Bubble coalescence model for phase-resolving simulations using an Immersed Boundary Method

In bubble-laden flows with large local or global void fraction the distance between bubbles is small so that these interact with a certain probability. During interaction, the bubble can either bounce or undergo coalescence, depending on the nature of the interaction. Coalescence as well as bubble breakup alter the bubble size distribution and consequently change the dynamics of individual bubbles and hence the characteristics of the entire multiphase system, e.g. turbulent statistics and coherent structures [9]. Furthermore, bubble shape oscillations related to the merging of two bubbles induce turbulent fluctuations with velocities larger than the rise velocity of the bubble [15]. This highlights the need for adequate representation of coalescence and breakup in this type of simulation and constitutes the motivation of the present work. Here, we will only consider coalescence as this occurs more frequently in the flows investigated. To this date, no consensus is found in the literature on how to realistically predict coalescence [4]. However, there is general agreement that van der Waals forces in the thin film between the two interacting bubbles need to become important to yield coalescence [2, 4]. These forces have a range of about 10 60 nm. Compared to the size of a bubble, typically with diameter 100 μm 10 mm, a gap of several orders of magnitude would have to be bridged if the rise of the bubble and the film thinning were to be resolved in the same simulation. Due to the limitation in grid size resulting from limited computational resources, a method for the simulation of bubble-laden flows cannot resolve the processes in the liquid film between the bubbles and hence cannot accurately predict coalescence. To create a model for bubble coalescence without resolving the microscopic processes inside the fluid film, but resolving the geometry of the bubbles requires two features. One is a criterion for coalescence that accounts for the evolution of the film. The other is a representation of the bubble surface which allows to use this information. A Front Tracking Method together with an Immersed Boundary Method provides such a framework and is used here. When two bubbles come sufficiently close for the surfaces to touch they interact. This interaction can then be subdivided into collisions, where the bubbles bounce back, and coalescence events. The coalescence process is understood as the merging of the bubbles, as well as the subsequent shape oscillations resulting from it. The coalescence model proposed here is applicable to phaseresolving simulations of many bubbles in turbulent flows. In [13] the suitability of the method is demonstrated by a simulation of two adjacent bubble chains.