As a first step towards a new approach for the simulation of two-phase flows, the objective of this work is to check out the prediction of a model dedicated to large and distorted bubbles on two bubble coalescence cases. The multifield hybrid approach for two-phase flow modelling consists in dealing separately with the small and spherical bubbles, treated with a dispersed approach, and with the large and distorted ones, whose interface is located. The overall method relies also on an existing building block, consisting in a set of averaged models dedicated to dispersed bubbles, which has already been validated and has given a reasonable agreement with experimental data in cases where the spherical shape assumption is still valid for the dispersed phase. This paper aims to assess a conservative interface locating method based on level set adapted to two-fluid model for two-phase flows. The interface locating method is a part of a model dedicated to the simulation of large and distorted bubbles. At different liquid viscosities and densities, the model provides reasonable predictions of terminal velocities and shapes for rising bubble experiments. The main outcome is the simulation of bubble coalescence where the distortion of the interface during the coalescence phenomenon is followed. The ability to simulate coalescence phenomena correctly is an important issue in the modelling of slug flows with interface locating methods.
bubble rising, coalescence, interface sharpening, multifield model, surface tension
 Weisman, J. & Kang, S.Y., Flow pattern transitions in vertical and upwardly inclined lines. International Journal of Multiphase Flow, 7, pp. 271–291, 1981. doi: http://dx.doi.org/10.1016/0301-9322(81)90022-7
 Bestion, D., Applicability of two-phase CFD to nuclear reactor thermalhydraulics and elaboration of best practice guidelines. Nuclear Engineering and Design, 253, pp. 311–321, 2012. doi: http://dx.doi.org/10.1016/j.nucengdes.2011.08.068
 Mimouni, S., Archambeau, F., Boucker, M., Laviéville, J. & Morel, C., A second order turbulence model based on a Reynolds stress approach for two-phase boiling flow and application to fuel assembly nalysis. Nuclear Engineering and Design, 240, pp. 2225–2232, 2009. doi: http://dx.doi.org/10.1016/j.nucengdes.2009.11.020
 Denefl e, R., Mimouni, S., Caltagirone, J.P. & Vincent, S., Multifi eld hybrid approach for bubble to slug fl ow transition modelling. Proceedings of AFM2012: 9th International Conference on Advances in Fluid Mechanics, Split, Croatia, 2012.
 Clift, R., Grace, J.R. & Weber, M.E., Bubbles, Drops, and Particles, Academic Press: New York, 1978.
 Raymond, F. & Rosant, J.M., A numerical and experimental study of the terminal velocity and shape of bubbles in viscous liquids. Chemical Engineering Science, 55, pp. 943–955, 2000. doi: http://dx.doi.org/10.1016/S0009-2509(99)00385-1
 Hua, J. & Lou, J., Numerical simulation of bubble rising in viscous liquid. Journal of Computational Physics, 222, pp. 769–795, 2007. doi: http://dx.doi.org/10.1016/j.jcp.2006.08.008
 Koebe, M., Bothe, D. & Warnecke, H.J., Direct simulation of air bubbles in water/glycerol mixtures: shapes and velocity fi elds. Proceedings of FEDSM’03: 4th ASMEJSME Joint Fluids Engineering Conference, Honolulu, Hawaii, USA, 2003.
 Hyman, J.M., Numerical methods for tracking interfaces. Physica D, 12, pp. 396–407, 1984. doi: http://dx.doi.org/10.1016/0167-2789(84)90544-X
 Gingold, R.A. & Monaghan, J.J., Smoothed particle hydrodynamics - theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society, 181, pp. 375–389, 1977.
 Unverdi, S.O. & Tryggvason, G., A front-tracking method for viscous, incompressible, multi-fl uid fl ows. Journal of Computational Physics, 100, pp. 25–37, 1992. doi: http://dx.doi.org/10.1016/0021-9991(92)90307-K
 Hirt, C.W. & Nichols, B.D., Volume of fl uid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39, pp. 201–225, 1981. doi: http://dx.doi.org/10.1016/0021-9991(81)90145-5
 Osher, S. & Sethian, J.A., Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 79, pp. 12–49, 1988. doi: http://dx.doi.org/10.1016/0021-9991(88)90002-2
 Sussman, M. & Puckett, E., A coupled level set and volume-of-fl uid method for computing 3D and axisymmetric incompressible two-phase fl ows. Journal of Computational Physics, 162, pp. 301–337, 2000. doi: http://dx.doi.org/10.1006/jcph.2000.6537
 Vincent, S., Caltagirone, J.P., Lubin, P. & Randrianarivelo, T.N., An adaptative augmented Lagrangian method for three-dimensional multimaterial fl ows. Computers and Fluids, 33, pp. 1273–1289, 2004. doi: http://dx.doi.org/10.1016/j.compfl uid.2004.01.002
 Olsson, E. & Kreiss, G., A conservative level set method for two phase fl ow. Journal of Computational Physics, 210, pp. 225–246, 2005. doi: http://dx.doi.org/10.1016/j.jcp.2005.04.007
 Chen, L., Li, Y. & Manasseh, R., The coalescence of bubbles – a numerical study. Proceedings of Third International Conference on Multiphase Flow: ICMF’98, Lyon, France, 1998.
 Brereton, G. & Korotney, D., Coaxial and oblique coalescence of two rising bubbles. Proceedings of AMD-Vol. 119: The ASME Applied Mechanics Conference, Colombus, OH, USA, 1991.
 Singh, R. & Shyy, W., Three-dimensional adaptive grid computation with conservative, marker-based tracking for interfacial fl uid dynamics. 44th Aerospace Science Meeting, Reno, MV, USA, 2006.
 van Sint Annaland, M., Deen, N. & Kuipers, J., Numerical simulation of gas bubbles behaviour using a three-dimensional volume of fl uid method. Chemical Engineering Science, 60, pp. 2999–3011, 2005. doi: http://dx.doi.org/10.1016/j.ces.2005.01.031
 Patankar, S.V. & Spalding, D.B., A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic fl ows. International Journal of Heat and Mass Transfer, 15, pp. 1787–1806, 1972. doi: http://dx.doi.org/10.1016/0017-9310(72)90054-3
 Ishii, M. & Hibiki, T., Thermo-fl uid Dynamics of Two Phase Flow, Springer-Verlag, 2006. doi: http://dx.doi.org/10.1007/978-0-387-29187-1
 Brackbill, J., Kothe, D. & Zemach, C., A continuum method for modeling surface tension. Journal of Computational Physics, 100, pp. 335–354, 1992. doi: http://dx.doi.org/10.1016/0021-9991(92)90240-Y