Numerical investigations in Rayleigh breakup of round liquid jets with VOF methods

Simulations of the growth of a capillary instability and of the breakup of a jet were carried out using a one-fluid model to describe the two-phase flow motion and a VOF approach to capture the interface. The model considered each phase as fictitious sub-domains and accounted implicitly for jump conditions at the interface through a unique set of equations for which a source term of surface tensions appeared in momentum equations. The predominance of capillary effects in the breakup mechanism required to accurately describe the surface tension contribution. The Brackbill surface model was chosen because of its simplicity to represent tension forces, although it was known to generate parasitic currents susceptible to limit its precision. The flow incompressibility was ensured with an augmented Lagrangian method in case of sequential calculations and by a predictor/corrector approach for 3D simulations that required parallel computations. As a first step, the numerical methods were validated by simulating the growth of a capillary instability and comparing results to those predicted by the Rayleigh theory for capillary instabilities. The consistency of the Brackbill surface tension model and the accuracy of the methods were evaluated via a convergence study. As a second step, the simulation of a jet breakup was carried out using water as injected liquid and compressed carbon dioxide as surrounding medium. It was shown that the simulation predicted accurately the breakup length and the droplet size evidenced experimentally in literature.