Volume of fluid method

The computational fluid dynamics investigations listed here are all based on the so-called volume-of-fluid method (VOF) used to follow the dynamics of the disperse/ continuous phase interface. The VOF method is a technique that represents the interface between two fluids defining an F function. This function is chosen with a value of unity at any cell occupied by disperse phase and zero elsewhere. A unit value of F corresponds to a cell full of disperse phase, whereas a zero value indicates that the cell contains only continuous phase. Cells with F values between zero and one contain the liquid/liquid interface. In addition to the above continuity and Navier-Stokes equation solved by the finite-volume method, an equation governing the time dependence of the F function therefore has to be solved. A constant value of the interfacial tension is implemented in the summarized algorithm, however, the diffusion of emulsifier from continuous phase toward the droplet interface and its adsorption remains still an important issue and challenge in the computational fluid-dynamic framework. 

Hirt, C.W. and Nichols, B.D. (1981), Volume of fluid method for the dynamics of three boundaries, J. 

In this chapter, we focus on the first stage of clogging and investigate the impaction of non-Newtonian power-law fluids on thin fibers. We aim to obtain the threshold radius of impacting droplets in different impact velocities. Effect of shear-thinning and shear-thickening behavior of droplets is evaluated and compared with corresponding Newtonian fluids. For this purpose, volume of fluid method is used and open source OpenFOAM software is applied for simulations. 

Hirt and Nichols [12] demonstrated the volume of fluid (VOF) method and started a new trend in multiphase flow simulation. It relies on the definition of an indicator function y. This function allows us to know whether one fluid or another occupies the cell, or a mix of both. In the conventional volume of fluid method [12], the transport equation for an indicator function y, representing the volume fraction of one phase, is solved simultaneously with the continuity and momentum equations as follows ... 

In this sub-section the basis elements of the volume of fluid method are described. In general the VOF model is composed of a set of continuity and momentum equations, as well as a transport equation for the evolution of a... 

In the context of fluid flow, the Navier-Stokes Eqs. 14 and 17 are integrated numerically, together with the advectiOTi equation D/Dt = 0 for the level set function (i.e., Eq. 24 or 25 with a = 0 and b = 0), and the re-initializafimi Eq. 26 is applied periodically or at every time step to keep the level set function well behaved. While this is more straightforward than the procedures involved in the volume-of-fluid method, it has been found that the VOF method has better mass conservation properties than the simple level set method. 

Sussman M, Puckett EC (2000) A coupled level set and volume of fluid method for computing 3D and axisymmetric incompressible two-phase flows. J Comput Phys 162 301-337... 

VOF Volume of fluid method, numerical method for the treatment of... 

Huang, H., Meakin, R, Liu, M.B. Computer simulation of two-phase immiscible fluid motion in unsaturated complex fractures using a volume of fluid method. Water Resources Research 41(12), W12413 (2005)... 

Sussman, M., Puckett, E.G. A Coupled Level Set and Volume of Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows. Journal of Computational Physics 162, 301-337 (2000)... 

Deen, N.G., vanSint Armaland, M., and Kuipers, J.A.M. (2005) Numerical simulation of gas bubbles behaviour using a three-dimensional volume of fluid method. Chem. Eng. Sci., 60, 2999-3011. 

Jeong, J.H. and Yang. D.Y. (1998) Finite element analysis of transient fluid flow with free surface using VOF (volume-of fluid) method and adaptive grid. Int. J. Numer. Methods Fluids, 26,1127—1154. 

Jet/Sheet Fragmentation Model 18.2.1 Volume of Fluid Method... 

Keywords Resorcinol-fonnaldehyde hydrogels Mechanical deformation Phase distribution Volume-of-fluid method X-ray microtomography... 

Fig. 5 Concept of the volume-of-fluid method for convective gel drying simulation. The figure shows a partially dried particle aggregate, a portion of the voxel grid as well as quantities used in the simulation the phase volume fractions/j (solid),/h, (liquid),/ (gas), from which singlephase, two-phase and three-phase cells can be distinguished, the outward-pointing unit normal vectors of the solid and liquid phases (Wj, ,), the contact angle 6, the mean curvature of the liquid-gas interface k and the capillary forces Fc (taken from [23])...

Baltussen MW, KuipersJAM, Deen NG A critical comparison of surface tension models for the volume of fluid method, Chem Eng Sd 109 65—74, 2014. 

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