A simple expression for the normal spectral emittance of open-cell foams composed of optically thick and smooth struts

Abstract

A set of 96 open-cell foams with growing porosities (0.35–0.95) and growing pore nominal diameters (0.4–2.6 mm) was artificially generated to firmly connect their normal spectral emittances to their textural features. This work is strictly focused on foams that are composed of opaque struts with optically smooth surfaces. To compute the normal spectral emittances, a Monte Carlo Ray Tracing code was carefully used through an indirect method based on Kirchhoff's laws. The Monte Carlo Ray Tracing code considers the complex refractive index of the solid phase constituting the struts foams. Particular attention is therefore paid to performing the calculation with absorption indices (0.5–8) that preserve the opacity of each strut. From a thorough analysis of the ray transport within all the foams, where the Representative Elementary Volumes used for computing the homogenized radiative properties were known beforehand, a general and simple law is established that connects the normal spectral emittance, on the one hand, and the open porosity and the complex index of refraction, on the other hand. In the field of the thermal conversion of solar energy, for example, the new law gives relevant insight on the radiative performance of highly porous foams that are virtually coated with materials that are known for possessing an undeniable spectral selectivity when they are shaped as dense samples.