Remi Coquard

Radiative Characteristics of Beds of Spheres Containing an Absorbing and Scattering Medium

The aim of this paper is to characterize the radiative behavior of beds made of spherical particles containing an homogeneous absorbing and scattering medium whose radiative properties (extinction coefficient, scattering albedo, and scattering phase function) are known. In the beds studied, the spherical particles could be far apart, close to each other, or even compressed. When the particles are sufficiently distant from each other to scatter independently, the radiative properties of the whole bed are determined from the radiative characteristics of one particle alone. These characteristics are determined using a Monte Carlo procedure applied to one bead alone. On the other hand, when particles get closer to each other independent scattering theory is no longer valid, and dependent scattering effects have to be taken into account. We then apply a Monte Carlo procedure to the whole bed and identify the extinction coefficient, scattering albedo, and scattering phase function of the equivalent homogeneous absorbing and scattering medium that best matches the radiative behavior of the bed. The simulation permits us to characterize the evolution of the radiative properties of the bed with the inside medium properties and the characteristics of the bed. Moreover, we investigate the limit of validity of the independent scattering hypothesis.

Numerical Investigation of the Radiative Properties of Polymeric Foams from Tomographic Images

Polymeric closed-cell foams are widely used in various applications where their insulating performance is of interest. In most of these applications, radiation propagation is an important mode of heat transfer. That is the reason why many studies have already been performed in the prediction of the radiative behavior. Until now, these studies were based on ideal representations of the cellular structure that simplify the real porous morphology. However, the recent development of x-ray tomography allows envisaging a noticeable improvement in the morphological characterization of these materials, which can be used to achieve a better numerical estimation of their radiative properties. To fulfill this objective, a numerical method for computing the directional radiative properties of particulate media based on ray-tracing procedures has been developed. The method to three-dimensional binary representations of the cellular structures obtained from x-ray tomography on plastic foams has been applied. The comparison between the spectral radiative properties computed by the simplified models of the literature and by our original models permits us to determine which assumptions are the most detrimental to the reliability of the simplified models.

Effective conductivity of Voronoi’s closed- and open-cell foams: analytical laws and numerical results

AbstractThe conductive heat transfer in high-porosity cellular materials is generally treated by defining a homogeneous effective thermal conductivity. Numerous empirical and semiempirical models as well as numerical investigations have already been conducted to estimate this conductivity. These previous investigations were based on simplifications of the morphology of the cellular structure and/or of the method of solution of the heat transfer problem. Moreover, they were developed specifically for a type of foam, thus limiting their range of applicability. In order to improve the theoretical knowledge on this field, we have developed an innovative approach combining Voronoi methods for the generation of representative cellular materials and the finite element method (FEM) for solving the conductive heat transfer. The structures generated are able to reproduce the discriminating details of the microstructure and cover the whole range of open-cell or closed-cell foams commonly used in scientific or industrial applications. The influence of the structural parameters on the effective conductivity is analyzed. Based on this assessment, new simplified analytical relations are deduced accounting for the composition and structural parameters of the material. The validity of these laws has been verified by comparisons with “tomographic” results obtained from 3D tomographic data of real open-cell and closed-cell foams. The analytical correlations are potentially very useful for numerous applications.

Radiative Transfer in Two-Phase Dispersed Materials

This chapter presents the treatment of radiative transfer in two-phase dispersed media in the framework of radiative transfer theory. With this aim, two modeling approaches, under the geometric optic hypothesis, are described and then compared. The first one is the traditional treatment of dispersed media as continuous and homogeneous systems, referred to here as the Homogeneous Phase Approach (HPA). The radiation propagation is characterized by effective radiative properties and modeled by the conventional Radiative Transfer Equation (RTE). The second approach is based on a separate treatment of radiative transfer in the continuous and dispersed phases, referred as the Multi-Phase Approach (MPA). In this approach, each constituting phase has its own effective radiative properties and temperatures. For each approach, the methods for predicting the radiative properties are reviewed. The radiative transfers through typical two-phase dispersed media, such as glass containing bubbles, packed bed of opaque spheres, and packed-bed of semitransparent spheres, are analyzed. The results of transmittances and reflectances from these predictive approaches are compared with available experimental data or Monte Carlo (MC) simulation.

Application of the Hot-Plane Method to Low-Density Thermal Insulators

low-density thermal insulators. To better understand the influence of the radiative contribution, we developed a three-dimensional simulation of transient coupled heat transfer and made hot-plane measurements on low-density expanded polystyrene foam. The analysis of theoretical and experimental results shows that classical hot-plane apparatuses are poorly adapted to low-density insulators. However, if a hot-plane apparatus with sufficiently large dimensions andlow thermal inertiais used, the estimated equivalent thermalconductivity is in closeagreement with that estimated by the guarded hot-plate method.