Comparison of upper boundary treatments for bubble column simulations with the two-fluid model

A better understanding of multiphase flows is increasingly relevant for industrial applications, in particular with respect to the transition of the chemical and process engineering industry towards green energy. Therein, bubble columns play an important role. Hence, they have been subject to numerical simulations for decades. The literature is characterized by a large variety of numerical methods, interfacial closure terms, boundary conditions, and more. The current paper makes the attempt to exclude one parameter, namely the treatment of the upper boundary, from the discussions around the modelling of those bubble columns. Three different boundary conditions, a degassing boundary condition, a gas-only outlet boundary condition, and an outlet boundary condition are compared. Furthermore, two modelling strategies with a different number of numerical phases to include the physics of the free surface, are investigated. The five different treatments are implemented into the same numerical solver, and are then applied to four different bubble column experiments. All simulations are set up as consistent as possible, to exclude the influence of other parameters, e.g., the numerical method. Three different modelling strategies for the bubble size distribution have been checked as well, namely a monodisperse, a fixed-polydisperse and a poly-disperse one, the latter including bubble breakup and coalescence. The results show for bubble columns no significant influence of the treatment of the upper boundary. However, a prerequisite for an accurate analysis is stable statistics, which are found to require a very long averaging time for the bubble columns investigated here.