Modeling high-speed viscous liquid sheet atomization

Abstract A linear stability analysis is presented for a liquid sheet that includes the effects of the surrounding gas, surface tension and the liquid viscosity on the wave growth process. An inviscid dispersion relation is used to identify the transition from a long wavelength regime to a short wavelength regime, analogous to the first and second wind induced breakup regimes of cylindrical liquid jets. This transition, which is found to occur at a gas Weber number of 27/16, is used to simplify the viscous dispersion relation for use in multi-dimensional simulations of sheet breakup. The resulting dispersion relation is used to predict the maximum unstable growth rate and wave length, the sheet breakup length and the resulting drop size for pressure-swirl atomizers. The predicted drop size is used as a boundary condition in a multi-dimensional spray model. The results show that the model is able to accurately predict liquid spray penetration, local Sauter mean diameter and overall spray shape.