Axisymmetric free-surface flow simulation using the moving surface mesh particle method and application to drop formation

Abstract

It is difficult to accurately simulate axisymmetric free-surface flows with surface tension and topological changes, such as drop formation through a nozzle. A promising numerical method that can achieve this goal is the moving surface mesh particle method. It incorporates a moving surface mesh to explicitly represent a free-surface boundary, which enables accurate free-surface tracking and surface tension calculation. In the present study, this method is extended to an axisymmetric coordinate system. In the axisymmetric simulation, particles moving in a Lagrangian fashion result in significantly non-uniform particle distributions, leading to numerical instabilities. To circumvent this issue, a new algorithm is developed for determining the particle movement in an ALE fashion by considering a two-dimensional continuity equation. Moreover, in order to deal with the topological change arising from breakup of liquid domain, a simple algorithm employing surface mesh splitting is developed. The proposed method is verified using fundamental test cases such as axisymmetric cavity flow, axisymmetric patch test, spherical droplet oscillation, and hanging droplet. Therein, precise agreements to reference solutions are confirmed. Furthermore, the proposed method is applied to the numerical simulation of dripping faucet. As a result, complex drop formation phenomena are successfully simulated with reasonable computational cost. The numerical results are also shown to agree well with the experimental measurement in the literature, from which the validity of the proposed method is demonstrated.