N} method is extremely inefficient in problems where the particle physics is dominated by streaming. The ray-effect eventually produced by the insufficient angular discretization, appears to be extremely persistent with respect to the refinement of the angular quadrature. The MP{sub N} method, that relies on continuous angular representation, offers a robust remedy to such an issue. MP{sub N} is based on the decomposition of the unit sphere into solid angles and on a piecewise continuous definition of interface fluxes, which are expanded in polynomials in each solid angle. This allows propagating more than one angular degree of freedom simultaneously while maintaining unaltered the block-diagonal pattern of the displacement plus removal operator. The method is therefore well suited for the flux resolution by means of a conventional sweep algorithm. Furthermore, unlike the S{sub N} method, MP{sub N} does not rely on discrete directions and, thus, on an angular quadrature formula, but rather constructs a set of linear equations solving for the angular moments of the flux for all discrete solid angles within the sweep. MP{sub N} shows an error convergence rate higher than S{sub N} at the expense of an increased size of the coefficient matrices, so of the computational cost. Although MP{sub N} is not free from ray-effect, the latter is effectively mitigated and less persistent with respect to the increase of the angular refinement order. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Thermomechanics coupling to Monte Carlo particle transport on unstructured mesh geometries using Cardinal
Geometry deformation due to thermal expansion influences neutron transport in many systems. Studying this phenomenon involves coupling models for neutronics, thermal hydraulics, and solid mechanics. To enable high fidelity modeling of these coupled physics, new capabilities were introduced in Cardinal, coupling OpenMC Monte Carlo particle transport models with MOOSE thermomechanical physics on unstructured moving-mesh geometries. In this work, we present a fully open-source capability leveraging on-the-fly mesh skinning to automatically regenerate OpenMC geometry, which allows multiphysics feedback from temperature, density, and geometry changes. The new capability is verified using an analytic benchmark slab problem, which couples S 2 neutron transport with thermal conduction, convective boundary conditions, Doppler-broadened cross sections, and nonlinear thermal expansion effects along the heated slab. Cardinal reproduces the analytic solutions for the neutron flux, heating, k eff , and temperature with demonstrated convergence in various error terms including mesh resolution and cross section temperature library spacing. For the nominal benchmark conditions and with a fine mesh, maximum relative errors for neutron flux, temperature, and heating are lower than 1%, while errors in integral quantities such as k eff and slab length are within 1 pcm and 48 µm, respectively. This work (i) presents a new numerical approach to thermomechanics coupling with OpenMC models, (ii) is the first (to our knowledge) to utilize a mechanical partial differential equation (PDE) solution to solve the (Griesheimer and Kooreman, 2022) analytic benchmark, and (iii) develops this verified capability within an open-source package.
97 - MATHEMATICS AND COMPUTING↗
Fluoride-Cooled High-Temperature Pebble-Bed Reactor Reference Plant Model
In this report we present work performed in Fiscal Year 2022 that demonstrates the modeling and simulation of a fully coupled neutronics thermal hydraulics reference plant model for a fluoride-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’s high-performance computer, which natively and seamlessly couples Griffin, Pronghorn, and the BISON Multiphysics Object-Oriented Simulation Environment based applications. Griffin provides reactor physics capabilities, including depletion to the equilibrium core, k-eigenvalue, adjoint, and transient. The unique direct equilibrium core capability in Griffin is based on a streamline methodology to spatially deplete the pebbles into burnup groups. Pronghorn solves the porous medium equations for the fluid regions and conduction in the solid regions and incorporates a fluidic diode model to simulate the transition from forced to natural convection during accident scenarios. MOOSE modules solves thermal conduction problems for the pebbles and tristructural isotropic 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, moderator, and reflector temperatures as as well as the FLiBe salt density. Here, we present results for the uncoupled equilibrium core and perform comparisons to equivalent Monte Carlo models. The power distributions and kinetic parameters obtained with Griffin are consistent with those computed with Griffin. We demonstrate a noticeable improvement with the use of discrete ordinates method (SN) transport. The coupled steady-state equilibrium core provides the initial condition for two time-dependent problems: a control rod withdrawal event and an unprotected loss of flow event. In both cases, the reactor design is self-stabilizing and the solutions are consistent with the expected physics. Although this model is prototypical regarding BlueCRAB’s capabilities, its results are consistent with published work by Kairos Power and other research entities. Significant improvements to the model are planned in future work.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Two-moment Neutrino Flavor Transformation with Applications to the Fast Flavor Instability in Neutron Star Mergers
Abstract Multi-messenger astrophysics has produced a wealth of data with much more to come in the future. This enormous data set will reveal new insights into the physics of core-collapse supernovae, neutron star mergers, and many other objects where it is actually possible, if not probable, that new physics is in operation. To tease out different possibilities, we will need to analyze signals from photons, neutrinos, gravitational waves, and chemical elements. This task is made all the more difficult when it is necessary to evolve the neutrino component of the radiation field and associated quantum-mechanical property of flavor in order to model the astrophysical system of interest—a numerical challenge that has not been addressed to this day. In this work, we take a step in this direction by adopting the technique of angular-integrated moments with a truncated tower of dynamical equations and a closure, convolving the flavor-transformation with spatial transport to evolve the neutrino radiation quantum field. We show that moments capture the dynamical features of fast flavor instabilities in a variety of systems, although our technique is by no means a universal blueprint for solving fast flavor transformation. To evaluate the effectiveness of our moment results, we compare to a more precise particle-in-cell method. Based on our results, we propose areas for improvement and application to complementary techniques in the future.
Astronomy & Astrophysics↗