Measurement and Use of Reflectance Function Based on the Discrete-Ordinates Method

An experimental scatterometer based on the angular discretization of the discrete-ordinates or SN method was constructed to account for the directional property of reflectance of metallic foils and their interaction with a high-temperature insulating material. Solution of the radiative heat-transfer equation is given in terms of the S4 approximation taking into consideration a linear-anisotropic scattering function for the scattering characteristics of the fiber and including the directional properties of the foils as part of the boundary condition limits. Special treatment in the SN method is required when dealing with directionally incident radiation in order to simulate the experimental conditions. The reflectance distribution function for the metallic surfaces showed to have a strong specular reflection and a weak diffuse component for all 12 incident directions in the spectral/gray model. Prediction of the reflectance function in fiber insulation while using measured reflectance data of the type of foil backing utilized provided good qualitative agreement. This is in lieu of the approximation in the scattering function and the directional biasing of the quadrature. However, using the full directional reflectance data helps to diminish this directional biasing (even intensity hemispherical distribution), which, in turn, leads to more consistent prediction of properties or to more accurate radiative-transfer calculations.