On the basis of the level set method, a new numerical method for predicting the evolution and the primary capillary breakup of a cylindrical liquid jet is presented. In such context, the only driving forces existed are considered to be the surface tension and the viscous forces, where the aerodynamic force is neglected. The evolution of the liquid jet and the subsequently dynamics including breakup are predicted by solving the Navier-Stokes equations using the control volume approach on a non-staggered grid system. The solution of the governing equations is performed only on the liquid phase, where specified boundary conditions for velocity components and pressure are defined on the moving interface. The topological changes of the moving interface is described via the level set method, which simultaneously, provides an accurate and robust modeling of the interfacial stresses which drive the internal flow. The numerical method is validated towards the analytical solution of the linear and nonlinear theories developed for predicting the evolution of the axisymmetric liquid jet under different conditions. The obtained results demonstrated the effects of the disturbance wave number, the disturbance amplitude, and the dynamics viscosity on the evolution and breakup of liquid jets. The formation of the satellite and sub-satellite droplets is also predicted which has been recognized as a highly nonlinear phenomenon in jet breakup process. The breakup process in the viscous regime is shown to be a self-repeating mechanism, which leads to the formation of sub-satellite droplets. The agreement with the analytical as well as the previous experimental measurements in inviscid and viscous regimes reveals the capability of the developed numerical method in predicting the liquids jet dynamics in different flow regimes.
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