Azimuthal shear instability of a liquid jet injected into a gaseous cross-flow

Abstract

AbstractWe investigate azimuthal instabilities which exist on the periphery of a non-turbulent liquid jet injected transversely into a gaseous cross-flow. We predict that the temporal growth of such instabilities may lead to the formation of interface corrugations, which are eventually sheared off of the jet surface (known as the jet ‘surface breakup’). In this study we employ temporal linear stability analyses to understand the nature of these instabilities. The analysis is based on a continuous formulation of momentum equations in which the jet and cross-flow are considered to be slightly miscible at the vicinity of the interface. We identify the shear instability as the primary destabilization mechanism in the flow. This inherently inviscid mechanism opposes the previously suggested mechanism of surface breakup (known as ‘boundary-layer stripping’), which is based on a viscous interpretation. The results show that the wavelengths of instabilities increase by moving away from the jet windward stagnation point toward the leeward point. We also investigate the influence of the jet-to-cross-flow density ratio on the flow stability and find that a higher ratio leads to formation of instabilities with higher wavenumbers on the jet surface. The results show that the density may have a non-monotonic stabilizing/destabilizing effect on the flow.