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DOE OSTI2025

Equilibrium Core Model for Micro Pebble Bed Reactors Using OpenMC

Estimating the equilibrium state for pebble bed reactors (PBRs) presents complex challenges as it requires simultaneous consideration of changes in the pebbles’ movement as well as their fuel compositions. Whereas traditional approaches use multigroup diffusion codes for neutronics calculations of PBRs’ equilibrium state, the double-heterogeneity of PBRs complicates neutron cross-section generation. Continuous-energy Monte Carlo (MC) methods are better suited for detailed PBR analysis because of their natural handling of double-heterogeneity, but they demand substantially more computational resources. Here, this study introduces a novel method for efficiently estimating the equilibrium state in small and micro PBRs with reduced computational cost. The method is anticipated to accelerate the processes of core design and performing parametric studies for utilizing advanced fuel and structural materials. The HTR-10 reactor design was used for validating the method’s predictions and evaluating its computational efficiency. When compared to reference calculation values from the literature, criticality (k-effective) was predicted to be approximately within the margin of error of the MC transport calculation, average core power density (in megawatts per cubic meter) was predicted within 2.5% relative error, and maximum thermal flux (10 13 n/cm 2 .s −1 ) was predicted within 1.8% relative error. The calculated inventory of fission products and fuel composition in the equilibrium core were within 15% and 16.6%, respectively, when compared to reported values from the literature. The difference is attributed to variance in the considered values of the core temperature, which was found to significantly affect the depletion analyses.

Equilibrium core↗

DOE OSTI2023

Probability of Initiation in Neutron Transport

We discuss the numerical solution of the nonlinear integro-differential equation for the probability of a divergent neutron chain in a stationary system (i.e., the probability of initiation (POI)). We follow the development described in Bell’s classic paper on the stochastic theory of neutron transport. As noted by Bell, the linearized form of this equation resembles the linear adjoint neutron transport equation. A matrix formalism for the discretized steady state (or forward) neutron equation in slab geometry is first developed and is then used to derive the discrete adjoint equation. A main advantage of this discrete development is that the resulting discrete adjoint equation does not depend upon how the multigroup cross sections for the forward problem are obtained. That is, we derive the discrete adjoint directly from the discrete forward equations rather than discretizing directly the adjoint equation. This also guarantees that the discrete adjoint operator is consistent with the inner product used to define the adjoint operator. We discuss three approaches for the numerical solution of the POI equations, and present numerical results on several test problems. The three solution methods are a simple fixed-point iteration, a second approach that is akin to a nonlinear Power iteration, and a third approach which uses a Newton-Krylov nonlinear solver. We also give sufficient conditions to guarantee the existence and uniqueness of nontrivial solutions to our discrete POI equations when the discrete system is supercritical, and that only the trivial solution exists when the discrete system is subcritical. Our approach is modeled after the analysis presented for the continuous POI equations by Mokhtar-Kharroubi and Jarmouni-Idrissi, and by Pazy and Rabinowitz.

42 ENGINEERING↗

DOE OSTI2024

A Variable Eddington Factor Model for Thermal Radiative Transfer with Closure Based on Data-Driven Shape Function

Here, a new variable Eddington factor (VEF) model is presented for nonlinear problems of thermal radiative transfer (TRT). The VEF model is data-driven and acts on known (a-priori) radiation-diffusion solutions for material temperatures in the TRT problem. A linear auxiliary problem is constructed for the radiative transfer equation (RTE) whose emission source and opacities are evaluated at these known material temperatures. The solution to this RTE approximates the specific intensity distribution in phase-space and time. It is applied as a shape function to define the Eddington tensor for the presented VEF model. The shape function computed via the auxiliary RTE problem will capture some degree of transport effects within the TRT problem. The VEF moment equations closed with this approximate Eddington tensor will thus carry with them these captured transport effects. In this study, the temperature data comes from multigroup P 1 , P 1/3 , and flux-limited diffusion radiative transfer models. The proposed VEF model can be interpreted as a transport-corrected diffusion reduced-order model. Numerical results are presented on the Fleck-Cummings test problem which models a supersonic wavefront of radiation. The VEF model is shown to improve accuracy by 1–2 orders of magnitude compared to the considered radiation-diffusion model solutions to the TRT problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2011

SHOCK BREAKOUT IN TYPE II PLATEAU SUPERNOVAE: PROSPECTS FOR HIGH-REDSHIFT SUPERNOVA SURVEYS

Shock breakout is the brightest radiative phenomenon in a supernova (SN) but is difficult to be observed owing to the short duration and X-ray/ultraviolet (UV)-peaked spectra. After the first observation from the rising phase reported in 2008, its observability at high redshift is attracting enormous attention. We perform multigroup radiation hydrodynamics calculations of explosions for evolutionary presupernova models with various main-sequence masses M {sub MS}, metallicities Z, and explosion energies E. We present multicolor light curves of shock breakouts in Type II plateau SNe, being the most frequent core-collapse SNe, and predict apparent multicolor light curves of shock breakout at various redshifts z. We derive the observable SN rate and reachable redshift as functions of filter x and limiting magnitude m {sub x,lim} by taking into account an initial mass function, cosmic star formation history, intergalactic absorption, and host galaxy extinction. We propose a realistic survey strategy optimized for shock breakout. For example, the g'-band observable SN rate for m {sub g',lim} = 27.5 mag is 3.3 SNe deg{sup -2} day{sup -1} and half of them are located at z {>=} 1.2. It is clear that the shock breakout is a beneficial clue for probing high-z core-collapse SNe. We also establish ways to identify shock breakout and constrain SN properties from the observations of shock breakout, brightness, timescale, and color. We emphasize that the multicolor observations in blue optical bands with {approx}hour intervals, preferably over {>=}2 continuous nights, are essential to efficiently detect, identify, and interpret shock breakout.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

RADIATION TRANSPORT FOR EXPLOSIVE OUTFLOWS: OPACITY REGROUPING

Implicit Monte Carlo (IMC) and Discrete Diffusion Monte Carlo (DDMC) are methods used to stochastically solve the radiative transport and diffusion equations, respectively. These methods combine into a hybrid transport-diffusion method we refer to as IMC-DDMC. We explore a multigroup IMC-DDMC scheme that in DDMC, combines frequency groups with sufficient optical thickness. We term this procedure ''opacity regrouping''. Opacity regrouping has previously been applied to IMC-DDMC calculations for problems in which the dependence of the opacity on frequency is monotonic. We generalize opacity regrouping to non-contiguous groups and implement this in SuperNu, a code designed to do radiation transport in high-velocity outflows with non-monotonic opacities. We find that regrouping of non-contiguous opacity groups generally improves the speed of IMC-DDMC radiation transport. We present an asymptotic analysis that informs the nature of the Doppler shift in DDMC groups and summarize the derivation of the Gentile-Fleck factor for modified IMC-DDMC. We test SuperNu using numerical experiments including a quasi-manufactured analytic solution, a simple 10 group problem, and the W7 problem for Type Ia supernovae. We find that opacity regrouping is necessary to make our IMC-DDMC implementation feasible for the W7 problem and possibly Type Ia supernova simulations in general. We compare the bolometric light curves and spectra produced by the SuperNu and PHOENIX radiation transport codes for the W7 problem. The overall shape of the bolometric light curves are in good agreement, as are the spectra and their evolution with time. However, for the numerical specifications we considered, we find that the peak luminosity of the light curve calculated using SuperNu is ∼10% less than that calculated using PHOENIX.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

A Study of Low-Temperature Neutron Star Atmospheres

We present a study of how a low-temperature accreted atmosphere influences the emitted X-ray spectrum of a neutron star. The atmosphere models and spectra were computed with Zcode, a multigroup radiation transfer code developed at the Los Alamos National Laboratory. Though the underlying hot neutron star behaves as a blackbody, the atmosphere shifts the peak of spectrum away from a blackbody and toward higher energies, producing an emitted spectrum similar to a dilute blackbody. Quantifying the effects of this atmosphere will remove a source of uncertainty in X-ray observations and better constrain the mass-radius relation for neutron stars and thus the equation of state of dense matter. We present a suite of these atmospheres with varying compositions and temperatures as well as the resulting spectra.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

Observation of Nonlocal Heat Flux Using Thomson Scattering

Here, nonlocal heat flux was measured in laser-produced coronal plasmas using a novel Thomson scattering technique. The measured heat flux was smaller than the classical values inferred from the measured plasma conditions in regions with large temperature gradients and agreed with classical values for weak gradients. Vlasov–Fokker–Planck simulations self consistently calculated the electron distribution functions used to reproduce the measured Thomson scattering spectra and to determine the heat flux. Multigroup nonlocal simulations overestimated the measured heat flux.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2011

Investigations of laser plasmas dynamics by means of real and virtual Langmuir probes

In this paper we propose a novel technique for LPP-Laser Produced Plasmas investigation, combining high time resolved measurements using compact Langmuir Probes with the output of a theoretical model called HYBLAS developed on purpose, which is able to simulate the charged particles collected by a so-called virtual probe. It will be shown that with an appropriate experimental set-up and with the use of a Matlab software able to accurately analyze the experimental I-V curves, laser plasmas can be investigated properly even if the probe is placed very close to the target surface. This permits not only to study the plume expansion with a high temporal resolution, but also to estimate correctly the self-generated coulomb electric field inside the plume and to detect the inner structure of the the first upcoming expanding plasma. HYBLAS is able to predict and describe the plume expansion at relatively low power densities and is a powerful method to compare directly the experimental current signals with the numerical results if the initial conditions are settled properly. A direct comparison of the theoretical data with the experimental ones realized on different metal targets shows that our method is able to predict properly the overall plasma expansion in the nanosecond laser pulse duration regime. The virtual probe method was moreover tested by comparing the numerical results with another numerical code called MULTI, which simulate the expansion by combining the hydrodynamics equations to a multigroup method in order to include the radiation transport. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Accelerated Deterministic Phonon Transport With Consistent Material Temperature and Intensities

Abstract We present a method for deterministically solving the frequency and temperature dependent phonon radiative transport (PRT) equation in the single-mode relaxation time (SMRT) approximation in the self-adjoint angular flux (SAAF) form. To handle the nonlinear coupling between the phonon intensities and the material temperature, we apply a linearization approach that is similar to one in thermal radiative transport. This procedure leads to the PRT equation with pseudo-scattering. The method presented includes acceleration of both the inner pseudo-scattering source iterations and outer temperature iteration with a gray diffusion synthetic acceleration (DSA) and Anderson acceleration, respectively. We use the finite-element method to discretize the PRT equation in space and the method of discrete ordinates (SN) for angular discretization. The proposed method is verified by a gray method of manufactured solutions problem and demonstrated on a problem using temperature and direction dependent multigroup data from lithium aluminate (LiAlO2). The iterative performance of the acceleration method in each test is then compared to the unaccelerated method.

Engineering↗

DOE OSTI2024

Performance Portable Graphics Processing Unit Acceleration of a High-Order Finite Element Multiphysics Application

The Lawrence Livermore National Laboratory (LLNL) will soon have in place the El Capitan exascale supercomputer, based on advanced micro devices (AMD) graphics processing units (GPUs). As part of a multiyear effort under the National Nuclear Security Administration (NNSA) Advanced Simulation and Computing (ASC) program, we have been developing marbl, a next generation, performance portable multiphysics application based on high-order finite elements. In previous years, we successfully ported the Arbitrary Lagrangian–Eulerian (ALE), multimaterial, compressible flow capabilities of marbl to nvidia GPUs as described in Vargas et al. Here, in this paper, we describe our ongoing effort in extending marbl's GPU capabilities with additional physics, including multigroup radiation diffusion and thermonuclear burn for high energy density physics (HEDP) and fusion modeling. We also describe how our portability abstraction approach based on the raja Portability Suite and the mfem finite element discretization library has enabled us to achieve high performance on AMD based GPUs with minimal effort in hardware-specific porting. Throughout this work, we highlight numerical and algorithmic developments that were required to achieve GPU performance.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

COUPLING OF RELAP5-SCDAP MOD4.0 AND NEUTRONIC CODES

High-fidelity and accurate nuclear system codes play a key role in the design and analysis of complex nuclear power plants, which consist of multiple subsystems, such as the reactor core (and its fuel, burnable poisons, control elements, etc.), the reactor internal structures, the vessel, and the energy conversion subsystem and beyond to grid demand. Most commonly the interplay between these various subsystems is modeled using coupled codes, each of which represents one of the subsystems. And the most common direct coupling is that of thermal-hydraulics and neutronics codes. The subject of this paper is the coupling of codes that model not only thermal-hydraulics and neutronics, but also structural components damage. Furthermore, the neutronic component is not limited to the sole core solver. The coupled code system encompasses thermal-hydraulics, material performance of the fuel, neutronic solver, and neutronic data preparation. Thus, this paper presents a framework for coupling RELAP5/SCDAPSIM/MOD4.0 with a suite of neutron kinetics codes that includes NESTLE, DRAGON and a version of the ENDF library. The version of the RELAP5/SCDAPSIM/MOD4.0 code used in this work is one developed by Innovate System Software (ISS) as part of the international SCDAP Development and Training Program (SDTP) for best-estimate analysis to model reactor transients including severe accident phenomena. This RELAP5/SCDAPSIM/MOD4.0 code version is also capable of predicting nuclear fuel performance. It uses nodal power distributions to calculate mechanical and thermal parameters such as heat-up, oxidation and meltdown of fuel rods and control rods, the ballooning and rupture of fuel rod cladding, the release of fission products from fuel rods, and the disintegration of fuel rods into porous debris and molten material. On the neutronics side, this work uses the NESTLE and DRAGON codes. NESTLE is a multi-dimensional static and kinetic neutronic code developed at North Carolina State University. It solves up to four energy groups neutron diffusion equations utilizing the Nodal Expansion Method (NEM) in Cartesian or hexagonal geometry. The DRAGON code, developed at Ecole Polytechnique de Montreal, performs lattice physics calculations based on the neutron transport equation and is capable of using very fine energy group structures. In this work, we have developed a coupling approach to exchange data among the various modules. In the coupling process, the generated nuclear data (in fine multigroup energy structure) are collapsed down into two- or four-group energy structures for use in NESTLE. The neutron kinetics and thermal-hydraulics modules are coupled at each time step by using the cross-section data. The power distribution results of the neutronic calculations are transmitted to the thermal-hydraulics code. The spatial distribution of coolant density and the fuel-moderator temperature, which result from the thermal-hydraulic calculations, are transmitted back to the neutron kinetics codes and then the loop is closed using new neutronics results. Details of the actual data transfers will be described in the full length paper.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2010

Calculation of thermal fluxes of plasma torch reradiation under the action of laser radiation on a condensed target

The problem of laser deposition with allowance for thermal radiation transport inside and outside the laser torch is considered in a multigroup approximation. The energy fluxes of laser torch thermal radiation onto a target in the far and near zones are calculated as functions of time and the character of the exposure. It is shown that absorption of thermal fluxes in the substrate and target in the course of laser deposition results in their substantial heating. The possibility of diagnosing thermal radiation fluxes from the laser torch by using photodetectors is demonstrated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

NJOY2016

NJOY2016 is used to convert evaluations in the Evaluated Nuclear Data Files (ENDF) format into forms useful for practical applications such as fission and fusion reactor analysis, criticality safety, radiation shielding, nuclear waste management, nuclear medicine procedures, and more. It begins with the generation of pointwise libraries, including reaction and resonance reconstruction, Doppler broadening, radiation heating and damage, thermal scattering data, unresolved resonance data, and gas production. It reviews the production of libraries for the continuous-energy Monte Carlo code MCNP, multigroup neutron, photon, and particle cross sections and matrices, and photon interaction data. Uncertainty information for ENDF data is processed, including the capability for calculating covariances of resonance data, angular distributions, energy distributions, and radioactive nuclide production. NJOY can prepare and process thermal scattering data evaluations into application libraries. It can also plot cross sections, angular distributions and secondary emission spectra.

Kahler III, A. C. (Skip)↗

DOE OSTI2017

Branson: A Mini-App for Studying Parallel IMC, Version 1.0

This code solves the gray thermal radiative transfer (TRT) equations in parallel using simple opacities and Cartesian meshes. Although Branson solves the TRT equations it is not designed to model radiation transport: Branson contains simple physics and does not have a multigroup treatment, nor can it use physical material data. The opacities have are simple polynomials in temperature there is a limited ability to specify complex geometries and sources. Branson was designed only to capture the computational demands of production IMC codes, especially in large parallel runs. It was also intended to foster collaboration with vendors, universities and other DOE partners. Branson is similar in character to the neutron transport proxy-app Quicksilver from LLNL, which was recently open-sourced.

Long, Alex↗

DOE OSTI2018

SCEPTRE v. 2.0 (Sandia Computational Engine for Particle Transport for Radiat

SCEPTRE solves the linear Boltzmann transport equation for general one-, two- and three-dimensional unstructured-mesh Cartesian geometries. SCEPTRE can handle any particle type for which multigroup-Legendre cross sections are available. However, the code is designed primarily to model the transport of photons, electrons, and positrons through matter. SCEPTRE 2.0 includes several auxiliary packages for pre- and post-processing, regression testing, stochastic radiation transport, thermal radiation transport, and charged-particle transport in the presence of electromagnetic fields. SCEPTRE 2.0 includes sophisticated transport-synthetic acceleration and ray-effects mitigation capabilities.

Pautz, Shawn↗

DOE OSTI2021

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.↗

DOE OSTI2026

ndi

The Nuclear Data Interface (NDI) is an application programming interface (API) that allows access to standard nuclear data parameters while hiding the underlying details of the data libraries and their storage. It allows access to multigroup transport data (neutron and gamma), thermonuclear burn data, dosimetry data, production/depletion chain data, radiochemistry data, and secondary neutron multiplicity data. The name NDI refers to both the code and data formats supported by the code.

Saller, Thomas↗

DOE OSTI2025

SEFOR Core I-E

This repository contains the VTB model developed for the Southwest Experimental Fast Oxide Reactor (SEFOR) core configuration I-E using the NEAMS tools. The MOOSE Reactor Module was employed to set up the geometry mesh, MC2-3 was applied to generate multigroup cross sections at various temperatures, and Griffin was used to calculate the k-eff values of Core I-E across these temperature conditions. To validate the deterministic results from Griffin, reference solutions were obtained with the Monte Carlo code Shift. The reactivity feedback was then derived and compared against SEFOR experimental data from isothermal tests in order to assess the performance of Griffin. Reproducing these results requires licensed access to several code systems, including Shift, Griffin, and MC2-3. Instructions for obtaining and accessing these codes can be found at the following locations: https://www.ornl.gov/scale/releases for SCALE/Shift, https://mooseframework.inl.gov/ncrc/applications/ncrc_root_griffin.html for Griffin, and https://www.anl.gov/nse/mc23 for MC2-3.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗