Free-rising air bubble: two-phase surface tracking

Problem description

Air bubble freely rising in a steady tank of water. The position of the computational domain is adjusted such that the bubble always remains
centred; the effect of free-rising velocity is taken into account using a non-inertial reference frame adjustment.

Physics and modelling

Laminar flow of air and water with high surface tension. The computational domain consists of two meshes with a matching boundary,
representing the free surface. The solution procedure includes the solution of the fluid flow in both phases and the adjustment of the free surface position as
a function of the flow solution. Here, the pressure boundary condition on both sides is adjusted such that the pressure jump corresponds to the local surface
tension effect and the position of the free surface is calculated from the “no-through-flow condition”. During each time-step, the procedure is repeated until both
conditions are satisfied simultaneously.

Automatic mesh motion capability of OpenFOAM is used in both phases: the volume mesh is automatically adjusted based on the calculated deformation of the free
surface.

In future work, the effect of surfactant chemicals and their transport along the free surface will also be included. The simulation in question has been performed
in 2-D; equivalent 3-D simulations for a range of diameters have also been performed.

OpenFOAM solver

bubbleSurfSimpleIcoFoam

Animations

The animation shown the time-sequence of a stationary bubble rising from rest in a quiescent tank. The cause of deformation of the free surface (yellow)
is the change in the pressure field around it. The nominal bubble diameter is 2.5 mm. Note that the variation in the pressure level inside the bubble cannot be
presented: this is a consequence of the pressure jump due to the surface tension.

The figures below illustrate the pressure and velocity fields at three points during the calculation. Note the effect of the vertex shedding on the surface pressure
and the shape of the bubble.

Author

Mr. eljko Tukovi, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Croatia; in collaboration with Nabla Ltd. For more
information please contact Nabla Ltd.