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Highly porous cellular media such as plastic, ceramic and metal foams present specific characteristics that make them interesting for a number of applications related to thermal engineering. In many of these applications, thermal radiation heat transfer can have a significant, ranging from a 20–30% effect for plastic foam insulation to becoming the predominant mode of heat transfer at higher temperatures. To model radiation heat transfer in these media, accurate models of radiation and microscopic structure of the foam are required. Over time, the state of the art has evolved from basic approaches using radiative conductivity to multi-scale models based on equivalent homogeneous media and the Radiative Transfer Equation, with more recent techniques such as MPA and GRTE allowing to model multiple phases, non-Beerian behavior, and history effects. Still, comparisons of homogenized models with reference results are sparse in literature, and results mixed. Furthermore, what more advanced models afford in accuracy they lose in simplicity, leading to cumbersome calculations. In this paper, we combine in a novel way hybrid direct-inverse identification of radiative properties and accounting of history effects, to present modified and improved version of the standard Homogenous Phase Approach (HPA+) and Multi Phase Approach (MPA+), with the intent of increasing accuracy while keeping maximum simplicity. We then compare existing and new models with a reference model based on Monte Carlo Ray Casting. In the comparison, we consider a varied set of porous morphologies and boundary conditions. The improved models consistently outperform existing homogenized models.

Expanded PolyStyrene (EPS) foams are very widely used as thermal insulators, especially for the Building insulation. Therefore, the heat transfer in these materials has been extensively studied and optimised. Nevertheless, due to their very low density, the IR thermal radiation propagating through their porous structure still contributes significantly to the total heat transfer. In order to increase their insulation performances even more, the addition of particles strongly interacting with IR radiation in the polymer matrix is very promising. We have investigated this solution from the theoretical and experimental points of view. The influences of the presence of particles on both the conductive and radiative properties of the opacified foams have been modelled. A parametric study allows us to highlight the key properties required to make the opacifying particles efficient and to evaluate the corresponding potential savings. Alongside, several powders have been tested experimentally by incorporating them into polystyrene thin films. Spectrometric measurements conducted on these films allow us to identify their radiative properties, evaluate the reduction of equivalent conductivity and confirm the efficiency of the solution. This investigation then constitutes a useful tool for selecting appropriate opacifiers.

International audience; Accurate numerical simulation of the effective thermal conductivity (ETC) of 3D pore-scale foam models requires a judicious choice of boundary conditions, as the computational domains are often smaller than the representative volume element, giving rise to considerable edge effects. Within the finite element homogenization framework, a set of mixed boundary conditions are considered alongside the usual uniform and periodic boundary conditions. Validity criteria and order relations, demonstrated from entropy-based principles, are numerically verified on unit cell-based geometries, random virtual periodic foams, and non-periodic tomography-reconstructed foams of equivalent microstructure. A statistical treatment based on the integral range provides confidence intervals for the estimated ETC. For foam samples with random homogeneous porosity, the mixed boundary conditions are shown to fulfill the macrohomogeneity condition and thus provide thermodynamically valid ETC estimates. For periodic foams with irregular microstructure, the ETC is very slightly underestimated under the mixed boundary conditions. For nonperiodic geometries, it is shown that periodic boundary conditions-commonly viewed as the referenceunderestimate the ETC due to boundary geometry mismatch, while the mixed boundary conditions give a more accurate and precise estimate.

This paper presents a micromechanical modeling for predicting the effective linear elastic properties of irregular open-cell foams using the periodic computational homogenization method. The tomography images are analyzed to obtain the morphological description of the irregular open-cell structure. An approach based on Voronoi diagram is used to generate realistic periodic foam structures with the morphological parameters. Hill’s lemma computational homogenization approach is performed to predict the effective elastic properties. In this paper, we focus especially on the determination of the Representative Volume Element (RVE) and the importance of choosing the RVE parameters, i.e. the number of realizations and the volume of RVE, on the accuracy of models. The efficiencies of different approaches are discussed. Some recommendations and improvements are proposed.

We compare two methods of characterizing the radiative behavior of 22 % porous sintered alumina disks containing μ m-sized pores on the 1 µm to 7 µm wavelength range up to very high temperatures. The first consists of direct spectroscopic measurements of the normal-hemispherical reflectance and transmittance at room temperature, as well as the normal emittance up to 1300 ∘ C. The second is a two-step multi-scale numerical approach: the volume radiative properties and surface reflectivity are first determined from physical optics computations on tomography-reconstructed microstructures, then applied to the resolution of the radiative transfer equation on an equivalent homogeneous medium to obtain the spectral reflectance, transmittance, and emittance. Uncertainties in the numerical results, mainly due to microstructural variability, are quantified through sensitivity studies. The good agreement between the experimental and numerical results confirm the ability of our proposed numerical approach to give accurate predictions of the high-temperature radiative behavior of porous ceramics.

We propose a physical optics approach to compute the volume radiative properties and surface reflectivity of porous ceramics composed of a weakly absorbing solid matrix containing low fractions of heterogeneities (pores or particles). Our approach accounts for dependent scattering between heterogeneities that are small and close to each other compared to the wavelength, and only requires the 3D microstructure and complex refractive indexes of constituent phases as input. We performed numerical validation of our models on reference microstructures with known solutions, and showed that an accuracy of 5% is achieved. We then applied our approach to compute the spectral volume and surface radiative properties of tomography-reconstructed porous alumina samples of various porosities up to 30%. Microstructure-property relations are extracted from numerical results, and are compared to several analytical relations in order to assess their applicability in the studied material.

The aim of this study is to investigate the influences of morphological parameters on the effective elastic properties of open-cell foam. We develop an innovative approach combined with Voronoi diagram for the generation of representative cellular materials. The generated structures are able to represent the details of the microstructure and cover a large range of open-cell foams commonly used in industrial applications. A micromechanical modeling based on Hill’s lemma approach is implemented for predicting the effective elastic properties. The influences of the morphological parameters on the elastic effective properties are analysed. Based on these assessments, new generic analytical laws are deduced for Kelvin open-cell foam structures by considering their morphological parameters.

The 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.

International audience

International audience; This study deals with the development of a partitioned coupling strategy at the fluid–solid interface for weakly transient heat transfer problems. The thermal coupling is carried out by an iterative procedure (strong coupling) between a transient solid and a sequence of steady states in the fluid. Continuity of temperature and heat flux is ensured at each coupling time step. Emphasis is put on the choice of interface conditions at the fluid–solid interface. Two fluid–solid transmission procedures are considered in this paper: Dirichlet–Robin and Neumann–Robin conditions. These conditions are theoretically examined and it is shown that the Biot number is a key parameter for determining relevant interface conditions. Stability diagrams are provided in each case and the most effective coupling coefficients are highlighted and expressed. Numerical thermal computations are then performed for two different Biot numbers. They confirm the efficiency of the interface conditions in terms of accuracy, stability and convergence. At the end of this paper a comparison between a partitioned and a monolithic approach is presented.

International audience; The effects of microstructure on the thermal conductivity of open-cell structures are investigated using a numerical approach. They include sample size, cell arrangement, and non-uniformity of strut cross-sectional area. The approach combines the Laguerre-Voronoi tessellation method for generating volumetric digitalized foam samples and the finite-element method for solving the heat transfer problem and thus for computing thermal properties. It is shown that (i) the apparent thermal conductivity is size dependent for small sample volumes. The size effect becomes negligible when the volume element representing the sample contains more than nine cells along the edge side and we can refer to effective thermal conductivity. (ii) The non-uniformity of axial strut cross-sectional area causes a strong thermal resistance along the strut axis and consequently, a decrease of the effective thermal conductivity. And (iii) From comparison between regular Kelvin's cells and random monomodal cell structures, the arrangement of cells has little influence on the effective thermal conductivity of open-cell foams. This is explained by the similarity of their tortuosity values (skeleton tortuosity about 1.4). The suitability of the current approach for predicting effective thermal conductivity of open-cell foams is confirmed by the satisfactory agreement between numerical calculations and measurements over the porosity range 75-96%. (C) 2015 Elsevier Masson SAS. All rights reserved.

Juncus maritimus fibers present an interesting cellular porous microstructure useful for thermal insulating properties. The elaboration and experimental characterization of composite materials based on different Juncus maritimus fibers content (0, 2, 5, 7 and 10 by mass) are investigated. We show that optimized composite materials can be elaborated from a simple chemically treatment of fibers. The thermo-physical properties (thermal conductivity, thermal diffusivity, and density) of both mortar composites with the raw and chemically treated fibers, were evaluated experimentally. Also, the water absorption uptake and mechanical strengths were performed to evaluate the chemical surface modification effects on the performances of the composites. As a result, due to their porous cellular microstructure, the use of Juncus maritimus fibers enhances the thermal insulating and lightness performances of reference mortar but affects negatively its mechanical strengths. The moisture effect tests reveal that thermal conductivity and density of the saturated composites are two times higher than that in a dry state. The chemical surface modification of used Juncus maritimus fibers improves the flexural and compressive strengths, decreases the water uptake of resulting composites with a low water diffusion coefficient. Thus, these new treated bio-cellular fibers composites can be used as structural and insulating lightweight concrete.

This paper focuses on the computational modeling of the effective elastic properties of irregular closed-cell foams. The recent Hill&rsquo, s lemma periodic computational homogenization approach is used to predict the effective elastic properties. Three-dimensional (3D) rendering is reconstructed with the tomography slices of the real irregular closed-cell foam. Its morphological description is analysed to generate realistic numerical closed-cell structures by the Voronoi-based approach. The influences of the Representative Volume Element (RVE) parameters (i.e., the number of realizations and the volume of RVE) and the relative density on the effective elastic properties are studied. Special emphasis is placed on the appropriate choice of boundary conditions. Satisfying agreements between the homogenized results and the experimental results are observed.

Radiative heat transfer is analyzed in participating media consisting of long cylindrical fibers with a diameter in the limit of geometrical optics. The absorption and scattering coefficients and the scattering phase function of the medium are determined based on the discrete-level medium geometry and optical properties of individual fibers. The fibers are assumed to be randomly oriented and positioned inside the medium. Two approaches are employed: a volume-averaged two-intensity approach referred to as multi-RTE approach and a homogenized single-intensity approach referred to as the single-RTE approach. Both approaches require effective properties, determined using direct Monte Carlo ray tracing techniques. The macroscopic radiative transfer equations (for single intensity or two volume-averaged intensities) with the corresponding effective properties are solved using Monte Carlo techniques and allow for the determination of the radiative flux distribution as well as overall transmittance and reflectance of the medium. The results are compared against predictions by the direct Monte Carlo simulation on the exact morphology. The effects of fiber volume fraction and optical properties on the effective radiative properties and the overall slab radiative characteristics are investigated. The single-RTE approach gives accurate predictions for high porosity fibrous media (porosity about 95%). The multi-RTE approach is recommended for isotropic fibrous media with porosity in the range of 79−95%.

This article deals with the development of a multiaxial “plasticity” criterion for the simulation of the macroscopic behavior of light closed-cell foams. The paper proposes a numerical methodology for the determination of the mechanical macroscopic properties given the geometry of the cells (whose walls are assumed to be thin) and the properties of the bulk material. The focus is on foams with relative densities ranging from 0.0526 to 0.1525. The bulk material is assumed to be isotropic with perfectly plastic behavior. We consider tetrakaidecahedron cells having three planes of symmetry in three orthogonal directions. As expected for a material having a cubic symmetry, one observes that the elastic homogenized material is fully described by three parameters ( E ∗ , ν ∗ , G ∗ ) and not only two as for the isotropic bulk material ( E , ν ). We propose a formula which, starting from only a knowledge of the two elastic properties and density of the bulk material, leads to the three macroscopic elastic properties of the thin-wall regular tetrakaidecahedral foam. Their yield and failure strengths in tension, compression and shear are also calculated. Two types of macroscopic behavior can be clearly identified. The first type characterizes foams made of a high-yield-strength bulk material: the foam’s macroscopic behavior is determined mainly by buckling of the cell walls. The second type applies when the bulk material has a low yield strength. In that case, yielding of the cell walls is the main failure mechanism. A loading surface of the Wang and Pan form is proposed for all these cases, both in the early nonlinear stage and at ultimate failure. Lastly the effect of irregularity of the geometries on the load surface is presented for the two previous extreme cases. It is observed that these irregularities play a crucial role in tensile case for the lightest foams having the highest yield strength. It is interesting to note that such a loading surface also leads to a good approximation of the “yield” strength obtained experimentally for both open-cell foams Combaz et al. (2010, 2011) and closed-cell foams Wang and Pan (2006).

This paper presents temperature dependent thermal diffusivity measurements of NiCrAl and mullite foam solid skeletons. The photoreflectance microscopy (PM) technique is used to characterize these skeletons at the microscopic scale. The characterized homogeneous zone area does not exceed 100 μm 2 . A singular sample preparation has been realized to take into account the brittleness and the optical semi-transparency of the mullite foam lumps. This specific sample preparation as well as the details of the technique are described in this article.

A simple analytical approach for estimating the total heat transfer inside new cellulose-based aerogels has been investigated. The model accounts for the characteristic solid matrix at the nanometric scale by using a cellular representation of the nanofoam porous structure. The radiation-conduction heat transfer is taken into account. Previous analytical correlation for the fluid phase is used to model the conduction heat transfer in gas. New analytical formulations based on mean free path theory combined with phonon tracking approach are proposed to model the conduction heat transfer in the solid phase at the nanometric scale. The contribution of radiation heat transfer is obtained from Rayleigh scattering approach combined to the Rosseland approximation. These analytical relations validated experimentally are expected to be useful for researchers aiming at developing new insulating organic aerogels since they permit to determine conduction-radiation equivalent conductivity as a function of cell dimensions, phonon and optical properties of cellulose.

Closed-cell polymer foams are well-known for their thermal capabilities, but works on the mechanical behavior of these materials are scarce, especially concerning the influence of the foam's microstructure. The objective of this study is to investigate the influence of the relative density and irregularity of Voronoi closed-cell foam structures on their elastic characteristics (such as the Young's modulus and the Poisson's ratio) and plastic characteristics (such as elastic limits and collapse stresses). New laws are proposed in order to approximate the macroscopic mechanical behavior of Voronoi closed-cell foams under uniaxial tension and compression.

International audience; Gypsum plaster is a building material used in walls or false ceilings. The aim of this paper consists on the improvement of thermal properties and lightness of gypsum plaster by combining it with granular cork collected from Moroccan Maamora’s forest. This composite material is intended to be used in false ceiling such as cork–gypsum board instead of plasterboard; its use will be a contribution to improve energy efficiency in buildings. By varying the granular cork size, an experimental investigation of thermal proprieties of gypsum based composite material with embedded granular cork was mainly performed using the asymmetrical transient Hot Plate method. A comparative study based on other experiments (Differential Scanning Calorimeter and Steady state Hot Plate) was realized and the thermal conductivity results were confronted to different theoretical models of equivalent thermal conductivity determination. The experimental results exhibit a good agreement with the weighted geometric mean equation.

This paper presents an analytical formulation of radiative properties of statistically isotropic and homogeneous dispersed media in the geometric optic regime. It attempts to overcome the powerful but time consuming approaches based on ray-tracing Monte Carlo technique and advance the existing analytical models. We show that simple analytical formulas, allow to capture the main extinction mechanisms in a dispersed medium. The suitability of the proposed model is discussed through two comparative studies: firstly, with the ray-tracing Monte Carlo approach on radiative properties of packed beds of spheres and matrixes enclosing spherical cavities; and secondly, with the direct Monte Carlo simulation and literature data on hemispherical transmittances of packed beds of opaque and semi-transparent spheres. The computation time of the analytical approach is shown to be less significant than those of the ray-tracing Monte Carlo method.

International audience; This study aims to study the thermal properties and the microstructure of composite materials based on mortar combined with Juncus maritimus fibers. Effective thermophysical properties of the composite materials containing Juncus maritimus fibers are experimentally and theoretically investigated. To better understand the morphology of these new composites, the corresponding microstructures were characterized in 2D by scanning electron microscope and in 3D using micro computed tomography. The local thermal conductivity of the Juncus maritimus fibers was identified using theoretical models and experimental measurement of the effective thermal conductivity of packed bed of crushed fibers. The thermal conductivity of the mortar matrix at given porosity was also determined using experimental measurement data and a theoretical model. The most appropriate analytical laws to predict effective thermal conductivity of mortar composites containing fibers are deduced from experimental thermal conductivity results.

International audience; There is currently a growing interest in nano-structured silica based materials due to their remarkable thermal properties. These materials are notably used in Vacuum Insulating Panels (VIP). Their exceptional insulating performances have been demonstrated experimentally for a relatively long time. But the heat transfer mechanisms occurring in this kind of materials remain relatively badly known due to the nanometric dimensions and to the complexity of the porous structure. Therefore, the present study aims to develop a numerical model for estimating the magnitude of conductive heat transfer inside nano-structured silicas using a realistic representation of their complex porous structure. The model takes into account the special porous morphology of the materials at both the nanometric and microscopic scale. Moreover, the conduction heat transfer at the nanometric scale is treated using a numerical resolution of the Boltzmann equation since the validity of the macroscopic laws is then questionable. The computations are conducted using phonon properties of silica obtained in the literature. A parametric study allows us to analyse the influence of structural characteristics and thermo-physical properties on the insulating performances and thus to highlight the most important parameters.

A vacuum insulation panel (VIP) is a very efficient thermal insulation system for buildings. It is constituted of an evacuated porous core material, enveloped in a gas barrier membrane. The total conductivity measured is as low as 5 mW/(m K). The high performance is due to the low pressure inside the panel and the gas barrier envelope plays a key role in maintaining the vacuum during the whole VIP service life. Indeed, due to the permeation of atmospheric gases through the envelope, a slow increase of pressure and humidity occurs over time, which involves a thermal conductivity increase in the mean time. This review paper details the mass transfer models used to predict the permeation rates of gases through the VIP envelope. The sorption–diffusion model for gas permeation through polymer membranes is presented as well as alternative permeation models. The parameters which play a key role for mass transfer are detailed. The adaptation of the permeation models from homogeneous polymer membranes to multilayer gas barrier membranes is then presented, including an important section about metal-coated polymer films. The conclusions of the works based on several approaches are reported.

The elaboration and characterization of hydrophobic melamine-based sponges are presented. Sponges were obtained by single-step carbonization of commercial melamine foam having a 3D interconnected network. We show that optimized sponges can be elaborated from a simple pyrolysis treatment with rather low temperatures of 500–600 °C. These materials exhibited excellent absorption capacities (they absorbed 90 to 200 times their own weight), a very high porosity of 99.5%, a low density around 7 mg/cm3 and water contact angles ranging from 120° to 140° close to superhydrophobicity. The relationship between hydrophobicity and physicochemical evolution on heat treatment (carbonization process, diffusion of additives, porosity evolution) was studied in detail. The as-prepared carbon sponges are compressible up to 80% with a Young’s modulus ranging from 0.58 kPa to 0.80 kPa, and keep part of their elastic properties after a hundred compression-decompression cycles. The carbonized sponges were characterized by thermogravimetric analysis (TGA), infra-red spectroscopy (FTIR), Raman spectroscopy, elemental analysis (EA), X-ray photoelectron spectroscopy (XPS) and scanning electronic microscopy (SEM). These characteristics make these materials promising absorbents for water depollution: oil-spill clean-ups or removal of oils and organic solvents from water, especially for the recovering of the pollutant by simple squeezing of the absorbent.

Purpose – The purpose of this paper is to investigate the impact of ligament shape on radiative behavior, with a specific focus on the inter-dependence among porosity, ligament shape and radiative characteristics. Design/methodology/approach – Using Surface Evolver to generate a base structure and then coherently modifying it, the model presented in this paper aims to tackle these challenges in an improved fashion, all the while making it possible to systematically assess the influence of ligament shape on radiation heat transfer in foams, focussing on the porosity-dependence of ligament shape. Findings – It is found that the prediction of numerical models, at constant size and specific surface of the cells, is strongly affected by the dependence of ligament shape on the porosity. Research limitations/implications – The above said dependence has, therefore, to be accounted for in robust modeling of radiation in foams with a wider range of porosities. Originality/value – The radiative behavior of metal foa...

International audience; Due to their excellent thermal insulation properties, low-density polyvinyl chloride (PVC) foams find applications in a wide variety of technological fields. They are notably used as thermal insulation in fuel tanks of Ariane rockets at very low temperatures. For this application, a relatively high mechanical strength is also required since the foams undergo significant mechanical loads during the flight. As a consequence, the mechanical strain undergone by the foams may affect their thermal behavior and vice versa, leading to a coupling between the mechanical and thermal properties. That is the reason why, in order to improve the modeling of the mechanical and thermal behaviors and to better understand their mutual influences, an original thermal model has been developed that is based on a shell mesh of the porous structures of PVC foams obtained by X-ray tomography. This permits the quick computation of the temperature field prevailing in the solid and fluid phases constituting the material and of the equivalent thermal transfer properties. The temperature field and thermal properties could then be used as entrance data of a mechanical finite-element computation. The effective thermal conductivities computed for non-deformed structures were compared with various correlations in the literature. Thereafter, the numerical model was applied to deformed structures obtained from mechanical finite-element computations modeling various mechanical loads. The analysis of the results highlights the major modifications of the thermal properties brought by different types of mechanical loads.

In addition to the multiple actual or possible applications of metal and ceramic foams in various technological fields, their thermal properties make them a good candidate for utilization as fire barriers. Several studies have shown experimentally their exceptional fire retardance due to their low apparent thermal conductivity. However, while the thermal properties of this porous material have been widely studied at ambient temperature and are, at present, well-known, their thermal behaviour at fire temperatures remains relatively unexplored. Indeed, at such temperatures, the major difficulties are not only due to the fact that thermal measurements are rendered fussy since heavy equipments are required but also stem from the fact that a significant part of the heat transfer occurs by thermal radiation which is much more difficult to evaluate than conductive heat transfer. Therefore, the present chapter is written with a view to report progress on the knowledge of heat transfer in open cell foams and to enlighten the reader on the mechanisms of heat transfer at high temperatures. A first part is devoted to the review of the prior published works on the experimental or theoretical characterisations of radiative and conductive heat transfers from ambient to high temperatures. By taking inspiration from the concepts and models presented in these previous works, we propose, in a second part, a model of prediction of the conductive and radiative contributions to heat transfer at fire temperatures. This analytical model is based on numerical simulations applied to real foams and takes into account the structure of the foam and the optical and thermal properties of the constituents. In a third part, we propose an innovative experimental technique of characterization of heat transfer in foams at high temperatures which permit to evaluate independently the radiative and conductive contributions from a unique and simple measurement. The experimental results obtained on several metal and ceramic foams are compared to the results predicted by our numerical model. The good adequacy between experimental and theoretical results show the consistency of both approaches.

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.

The radiative properties of extruded polystyrene foams (XPS) were predicted using morphological data and optical properties of bulk medium. A particular attention was paid on the modelling of the radiative properties of struts, which are located at the junctions between cell walls. The radiative properties of XPS foams were determined by adding the contributions of each particle (walls and struts) using the independent scattering hypothesis. Hemispherical reflectance and transmittance measurements were made in addition to total thermal conductivity measurements. Comparisons were made between theoretical and experimental results and some improvements were suggested to better improve modelling of foam radiative properties.

A combination of analytical and phonon-tracking approaches is proposed to predict thermal conductivity of porous nanostructured thick materials. The analytical approach derives the thermal conductivity as function of the intrinsic properties of the material and properties characterizing the phonon interaction with pore walls.

The conductive heat transfer in heterogeneous cellular materials is generally treated by defining the homogeneous effective thermal conductivity. For high-porosity foams, a very large number of empirical or semi-empirical models have already been proposed to evaluate this conductivity. Each approach considered different cellular morphologies and used different solution methods, leading to noticeable discrepancies. In order to estimate the reliability of these models, a numerical finite volume method computing the effective thermal conductivity of discretised two-phase heterogeneous materials was developed. It was applied to different regular open or closed cellular structures and to structures generated from tomographic images of polyvinyl chloride, expanded polystyrene and NiCrAl foams. The comparison with the results of the different models allows their degree of reliability and their domain of applicability to be estimated quantitatively.

Due to their interesting thermal, mechanical and exchange properties, solid metal or ceramic foams have shown a strong development in numerous technological fields for which the knowledge of their thermal properties is of primary importance. In order to investigate the coupled conductive/radiative heat transfer in this kind of materials, we propose an identification method using thermograms obtained from laser-FLASH measurements. This permits us to evaluate, at ambient and high temperatures, the effective thermal conductivity and two global radiative properties of various metal or ceramic foams, describing the thermal behavior of their equivalent homogeneous semi-transparent materials. This new method of characterization of solid foams is promising since conduction and radiation contributions to heat transfer can be evaluated from a unique experiment.

International audience; Superinsulating materials are currently of much interest because of the price of energy on the one hand and CO 2 emissions attributed to offices and houses cooling and heating on the other hand. In this work, we aim at understanding and modeling the radiative transfer within silica nanoporous matrices that are the principal components of nanoporous superinsulating materials. We first elaborate samples of various thicknesses from a pyrogenic silica powder. These samples are characterized using two spectrophotometers on the whole wavelength range [250 nm; 20 µm]. Using a parameter identification technique, we compute the radiative properties of the various samples. Then, our samples being made of packed quasi-spherical particles, we use the Mie theory to model the radiative properties of these materials. Due to the observed discrepancies between the experimental radiative properties and those computed from the Mie theory with a uniform value of 10 nm for the scatterer diameter (value derived from TEM images), we determine an effective scatterer diameter that allows a good agreement between the experimental radiative properties and the Mie results. Nevertheless, in the short wavelength range, the Mie theory gives results that significantly differ from the experimental radiative properties. This behavior is attributed to structure effects as the wavelength is of the same order of magnitude as the diameter of the scatterer that is now regarded as an aggregate of nanoparticles. Hence, to take into account these effects, we use the discrete dipole approximation (DDA). The DDA extinction coefficient spectra appear to be much closer to the experimental results than the Mie spectra, and these first results are quite encouraging.

Two metallic foams exhibiting a similar porosity but different cell sizes have been characterized using X-ray tomography. The images have been processed and analysed to retrieve the morphological properties required for the calculation of the radiative properties such as the extinction coefficient. The multiple possibilities of using the X-ray tomography method rather than conventional optical methods like SEM have been quantified. The extinction coefficient has then been determined from two approaches. First, the resulting morphological properties have been used as the input data of the conventional independent scattering theory. A special emphasis is put on the determination of morphological properties and their influence on the results. In the second approach, an original method is also proposed in order to determine the extinction coefficient of highly porous open cell metal foams, from the tomographic images and without any calculation or hypothesis. Results show a good agreement with the extinction coefficient obtained from experimental measurements. Our novel method enables to reduce uncertainties considerably.

This study is interested in the heat conduction in porous metallic/ceramic foams characterized by their complex morphology and the large difference between the thermal conductivities of the fluid and solid phases. We have developed two numerical simulations of the heat conduction in a 3-D two-phase material based on the Finite Element Method and on the Lattice-Boltzmann Method. The foam microstructure is modeled by various polyhedral open cells formed by solid struts with different shapes. The accordance between the results of the two numerical methods is excellent. The simulations allow to investigate theoretically the influence of the structural parameters on the magnitude of heat conduction.

Among all the transient techniques of measurement of the thermal conductivity, the hot-wire method is an interesting alternative to the standard guarded hot-plate method. However, it has been proved to be poorly adapted to low-density thermal insulators notably due to edge effects, which disturb the temperature rise. To overcome this problem, the hot-ring method, which is very close to the hot-wire technique, could be interesting as it does not make any assumptions on the dimensions of the heating elements. In order to investigate the use of this method for measurements on low-density thermal insulators we conducted a theoretical and experimental study on several expanded polystyrene (EPS) foam samples. The numerical model developed solves the 2-D axisymmetric heat transfer around the ring taking into account the conduction–radiation coupling and the inertia of the element. Numerical and experimental results show that classical hot-ring apparatus are poorly adapted to measurements on low-density insulators owing to the thermal inertia of the elements. However, we developed a modified identification procedure eliminating the influence of the inertia of the apparatus on the measured thermal conductivity. This new procedure gives accurate results even for EPS foams, which could not be considered as optically thick. Thus, the hot-ring technique could be extended to low-density thermal insulators.

The use of the hot wire method for thermal conductivity measurement has recently known a significant increase. However, this method is theoretically not applicable to materials where radiative heat transfer is not negligible such as low-density thermal insulators. In order to better understand the influence of radiative contribution, we developed a two dimensional simulation of transient coupled heat transfer and made hot-wire measurements on low-density Expanded PolyStyrene (EPS) foams. The analysis of theoretical and experimental results shows that classical hot-wire apparatus are poorly adapted to low-density insulators. However, if an appropriate hot-wire apparatus is used, the estimated equivalent thermal conductivity is in close agreement with that estimated by the guarded hot-plate method.

Recently a new experimental set-up for measuring the directional spectral emittance has been developed. Both sides of packed opaque spheres are simultaneously heated with identical power laser beams (CO2 10.6 μm) and the isothermal condition in the medium is assumed. In this paper we consider the coupled conduction-radiation equations to investigate the effect of the temperature nonuniformity on the calculated value of the emittance and to verify if the isothermal assumption is valid. Moreover, the sensitivity of the emittance and the temperature profile to the values of parameters (such as the porosity, the face temperatures, and the particle hemispherical reflectivity, etc.) is studied.

As dispersed materials generally are semi-transparent media which absorb, emit and scatter thermal radiation, the predictive modeling of thermal processes involving such kind of materials requires the knowledge of a number of radiative properties to feed the models. These properties cannot be directly measured but are identified from a set of experimental data of radiative flux collected from a sample submitted to appropriate experimental conditions. This paper focuses on identification methodology for thermal radiation properties of dispersed media such as fibers, foams, pigmented coatings, ceramics. After a brief introductive overview of the subject, the parameter identification methodology and two experimental facilities used for radiative properties determination are firstly described. As the identification process involves a solution model for the Radiative Transfer Equation inside the sample, some attention is then paid to the development of RTE solution models well matched to this specific purpose. Two examples of application are described before concluding on the advantages, limitations and remaining difficulties connected to this new and promising metrology of thermal radiative properties of dispersed media.

Spectral radiative properties (absorption coefficient, scattering coefficient, and phase function) of open-cell polyurethane foam are identified using a combination of hemispherical and bidirectional spectral transmittance and reflectance measurements in the infrared wavelength region 2-15 μm. The influence of the number of transmittance measurements on identification results is analyzed. The Gauss linearization technique is used in the identification method, and discrete ordinates method is applied to solve the radiative transfer equation.

Spectral radiative properties (absorption coefficient, scattering coefficient and phase function) of open cell polyurethane foam are determined from parameter identification method. This method uses spectral transmittance and reflectance measurements in the wavelength infrared region of 2– 15 μm . Different strategies of identification using different types of measurements (directional–hemispherical, combination of directional–directional and directional–hemispherical) are compared. The discrete ordinates method is used to solve the radiative transfer equation.

Spectral radiative properties (absorption coefficient, scattering coefficient, and phase function) of open-cell carbon foam have been determined experimentally. The identification method uses spectral transmittance and reflectance measurements and a prediction model based on a combination of geometric optics laws and diffraction theory. In the wavelength region 0.2-2 μm directional-hemispherical transmittance and reflectance measurements are used, and directional directional transmittance and reflectance measurements are used in the wavelength region 2-15 μm. Radiative properties are determined in the wavelength region from visible to infrared. Two approaches corresponding to two different types of measurements are compared for the determination of radiative properties. Moreover, experiments on a guarded hot-plate device are used to confirm that the proposed model is appropriate to predict the radiative heat transfer in such media.

Directional spectral emittance of an absorbing and scattering isothermal system of packed spheres is predicted by a radiative model based on the discrete ordinates method. Radiative properties for the bed of packed opaque spheres are obtained using geometric optics laws corrected with a scaling factor to take into account the dependent scattering. This model requires the knowledge of several parameters. Particle diameter and porosity can be easily obtained, but particle hemispherical spectral reflectivity is very difficult to obtain a priori. This particle reflectivity is determined by an identification method (Gauss method of linearization) applied to bidirectional spectral reflectance data obtained from an experimental device using a Fourier transform infrared spectrometer. Directional spectral emittance is measured using a direct radiometric technique that has been recently proposed. For a system of packed opaque spheres at high temperature, good agreement is observed between experimental results of directional spectral and computed theoretical data.

A method to determine radiative properties of open-cell foam insulation is described. The spectral volumetric absorption and scattering coefficients and the spectral phase function are predicted from the dimensions and hemispherical reflectivity of particles that constitute the solid structure by applying to these particles a combination of geometric optics laws and diffraction theory. Three types of carbon foam of different porosities are studied. Particle dimensions and porosity can be obtained from microscopic analysis, but solid hemispherical spectral reflectivity is very difficult to obtain directly. It is determined by the Gauss method of linearization, applied to bidirectional spectral transmittance data obtained from an experimental device using Fourier-transform infrared spectroscopy. Results obtained from this approach are consistent. Good agreement is observed between the experimental results of transmittance and reflectance and the theoretically predicted values computed from the identified values of particle hemispherical reflectivity.

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The hot-disk technique is a very practicable transient method of measurement of the thermal properties of solid materials. It has been applied successfully to a wide variety of materials. However, it is based on several approximations regarding the nature of the heat transfer. Notably, the probe is considered thermally neutral, and the heat transfer is assumed purely conductive. These two assumptions are questionable when dealing with low-density thermal insulators. In order to evaluate the accuracy of the method, we have generated numerically noised thermograms reproducing the thermal response that would be recorded when measurements are applied to those type of materials. Thereafter, the best-fitting procedure of the classical hot-disk technique was applied to these thermograms. The analysis of the identification results show that the presence of a radiative contribution do not affect the accuracy of the thermal properties identified. The conductivity measured actually corresponds to the equivalent conductivity. On the other hand, when the method is applied to materials with thermal inertia strongly different from the probe (≈2 order of magnitude lower or more), the accuracy of the method becomes questionable. This is notably the case for common insulators used in the building industry like polymer foam or mineral wools. The preceding conclusions have been validated by experimental measurements on a standard low-density XPS foam sample and a superinsulating silica areogel.

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