ON THE USE OF GRAY ASSUMPTION FOR MODELING THERMAL RADIATION THROUGH WATER SPRAYS

Abstract

The use of grey assumption to describe the attenuation of thermal radiation in fire/water spray interactions is investigated. The gas phase is assumed to be radiatively non-participating. Radiative fluxes obtained using mean Planck radiative properties are compared with those integrated over all the wavelengths. On a spectral basis, the radiative transfer equation (RTE) is obtained using the Mie absorption and scattering efficiencies, and the Henyey-Greenstein phase function is used to approximate the exact Mie phase function. RTE is solved using the finite-volume method. Results show the capability of the grey model to provide correct results for an optical thickness less than 2. For optically thicker media, an improved model is proposed. It consists in dividing the radiative intensity into three or more spectral bands and using individual mean Planck quantities for each band. Deviations from the reference spectral model results are estimated as well as the gain in computational time for a wide range of droplet sizes and concentrations. This "compromise solution" could be easily incorporated into CFD codes.