On the Importance of Modelling Bubble Dynamics for Point-mass Numerical Calculations of Bubble Columns

For decades, CFD (computational fluid dynamics) has been applied for numerical calculations of the rather complex flow in bubble columns using the two-fluid approach (Euler/Euler method) as well as the Euler/Lagrange approach, both based on the point-mass approximation. Numerous different models and closures have been proposed and used for describing the fluid dynamic forces acting on bubbles, modelling bubble induced turbulence (BIT) and transport of bubbles by turbulence structures (Sommerfeld, 2004). However, the dynamics of bubbles, i.e., oscillations and tumbling motion, is mostly neglected in such calculations since a physically based model in the frame of a point-particle approximation is not readily available. Such a model was developed, implemented in the frame of LES-Euler/Lagrange calculations (LES: Large Eddy Simulations) and validated based on detailed experiments (Sommerfeld and Broder, 2009). The temporal evolution of bubble eccentricity was randomly generated based on measured correlations for the mean and rms (root mean square) values of eccentricity in connection with a theoretical oscillation time scale. Naturally, the state-of-the-art fluid forces acting on the bubbles were considered and the transport of bubbles by sub-grid-scale-turbulence (SGS) was modelled by a Langevin approach, as well as turbulence modification by the bubbles being considered in the frame of the LES context. Similar to experimental observations, such a thorough model yielded a bubble tumbling motion even in the point-particle approximation. The correct anisotropic bubble fluctuating velocities were thereby reproduced and good agreement with experiments was obtained for all other velocities. Note that bubble velocity fluctuations were so far never considered for the validation of calculations, but they are of immense importance when also considering mass transfer. Hence, the bubbly dynamics model provided the correct bubble residence time and, as a result, a gas hold-up identical to measured values.