Effect of gas stream swirls on the instability of viscous annular liquid jets

A linear temporal instability analysis has been carried out for a viscous annular liquid jet moving in two swirling gas streams of unequal velocities with the gas stream swirling motion represented by free-vortex rotation. It is found that two modes of unstable surface waves exist, the para-sinuous and para-varicose mode. The results of the two limiting flow situations, which are a cylindrical liquid jet in a swirling gas stream and a swirling gas jet in a liquid stream, indicate that their instabilities are associated with the para-varicose mode on the outer interface and para-sinuous mode on the inner interface of the annular liquid jet, respectively. It is shown that the centripetal force induced by the inner gas stream rotation is destabilizing and enhances the jet instability, while the centripetal force produced by the outer gas stream rotation is stabilizing and reduces the instability of annular liquid jets. It is interesting to find that for a para-varicose mode an increase in the outer gas rotation not only reduces the upper cut-off wave number, but also increases the lower cut-off wave number, leading to the significant reduction in the unstable wave number range. The stabilizing effect of the outer gas rotation is much more significant for para-varicose mode, and the destabilizing effect of the inner gas rotation is much more influential for para-sinuous mode. In general, the para-sinuous mode has a much larger growth rate and is predominant in the annular liquid jet breakup process. Therefore, increasing the inner gas stream rotation can significantly enhance the breakup of annular liquid jets for practical spray applications.