Baseline closure model for dispersed bubbly flow: bubble coalescence and breakup

Computational Fluid Dynamics (often abbreviated as CFD) has been becoming one indispensable tool in solving and analyzing of problems that involve fluid flows. Moreover, owing to ever-increasing computer power, the physical scale that can be resolved in a CFD simulation gets smaller and smaller. For example, in a simulation of gas-liquid flows using interface-tracking or interface-capturing methods gas-liquid interfaces can be resolved, where closure models neither for bubble-liquid nor for bubble-bubble are needed. However, the spread of such kind of approaches is retarded by the huge computational consumption. So far it can only be applied to quite small systems, where only a small number of bubbles and thus simple regular interfaces are included.
For problems at engineering or industrial scale, the Euler-Euler or two-fluid model (TFM) is still the most attractive one. However, new issues arise from the complete smearing of gas-liquid interfaces. In a TFM simulation results rely heavily on the applied closure relations, which reconstruct the information of bubble-liquid and bubble-bubble interactions. Furthermore, the effect of all the closures is coupled with each other. As a result, to assess the performance of one certain closure relation, e.g. coalescence and breakup of bubbles, under various flow conditions, a common set of other models should be defined. Otherwise, the wish of generally-applicable closures for TFM will always remain a dream.
On the other hand side, due to a variety of flow regimes and the complicated nature of physics, there exists not yet a consensus set of closure models, even for the simplest case of adiabatic bubbly flow. Rzehak et al. (2013) has taken the first step towards the goal by defining a so-called baseline model, which collects the best or most promising relations from the open literature for adiabatic bubbly flows. It includes bubble forces, bubble-induced turbulence (BIT), and bubble coalescence and breakup. The baseline model provides a common basis for further improvement and development of closure relations.
The focus of the present work is put on the new closures for bubble coalescence and breakup included in the baseline model, which was proposed originally in Liao et al. (2011). In order to guarantee the transferability all important mechanisms that lead to bubble coalescence and breakup are taken into account. In addition, the breakup model avoids successfully uncertainty introduced by separate daughter bubble size distribution functions. These have been believed to be major limitations in most existing models published in the open literature.
One major difficulty encountered in the validation of new bubble coalescence and breakup models is the superposition between coalescence and breakup as well as between multiple mechanisms in the reality. The strategy adopted in the current work is to select validation cases, where only coalescence is most important while the uncertainty brought by breakup is as few as possible. In addition, coalescence due to wake entrainment and eddy capture is negligible. Some test cases that satisfy the criterion approximately are found in the MTLoop experiments for air-water upward vertical pipe flows, which were carried out at the Helmholtz-Zentrum Dresden – Rossendorf a few years ago.
In the simulation, the new closures for bubble coalescence and breakup are implemented in the MUSIG approach (Krepper et al., 2008) provided by ANSYS CFX 14.0. With aid of measured evolution of bubble size distributions along the pipe, the performance of the new model within the baseline model is evaluated for several superficial gas and liquid velocities. The comparison between predictions and measurements demonstrates a promising agreement for all the investigated cases. In addition, considerable improvement against the default closure models available in ANSYS CFX is achieved. Nevertheless, huge validation work is still required to evaluate the breakup model as well as other coalescence mechanisms such as wake entrainment.