An interface-capturing method for incompressible two-phase flows. Validation and application to bubble dynamics

• Published in: International journal of multiphase flow Vol. 33; no. 2; pp. 109 - 133
• Main Authors: Bonometti, Thomas, Magnaudet, Jacques
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.02.2007; Elsevier
• Subjects: Bubbly flow; Computational methods in fluid dynamics; Engineering Sciences; Exact sciences and technology; Fluid dynamics; Fluid mechanics; Fluids mechanics; Front capturing; Fundamental areas of phenomenology (including applications); Interface tracking; Mechanics; Multiphase and particle-laden flows; Nonhomogeneous flows; Physics; Two-phase flow; Volume of Fluid; Volume of Fluid; Bubbly flow; Interface tracking; Two-phase flow; Front capturing; Gas liquid interface; Volume fraction; Bubble ascent; Digital simulation; Algorithms; Modelling; Bubble flow; Incompressible fluid; Mesh generation; Navier-Stokes equations
• ISSN: 0301-9322; 1879-3533
• DOI: 10.1016/j.ijmultiphaseflow.2006.07.003

We report on the development and applications of an interface-capturing method aimed at computing three-dimensional incompressible two-phase flows involving high density and viscosity ratios, together with capillary effects. The numerical approach borrows some features to the Volume of Fluid method (since it is essentially based on the transport of the local volume fraction of the liquid) as well as to the Level Set technique (as no explicit reconstruction of the interface is carried out). The transport of the volume fraction is achieved by using a flux-limiting Zalesak scheme and the fronts are prevented from spreading in time by a specific strategy in which the velocity at nodes crossed by the interface is modified to keep the thickness of the transition region constant. As shown on several test cases, this algorithm allows the interface to deform properly while maintaining the numerical thickness of the transition region within three computational cells whatever the structure of the local flow field. The full set of governing equations is then used to investigate some fundamental aspects of bubble dynamics. More precisely we focus on the evolution of shape and rise velocity of a single bubble over a wide range of physical parameters and on head-on and side-by-side interactions between two rising bubbles.