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The thermal radiative transfer equations (TRT) model many important phenomena of interest at LANL. The TRT equations model time-dependent thermal radiation through a medium, i.e., how thermal radiation loses energy by absorption, gains energy via emission processes, and redistributes energy via scattering.
A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor) equations for moments of the radiation intensity and (ii) the normalized Boltzmann transport equation (BTE). The multilevel system of moment equations is derived by projection of the BTE onto a sequence of subspaces which represent elements of the phase space of the problem. Exact closure for the moment equations is provided by the Eddington tensor. A Petrov-Galerkin (PG) projection of the normalized BTE is formulated using a proper orthogonal decomposition (POD) basis representing the normalized radiation intensity over the whole phase space and time. The Eddington tensor linearly depends on the solution of the normalized BTE. By linear superposition of the POD basis functions, a low-rank expansion of the Eddington tensor is constructed with coefficients defined by the PG projected normalized BTE. The material energy balance (MEB) equation is coupled with the effective gray low-order equations which exist on the same dimensional scale as the MEB equation. The resulting TRT ROM is structure and asymptotic preserving. A detailed analysis of the ROM is performed on the classical Fleck-Cummings (F-C) TRT multigroup test problem in 2D geometry. Numerical results are presented to demonstrate the ROM's effectiveness in the simulation of radiation wave phenomena. Importantly, the ROM is shown to produce solutions with sufficiently high accuracy while using low-rank approximation of the normalized BTE solution. Essential physical characteristics of supersonic radiation wave are preserved in the ROM solutions.
We apply a nonlinearly preconditioned, quasi-Newton framework to accelerate the numerical solution of the thermal radiative transfer (TRT) equations. This framework was inspired by the unpublished method that has existed for years in Teton, Lawrence Livermore National Laboratory’s deterministic TRT code. In this paper, we cast this iteration scheme within a formal nonlinear preconditioning framework and compare its performance against other iteration schemes in the framework. With proper choices of iteration controls for the various levels of the solver, we can recover the standard linearized one-step method, a full nonlinear Newton scheme, as well as the method in Teton. In brief, the nonlinear preconditioning TRT scheme formally eliminates the material temperature equation from the nonlinear system in a nonlinear analog of a Schur complement. This nonlinear elimination step involves solving a decoupled nonlinear equation for each spatial degree of freedom and is therefore inexpensive. By applying a quasi-Newton iteration scheme on the new system, we obtain a three-level iteration scheme that is at least as efficient as commonly used TRT schemes. The new method allows full convergence to the nonlinear backward Euler time-discretized system, increasing accuracy and robustness, while using a similar number of linear iterations as the more common linearized one-step methods Eq. (4).
We present a family of discretizations for the Variable Eddington Factor (VEF) equations that have high-order accuracy on curved meshes and efficient preconditioned iterative solvers. The VEF discretizations are combined with the Discontinuous Galerkin transport discretization from to form effective high-order, linear transport methods. The VEF discretizations are derived by extending the unified analysis of Discontinuous Galerkin methods for elliptic problems presented by Arnold et al. to the VEF equations. This framework is used to define analogs of the interior penalty, second method of Bassi and Rebay, minimal dissipation local Discontinuous Galerkin, and continuous finite element methods. The analysis of subspace correction preconditioners, which use a continuous operator to iteratively precondition the discontinuous discretization, is extended to the case of the non-symmetric VEF system. Numerical results demonstrate that the VEF discretizations have arbitrary-order accuracy on curved meshes, preserve the thick diffusion limit, and are effective on a proxy problem from thermal radiative transfer in both outer transport iterations and inner preconditioned linear solver iterations. We demonstrate that the VEF solution converges to the S N transport solution as the mesh is refined on both problems with smooth and non-smooth behavior in angle. Parallel performance studies show that the interior penalty VEF discretization's linear solve weak scales out to 1024 processors and strong scales well on a single node. Particular attention is paid to the parallel performance of the VEF algorithm when used in combination with a parallel block Jacobi transport sweep.
This research is focused on applying the NLem method to the full thermal radiative transfer (TRT) equations in the context of a Monte Carlo solution strategy. A framework has been developed for obtaining a solution to the TRT equations using the nonlinear elimination method (NLem) method. Current efforts are focused of the development and verification of the required Monte Carlo algorithm, diffusion algorithm, and material energy solver. Once all three pieces have been verified, the algorithms will then be coupled into a fully functioning method for applying NLem to the TRT equations.
Starting in 2019, the Lagrangian Applications Project (LAP) and the Transport Project set out to develop a new ALE/Lagrangian radiation-hydrodynamics (RH) capability in a new code product named LUMOS. This work was done under the guidance of the Advanced Simulation and Computing (ASC) program with the goal of producing software capable of leveraging the high-order thermal radiative transfer (TRT) solvers provided by the Jayenne and Capsaicin software projects. This capability supplements the existing gray diffusion solver that is currently available in LAP’s FLAG code [1, 2, 3] for RH. The remainder of this memo describes the coupling of the radiation and hydrodynamics solvers within LAP’s LUMOS code. Initially delivered in 2020 as part of an L2 milestone [4], this capability continues to mature in FY21 with more efficient and robust algorithms, new support for ALE, and support for mixed materials per cell. Today, LUMOS is provided as a standard end-user product in the suite of LAP tools provided in each release cycle. Code access can be requested at https://asc.lanl.gov.
Describing high-temperature plasmas requires inclusion of several nonlinear coupled physics, including ion kinetics - for each isotope species present in the plasma, electron kinetics, thermal radiative transfer (TRT), electromagnetic description, and nuclear reactions (fusion burn). Simulating plasmas in ICF hohlraums aims to solve kinetic ions (particles), fluid electrons, energetic electrons, electromagnetics, kinetic radiation (MG DP solver), and laser-plasma interactions.
System of equations derived by Fleck and Cummings to model time-dependent thermal radiative transfer (TRT) problems: Solution of radiation specific intensity (I), non-linearly coupled to material internal energy (U); Absorption and re-emission approximated by effective scattering events. Useful for high-energy density physics simulations: i.e., astrophysics, inertial confinement fusion (ICF). Whereas deterministic methods are fully discretized and free of statistical noise, Monte Carlo methods allow for dynamic sampling of the phase space at the price of statistical noise; Monte Carlo methods are also characterized by a slow $\frac{1}{√Ν}$ convergence rate.
Concerns over climate change have led to numerous efforts in developing low-carbon energy technologies. Pressurized oxy-combustion (POC) is a promising candidate to reduce carbon emission in power generation. Due to the strong impact of pressure on thermal radiation, heat transfer in POC differs significantly from the situation of conventional atmospheric pressure combustion. Thus thermal radiation in POC needs to be investigated to aid new combustor development. The present computational work is a step in this direction, initiating a systematic analysis of thermal radiation and heat transfer in a pilot-scale POC combustor, which has been developed at Washington University in St. Louis (WUSTL). In a POC process, pulverized coal is burned under elevated pressure and O2-CO2 environment. While most previous computational works on flame radiation focused on atmospheric pressure condition, this work considered a pressurized flame. Specifically, a 15-bar POC combustor of power 50 kW is modeled employing the Ansys FLUENT commercial platform, using both Reynolds-averaged Navier-Stokes (RANS) modeling and large-eddy simulation (LES). A recently published and validated global radiation model is used to predict the radiative property of the flue gas. The discrete ordinates (DO) radiation model is chosen to solve the radiative transport equation. Incident radiation on the walls of the combustor is identified and investigated. It is revealed that for this pilot-scale, pressurized combustor, thermal radiation exhibits similar patterns in the RANS and LES models. However, the magnitudes of radiation are different in both models, presumably because interactions between radiation and turbulence are embedded in the LES model but not in the RANS model. This difference thereby underlines the major goal of this research: investigating the impact of such turbulence-to-radiation coupling on thermal radiation in a pilot-scale POC setting. Most previous studies on turbulence-to-radiation interactions focused on bench-scale, atmospheric pressure flames. This work is the first effort to extend this study to a pilot-scale, pressurized flame.
We measured and modeled near infrared extinction of nuclear waste glasses from 300 °C to 1150 °C to enable predictive radiation heat transfer and thermal conductivity estimates. A composition and redox informed model resolved contributions from key chromophores (Fe+2-O-Fe+3, V+4, free and bonded ?Si-OH groups) and, when present, spinel particles that can cause strong scattering. The model reproduced measured absorption from room temperature up to 1150 °C, with minor discrepancies near 1 µm (likely due to possible trace impurities) and 2.5 µm (linked to uncertainty in hydroxy groups). Spectra showed silicate melts were semitransparent mainly in the 0.5–4.0 µm window, responsible for radiation thermal conductivity that generally increases with increasing temperature. We quantified the dependence of effective thermal conductivity on dissolved water and provided distributions across >100 LAW/HLW/DFHLW melts at 1150 °C, supporting improved melter heat transfer modeling.
System Analysis Module (SAM) is a system-level thermal hydraulics code being developed at Argonne National Laboratory for advanced nuclear reactor analysis. In addition to a wide range of interests from the advanced reactor design community, SAM has also been adopted by the United States Nuclear Regulatory Commission's suite of codes purposed for advanced reactor licensing. Nevertheless, the code is still under active development and new capabilities are being added to address various modeling and simulation challenges for advanced reactor analysis. One such phenomenon important to the thermal behavior of some advanced reactor concepts is radiative heat transfer (radHT). Conditions, such as high temperatures and long optical paths, increase the radiative contributions from solids and coolants alike. This paper discusses the development of radHT modeling in SAM and describes the new capabilities provided for thermal analysis. Depending on the geometry and temperatures of the system at hand, as well as the coolant in question, thermal transfer due to thermal radiation will vary dramatically. Therefore, the ability to model variable radiative systems was maintained as a priority during development of SAM radHT modeling. This newly developed simulation feature provides a flexible solid-to-fluid radiative heat transfer framework necessary for SAM to perform accurate analysis for advanced reactor designs. Test cases are also presented and shown to match analytical solutions, which demonstrate the radHT model's efficacy.
In this work, we present a new flux-fixup approach for arbitrarily high-order discontinuous Galerkin (DG) discretizations of the S N transport equation, and we demonstrate the compatibility of this approach with the Variable Eddington Factor (VEF) method. The new fixup approach is sweep-compatible: during a transport sweep (block Gauss-Seidel iteration in which the scattering source is lagged), a local quadratic programming (QP) problem is solved in each spatial element to ensure that the solution satisfies certain physical constraints, including local particle balance. In this paper, we describe two choices of physical constraints, resulting in two variants of the method: QP Zero (QPZ) and QP Maximum Principle (QPMP). In QPZ, the finite element coefficients of the solution are constrained to be nonnegative. In QPMP, they are constrained to adhere to an approximate discrete maximum principle. There are two primary takeaways in this paper. First, when the positive Bernstein basis is used for DG discretization, the QPMP method eliminates negativities, preserves high-order accuracy for smooth problems, and significantly dampens unphysical oscillations in the solution. The latter feature – the dampening of unphysical oscillations – is an improvement upon standard, simpler fixup approaches such as the approach described in (denoted as the “zero and rescale” (ZR) method in this paper). This improvement comes at a moderate computational cost, but it is not prohibitive. Our results show that, even in an unrealistic worst-case scenario where 83% of the spatial elements require a fixup, the computational cost of performing a transport sweep with fixup is only ~31% greater than performing one without fixup. The second takeaway is that the VEF method can be used to accelerate the convergence of transport sweeps even when a fixup is applied. When optically thick regions are present, transport sweeps converge slowly, regardless of whether a fixup is applied, and acceleration is needed. However, attempting to apply standard diffusion synthetic acceleration (DSA) to fixed-up transport sweeps results in divergence for optically thick problems. Our results show that the same is not true for VEF. When VEF is combined with fixed-up transport sweeps, the result is a scheme that produces a nonnegative solution, converges independently of the mean free path, and, in the case of the QPMP fixup, adheres to an approximate discrete maximum principle.
The Advanced Simulation and Computing (ASC) Transport project’s Jayenne Implicit Monte Carlo (IMC) transport library now includes an unstructured mesh capability and is available in a Lagrangian Applications Project (LAP) code. In this presentation, we discuss recent work by the LAP and Transport projects that provides an IMC transport capability for radiation hydrodynamics in the Lagrangian frame. Verification problems testing the new capabilities have been simulated and analyzed, i.e. Marshak wave, Mach 45, Su-Olsen, picket fence, and crooked pipe, both in one and two dimensions. We also present results on two stretch goal problems: a simplified COAX high energy density physics experiment and a supernova shock simulation. Finally, we identify current limitations and future work needed to bring a full capability to the user community.
In this document, the Advanced Simulation and Computing (ASC) Transport Project’s Jayenne team presents evidence that the Los Alamos National Laboratory (LANL) Level 2 milestone statement, Demonstrate a new unstructured mesh IMC x-ray transport capability in LAP codes, due Q4 FY20, has been satisfied with the release and integration of the Jayenne team’s Implicit Monte Carlo (IMC) solver libraries into the lumos multiphysics solver. The Jayenne project’s software includes the algorithms and features prescribed by the milestone description. The lumos software is maintained by the Lagrangian Applications Project (LAP) along with the hydrodynamics code flag and operates under the same ASC program as Jayenne. A set of demonstration problems has been specified, executed, and analyzed.
A system for transferring heat from a nuclear reactor comprises a nuclear reactor comprising a nuclear fuel and a reactor vessel surrounding the nuclear reactor and a heat transfer system surrounding the nuclear reactor. The heat transfer system comprises an inner wall surrounding the nuclear reactor vessel, first fins coupled to an outer surface of inner wall, an outer wall between the inner wall and a surrounding environment, and second fins coupled to an inner surface of the outer wall and extending in a volume between the outer surface of the inner wall and the inner surface of the outer wall, the outer surface of the inner wall and the first fins configured to transfer heat from the nuclear reactor core to the second fins and the inner surface of the outer wall by thermal radiation. The heat transfer system may be directly coupled to the nuclear reactor vessel, or may be coupled to an external reflector surrounding the nuclear reactor vessel. Related heat transfer systems and systems for selectively removing heat from a nuclear reactor are disclosed.
Here this study describes the makeup of and results from a simulation consisting of a lumped thermal model integrated with a dynamic algae growth model to simulate the microalgae productivity of an open-channel raceway cultivation system. The thermal model considers the dynamic effects of weather, light absorption, convective heat transfer, radiation heat transfer, conductive heat transfer, thermal capacitance, and water control strategies. The dynamic algae growth model solves a set of ordinary differential equations consisting of growth functions dependent on incident radiation, temperature, nutrient availability, basal metabolism, and losses due to dark- and photo-respiration. Relative errors in the predicted ash-free dry weight of Nannochloropsis oceanica are 12.5%, -6.1%, and 4.4% for three separate replicates of cultivation cycles (~4.2 m 2 ) performed at AzCATI during the ATP 3 Unified Field Studies in Fall, Spring, and Summer. This research demonstrates that thermal modeling is an essential contributor to the validation of microalgae growth models.
Concerns over climate change have led to numerous efforts in developing low-carbon energy technologies. Pressurized oxy-combustion (POC) is a promising candidate to reduce carbon emissions in power generation. Pressure strongly impacts thermal radiation, leading to a substantial difference in heat transfer between POC and conventional atmospheric pressure combustion. A good understanding of thermal radiation in POC is needed to aid new combustor development. The present work is a step in this direction, initiating a systematic analysis of thermal radiation and heat transfer in a pilot-scale POC combustor, which has been developed at Washington University in St. Louis (WUSTL). In a POC process, pulverized coal is burned under elevated pressure and O2-CO2 environment. Few researchers have investigated the thermal radiation of pressurized oxy-combustion. This work adopted the discrete ordinate model to simulate the radiation of a 1-D cylinder with predetermined conditions (temperature, pressure, gas compositions) to predict the influence of radiative properties of flue gas on the radiation in the combustor.