Three-dimensional simulations of a jet with finite element and VOF method

In this paper we present a novel approach for solving incompressible fluid jet simulations with a finite element Navier-Stokes solver coupled to a multilevel Volume-of-Fluid (VOF) method to describe the interface between the two fluids. In order to guarantee a high value of the ratio between the curvature radius and the computational cell dimension we introduce a grid with very high resolution only for the interface capturing and then project the resulting forces to a coarser grid where velocity and pressure fields are computed. In this way we overcome typical problems of the VOF approach such as numerical breakups that may be introduced by large grid resolutions. In general, very high resolution grids need large storage capacities. To avoid this, a new sparse matrix storage algorithm for the color function has been developed in order to memorize only the interface cells. Several simulations of three-dimensional jets are performed to show the high accuracy and robustness of the proposed scheme. The linear instabilty modes are investigated to reproduce analytical results. We recover that there exists a critical Weber number above which asymmetric instabilities develop. We simulate low Reynolds jets with given sinusoidal inflow source to reproduce the breakup with different frequencies. Close to the Rayleigh wavelength the jet breaks in a primary drop and a small thread that evolves in a satellite of spherical shape due to surface tension in agreement to experimental results. Increasing the inlet velocity the Weber number becomes bigger than the critical value and the jet develops asymmetrical threads and fingers that evolve in several droplets of small diameters.