The momentum transport and entrainment of a developing plane jet are dominated by coherent structures. Percipience about the formation, evolution, and interaction of these coherent structures for oscillating planar jets remains unclear. In the present study, numerical investigations are reported for analyzing spatially oscillating planar jets by solving Navier–Stokes equations coupled with the volume of fluid method to track the air–water interface. Coherent structures in the flow for Reynolds numbers (Re) 4500 and 500 are identified using Q-criterion. It is demonstrated that for oscillating jets, the spread and entrainment increase with an increase in Re. These jet characteristics are greatly influenced by the head vortices, which transform into a pair of hairpin vortices, which further undergo leapfrogging. This jet front dynamics is found to be dampened by viscous forces. The numerical results also suggest the existence of sideways hairpin vortices that expel the fluid by forming a channel and are significantly subdued at low Re. A peculiar merging of span-wise Kelvin–Helmholtz rollers at low Re is also reported in the present study. Furthermore, the dominant flow structures are identified and analyzed using proper orthogonal decomposition and dynamic mode decomposition. The results demonstrate the dominance of coherent structures at the downstream for higher Re with vortices in the near field at the jet peaks also contributing to the flow field dynamics.

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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.

Understanding the behavior of oscillating liquid jets in tandem is vital for improving the efficacy of numerous industrial applications. An interpretation of their behavior in the terms of development, associated instability, and interactions when used in tandem remains unclear. Therefore, the present study reports the numerical investigations on spatially oscillating liquid jets in tandem. Numerical simulations are carried out by solving Navier–Stokes equations coupled with volume of fluid method to track the air–water interface. The development of the tandem jets, growth in amplitude of oscillation, and interaction between the coherent structures is analyzed for both synchronous and asynchronous liquid jets in tandem. Moreover, the effect of nozzle spacing on these parameters is also reported in the present study. It is demonstrated that a decrease in the nozzle spacing destabilizes these jets and promotes an early merging between them. This decrease in nozzle spacing also improves the stream-wise entrainment of the surrounding fluid. Furthermore, synchronous jets are found to be more stable as compared to asynchronous jets owing to a relatively constant spacing between the two jets. Asynchronous jets provide better fluid entrainment than synchronous jets owing to their higher amplitude of oscillation and stronger jet front interactions. Moreover, it is demonstrated that these interactions at the jet front give rise to a staggered vortex front in asynchronous jets, whereas the vortex front remains symmetric in synchronous jets.

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