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Description
In the domain of thermal insulation at high temperatures, refractory porous or fibrous materials are of particular interest. In these materials, the conductive and convective heat transfer modes can be negligible and thus, the radiative transfer plays a key role that must be accurately quantified
In this work, we study a random array of overlapping infinite cylinders under vacuum, assumed to be representative of a felt of fibers. The solid phase is assimilated to a homogeneous cold dense participating (absorbing and non scattering) medium with a spectral complex optical index. The distribution of cylinders inside the calculation box is imposed to be statistically homogeneous and isotropic to ensure interesting morphological properties. To achieve this, an algorithm generates each cylinder axis as a µ-random chord of the calculation box. Analytical expressions for the average porosity, the overlapping ratio, the autocorrelation function and some chord lengths statistics are deduced.
A Monte Carlo ray tracing method is implemented to simulate the propagation of radiation inside the medium. Each ray enters the box following a direction that complies with the conditions of the incident illumination, and may be absorbed inside the cylinders, or reflected or refracted at the interfaces between the cylinders and the vacuum. The fractions of rays exiting the box provide the directional-hemispherical transmittance and reflectance values of the calculation domain. They serve as numerical measurements.
The radiative characterization is done based on rather recent methods formalized to various extents by several authors [1, 2, 3], where the generalized radiative properties of an equivalent homogeneous medium are determined and approximated numerically with the use of a Monte Carlo method. Yet, the originality of our work is in the analytical determination of these generalized radiative properties of our particular material. A “non-Beerian” behaviour of the medium is highlighted. The generalized radiative properties are then used in a radiative model, which is then solved with a Monte Carlo algorithm. The results of transmittances and reflectances issued from this approach are compared to our previous numerical measurements. The agreement between the two methods is not perfect in all the situations that we consider but the behaviors of the curves are always very consistent. Investigation and improvements of the method are still undergoing.
| References | [1] M. Tancrez, J. Taine, “Direct identification of absorption and scattering coefficients and phase function of a porous medium by a Monte Carlo technique”, International Journal of Heat and Mass Transfer, 47(2), 373-383, (2004). [2] Y. Dauvois, M. Zarrouati, D. Rochais, F. Enguehard, J. Taine, “Comments over homogenisation scales for interfacial emission and scattering by a divided medium: Beerian and non Beerian behaviours”, IJHMT, 103, 468-477, (2016). [3] L. Seyer, F. Enguehard, D. Rochais, “Deterministic and stochastic approaches for the modeling of conduction-radiation coupling within non-Beerian semi-transparent media”, JQSRT, 325, 109086, (2024). |
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| Country | France |
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