High-order azimuthal instabilities on a cylindrical liquid jet driven by temporal and spatial perturbations

Abstract

A method has been developed to drive a cylindrical liquid jet unstable for deformations with axial wavelengths shorter than the circumference of the jet and azimuthal mode numbers greater than $\text{0.}$ The benefit of this method is that a cylindrical liquid jet can be broken into a spray with an average diameter smaller than the diameter of the initial jet. The higher-order instabilities were created by establishing initial conditions for the jet in space and time at the nozzle. An electromechanical transducer creates the applied temporal initial condition which is a sinusoidally varying velocity perturbation added to the steady velocity of the jet. The amplitude of the velocity perturbation can be as large as the jet’s steady velocity and the energy in the applied velocity perturbation drives the instability. The spatial perturbation is created by placing perturbations in the circumference of the nozzle. As the velocity perturbation travels on the jet, its leading edge steepens and the trailing edge broadens in a manner analogous to the steepening of a pressure pulse in a compressible gas. If the driven velocity perturbation is sufficiently large, a shock or jump forms on the leading edge of the velocity pulse and the jet may break up into higher-order modes. A theoretical analysis of the breakup process, based on an adaptation of compressible fluid shock theory, is used to derive a fundamental lower bound on the spray’s Sauter mean diameter as a function of the velocity perturbation amplitude. Techniques for approaching the theoretical minimum spray diameter by using the higher-order modes to atomize liquid jets are discussed.