Numerical investigations on stability of the spatially oscillating planar two-phase liquid jet in a quiescent atmosphere

Abstract

The liquid jet when perturbed sinusoidally will lead to instability under certain conditions. Understanding the causes and consequences of such a behavior is still obscure. Hence, numerical investigations are reported in the present study for a two phase spatially oscillating planar jet in a quiescent air. Simulations are performed by solving the Navier-Stokes equations and using the volume of fluid method to track the air-water interface. It is demonstrated that an increase in amplitude of oscillation is caused due to the formation of a low pressure region created by the vortical structures in air near the leading edge of the jet when deflected. This two way coupling between air and water is analyzed with the help of enstrophy, divergence of the Lamb vector, and vortex forces. It is found through a parametric study that surface tension and viscosity stabilize the perturbations in an oscillating planar jet. On the other hand, an increase in Froude number (Fr) initially leads to an augmentation of perturbation amplitude and later causes its damping when surface tension forces become dominant. The numerical analysis for different inlet velocity profiles establishes that the jet is more stable when subjected to a parabolic inlet velocity profile as compared to a uniform profile due to lower relative velocity at the interface. The present work also reveals the role of capillary instability in addition to Kelvin-Helmholtz and Rayleigh-Taylor instabilities that induce primary breakup in the jet.