Numerical investigation of non-spherical droplet dynamics in viscous convective flows

A comprehensive computational model based on the Arbitrary Lagrangian Eulerian (ALE) numerical algorithm has been developed for the numerical simulation of non-spherical (deforming) evaporating droplet dynamics in viscous convective flows. This model has the ability to solve both incompressible and compressible (two-phase) fluid flows separated by a free surface where surface tension forces, phase change, mass and heat transfer are very important. Special treatment of surface tension forces and interface jump conditions were carefully developed in the modeling effort. This model has been used to study the dynamics of cylindrical/spherical droplet shape free oscillation, nonevaporating and evaporating droplets undergoing deformation/breakup and oscillation dynamics under inviscid and/or viscous convective flows. The model developed has been validated by comparisons of droplet shape oscillation simulations to theoretical analysis. It has been shown that the numerically predicted droplet shape oscillation frequencies agree closely with those derived from linear theory. The surface pressure formula works well for the interface discontinuity. The results of spherical droplet deformation/oscillation simulation have also been compared to experimental results yielding good agreement. In the droplet deformation/breakup dynamics study, the numerically predicted breakup mode agrees well with experimentally derived criteria. The effects of droplet deformation on evaporation rates have been examined indicating that the non-spherical droplet evaporation rates are signiflcantly different from that of spherical droplets. Imposed inflow velocity fluctuations have a significant effect on the droplet evaporation rate both for spherical and nonspherical droplets. Potential applications of the present code to high pressure droplet dynamics, and microgravity free surface dynamics are discussed.