SPATIAL INSTABILITY ANALYSIS OF AN ANNULAR SWIRLING VISCOUS LIQUID JET

The effect of liquid viscosity on an annular swirling viscous liquid jet with different swirl strength values is studied with linear instability analysis. The spatial mode instability analysis for para-sinuous mode and para-varicose mode is carried out. An analytical form of dispersion relation is derived, which governs the disturbance growth for an annular swirling viscous liquid sheet with a solid vortex swirl velocity profile subjected to three-dimensional disturbances. The results show that, with higher swirl strength, the increase of viscosity hinders the breakup and makes the domain frequency and domain wave number smaller. However, at low swirl strength, the increase of viscosity speeds up the breakup, makes the domain frequency in the para-sinuous mode first decrease and then increase and makes the domain frequency in the para-varicose mode increase. Furthermore, at low swirl strength, the domain wave number in the para-sinuous mode first decreases and then increases, the domain wave number in the para-varicose mode increases with an increase in liquid viscosity.