Publications

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This milestone campaign was focused on coupling Sandia physics codes SIERRA low Mach module Fuego and RAMSES Boltzmann transport code Sceptre(Scefire). Fuego enables simulation of low Mach, turbulent, reacting, particle laden flows on unstructured meshes using CVFEM for abnormal thermal environments throughout SNL and the larger national security community. Sceptre provides simulation for photon, neutron, and charged particle transport on unstructured meshes using Discontinuous Galerkin for radiation effects calculations at SNL and elsewhere. Coupling these ”best of breed” codes enables efficient modeling of thermal/fluid environments with radiation transport, including fires (pool, propellant, composite) as well as those with directed radiant fluxes. We seek to improve the experience of Fuego users who require radiation transport capabilities in two ways. The first is performance. We achieve this through leveraging additional computational resources for Scefire, reducing calculation times while leaving unaffected resources for fluid physics. This approach is new to Fuego, which previously utilized the same resources for both fluid and radiation solutions. The second improvement enables new radiation capabilities, including spectral (banded) radiation, beam boundary sources, and alternate radiation solvers (i.e. Pn). This summary provides an overview of these achievements.

The goal of this milestone is to demonstrate effective coupling between the Sierra low-Mach module Fuego and the RAMSES Boltzmann transport (particle and radiation) code Sceptre.

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Radiation heat transfer is an important phenomenon in many physical systems of practical interest. When participating media is important, the radiative transfer equation (RTE) must be solved for the radiative intensity as a function of location, time, direction, and wavelength. In many heat-transfer applications, a quasi-steady assumption is valid, thereby removing time dependence. The dependence on wavelength is often treated through a weighted sum of gray gases (WSGG) approach. The discrete ordinates method (DOM) is one of the most common methods for approximating the angular (i.e., directional) dependence. The DOM exactly solves for the radiative intensity for a finite number of discrete ordinate directions and computes approximations to integrals over the angular space using a quadrature rule; the chosen ordinate directions correspond to the nodes of this quadrature rule. This paper applies a projection-based model-reduction approach to make high-order quadrature computationally feasible for the DOM for purely absorbing applications. First, the proposed approach constructs a reduced basis from (high-fidelity) solutions of the radiative intensity computed at a relatively small number of ordinate directions. Then, the method computes inexpensive approximations of the radiative intensity at the (remaining) quadrature points of a high-order quadrature using a reduced-order model constructed from the reduced basis. Finally, this results in a much more accurate solution than might have been achieved using only the ordinate directions used to compute the reduced basis. One- and three-dimensional test problems highlight the efficiency of the proposed method.

Concurrent sound associated with very bright meteors manifests as popping, hissing, and faint rustling sounds occurring simultaneously with the arrival of light from meteors. Numerous instances have been documented with â '11 to â '13 brightness. These sounds cannot be attributed to direct acoustic propagation from the upper atmosphere for which travel time would be several minutes. Concurrent sounds must be associated with some form of electromagnetic energy generated by the meteor, propagated to the vicinity of the observer, and transduced into acoustic waves. Previously, energy propagated from meteors was assumed to be RF emissions. This has not been well validated experimentally. Herein we describe experimental results and numerical models in support of photoacoustic coupling as the mechanism. Recent photometric measurements of fireballs reveal strong millisecond flares and significant brightness oscillations at frequencies ≥40 Hz. Strongly modulated light at these frequencies with sufficient intensity can create concurrent sounds through radiative heating of common dielectric materials like hair, clothing, and leaves. This heating produces small pressure oscillations in the air contacting the absorbers. Calculations show that â '12 brightness meteors can generate audible sound at ∼25 dB SPL. The photoacoustic hypothesis provides an alternative explanation for this longstanding mystery about generation of concurrent sounds by fireballs.

The dispersion and connectivity of particles with a high degree of polydispersity is relevant to problems involving composite material properties and reaction decomposition prediction and has been the subject of much study in the literature. This work utilizes Monte Carlo models to predict percolation thresholds for a two-dimensional systems containing disks of two different radii. Monte Carlo simulations and spanning probability are used to extend prior models into regions of higher polydispersity than those previously considered. A correlation to predict the percolation threshold for binary disk systems is proposed based on the extended dataset presented in this work and compared to previously published correlations. A set of boundary conditions necessary for a good fit is presented, and a condition for maximizing percolation threshold for binary disk systems is suggested.

The discrete ordinates method is a popular and versatile technique for solving the radiative transport equation, a major drawback of which is the presence of ray effects. Mitigation of ray effects can yield significantly more accurate results and enhanced numerical stability for combined mode codes. When ray effects are present, the solution is seen to be highly dependent upon the relative orientation of the geometry and the global reference frame. This is an undesirable property. A novel ray effect mitigation technique of averaging the computed solution for various reference frame orientations is proposed.

Participating media radiation (PMR) in weapon safety calculations for abnormal thermal environments are too costly to do routinely. This cost may be s ubstantially reduced by applying reduced order modeling (ROM) techniques. The application of ROM to PMR is a new and unique approach for this class of problems. This approach was investigated by the authors and shown to provide significant reductions in the computational expense associated with typical PMR simulations. Once this technology is migrated into production heat transfer analysis codes this capability will enable the routine use of PMR heat transfer in higher - fidelity simulations of weapon resp onse in fire environments.

The common methods for finding the local radiative flux divergence in participating media through solution of the radiative transfer equation are outlined. The pros and cons of each method are discussed in terms of their speed, ability to handle spectral properties and scattering phenomena, as well as their accuracy in different ranges of media transport properties. The suitability of each method for inclusion in the energy equation to efficiently solve multi-mode thermal transfer problems is discussed. Finally, remaining topics needing research are outlined.

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High-speed photometric observations of meteor fireballs have shown that they often produce high-amplitude light oscillations with frequency components in the kHz range, and in some cases exhibit strong millisecond flares. We built a light source with similar characteristics and illuminated various materials in the laboratory, generating audible sounds. Models suggest that light oscillations and pulses can radiatively heat dielectric materials, which in turn conductively heats the surrounding air on millisecond timescales. The sound waves can be heard if the illuminated material is sufficiently close to the observer’s ears. The mechanism described herein may explain many reports of meteors that appear to be audible while they are concurrently visible in the sky and too far away for sound to have propagated to the observer. This photoacoustic (PA) explanation provides an alternative to electrophonic (EP) sounds hypothesized to arise from electromagnetic coupling of plasma oscillation in the meteor wake to natural antennas in the vicinity of an observer.

Two of the most popular deterministic radiation transport methods for treating the angular dependence of the radiative intensity for heat transfer: The discrete ordinates and simplified spherical harmonics approximations are compared. A problem with discontinuous boundary conditions is included to evaluate ray effects for discrete ordinates solutions. Mesh resolution studies are included to ensure adequate convergence and evaluate the effects of the contribution of false scattering. All solutions are generated using finite element spatial discretization. Where applicable, any stabilization used is included in the description of the approximation method or the statement of the governing equations. A previous paper by the author presented results for a set of 2D benchmark problems for the discrete ordinates method using the PN-TN quadrature of orders 4, 6, and 8 as well as the P1, M1, and SP3 approximations. This paper expands that work to include the Lathrop-Carlson level symmetric quadrature of order up to 20 as well as the Lebedev quadrature of order up to 76 and simplified spherical harmonics of odd orders from 1 to 15. Two 3D benchmark problems are considered here. The first is a canonical problem of a cube with a single hot wall. This case is used primarily to demonstrate the potentially unintuitive interaction between mesh resolution, quadrature order, and solution error. The second case is meant to be representative of a pool fire. The temperature and absorption coefficient distributions are defined analytically. In both cases, the relative error in the radiative flux or the radiative flux divergence within a volume is considered as the quantity of interest as these are the terms that enter into the energy equation. The spectral dependence of the optical properties and the intensity is neglected.

The simplified spherical harmonics (SPn) approximation to the radiative transport equation (RTE) is a computationally efficient deterministic solution method that may be derived either as an asymptotic correction to the diffusion approximation or as a 3D analog to the 1D spherical harmonics (Pn) or discrete ordinates (Sn) approximations. It is used to approximate the effects of participating media radiation. In order to trust the output of a given implementation for a high consequence application, code verification activities must be undertaken to build confidence in the results generated. The method of manufactured solutions is a widely accepted code verification technique in which a solution is assumed and arbitrary source terms are derived such that the code should converge to the prescribed solution. This convergence rate is then confirmed. In this paper we consider the set of coupled PDEs representative of radiation/conduction problems. The RTE is approximated using the “canonical” SPn equations with Mark boundary conditions. All boundaries are diffuse and emissivities range from 0 to 1. A set of manufactured solutions are presented for 1D-planar, 2D-planar, 2D-axisymmetric, and 3D-radially symmetric geometries. These manufactured solutions are used to verify the convergence rate of the conduction and simplified spherical harmonics approximations implemented in Sierra Aria, a highly scalable thermal analysis code.

Thermal analysts address a wide variety of applications requiring the simulation of radiation heat transfer phenomena. There are gaps in the currently available modeling capabilities. Addressing these gaps would allow for the consideration of additional physics and increase confidence in simulation predictions. This document outlines a five year plan to address the current and future needs of the analyst community with regards to modeling radiation heat transfer processes. This plan represents a significant multi-year effort that must be supported on an ongoing basis.

The discrete ordinates method is a popular and versatile technique for deterministically solving the radiative transport which governs the exchange of radiant energy within a fluid or gas mixture. It is the most common 'high fidelity' technique used to approximate the radiative contribution in combined-mode heat transfer applications. A major drawback of the discrete ordinates method is that the solution of the discretized equations may involve nonphysical oscillations due to the nature of the discretization in the angular space. These ray effects occur in a wide range of problems including those with steep temperature gradients either at the boundary or within the medium, discontinuities in the boundary emissivity due to the use of multiple materials or coatings, internal edges or corners in non-convex geometries, and many others. Mitigation of these ray effects either by increasing the number of ordinate directions or by filtering or smoothing the solution can yield significantly more accurate results and enhanced numerical stability for combined mode codes. When ray effects are present, the solution is seen to be highly dependent upon the relative orientation of the geometry and the global reference frame. This is an undesirable property. A novel ray effect mitigation technique is proposed. By averaging the computed solution for various orientations, the number of ordinate directions may be artificially increased in a trivially parallelizable way. This increases the frequency and decreases the amplitude of the ray effect oscillations. As the number of considered orientations increases a rotationally invariant solution is approached which is quite accurate. How accurate this solution is and how rapidly it is approached is problem dependent. Uncertainty in the smooth solution achieved after considering a relatively small number of orientations relative to the rotationally invariant solution may be quantified.