Volume of fluid methods for immiscible-fluid and free-surface flows
This article reviews and analyzes a number of numerical methods to track interfaces in multiphase flows. Several interface tracking methods can be found in literature: the level-set method, the marker particle method, the front tracking method and the volume of fluid method (VOF) to name a few. The volume of fluid method has an advantage of being conceptually simple, reasonably accurate and phenomena such as interface breakup and coalescence are inherently included. Over the years a number of different techniques to implement the VOF method have been devised. This article gives a basic introduction to the VOF method and focuses on four VOF methods: flux-corrected transport (FCT) by Boris et al. [J.P. Boris, D.L. Book, Flux-corrected transport. I: SHASTA, a fluid transport algorithm that works, J. Comput. Phys. 11 (1973) 38-69], Lagrangian piecewise linear interface construction (L-PLIC) by van Wachem and Schouten [B.G.M. van Wachem, J.C. Schouten, Experimental validation of 3-d Lagrangian VOF model: bubble shape and rise velocity, AIChE 48 (12) (2002) 2744-2753], Compressive interface capturing scheme for arbitrary meshes (CICSAM) by Ubbink [O. Ubbink, Numerical prediction of two fluid systems with sharp interfaces, Ph.D. Thesis, Imperial College of Science, Technology and Medicine, 1997] and inter-gamma scheme by Jasak and Weller [H. Jasak, H.G. Weller, Interface-tracking capabilities of the InterGamma differencing scheme, Technical Report, Imperial College, University of London, 1995]. A detailed description of these schemes is given and implemented into an in-house fully coupled solver. Further, the performance of these schemes is examined employing a number of tests to analyze their strengths and weaknesses. Their advantages and limitations are discussed. (C) 2008 Elsevier B.V. All rights reserved.
Influence of surface tension implementation in Volume of Fluid and coupled Volume of Fluid with Level Set methods for bubble growth and detachment
A simple coupled Volume of Fluid (VOF) with Level Set (LS) method (S-CLSVOF) for improved surface tension implementation is proposed and tested by comparison against a standard VOF solver and experimental observations. A CFD Open source solver library (OpenFOAM®) is used for the VOF method, where the volume fraction is advected algebraically using a compressive scheme. This method has been found not to be suitable for problems with high surface tension effects and it is extended by coupling it with a LS method which is used to calculate the surface tension and the interface curvature. Two test cases; a circular bubble at equilibrium and a free bubble rise, are studied first to examine the accuracy of the S-CLSVOF method. The problem of 3D axi-symmetrical air bubble injection into quiescent water using different volumetric flow rates is then considered to assess the method under challenging capillary dominant conditions. An experimental study has been performed to validate the numerical methods with reference to the geometrical characteristics of the bubble during the full history of formation. The exponential power law controlling the detachment process is investigated. In addition, the influence of the static contact angle imposed at the rigid wall is considered. The results have shown that the coupling code (S-CLSVOF) improves the accuracy of the original VOF method when the surface tension influence is predominant. The two methods provide similar results during the detachment stage of the process due to the large increase of the gas inertia effect. Finally, the static contact angle boundary condition was shown to allow accurate modeling provided that the imposed static contact angle is less than the minimum instantaneous values observed experimentally.
Benchmark numerical simulations of segmented two-phase flows in microchannels using the Volume of Fluid method
We present an extensive analysis of the performance of the Volume of Fluid (VOF) method, as implemented in OpenFOAM, in modeling the flow of confined bubbles and droplets (“segmented flows”) in microfluidics. A criterion for having a sufficient grid solution to capture the thin lubricating film surrounding non-wetting bubbles or droplets, and the precise moment of breakup or coalescence is provided. We analyze and propose optimal computational settings to obtain a sharp fluid interface and small parasitic currents. To show the usability of our computational rules, numerical simulations are presented for three benchmark cases, viz. the steady motion of bubbles in a straight two-dimensional channel, the formation of bubbles in two- and three-dimensional T-junctions, and the breakup of droplets in three-dimensional T-junctions. An error analysis on the accuracy of the computations is presented to probe the efficacy of the VOF method. The results are in good agreement with published experimental data and experimentally-validated analytical solutions.
Numerical simulation of wavy falling film flow using VOF method
Surface wave dynamics of vertical falling films under monochromatic-frequency flowrate-forcing perturbations is computed by the direct simulation of Navier-Stokes equations using the Volume of Fluid (VOF) method to track free surfaces and the Continuum Surface Force (CSF) model to account for dynamic boundary conditions at free surfaces. The numerical VOF-CSF model is completely formulated, and more attention is given to understanding instabilities of thin films. At low frequency and high flowrate, the small inlet disturbance develops into large solitary waves preceded by small capillary bow waves. The circulation flow compatible with the solitary wave size is observed in the solitary peak. On the other hand, at high frequency and low Re, small-amplitude waves in nearly sinusoidal shape without fore-running capillary waves are formed on the surface. The quasi-periodic waveforms are found to occur at the nearly sinusoidal wave regime. The slight increase in wave-amplitude and wavelength, and decrease in residual thickness as waves evolves downstream are observed for both solitary waves and sinusoidal types. The variation of velocity and pressure along a wave are strong at the wave trough and capillary wave region, due to the large surface curvature there. The pressure variation perpendicular to the wall is negligible and only a small variation is observed at the solitary wave trough and capillary region.
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