On the shapes of swirling annular jets of a liquid

Abstract

Annular jets of an incompressible liquid moving in a gas at rest are of interest for applications. A critical analysis of the investigations into jets from centrifugal nozzles is contained in [1]. These investigations elucidated the experimentally observed “tulip” and “bubble” jet shapes, and also predict the existence of annular jets of periodic shape. However, simplifications of the flow details are made to obtain the results. For example, in the equations describing the equilibrium of the forces acting on the film, no allowance is made for forces that arise on account of the curving of its shape in the meridional sections nor for the variability of the tangential velocity component in the field of the centrifugal forces. In the present paper, the method of [2] is used to derive equations that describe the flow of swirling annular jets of liquid with uniform profile of the longitudinal velocities in an undisturbed ideal medium with allowance for surface tension and gravity forces and also the pressure difference outside and within the jet. The results of calculations are given that illustrate the dependence of the jet shapes on the relative contributions of the capillary and inertial forces and also the pressure difference, the intensity of the initial swirling, the angle at which the liquid leaves the nozzle, and the gravity force.