Implementation of Linear Hydrodynamic Instability Theory on a Hollow Cone-shaped Liquid Sheet of a Swirl Injector

In the atomization process, small disturbances grow in liquid jet or sheet and eventually cause to disintegrate it into ligaments and smaller droplets. Concerning to the motion of waves on the liquid sheet surface, the stage of primary breakup is deterministic and can be predicted by instability analyzes. In early studies, the theories of linear and weakly nonlinear instability have been implemented on a cylindrical liquid sheet and the effect of spray cone angle was not included in the model. Therefore, in this paper in order to improve the model, the linear instability theory is implemented on a cone-shaped liquid sheet for the first time, and therefore radial velocities of liquid and gas phases are also considered moreover than axial and tangential velocities. The results of this improved model such as maximum wave growth rate and its corresponding wave number can be used to estimate mean droplet diameter and breakup length.