Theoretical breakup model in the planar liquid sheets exposed to high-speed gas and droplet size prediction

This paper makes an effort to describe the atomization in the air-blast breaking liquid sheet, with an emphasis on the establishment of the theoretical model capable of quantitatively predicting the performance of the atomizer. The phenomenological two-staged breakup model for a cylindrical jet exposed to the high-speed gas has been extended to the planar sheet, combined with a classical linear stability analysis whether gas compressibility and viscosity are included. By means of the full-wave integral, explicit expression of the Sauter Mean Diameter (SMD) for incompressible gas is obtained, as well as implicit ones for compressible and viscous gas conditions. Based upon the breakup model, results of the SMD are shown to coincide favorably with previous experimental data. Typically, the gas compressibility and viscosity in the first breakup stage have almost no influence on the ultimate value of mean droplet size, elucidating the validity and applicability of the explicit expression of the incompressible gas in the breakup model.