Spatial characterization of the flapping instability of a laminar liquid jet fragmented by a swirled gas co-flow

Abstract

A liquid jet destabilized by a co-flowing gas jet is subjected to several instabilities that are responsible for its fragmentation into a spray of fine droplets. At the large scale, the difference in the velocities of the gas and liquid phases lead to a meandering motion of the liquid jet called the flapping instability. Flapping is suspected to play a role in the spatio-temporal characteristics of the clouds of droplets further downstream, as it periodically brings a portion of the liquid phase away from the centerline and into the gas jet. While the scaling law determining the frequency associated to flapping has recently been proposed, a study of its spatial characteristics is lacking in the literature. Two-view high-speed back-lit imaging is used to obtain 3D time-resolved measurements of the liquid phase. The trajectories of the bulk of the liquid is computed using barycenter of the liquid presence. Such trajectories are phase averaged over many flapping periods to yield flapping orbits. In the regime of shear break-up atomization, a transition in the shape of the flapping orbits, from planar to circular, is observed along variations of the gas-to-liquid dynamic pressure ratio (also called momentum ratio) as well as the swirl ratio (ratio of the azimuthal to longitudinal components of the gas jet). This is characterized using the shape factor of the flapping orbits, as well as the flapping amplitude. The latter is found to decrease with dynamic pressure ratio but is larger when swirl is added to the gas jet. The transition appears to be related to the formation of bags along the liquid jet, that originate from interfacial instabilities and opposes the existence of a preferential flapping direction.