Theoretical model for swirling thin film flows inside nozzles with converging-diverging shapes

A quasi-one-dimensional model was developed to describe a swirling, thin, liquid film inside nozzles with different wall profiles. The model quantifies the effects of swirl strength, initial film thickness, and Reynolds and Weber numbers on the film thickness along the nozzle surface. Moreover, the model allows for a rapid (at least, qualitative) evaluation of different effects, e.g. of the swirl strength and nozzle geometry, and can serve as a benchmark case for the subsequent more involved numerical simulations. Steady-state solutions are presented as a function of various parameters. The effect of the nozzle geometry on film thickness is explored. As swirling flow entered the expanding (diverging) section of the nozzle, film thickness decreased to satisfy continuity (to conserve mass). Conversely, film thickness increased upon entering the contracting (converging) region of the nozzle. Geometric effects controlled film thicknesses much more than other flow parameters. This quasi-one-dimensional model for a swirling thin film can be useful for designing a swirl jet used in various industrial applications.