Influence of surface tension implementation in Volume of Fluid and coupled Volume of Fluid with Level Set methods for bubble growth and detachment

Abstract

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.