Numerical investigation of secondary instabilities along helical disturbances in a swirling liquid jet*

This work is an approach to understanding the generation of secondary instabilities developing along the helical disturbance in a rotating liquid jet injected in a quiescent gaseous phase. Three-dimensional numerical simulations are performed to find the fundamental flow behavior of the swirling liquid jet for axial Reynolds numbers of 50≤ Re ≤ 300 and swirl numbers range of 0.50≤ S ≤ 1.55 corresponding to two control parameters, the mean injection velocity and angular velocity applied at the nozzle inlet. There are two main objectives of this paper (1) To explain the physical mechanism behind the evolution of the secondary instabilities at the interface and (2) To understand the impact of varying rotation rates on the generation of these secondary instabilities. The results indicate that initial small bulges form along each helical disturbance, which subsequently grow into thick liquid sheets and ligaments under the action of centrifugal force. Further, the liquid sheets and ligaments disintegrate into smaller satellite drops giving rise to smaller droplets. Also, the growth of secondary instabilities along helical disturbance strongly depends on the injection velocity applied at the inlet. As the injection velocity dominates over the rotation applied at the inlet, the generation of the secondary instabilities occurs at farther downstream locations compared to lower injection velocities. A parameter space plot is suggested to demarcate the Reynolds number and swirl number range for which secondary instabilities could be observed. Also, vortex structures are identified with Q-criterion to demarcate rotational dominance zones, which lie along the helical disturbance appearing at the interface giving rise to secondary instabilities. The thickness of axial and azimuthal shear layers is studied to explore the unstable helical disturbances at the interface.