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Hybrid Methodology for Retrieving Thermal Radiative Properties of Semi-Transparent Ceramics Benjamin Bouvry, Leire del Campo, Domingos De Sousa Meneses, Olivier Rozenbaum, Romain Echegut, David Lechevalier, Michel Gaubil, and Patrick Echegut J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b09693 • Publication Date (Web): 22 Jan 2016 Downloaded from http://pubs.acs.org on February 1, 2016
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The Journal of Physical Chemistry
Hybrid Methodology for Retrieving Thermal Radiative Properties of Semi-Transparent Ceramics Benjamin Bouvry§,+, Leire del Campo§, Domingos De Sousa Meneses*,§, Olivier Rozenbaum*, Romain Echegut§, David Lechevalier#, Michel Gaubil+, Patrick Echegut§
§
CNRS, CEMHTI UPR3079, Univ. Orléans, F-45071 Orléans, France
*
ISTO, Université d’Orléans, CNRS, BRGM, 1A rue de la Ferollerie, 45100 Orléans, France
+
Saint-Gobain CREE, 550 avenue Alphonse Jauffret, 84306 Cavaillon cedex, France
#
Saint-Gobain NRDC, 9 Goddard Road, Northborough, MA 01532, USA
* Corresponding author:
[email protected], phone number: +33 2 38 25 55 34
Abstract Semi-transparent materials, like silica or alumina, are highly used by high-temperature industries as refractory materials in blast or glass-making furnaces, firstly for their good mechanical properties. The knowledge of their radiative properties is also essential to improve thermal transfers. However, characterizing experimentally the high temperature dependence of radiative properties of semi-transparent ceramic materials remains nowadays a difficult task. This paper reports a hybrid methodology to address this problem. The approach relies on two or more experimental emittance measurements, performed by infrared spectroscopy on samples of increasing thicknesses, and application of emittance models. The efficiency of the method is illustrated by using experimental data obtained on Jargal M samples, an industrial electrofused ceramic, and a virtual media built from X-ray computed tomography images.
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Two emittance models, a model from the literature and a new model proposed in this work, are selected to be a part of the hybrid methodology, since they allow retrieving complementary information on the optical and scattering properties of the materials. Both models show a good efficiency to reproduce emittance behavior of the industrial and virtual samples. Parameters are extracted from these models to improve our knowledge of the characteristic thickness of radiative transfer into semi-transparent materials and the emittance value of semi-infinite media.
1 Introduction Semi-transparent materials like glass and ceramics are used for numerous applications, e.g., in aeronautics, aerospace, defense, for thermal shields or missile heads1, or high-temperature industries. Semi-transparent materials, for example silica, alumina or zirconia, are used by high-temperature industries as refractory materials in blast or glass-making furnaces to decrease thermal loss and maintain high temperatures2. In spite of their wide uses, the understanding of their radiative properties remains incomplete. Indeed, thermal transfers in this type of material are a complex issue, since a lot of textural parameters influence photon trajectory and their absorption. It is well-known that material surface properties have a major role on the emissivity value, especially in the far-infrared region called opaque region3-6. But to completely describe the optical and thermal properties of semi-transparent materials at room and high temperatures, the whole thermal spectral range has to be considered. Thus, we focus this study in the semitransparent region, the region from the mid-infrared to the visible range, where light travels far under the material surface, and where the whole volume and topology of the material affect the light propagation. Indeed, texture, pore size and its distribution, are known to influence radiative properties of semi-transparent materials7-12.
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The Journal of Physical Chemistry
Experimental determination of a sample emittance by infrared spectroscopy is not accurate for large samples in case of semi-transparent media. The size of the samples characterized by spectroscopy is usually around a few millimeters thick, which is off from actual industrial applications, i.e., sample thicknesses from centimeters to several tenths of centimeters. For example, the typical thickness of refractory materials used in glass furnace superstructures is about 300 mm. The laboratory setups are mainly limited by the heating system used to reproduce material thermal conditions and to characterize precisely their radiative behavior. Indeed, a heating system by element brings a parasite flux during the analysis whereas a CO2 laser, often used to heat semi-transparent materials up to the fusion temperature, do not but allows only keeping an homogeneous temperature on samples of about 5 mm thick and 8 mm in diameter. For measurements at room temperature, bigger samples can be analyzed because temperature heterogeneity is no more an issue. Therefore, samples with a thickness up to about 10 mm can be characterized by using an integrating sphere, but this remains much lower than the thickness of real industrial blocks. For the last decades, several numerical approaches or models, like the Kubelka-Munk model13, two-flux and four-flux models14 have been used in order to provide mathematical formulations of radiative transfers and to complete our understanding of these processes. A review of the different existing models is given by Wang15. These models allow simulating light absorption and light scattering in semi-transparent media and have been used in recent works16-21. All these models are based on approximations which can lead to severe variations of absorption and scattering coefficients depending on the spectral range considered or the thickness of media. This study aims at estimating the emittance values of samples thicker than the ones currently measured in laboratory and at estimating the sample thickness responsible for the radiative response of semi-transparent materials. For that purpose, we propose a hybrid methodology,
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combining experimental measurements on a set of samples of increasing thicknesses and emittance models. We use a Modified Two-Flux Approximation (MTFA) model and a new simplified model, called Exponential Approximation (EA) model. Validation and comparison of the two models are done using experimental emittance results at room temperature, a temperature allowing radiative response for high sample volumes. Thereafter, a numerical procedure is proposed to validate radiative behavior as observed by the predictive models on a various range of thicknesses and porosities. A combination of a ray tracing procedure and a Monte-Carlo method is applied on numerical samples, based on an approximate sample texture for which pores are simplified by ellipsoids. The focus is done on an alumina-based refractory material, called Jargal M, used in superstructure in high temperature glass furnaces dedicated to high quality glass.
2 Experiment 2.1
Sample characterization
Jargal M is a fused cast refractory material produced by Saint-Gobain SEFPRO. It is a multiphase material made of about 55% β-alumina (Na2O-11Al2O3), 43% α-alumina, and a small amount of other phases located mainly at the grain boundaries. The Jargal M composition, as measured by X-ray fluorescence analysis, is given in Table 1. Table 1. Composition of the Jargal M samples. Elements (wt %) Al2O3
CaO
SiO2
Na2O
ZrO2
Fe2O3
95
0.13
0.72
3.89
0.08
