Development and application of a simplified radiative transport equation in water curtain systems

Abstract

In this study, a simplified radiative transfer equation (RTE) for water curtain is introduced. The scattering phase function, asymmetric factor, single scattering albedo, and efficiency factors are investigated with non-gray and gray medium, respectively. The prediction values by a simplified equation are compared with previous results by the two-flux, P3 and F9 methods in non-gray medium. The deviations of reduced intensities are less than 10%. As the droplet size increases more than 100 μm, the asymmetry factor, scattering phase function, and scattering albedo are converged as 0.975, 0.992 and 0.501, respectively. Thus, a more simplified equation for the reduced intensity of radiation can be determined with the exponential function of optical depth.To correlate the relations between the flow characteristics of water curtain and the optical depth, the droplet mean diameter and the number density are analyzed with a modified gamma distribution function. In addition, the FTIR spectrometer is calibrated to obtain the spectral intensity in the thermal infrared and large droplet region.Finally, the important engineering parameters such as the mass flow rate, the droplet mean diameter, the number density, the optical depth, and the reduced intensity are systematically investigated. It can be predicted that optical depth (τ > 0.89), number density (N > O(4 × 106 m−3)), droplet mean radius (rm < 180 μm) and flow rate (Qflow > 1.2 kg/s) are determined to reduce the radiation intensity less than 50% for the selected water curtain nozzle in this study.