Application of finite volume particle method for axisymmetric modeling of droplet formation in dripping and Rayleigh regimes

Abstract

An axisymmetric model has been developed in the finite volume particle method (FVPM). FVPM is a conservative, consistent, meshless particle method that incorporates properties of both smoothed particle hydrodynamics (SPH) and the mesh-based finite volume method (FVM). The surface tension effect amplifies capillary instability which is the main mechanism in dripping and jet disintegration. The simulations are performed in 2D cylindrical coordinates by only considering the liquid flow (one phase). The model is validated for free liquid droplet evolved from cylindrical state, dripping from a capillary tube, Rayleigh instability of capillary liquid cylinder columns, and Rayleigh breakup of viscous jets. The FVPM-predicted pressure and oscillating period are in good agreement with theoretical solution for a free droplet. The FVPM-computed dripping length shows good consistency with provided experimental data in literature. The predicted growth rate of capillary instability is in good agreement with analytical solutions for flows with different orders of Ohnesorge numbers. The numerical breakup length of jet with Weber numbers between 2.5 and 40 has been determined with good accuracy based on analytical experimental solution.