Dominique Baillis

Modified two-flux approximation for identification of radiative properties of absorbing and scattering media from directional-hemispherical measurements

A modified two-flux approximation is suggested for calculating the hemispherical transmittance and reflectance of a refracting, absorbing, and scattering medium in the case of collimated irradiation of the sample along the normal to the interface. The Fresnel reflection is taken into account in this approach. It is shown that the new approximation is rather accurate for the model transport scattering function. For an arbitrary scattering medium, the error of the modified two-flux approximation is estimated by comparison with the exact numerical calculations for the Henyey-Greenstein scattering function in a wide range of albedos and optical thicknesses. Possible applications of the derived analytical solution to identification problems are discussed.

Spectral Radiative Properties of Open-Cell Foam Insulation

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.

Use of Mie theory to analyze experimental data to identify infrared properties of fused quartz containing bubbles

An improved method used to determine the absorption and scattering characteristics of a weakly absorbing substance containing bubbles is suggested. The identification procedure is based on a combination of directional-hemispherical measurements and predictions of Mie-scattering theory including approximate relations for a medium with polydisperse bubbles. A modified two-flux approximation is suggested for the calculation of directional-hemispherical transmittance and reflectance of a refracting and scattering medium. The complete identification procedure gives not only the spectral radiative properties but also the volume fraction of bubbles and the characteristics of possible impurity of the medium. This procedure is used to obtain new data on near-infrared properties of fused-quartz samples containing bubbles.

Determination of Spectral Radiative Properties of Open Cell Foam: Model Validation

Spectral radiative properties (absorption coefe cient, scattering coefe cient, and phase function ) of open cell carbonfoamaredeterminedexperimentally. Theidentie cation method usesspectral transmittanceand ree ectance measurements and a prediction model based on a combination of geometric optics laws and of diffraction theory. In the wavelength region of 0.1 -2.1 πm, directional -hemispherical transmittance and ree ectance measurements are used, whereas directional -directional transmittance and ree ectance measurements are used in the wavelength regionof2-15 πm.Thus, radiativepropertiesaredeterminedin thewavelengthregionfromvisibletoinfrared.The two approaches corresponding to the two different types of measurement (directional -directional and directional - hemispherical ) are compared for the determination of radiative properties. Moreover, experiments performed on a guarded hot-plate-typedeviceareused to cone rm thattheproposed model is appropriate to predict the radiative heat transfer in such media. isputonthedeterminationofradiativepropertiesofopencellcarbon foam. The radiative properties of foam that are required for solving the radiative transfer equation are the spectral volumetric scatter- ing and absorption coefe cients and the spectral volumetric phase function. Recently, Baillis et al. 3 have adopted a new approach to determine such properties. Radiative properties were obtained from morphological data, such as porosity, particle sizes, and f s param- eter, and from solid hemispherical ree ectivity. Particle dimensions and porosity can be obtained from microscopic analysis, but solid hemispherical spectral ree ectivities are very dife cult to obtain di- rectly.Baillisetal. 3 havedeterminedsolidhemisphericalree ectivity andmorphologicalparameter f s withanidentie cationmethod.This method used spectral directional -directional experimental results of transmittance and ree ectance obtained for several measurement directions and for several wavelengths in the range 2 -15 l m. A good agreement was observed between experimental and theoret- ical results. These results are encouraging, but they do not permit validation of the model. Moreover, for high-temperature applica- tions, it is necessary to determine radiative properties in the region of visible and near-infrared wavelengths. In this paper, a device with an integrating sphere is used to measure spectral directional - hemispherical transmittance and ree ectance in the wavelength re- gion of 0.2-2.1 l m. The radiative properties predictive model and the identie cation method used to determine the unknown parameters are briee y de- scribed.Thenapplication toacarbonfoamsampleof98.75%poros- ity permits the study and validation of the model. This section rep- resents the most innovative part of this work. 1) Sensitivity of different parameters (porosity, particle di- mensions, etc. ) on hemispherical ree ectance and transmittance is studied. 2) Identie cation results obtained from the two approaches cor- responding to two different types of measurements (hemispherical or directional) are compared to each other. The values of f s iden- tie ed are also compared with the value of f s determined from a microscopic analysis. 3) Finally, experiments on a guarded hot-plate-type device allow comparison of the experimental and theoretical conductivities (ac- countingforradiativetransfer,obtainedfromtheradiativeproperties in the wavelength region of 0.2 -15 l m). Results are also compared with simpler models that neglect scattering.

Identification of spectral radiative properties of polyurethane foam from hemispherical and bi-directional transmittance and reflectance measurements

Abstract 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.

Experimental characterization of thermal radiation properties of dispersed media

Abstract 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.

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.

Improved Inverse Method for Radiative Characteristics of Closed-Cell Absorbing Porous Media

Radiative characteristics such as the extinction coefficient, the scattering albedo, and the scattering phase function of fused quartz containing closed cells are determined by using an inverse method based on theoretical and experimental bidirectional transmittances. The theoretical transmittances are obtained by solving the radiative transfer equation with the discrete ordinate method. Improvements have been made over previously reported experimental determination of porous fused quartz radiative characteristics by using a more accurate phase function and an adaptive quadrature to compute more precisely the intensities in the measurement directions. In addition, a two-step inverse method to compute accurately and simultaneously the radiative parameters has been developed. The results are shown to be independent of samples thickness. Exhaustive comparison between experimental measurements of hemispherical transmittance and reflectance and computational results using the retrieved radiative characteristics shows good agreement. The retrieved absorption coefficient of porous fused quartz appears to be more realistic than that reported in our earlier publication.

Experimental Determination and Modeling of the Radiative Properties of Silica Nanoporous Matrices

Experimental Determination and Modeling of the Radiative Properties of Silica Nanoporous Matrices Superinsulating materials are currently of interest because the heating and cooling of houses and offices are responsible for an important part of CO 2 emissions. In this study, we aim at modeling the radiative transfer in nanoporous silica matrices that are the principal components of nanoporous superinsulating materials. We first elaborate samples from different pyrogenic amorphous silica powders that slightly differ one from another in terms of specific surface, nanoparticle diameter, and composition. The various samples are optically characterized using two spectrometers operating on the wavelength range (250 nm; 20 ␮m). Once the hemispherical transmittance and reflectance spectra are measured, we deduce the radiative properties using a parameter identification technique. Then, as the considered media are made of packed quasispherical nanoparticles, we try to model their radiative properties using the original Mie theory. To obtain a good agreement between experiment and theory on a large part of the wavelength range, we have to consider scatterers that are up to five times larger than the primary nanopar-ticles; this is attributed to the fact that the scatterers are not the nanoparticles but aggregates of nanoparticles that are constituted during the fabrication process of the powders. Nevertheless, in the small wavelength range (␭ smaller than 1 ␮m), we can never get a satisfactory agreement using the Mie theory. This disagreement is attributed to the fact that the original Mie theory does not take into account the nanostructure of the aggregates. So we have developed a code based on the discrete dipole approximation that improves the modeling results in the small wavelength range, basing our computations on aggregates generated using the diffusion-limited cluster-cluster aggregation algorithm in order to ensure a fractal dimension close to what is usually found with aggregates of silica nanoparticles.

Monte Carlo simulation of cross-plane thermal conductivity of nanostructured porous silicon films

This paper presents a Monte Carlo (MC) modeling of heat conduction in heavily doped (p+ and n+) porous silicon (PS) films known as mesoporous silicon (meso-PS). A three-dimensional pore network generator is developed to better reproduce the structure of low porosity (fv<50%) meso-PS. The submicron scale heat conduction modeled by the Boltzman transport equation is simulated using the MC method in which the nonlinear phonon dispersion curves of bulk silicon and the phonon lifetime dependent on temperature, frequency, and polarization are taken into account. The proposed method has been applied to predict the effect of the porosity (10%–47%), pore sizes (10–20nm), pore arrangement (p+- and n+-type), temperature (50–500K), and film thickness (50nm–1μm) on the cross-plane thermal conductivity of meso-PS films. Moreover, the simulation results enable to deduce the scattering mean free path (MFP) of phonons in the PS and the scattering MFP due to phonon-pore wall interaction. At room temperature, the thermal co...