3D numerical modelling of the propagation of radiative intensity through a X-ray tomographied ligament. (June 2017) - Le Hardy, David; Badri, Mohd Afeef; Rousseau, Benoit; Chupin, Sylvain; Rochais, Denis; Favennec, Yann
Abstract: In order to explain the macroscopic radiative behaviour of an open-cell ceramic foam, knowledge of its solid phase distribution in space and the radiative contributions by this solid phase is required. The solid phase in an open-cell ceramic foam is arranged as a porous skeleton, which is itself composed of an interconnected network of ligament. Typically, ligaments being based on the assembly of grains more or less compacted, exhibit an anisotropic geometry with a concave cross section having a lateral size of one hundred microns. Therefore, ligaments are likely to emit, absorb and scatter thermal radiation. This framework explains why experimental investigations at this scale must be developed to extract accurate homogenized radiative properties regardless the shape and size of ligaments. To support this development, a 3D numerical investigation of the radiative intensity propagation through a real world ligament, beforehand scanned by X-Ray micro-tomography, is presented in this paper. The Radiative Transfer Equation (RTE), applied to the resulting meshed volume, is solved by combining Discrete Ordinate Method (DOM) and Streamline upwind Petrov-Garlekin (SUPG) numerical scheme. A particular attention is paid to propose an improved discretization procedure (spatial and angular) based on ordinate parallelization with the aim to reach fast convergence. Towards the end of this article, we present the effects played by the local radiative properties of three ceramic materials (silicon carbide, alumina and zirconia), which are often used for designing open-cell refractory ceramic foams. Abstract : Highlights: The propagation of the radiative intensity of a real ligament is numerically modelled. DOM combines with SUPG method is used to solve the RTE. Treatment of the specularity by partition is performed for complex geometry. Radiative quantities are computed with prescribed effective radiative properties.