Breakup of swirling films issued from a pressure-swirl atomizer

Applications of pressure-swirl atomizers are found in liquid rockets, gas turbines, internal combustion engines, agriculture, food drying, pharmaceutical industry, etc. Despite extensive experimental and numerical studies, understanding of their breakup mechanism is still incomplete. Herein, we present a new theoretical breakup model of a swirling film/sheet issued from a pressure-swirl atomizer based on the quasi-one-dimensional equations of the dynamics of free swirling inviscid liquid films surrounded by viscous gas. These equations are supplemented by a novel model of the hole formation in the swirling film due to turbulent pulsations in the surrounding gas. After nucleation, the hole increase in size is driven by surface tension according to the Taylor-Culick mechanism that ultimately results in a complete breakup of an intact film and formation of a network of ligaments which eventually breakup due to the capillary instability. In particular, if the number of the holes is sufficiently high that their area locally reaches 50 % of the surface area of the liquid sheet (i.e., the ratio of holes approaches to η = 0.5), a complete breakup of the swirling sheet occurs, according to the percolation theory. Based on the above-mentioned model, the diverging shape, thickness, spreading angle, longitudinal and swirling velocities in the swirling liquid films, as well as their breakup lengths are predicted for different values of the governing dimensional parameters and the corresponding dimensionless groups. In particular, it is predicted that increasing the exit longitudinal velocity (V_τ,e), or the exit nozzle radius (R_e), or thinning the exit film thickness (h_e) results in shorter breakup lengths. Reducing the liquid surface tension also reduced the breakup length. In addition, an increase in gas kinematic viscosity (ν_g) or density (ρ_g) reduced the breakup length.