Modeling and direct numerical simulation of mass transfer from rising gas bubbles

Mass transfer at fluid interfaces is a widespread phenomenon in industrial applications. In particular, the optimization of apparatuses in Chemical Engineering requires a detailed knowledge of the relevant physical phenomena at the interface. Since only a minimum of simplifying assumptions has to be made, Direct Numerical Simulation is an adequate tool for investigating the mechanisms of mass transfer, mixing and chemical reaction in interface vicinity. A detailed simulation of entire chemical reactors, however, will not be feasible in the near future, owing to the enormous computational power required for simulations. Therefore, the focus in this PhD thesis is on mass transfer from single bubbles. Three central difficulties for the simulation of non-reactive species transfer are discussed. The main goal is to develop numerical methods for the simulation of mass transfer from single rising gas bubbles. Emphasis is put on the validation of the developed approaches, where some of the reference cases had to be developed first. The central phenomenon which is investigated is the conjugate mass transfer of a species at the interface. For this purpose, a conservative unsplit method is developed which is able to compute local Sherwood numbers at fluid interfaces. Furthermore, a simplified model for the influence of an insoluble surfactant on bubble hydrodynamics is derived. This simplified approach leads to a Navier-type boundary condition at the interface. The numerical method derived from this model is validated by comparison with experimental results on the terminal rise velocity of surfactant laden bubbles. Moreover, correlations for the terminal rise velocity are used to compare the simulated bubble rise velocities with. The third numerical approach implements mass transfer accompanied by volume effects. To derive this approach, spatial averaging techniques are employed to derive the equations which are suitable for numerical computations of multi-component mass transfer. The developed numerical methods are all validated and implemented in the two-phase flow solver FS3D which has originally been developed at the University of Stuttgart. The presented numerical approaches are finally applied to different problems of bubble rise and mass transfer. Among others, mass transfer from a small gas bubble (dB =0.8 mm) with a contaminated interface rising in water is simulated. Furthermore, the influence of bubble deformation on rise velocity of a bubble with contaminated interface is investigated and, finally, the shrinking of a Taylor bubble due to mass transfer, moving in a square minichannel is simulated.