Dual-scale 3-D approach for modeling radiative heat transfer in fibrous insulations

摘要

In this work, a dual-scale computationally-affordable 3-D method is developed to simulate the transfer of radiative heat through fibrous media comprised of fibers with different diameters and orientations. The simulations start by generating a virtual fibrous material with specified microstructural properties and then compute the radiative properties of each fiber (i.e., effective phase function, as well as scattering and absorption coefficients) in the structure using the Mie Scattering theory. Considering independent scattering formulations for our fibrous media (media with high porosities), the radiative properties of the insulation material are computed by summing up the radiative properties of each individual fiber, after transforming the phase function values from the fiber's local 3-D coordinates system to a fixed global coordinates system. The radiative properties of the media are then used in the Radiative Transfer Equation (RTE) equation, an integro-differential equation obtained for computing the attenuation and augmentation of an InfraRed ray's energy as it travels through a fibrous medium. Using the Discrete Ordi-nate Method (DOM), the RTE is then discretized into a system of twenty four coupled partial differential equations and solved numerically using the FlexPDE program to obtain the rate of heat transfer through the entire thickness of the media. Studying media with different microstructural properties, it was quantitatively shown that increasing solid volume fraction, thickness, or fibers' through-plane orientation increases the rate of heat transfer through insulation. With regard to the role of fiber diameter, it was found that there exists a fiber diameter for which radiation heat transfer through a fibrous media is minimal, ranging between 3 and 10 μm for glass fibers operating in a temperature range of about 340-750 K.