When bubbles are continuously released from a located source at the bottom of a fluid layer initially at rest, a plume is produced. The motion of the carrier fluid is initiated and driven by buoyancy of the bubble cloud. In the present study, a detailed analysis of the bubble plume transition is investigated. The continuous phase flow is obtained by direct numerical resolution of Navier-Stokes equations forced by the presence of bubbles. Collective effects induced by the presence of bubbles are modelled by a spatio-temporal distribution of momentum. Time evolution of the dispersed phase is solved by lagrangian tracking of all the bubbles. Focused on the description of plume transition, several configurations (plume widths, fluid viscosity, injection rate) are investigated. During the laminar ascension of the plume, fluid velocity profiles can be non-dimensionalised on a single auto-similar evolution. Dimensional analysis provides a prediction of the limit rising velocity of the plume top. This prediction has been confirmed by our numerical simulations. Furthermore, our first results point out the symmetry breaking induced by plume instability which appears beyond a critical transition height. Various data show that the Grashof number based on injection conditions is the key parameter to predict the transition of the plume. Our results agree very well with recent experimental data. Comparison with experiments on thermal plumes in air shows that the bubble plume is more unstable. This feature should be related to the lack of diffusion in the lagrangian transport of density gradient by the bubble cloud and to the slip velocity between the two phases.

This content is only available via PDF.
You do not currently have access to this content.