Table of contents

This volume of Journal of Physics: Conference Series is based on papers presented at the Eurotherm Conference 105: Computational Thermal Radiation in Participating Media V, which was held in Albi, France on 1-3 April 2015. This seminar was the fifth in a series after Nancy, France (Eurotherm Seminar 95, April 2012), Mons, Belgium (Eurotherm Seminar 73, April 2003), Poitiers, France (Eurotherm Seminar 78, April 2006) and Lisbon, Portugal (Eurotherm Seminar 83, April 2009).

Around 40 contributions were received during the conference preparation that have been submitted to oral presentations. A selection process based on two peer-reviews of the full papers finally resulted in the acceptance of 36 for oral presentations (including 2 plenary lectures). These 2 plenary lectures and 10 other papers have been selected for a special issue in a journal related to radiative heat transfer and will not be presented in this volume.

The conference was attended by almost 60 scientists from 15 different countries: Australia, Belgium, Canada, China, France, Germany, Poland, Portugal, Russia, Switzerland, The Netherlands, Sweden, Tunisia, Turkey and USA.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

The main restriction of k-distribution approaches for applications in radiative heat transfer in gaseous media arises from the use of a scaling or correlation assumption to treat non-uniform situations. It is shown that those cases can be handled exactly by using a multidimensional k-distribution that addresses the problem of spectral correlations without using any simplifying assumptions. Nevertheless, the approach cannot be suggested for engineering applications due to its computational cost. Accordingly, a more efficient method, based on the so-called Multi-Spectral Framework, is proposed to approximate the previous exact formulation. The model is assessed against reference LBL calculations and shown to outperform usual k-distribution approaches for radiative heat transfer in non-uniform media.

In simulations of periodic or symmetric geometries, computational domains are reduced by imaginary boundaries that present the symmetry conditions. In Photon Monte Carlo methods, this is achieved by imposing specular reflective boundary conditions for the radiative intensity. In this work, a similar specular reflective boundary condition is developed for Discrete Ordinate Methods. The effectiveness of the new boundary condition is demonstrated by multiple numerical examples including plane symmetry and axisymmetry.

The radiative characterization of heterogeneous media with complex morphologies on multiple scales is of interest in a variety of areas such as solar energy conversion technologies or environmental sciences. An in-depth understanding and decoupling of the multi-scale morphological effects, bulk material properties, and operating conditions on the macroscopic behaviour provides pathways for morphology tailoring on multiple scales for improved application performance. We introduce a multi-scale methodology for the characterization of the spectral radiative transport in heterogeneous media with complex morphologies on two distinct scales characterized by size parameters (π-diameter/wavelength) significantly above and below one. The methodology incorporates the exact morphology at the various scales and utilizes volume-averaging approaches with the corresponding effective properties to couple the scales. At the large scale the volume-averaged coupled radiative transfer equations are solved utilizing i) effective radiative transport properties obtained by direct Monte Carlo simulations at the middle scale (mm range), and ii) averaged bulk material properties obtained at the small scale (submicron scale) by discrete dipole approximation calculations. The method is exemplary applied to snow containing agglomerated soot impurities. A quantification and decoupled understanding of the morphological effect on the radiative transport is achieved and a significant influence of the dual-scale morphology on the macroscopic optical behaviour is observed.

This paper deals with the estimation of radiative property distributions of participating media from a set of light sources and sensors located on the boundaries of a medium. This is the so-called diffuse optical tomography problem. Such a non-linear ill-posed inverse problem is solved through the minimization of a cost function which depends on the discrepancy, in a least-square sense, between some measurements and associated predictions. In the present case, predictions are based on the diffuse approximation model in the frequency domain while the optimization problem is solved by the L-BFGS algorithm. To cope with the local convergence property of the optimizer and the presence of numerous local minima in the cost function, a wavelet multi-scale method associated with the L-BFGS method is designed.

We present the kspectrum, scientific code that produces high-resolution synthetic absorption spectra from public molecular transition parameters databases. This code was originally required by the atmospheric and astrophysics communities, and its evolution is now driven by new scientific projects among the user community. Since it was designed without any optimization that would be specific to any particular application field, its use could also be extended to other domains. kspectrum produces spectral data that can subsequently be used either for high-resolution radiative transfer simulations, or for producing statistic spectral model parameters using additional tools. This is a open project that aims at providing an up-to-date tool that takes advantage of modern computational hardware and recent parallelization libraries. It is currently provided by Méso-Star (http://www.meso-star.com) under the CeCILL license, and benefits from regular updates and improvements.

Inversion based on the radiative transfer equation (RTE) is generally highly CPU time consuming because the forward model itself is complicated to solve when the space dimension is greater than one, and because the inversion is based on a large number of forward model runs until convergence is reached. The goal of this paper is to set up some speed-up strategies specific of inversion when radiative transfer problems are dealt with. More specifically, the accurate identification of the volumetric radiative properties i.e. both the absorption and scattering coefficients is the objective of this study.

It was recently shown that null-collision algorithms could lead to grid-free radiative- transfer Monte Carlo algorithms that immediately benefit of computer-graphics tools for an efficient handling of complex geometries [1, 2]. We here explore the idea of extending the approach to heat transfer problems combining radiation, conduction and convection. This is possible as soon as the model can be given the form of a second-kind Fredholm equation. In the following pages, we show that this is quite straightforward at the stationnary limit in the linear case. The oral presentation will provide corresponding simulation examples. Perspectives will then be drawn concerning the extension to non-stationnary cases and non-linear coupling.

Numerical simulations of radiation received from a fire front were carried out in a situation of laboratory-scale fire. The fire front was determined at different instants based on camera images taken during a real experiment, and predicted in using a "small world network" propagation model. The fluxes were computed using either a ray tracing method with EDStaR, or a home-made reciprocal Monte Carlo method. Results were compared with available flux measurements using radiative heat flux gauges.

The knowledge of the normal spectral absorptances of open-cell foams used as volumetric solar receivers is required to finely compute their thermal efficiencies. For this purpose, absorptances of a set of virtual open-cell foams of varying porosities, beforehand generated by using a numerical generator, are computed thanks to a ray tracing code. This work details the contribution of the intrinsic optical properties of the solid phase to the normal spectral absorptance of open-cell foams, through the statistical analysis of both the path and the events undergone by a ray, which is permitted by the ray tracing code. This study allows us to propose a robust and linear relationship that links the normal spectral absorptance to the porosity and the intrinsic optical properties of the solid phase, which is considered as optically thick.

The porous morphology of ceramic foams can significantly influence its heat and mass transport phenomena. Ceramic foams with dual-scale porosity provide flexibility for tailoring the coupled transport characteristics for enhanced performance. We numerically characterized the radiative transport in porous ceria foams with dual-scale porosity, i.e. exhibiting pores in the millimeter range in the micrometer range. Ceria can act as a catalyst- equivalent in high temperature thermochemical reactions for the direct synthesis of solar fuels and its bulk material properties vary significantly with wavelength. The methodology used is based on Monte Carlo methods for the solution of the volume-averaged radiative transfer equations for the determination of macroscopic optical properties such as reflectance or transmittance of a 1D slab. The exact millimeter-scale structure was incorporated by effective transport properties obtained through collision-based Monte Carlo methods. The micrometer- range strut porosity was incorporated using Mie theory and assuming independent scattering. The results allow for guiding the synthesis of ceramic foams with dual-scale porosity for enhanced radiative transport characteristics.

The present paper deals with iterative algorithms coupled with finite element methods (FEM) to solve the Radiative Transfer Equation (RTE) within semi-transparent heterogenous materials where specular reflexions occur on their boundaries. As our intention is to use such solution for inversion, the forward model should be solved as fastly as possible. This communication compares, in terms of both accuracy and CPU, the Discontinuous Galerkin (DG) method with the Streamline Upwind Petrov-Galerkin (SUPG) method, both being coupled with the Discrete Ordinate Method. Next, several iteratives methods used to accelerate the convergence are compared. These methods are the Gauss-Siedel (GS), the Source-Iteration (SI) and the Successive Over-Relaxation (SOR) methods.

The paper presents a complex model of heat and mass transfer in a multi-layer protective clothing exposed to a flash fire and interacting with the human skin. The clothing was made of porous fabric layers separated by air gaps. The fabrics contained bound water in the fibres and moist air in the pores. The moist air was also present in the gaps between fabric layers or internal fabric layer and the skin. Three skin sublayers were considered. The model accounted for coupled heat transfer by conduction, thermal radiation and associated with diffusion of water vapour in the clothing layers and air gaps. Heat exchange due to phase transition of the bound water were also included in the model. Complex thermal and mass transfer conditions at internal or external boundaries between fabric layers and air gaps as well as air gap and skin were assumed. Special attention was paid to modelling of thermal radiation which was coming from the fire, penetrated through protective clothing and absorbed by the skin. For the first time non-grey properties as well as optical phenomena at internal or external boundaries between fabric layers and air gaps as well as air gap and skin were accounted for. A series of numerical simulations were carried out and the risk of heat injures was estimated.

Continuum-scale equations of radiative transfer and corresponding boundary conditions are derived for a multi-component anisotropic medium consisting of components in the range of geometrical optics. The derivations are obtained by employing the volumeaveraging theory. This study generalizes the previous derivations obtained for multi-component isotropic media.

Nongray radiation calculations are carried out for a case problem available in the literature. The problem is a non-isothermal and inhomogeneous CO₂-H₂O- N₂ gas mixture confined within an axisymmetric cylindrical furnace. The numerical procedure is based on the zonal method associated with the weighted sum of gray gases (WSGG) model. The effect of the wall emissivity on the heat flux losses is discussed. It is shown that this property affects strongly the furnace efficiency and that the most important heat fluxes are those leaving through the circumferential boundary. The numerical procedure adopted in this work is found to be effective and may be relied on to simulate coupled turbulent combustion-radiation in fired furnaces.

The accuracy of several non-gray global gas/soot radiation models, namely the Wide-Band Correlated-K (WBCK) model, the Spectral Line Weighted-sum-of-gray-gases model with one optimized gray gas (SLW-1), the (non-gray) Weighted-Sum-of-Gray-Gases (WSGG) model with different sets of coefficients (Smith et al., Soufiani and Djavdan, Taylor and Foster) was assessed on several test cases from the literature. Non-isothermal (or isothermal) participating media containing non-homogeneous (or homogeneous) mixtures of water vapor, carbon dioxide and soot in one-dimensional planar enclosures and multi-dimensional rectangular enclosures were investigated. For all the considered test cases, a benchmark solution (LBL or SNB) was used in order to compute the relative error of each model on the predicted radiative source term and the wall net radiative heat flux.

Applicability of an IR imaging/spectroscopy diagnostic was tested on a laboratory- scale flame. For this purpose, measurements were carried out on a V-shape flame developed along a wall, with the aim of evaluating the wall temperature and of identifying the flame properties (temperature and species concentrations). Infrared measurements with a multiband camera and a spectrometer were post-processed and compared, in particular, with thermocouple measurements carried out for the wall temperature. Simple evaluation involving a correction for the emissivity showed a quite good agreement when assessed against experimental data. An attempt to reconstruct a flame emission spectrum was also carried out, expecting a possible inverse identification of the flame properties. The method showed a promising behaviour on synthetic data built with a radiative transfer model for gas and wall radiation. However, the spectrum reconstruction method is not yet accurate enough to allow an identification of the flame properties in full confidence when applied to actual experimental data. First tests showed a correct qualitative behaviour, but model refinements are required at least for the flame radiation, before getting accurate flame properties.

The infrared signature modelling of rocket plumes is a challenging problem involving rocket geometry, propellant composition, combustion modelling, trajectory calculations, fluid mechanics, atmosphere modelling, calculation of gas and particles radiative properties and of radiative transfer through the atmosphere. This paper presents ONERA simulation tools chained together to achieve infrared signature prediction, and the comparison of the estimated and measured signatures of an in-flight rocket plume. We consider the case of a solid rocket motor with aluminized propellant, the Black Brant sounding rocket. The calculation case reproduces the conditions of an experimental rocket launch, performed at White Sands in 1997, for which we obtained high quality infrared signature data sets from DRDC Valcartier. The jet plume is calculated using an in-house CFD software called CEDRE. The plume infrared signature is then computed on the spectral interval 1900-5000 cm^-1 with a step of 5 cm^-1. The models and their hypotheses are presented and discussed. Then the resulting plume properties, radiance and spectra are detailed. Finally, the estimated infrared signature is compared with the spectral imaging measurements. The discrepancies are analyzed and discussed.

The Generalized SLW Method is presented, formulating the SLW method with the help of both the ALBDF and the Inverse ALBDF. The result is two equivalent symmetric models: the SLW Model and the Inverse SLW Model. The advantage of the unified dual formulation and of application of the ALBDF and the Inverse ALBDF is in more efficient implementation of the model and the elimination of the solution of the implicit equations for the absorption cross-sections in the construction of the spectral model in the case of nonisothermal media. The generalized approach explores all possibilities of the SLW method under both direct and inverse formulations including its limiting cases: the minimal one clear gas-one gray gas SLW-1 model, and the case when the number of gray gases approaches infinity termed the Exact SLW model. The present work outlines the steps in a unified construction of the generalized SLW model in isothermal and non-isothermal media, and compares different forms of the modelled radiative quantities in plane parallel media: directional total radiative flux, total emissivity, Planck mean and Rosseland mean absorption coefficients.

The transition from the incoherent to the coherent regime for thermal radiation between bodies trough a transparent medium is discussed. The canonical case of two parallel semi-infinite planar media is used as a basis to provide an insight into the physics and quantities ruling the distance at which coherent effects have an impact on the propagative component of the net heat flux exchanged. A practical criterion is proposed to define the distance below which radiation intensity framework should not be used, but instead fluctuational electrodynamics.

A diffuse approximation meshless method (DAM) is employed as a means of solving the coupled radiative and conductive heat transfer problems in semi-transparent refractive index media contained in 1D and 2D geometries. The meshless approach for radiative transfer is based on the discrete ordinates equation. Cases of combined conduction- radiation are presented, including plane parallel slab, square enclosure, and semicircular enclosure with an inner circle. The influence of the refractive index on the temperature distributions and heat fluxes is investigated. Results obtained using the proposed meshless method are compared with those reported in the literature to demonstrate the flexibility and accuracy of the method.