Numerical simulation of gas bubbles behaviour using a three-dimensional volume of fluid method

In this paper a three-dimensional (3D) volume of fluid (VOF) method is presented featuring (i) an interface reconstruction technique based on piecewise linear interface representation, (ii) a 3D version of the CSF model of Brackbill et al. [1992, Journal of Computational Physics 100, 335]. Our model can handle a large density and viscosity ratio and a large value of the surface tension coefficient. First the results of a number of test cases are presented to assess the correctness of the advection and interface reconstruction algorithms and the implementation of the 3D version of the CSF model. Subsequently the computed terminal Reynolds numbers and shapes of isolated gas bubbles rising in quiescent liquids are compared with data taken from the bubble diagram of Grace (1973). Finally results of two calculations are reported involving the co-axial and oblique coalescence of two gas bubbles. The computed bubble shapes compared very well with the experimentally observed bubble shapes of Brereton and Korotney [1991, In: Dynamics of Bubbles and Vortices Near a Free Surface, AMD-vol. 119. ASME, New York]