Optical thickness of emissivity for pool fire radiation

The evaluation of emissivity ε=1−exp(−κL) is important for predicting fire radiation heat transfer, where the flame in many actual scenarios is neither optically thin nor optically thick. In this work, the mean optical length of soot emissivity was focused on. Firstly, the formula of the optical correction factor was deduced, which was dependent on burner size, flame shape, geometrical configuration, soot volume fraction, flame temperature, and radiation flux. Secondly, burner size and air pressure were shown to have coupling effects on soot volume fraction as fv∝D0.4p1.4+0.2n (m˙″∝pn), which caused a high flame temperature and a low flame luminosity in a low air pressure for small-sized burners. Thirdly, in a low air pressure, the optical correction factor was indicated to be larger, which was dominated by the decrease in soot volume fraction. Finally, compared with the soot emissivities generated using the formula proposed in this work, the soot emissivities obtained using traditional formulas were larger. The overestimated difference increased with increasing burner diameter. In a low air pressure, soot emissivity was smaller mainly because of the decrease in soot volume fraction. The assumptions of optically thin would apply better for a small-sized burner in a low air pressure.