Nonlinear instability of an annular liquid sheet exposed to gas flow

Nonlinear instability and breakup of an annular liquid sheet has been modeled in this paper. The liquid sheet is considered to move axially and is exposed to co-flowing inner and outer gas streams. Also, the effect of outer gas swirl on sheet breakup has been studied. In the developed model a perturbation expansion method has been used with the initial magnitude of the disturbance as the perturbation parameter. This is a comprehensive model in that other geometries of planar sheet and a coaxial jet can be obtained as limiting cases of very large inner radius and inner radius equal to zero, respectively. In this temporal analysis, the effect of liquid Weber number, initial disturbance amplitude, inner gas-to-liquid velocity ratio, outer gas-to-liquid velocity ratio and outer gas swirl strength on the breakup time is investigated. The model is validated by comparison with earlier analytical studies for the limiting case of a planar sheet as well as with experimental data of sheet breakup length available in literature. It is shown that the linear theory cannot predict breakup of an annular sheet and the developed nonlinear model is necessary to accurately determine the breakup length. In the limiting case of a coaxial jet, results show that gas swirl destabilizes the jet, makes helical modes dominant compared to the axisymmetric mode and decreases jet breakup length. These results contradict earlier linear analyses and agree with experimental observations. For an annular sheet, it is found that gas flow hastens the sheet breakup process and shorter breakup lengths are obtained by increasing the inner and the outer gas velocity. Axially moving inner gas stream is more effective in disintegrating the annular sheet compared to axially moving outer gas stream. When both gas streams are moving axially, the liquid sheet breakup is quicker compared to that with any one gas stream. In the absence of outer gas swirl, the axisymmetric mode is the dominant instability mode. However, when outer gas flow has a swirl component higher helical modes become dominant. With increasing outer gas swirl strength, the maximum disturbance growth rate increases and the most unstable circumferential wave number increases resulting in a highly asymmetric sheet breakup with shorter breakup lengths and thinner ligaments.