Effect of anisotropy on thermal radiation transport in porous ceramics

Aiming at promoting the fundamental understanding on relationship between the radiative transfer mechanism and microstructure of thermal barrier coatings (TBCs), here in this study, we numerically demonstrate the anisotropy of radiative properties of air plasma sprayed (APS) TBCs for the first time. The anisotropic microstructures of APS TBCs are quantitatively reconstructed based on Ultra-Small-Angle X-Ray Scattering (USAXS) measurement by the Stony Brook University group (Li et al., J. Amer. Ceram. Soc., 92(2) p. 491-500, 2009), in which the microscale pores and cracks are treated as oblate spheroids with a preferred distribution of orientations. The anisotropic mesoscopic radiative properties, including scattering coefficient/mean free path and asymmetry factor, are computed using the discrete dipole approximation (DDA) to solve Maxwell's equations. To fully depict the effect of anisotropy on radiative transfer in a macroscopic scale, a random walk scheme is thus proposed to solve the anisotropic radiative transfer problem in such medium, and the macroscopic transport mean free path describing energy diffusion process is derived. Results are further compared with those under isotropic assumption. By considering external blackbody as thermal radiation sources for the coating, we show that anisotropy of radiative properties affects the transmitted radiative heat flux across it considerably, especially at high operating temperatures and for thick coatings. On the other hand, in moderate operating conditions, the simplistic approach can also give an acceptable approximation on heat transfer for the presented particular coating microstructure. The present work provides a fundamental framework for studying radiative transport in anisotropic porous media.