Improved Estimates of High-Temperature Fiber Bed Effective Emissivities from Variational Calculations

Rigorous variational upper bounds are presented for the effective bed emissivity (epsilon)eff of a model semi-infinite fiber bed made up of long, parallel, randomly placed, freely overlapping cylinders for two possible bed edges-fibers perpendicular and fibers parallel to the bed edge. Calculations of bed emissivity variational results for both cases provide significant improvement over first-order scattering upper bounds given in a previous paper. For high void fraction (phi)-1 and fiber surface emissivity values of (epsilon)s = 0.5, 0.3, and 0.1, respective bed emissivity upper bound reduction improvements of 4.14, 12.2, and 35.8% were generated for the latter bed edge structure, and 4.08, 11.3, and 32.2% were obtained for the former case. Along with the first-order scattering lower bounds on (epsilon)eff, improved estimates of bed emissivities were calculated for high-temperature, nonmetallic fiber beds with (epsilon)s >0.55. Bed emissivity enhancement factors ((epsilon)eff/(epsilon)s) of 1.27 for fibers parallel to the semi-infinite bed edge and 1.42 for fibers perpendicular to the bed edge were observed for high fiber bed porosity (phi)= 0.9 and (epsilon)s = 0.55. Results compared favorably with an experimental correlation and Monte Carlo simulations.