Droplet Collisions Using A Level Set Method:Comparisons Between Simulation AndExperiments

Abstract

Level Set methods are based on defining a continuous function where the zero level curve is the interface. That function is initialized as the signed distance to the interface in the computation field. Solving a convection equation allows one to follow the interface displacements in a given velocity field. One advantage is its ability to represent topological changes and geometrical information on the interface, such as the normal vector or curvature, which are obtained through a level set function gradient. To avoid the spreading and stretching of a level set, a re-distancing algorithm is applied to ensure that the function remains the signed distance to the interface. The Level Set method is coupled with the projection method for the direct numerical simulation of the incompressible Navier-Stokes equations. Spatial derivatives are estimated with the 2nd order central scheme, but convective terms are approximated by the 5th order WENO scheme discretization in order to get a robust behavior of the solution. Temporal derivatives are approximated with the Adams Bashforth scheme. The linear system deduced from the Poisson equation is solved with a multigrid algorithm for preconditioning the conjugate gradient method. To handle interface discontinuities the ghost fluid method is used. Numerical codes have been developed for 2D, 2Daxi and 3D geometries, with MPI parallelization. The results are presented for head-on droplets collisions in a coalescence regime and a reflexive regime with 2D axi-symmetric code, and for off-center droplets collision code in a separation regime for a large impact parameter with 3D code. Simulations provide realistic and various droplet collision behaviors and they correspond to experimental observations.