The aim of this study is to present a general method to investigate radiative transfer in disordered media with a subwave-length, anisotropic short-range order and provide a fundamental understanding on the interplay between polarized radiative transfer and microstructural anisotropy as well short-range order. We show the anisotropy of short-range order, described by an anisotropic correlation length in Gaussian random permittivity model, induces a significant anisotropy of radiative properties. Here the photon scattering mean free path is derived using the Feynman diagrammatic expansion of self-energy, and the transport mean free path and phase function are calculated based on the diagrammatic representation of the irreducible vertex in the Bethe-Salpeter equation. We further consider the transport of polarized light in such media by directly solving Bethe-Salpeter equation (BSE) for photons, without the use of traditional vector radiative transfer equation (VRTE). The present method advantageously allows us to elegantly relate anisotropic structural parameters to polarized radiative transport properties and obtain more fundamental physical insights, because the approximations in all steps of our derivation are given explicitly with reasonable explanations from the exact ab-initio BSE. Moreover, through a polarization eigen-channel expansion technique for intensity tensor, we show that values of transport mean free path in different polarization eigen-channels are rather different, which are also strongly affected by structural anisotropy and short-range order. As a conclusion, this study depicts some fundamental physical features of polarized radiative transfer in disordered media, and is also valuable for potential applications of utilizing anisotropic short-range order in disordered media in manipulation of polarized radiative transfer.

In this work, we present a new formula for the near-field thermal radiative transfer between two spheres. The formula is identical for coated or uncoated spheres and captures the effect of the coatings in the effective Mie reflection coefficients of the spheres. We also numerically demonstrate that silica coated silver spheres transition from silver-like conductance in the far-field to surface phonon polariton dominated silica-like behavior in the extreme near-field.

Radiative heat transfer is studied numerically for reacting swirling flow in an industrial gas turbine burner operating at a pressure of 15 bar. The reacting field characteristics are computed by Reynolds-averaged Navier-Stokes (RANS) equations using the k-ε model with the partially stirred reactor (PaSR) combustion model. The GRI-Mech 2.11 mechanism, which includes nitrogen chemistry, is used to demonstrate the the ability of reducing NO x emissions of the combustion system. A Photon Monte Carlo (PMC) method coupled with a line-by-line spectral model is employed to accurately account for the radiation effects. CO 2 , H 2 O and CO are assumed to be the only radiatively participating species and wall radiation is considered as well. Optically thin and PMC-gray models are also employed to show the differences between the simplest radiative calculation models and the most accurate radiative calculation model, i.e., PMC-LBL, for the gas turbine burner. It was found that radiation does not significantly alter the temperature level as well as CO 2 and H 2 O concentrations. However, it has significant impacts on the NO x levels at downstream locations.

Radiation absorption by a particle curtain formed in a solar free falling particle receiver is investigated using a Eulerian-Eulerian granular two-phase model to solve the two-dimensional mass and momentum equations (CFD). The radiative transfer equation is subsequently solved by the Monte-Carlo (MC) ray-tracing technique using the CFD results to quantify the radiation intensity through the particle curtain. The CFD and MC results provide reliable opacity predictions and are validated with the experimental results available in literature. The particle curtain was found to absorb the solar radiation efficiently for smaller particles at high flowrates due to higher particle volume fraction and increased radiation extinction. However, at low mass-flowrates the absorption efficiency decreases for small and large particles.

Near-field thermal radiation and van der Waal force between flat plates and curved surfaces have been probed in the past; however the peculiarities of radiative heat transfer and van der Waals stress due to fluctuations of electromagnetic fields for micro/nano-sized spherical objects have not been studied in great details. We demonstrate how fluctuational electrodynamics can be used to determine emissivity and van der Waals contribution to surface energy for various spherical shapes in a homogeneous and isotropic medium. The dyadic Green’s function formalism of radiative energy and fluctuation-induced van der Waals stress for different spherical configurations has been developed. We present the calculations for a single sphere, a bubble, a spherical shell and a coated sphere. We observe that emission spectrum ofmicro/nanoscale spheres displays several sharp peaks as the size of object reduces. Our calculations indicate that surface energy becomes size dependent (r-3) due to van der Waals phenomena for small radii.

Microscopic thin films are known to have narrow band selective thermal radiation whch have potential applications in selective emitter and absorbers. We propose a methodology to shift the wavelength selectivity in the desired location. Calculation of emissivity and near field radiation for different materials and structures is presented. Emissivity calculations are performed using the standard expressions for Fresnel reflection coefficients. For the near field thermal radiation, we use the analytical expression for transitivity between two half spaces obtained using the dyadic Greens function formalism. We use Maxwell-Garnett-Mie theory to calculate effective dielectric function of media doped with nanoparticles. We observe that spectrum of thermal radiation in far-field and in near-field can be altered using nanoparticles. Moreover spectral properties of mixtures can be characterized using refractive indices. Influence of nanoparticle size and concentration is also studied.

In designing industrial cylindrical furnaces, it is important to predict the radiative heat flux on the wall with high accuracy. In this study, we consider CO 2 and H 2 O which have strong absorption in the infrared range. The absorption coefficients of the gases are calculated by using the statistical narrow band (SNB) model. The spectrum is divided into 15 bands to cover all the absorption regions of the two non-gray gases. The radiative transfer equation is solved by the finite volume method (FVM) in cylindrical coordinates. To make the FVM more accurate, we discretize the solid angle into 80 directions with the S 8 approximation which is found to be both efficient and less time consuming. Based on the existing species and temperature fields, which were modeled by the FLUENT commercial code, the radiative heat transfer in a cylinder combustor is simulated by an in-house code. The results show that the radiative heat flux plays a dominant part of the heat flux to the wall. Meanwhile, when the gas is considered as nongray, the computational time is very huge. Therefore, a parallel algorithm is also applied to speed up the computing process.

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. The dependence on wavelength is often treated through a weighted sum of gray gases type approach. The discrete ordinates method is the most common method for approximating the angular dependence. In the discrete ordinates method, the intensity is solved exactly for a finite number of discrete directions, and integrals over the angular space are accomplished through a quadrature rule. In this work, a projection-based model reduction approach is applied to the discrete ordinates method. A small number or ordinate directions are used to construct the reduced basis. The reduced model is then queried at the quadrature points for a high order quadrature in order to inexpensively approximate this highly accurate solution. This results in a much more accurate solution than can be achieved by the low-order quadrature alone. One-, two-, and three-dimensional test problems are presented.

The S N quadrature set for the discrete-ordinates method is limited in overall discrete direction number in order to avoid physically unrealistic negative directional weight factors. Such a limitation can adversely impact radiative transfer predictions. Directional discretization results in errors due to ray effect, as well as angular false scattering error due to distortion of the scattering phase function. The use higher-order quadrature schemes in the discrete-ordinates method allows for improvement in discretization errors without an overall directional limitation. In this analysis, four higher-order quadrature sets (Legendre-Equal Weight, Legendre-Chebyshev, Triangle Tessellation, and Spherical Ring Approximation) are implemented for determination of radiative transfer in a 3-D cubic enclosure containing participating media. Radiative heat fluxes, calculated at low direction number, are compared to the S N quadrature and Monte Carlo predictions to gauge quadrature accuracy. Additionally, investigation into the reduction of angular false scattering with sufficient increase in direction number using higher-order quadrature, including heat flux accuracy with respect to Monte Carlo and computational efficiency, is presented. While higher-order quadrature sets are found to effectively minimize angular false scattering error, it is found to be much more computationally efficient to implement proper phase function normalization for accurate radiative transfer predictions.

A thermotropic material is modeled as an absorbing, thin slab containing anisotropic scattering, monodisperse, spherical particles. Monte Carlo ray tracing is used to solve the governing equation of radiative transfer. Predicted results are validated by comparison to the measured normal-hemispherical reflectance and transmittance of samples with various volume fraction and relative index of refraction. A parametric study elucidates the effects of particle size parameter, scattering albedo, and optical thickness on the normal-hemispherical transmittance, reflectance, and absorptance. The results are interpreted for a thermotropic material used for overheat protection of a polymer solar absorber. For the preferred particle size parameter of 2, the optical thickness should be less than 0.3 to ensure high transmittance in the clear state. To significantly reduce the transmittance and increase the reflectance in the translucent state, the optical thickness should be greater than 2.5 and the scattering albedo should be greater than 0.995. For optical thickness greater than 5, the reflectance is asymptotic and any further reduction in transmittance is through increased absorptance. A case study is used to illustrate how the parametric study can be used to guide the design of thermotropic materials. Low molecular weighted polyethylene in poly(methyl methacrylate) is identified as a potential thermotropic material. For this material and a particle radius of 200 nm, it is determined that the volume fraction and thickness should equal 10% and 1 mm, respectively.

This work presents an OpenFOAM implementation of the P N approximation for radiative heat transfer, including higher orders P 3 , P 5 , and P 7 . Also described is a procedure which enables the sequential numerical computations of the coupled partial differential equations (PDEs) by re-expressing the boundary conditions in matrix form so that individual boundary conditions can be associated with each PDE. The implementation of the software programs are verified with derived analytical solutions for 1-D slabs with constant and variable properties, and are also tested with various orientations in order to demonstrate the geometric invariance properties of the 3-dimensional P N formulation. A few examples taken from the literature are also considered in this work and could be taken as benchmark solutions for the P N approximations.

A new nongray radiation modeling library for combustion gases has been implemented in OpenFOAM. The spectral models for single species include gray, correlation tables and narrowband k -distributions. Mixing models for k -distributions include the multiplication and uncorrelated mixture models. Radiative transfer equation solvers for the library include spherical harmonics such as P 1 , SP 3 and SP 5 as well as the optically thin approximation. The performance of the different solution methods is compared for accuracy and speed as a tool for future model strategy selection.

In this work, a spectral collocation method is developed to simulate radiative transfer in a refractive planar medium. The space and angular domains of radiative intensity are discretized by Chebyshev polynomials, and the angular derivative term and the integral term of radiative transfer equation are approximated by spectral collocation method. The spectral collocation method can provide exponential convergence and obtain high accuracy even using few nodes. There is a very satisfying correspondence between the spectral collocation results and available data in literatures. Influence of the extinction coefficient, the scattering albedo, the scattering phase function, the gradient of refractive index and the emissivity of boundary are investigated for the plane-parallel scattering medium with variable refractive index.

Finite element method (FEM) numerical simulations of heat transfer for high-temperature regimes often require modeling of grey-body enclosure radiation where enclosure geometry definitions are obtained as part of the model grid generation process. Owing to the expense of solving the radiation problem, typical FEM approaches loosely couple the radiative transfer solution as boundary conditions to a standard conduction formulation. When the problem at hand is thermal-mechanical and relative motion occurs between enclosure surfaces, the simulation code is tasked with providing a means of updating the original enclosure surface geometry to reflect the deformed configuration. While this scenario is manageable for contiguously meshed discretizations, the difficulty of updating enclosure geometry is greatly increased when the model admits sliding. Here the analysis code must employ both mechanical and thermal contact, relying heavily on geometric search and contact constraints to enforce closure for the conduction formulation. General purpose large-deformation FEM structural codes employ surface contact utilities to provide geometric search and contact constraint definitions. This paper describes an ongoing effort to leverage contact utilities for solving the enclosure radiation problem in deforming and sliding mesh scenarios while having minimal impact to a traditional modeling approach. The current effort is divided into two areas, enclosure definitions and thermal contact, but the primary focus here is on enabling use of contact to provide definition of the enclosure. The proposed methodology is demonstrated on simple enclosure radiation models using SNL Sierra Mechanics Dash contact utilities and the Chaparral enclosure radiation library with Sierra Mechanics Structural and Thermal application codes. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energys National Nuclear Security Administration under contract DE-AC04-94AL85000.

Normalization of the scattering phase function is applied to the transient discrete ordinates method for ultrafast radiative transfer analysis in a turbid medium subject to a normal collimated incidence. Previously, the authors have developed a normalization technique which accurately conserves both scattered energy and phase function asymmetry factor after directional discretization for the Henyey-Greenstein phase function approximation in steady-state diffuse radiative transfer analysis. When collimated irradiation is considered, additional normalization must be applied to ensure that the collimated phase function also satisfies both scattered energy and asymmetry factor conservation. The authors’ technique is applied to both the diffuse and collimated components of scattering using the general Legendre polynomial phase function approximation for accurate and efficient ultrafast radiative transfer analysis. The impact of phase function normalization on both predicted heat fluxes and overall energy deposition in a model tissue cylinder is investigated for various phase functions and optical properties. A comparison is shown between the discrete ordinates method and the finite volume method. It is discovered that a lack of conservation of asymmetry factor for the collimated component of scattering causes over-predictions in both energy deposition and heat flux for highly anisotropic media.

This paper reports a numerical study on the thermal radiative transport in a cloud of dry water particles. Dry water is a water-in-air inverse foam which consists of micrometer-sized water droplets encapsulated by hydrophobic fumed-silica nanoparticles. The radiative properties of this novel material were estimated using the Mie theory for coated spheres. The radiative transport equation (RTE) was solved for a one-dimensional geometry using the discrete ordinates method. The effects of silica particle and water droplet size as well as the volume fraction of dry water particles on reducing radiative heat transfer were studied numerically. The results were compared with respect to two limiting cases: (i) system with no particles and (ii) silica particles with no water. The results showed that dry water reduced the local radiative heat flux as much as 20% more than that by silica particles alone. Additionally, reduction of the diameter of dry water particles from 75 to 25 μm reduced the radiative heat flux by 17%. Finally, parametric analysis showed that increasing the volume fraction of dry water by 10 times decreased the radiative heat flux by about 30% at the receiver end.

This study compares several band models for calculating the thermal radiation from the plume of a simulated rocket motor. First, a non-scattering plume is considered allowing one to use the line-of-sight integration (LOS). The results for three band models are compared. Next we study a scattering plume. The radiative heat transfer equation is solved numerically using the axisymmetric finite volume method (FV). Detailed analysis of the numerical scheme of the FV method demonstrated that it has a large numerical diffusion term which, although formally of the first order, in practice can cause large errors in calculating thermal signatures of hot jets. The numerical scheme was hence modified using what we call the “quasi-Cartesian” approach. We demonstrate that for a non-scattering media in the first order the numerical diffusion term vanishes and the modified scheme formally reduces to the integration along the line of sight resulting in a very good agreement between the FV and LOS predictions. The new method is then used to calculate radiation from a scattering plume and the results for two band models are compared.

A non-isothermal medium is modeled using the multilayer approach in which the continuous temperature distribution in a one-dimensional system as modeled as being piecewise constant. This has been shown to provide accurate results for a surprisingly small number of layers. Analysis is performed on a non-isothermal gray medium to attempt to characterize the ways in which the errors introduced by the multilayer modeling change with various physical parameters namely, the optical thickness and the temperature or emissive power gradient. A demonstration is made of how the multi-source k-distribution method is capable of evaluating the heat flux within a one-dimensional system with piecewise constant temperature distribution with line-by-line accuracy with a significant decrease in computational expense. The k-distribution method for treating the spectral properties of an absorbing-emitting medium represents a powerful alternative to line-by-line calculations by reducing the number of RTE evaluations from the order of a million to the order of ten without any significant loss of accuracy. For problems where an appropriate reference temperature can be defined, the k-distribution method is formally exact. However, when no appropriate reference temperature can be defined, the method results in errors. The multi-source k-distribution method extends the k-distribution method to problems with piecewise constant temperature and optical properties.

Recently, it has become possible to conduct line-by-line (LBL) accurate radiative heat transfer calculations in spectrally highly nongray combustion systems using the Monte Carlo method. LBL accuracy, in principle, adds little to the computational load as compared to gray calculations. However, when employing the Monte Carlo method, choosing appropriate emission wave numbers for statistical photon bundles can be numerically expensive. In this paper, a new scheme for wave number selection is proposed, significantly decreasing CPU requirements compared to previous work. The accuracy of the new method is established and its time requirements are compared against the previous method.

Currently infrared scanning technology has been successfully applied for the detection of a wide variety of defects in many applications provided that the surfaces have a high emissivity that doesn’t reflect radiation from outside sources. However, surfaces with low and variable emissivity present a challenge for the application of this technology because infrared cameras and sensors cannot differentiate between the emitted radiation from the surface of interest and those reflected from outside sources. The system presented is an attempt to reduce and/or remove the effects of reflected radiation to increase the system’s applicability beyond the limit of high emissivity surfaces. Physical hardware and computer software are used in concert with radiative heat transfer equations to first determine the emissivity of each point on the surface, then use that information obtained to accurately depict the surface temperature. While this newest iteration of the system development has addressed many important issues regarding accuracy, efficiency as well as performance enhancement in the removal of the artifacts of reflected radiation, the technique still has difficulties to be applied to most surfaces with variable emissivity.