A deterministic and viable coalescence model for Euler–Lagrange simulations of turbulent microbubble-laden flows

Abstract

The topic of the paper is the development of an enhanced film drainage model for the prediction of bubble coalescence in the context of the Euler–Lagrange approach relying on large-eddy simulations. The starting point is the coalescence model by Jeelani and Hartland (1991), which compared to other often used models has several benefits: (1) A temporally evolving contact surface is considered avoiding the strong simplification of a constant contact area. (2) For contaminated bubbles an initially inertia-dominated process followed by a viscous-controlled regime are distinguished. (3) The contact time of the bubbles results as a side product of the modeling assumptions and thus is consistent with the film drainage concept. The main reason why this improved coalescence model was not applied in the past is the specific circumstance that the implicit equation for the determination of the transition time between the two phases (inertial and viscous) cannot be determined analytically. This problem is eliminated in the present study by numerically solving this equation. However, to avoid a time-consuming procedure for each individual bubble collision, a regression function is set up for a pre-defined range of bubble diameters and relative collision velocities. This renders the coalescence model feasible for flows with a huge number of bubbles. In a first step, the new coalescence model is validated against the experiments of single bubble coalescence with a free surface by Zawala and Malysa (2011) and Kosior et al. (2014). For the different cases considered the coalescence model yields reasonable agreement with the experiments. Furthermore, it is demonstrated that the results are improved compared to more popular but simpler models available in the literature. Afterwards, the coalescence model is applied to four-way coupled Euler–Lagrange simulations of a bubble column with clean and contaminated bubbles considering two different sizes. Significant deviations are found between the different cases, which can be traced back to varying collision frequencies and the different coalescence mechanisms in effect. Thus, it is shown that on the one hand the enhanced coalescence model leads to reasonable results and on the other hand is highly efficient allowing to take a huge number of bubble collisions deterministically into account.