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

Abstract

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.