The instability and consequent atomization of a swirling viscous liquid jet emanated into gaseous surroundings and subjected to periodical surface disturbances is modelled and investigated. The theoretical analysis is based on a simplified mathematical formulation of the continuity and momentum equations in their conservative forms. Numerical solutions of the governing equations along with appropriate initial and boundary conditions are obtained through a robust finite-difference scheme. The computations yield real-time evolution of the interfacial profile and subsequent breakup characteristics of the liquid jet. It is found that the jet disintegrates into main and satellite drops, under all the conditions considered in the present study. The swirl enhances the instability of the jet and causes radial stretching of the main drops, whereas the satellite drops exhibit axial elongation. Increasing viscosity hinders jet instability and leads to main and satellite drop deformations that are similar to those produced by the swirl. The sizes of both main and satellite drops are diminished at higher disturbance wave numbers. A greater swirl strength induces a higher dominant wave number, and hence a reduced size of resultant main and satellite drops. Larger satellite drops and smaller main drops are produced as viscous forces are increased. The present model could be used as a guide for designing swirl injectors. [PUBLICATION ABSTRACT]
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