Modelling
of Drop Deformation:A
Combination of the VOF Method and the Finite Element Method
Danish Polymer Centre, Department of Chemical Engineering, Technical
The Volume of Fluid (VOF) method has been applied extensively for tracking interfaces when modelling the merging and breakup of droplets in dispersed systems. Most commonly the VOF method is coupled to a finite difference scheme or a finite volume scheme which limits the possibility to handle complex geometries. In our work we are interested in simulating the deformation and breakup of drops in complex flow fields which requires the solution of the flow variables in complex domains. We have therefore implemented the VOF method together with a finite element formulation of the Stokes equation. Interfacial tension is included using the continuous surface stress (CSS) formulation of Lafaurie et al. [1]. The CSS formulation is well suited for the finite element formulation because the interfacial stress tensor enters as a natural boundary condition. The interface between the continuous phase and the disperse phase is reconnected using piecewise linear interface calculation (PLIC). In order to make the VOF implementation compatible with the finite element formulation the interface normal is calculated using finite element shape functions. The finite element solver is based on hexahedral Q2P0 elements. By introducing 8 VOF cells per finite element (in 3D) the vertices of each VOF cell coincide with the finite element velocity nodes. Advection of the two phases is carried out by solving the transport equation dF/dt + r . (Fv) = 0 where F is the colour field associated with the VOF method and v is the velocity.
References
[1]Bruno Lafaurie,Carlo
Nardone, Ruben Scardovelli,
Stephane Zaleski, and Gianluigi Zanetti.Modelling
Merging and Fragmentation in Multiphase Flows with SURFER. Journal of
Computational Physics, 113:134-147, 1993.