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

Abstract

For decades, CFD (computational uid dynamics) has been applied for numerical calculations of the rather complex ow in bubble columns using the two-uid approach (Euler/Euler method) as well as the Euler/Lagrange approach, both based on the point-mass approximation. Numerous di erent models and closures have been proposed and used for describing the uid 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 Bröder, 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 uid 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 modi cation 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 uctuating velocities were thereby reproduced and good agreement with experiments was obtained for all other velocities. Note that bubble velocity uctuations 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 holdup identical to measured values.

Large Eddy Simulation of Bubble Column Bubbly Flow Considering Subgrid‐Scale Turbulent Diffusion Effects and Bubble Oscillation

“…It was affirmed that the bubble dynamics in the bubble column can be captured by using the adequate SGS‐TDF and SGS‐AMS models in Eulerian‐Eulerian LES modeling, when mimicking the bubble transport in the bubble column. This can imply that the modified SGS‐TDF and SGS‐AMS models may play an equivalent role in indicating the bubble fluctuating motion predicted by using the Euler/Lagrange LES modeling approach but with the stochastic dispersion model 4. Although the case presented in the present study is confined to a circular cylindrical bubble column, it was revealed that the proposed modeling can also be applied to other cases such as a square bubble column.…”

“…Comparison of the time‐averaged bubble axial velocity distribution at z = 325 mm by using three models with experimental and numerical data obtained from Sommerfeld et al. (dots: experimental data 4; dashes: E‐L simulation data 4). …”

“…By comparing the magnitude of the contribution from the drag, lift, and added mass forces, along the height, the ratio can reach around 12 % but gradually decreases with the height. The decrease in the ratio of the SGS‐TDF to the overall contribution from the drag, lift, and added mass forces along the column height reveals that the bubble lateral dispersion is highly affected by the TDF, implying that a stronger SGS‐TDF may promote the bubble group oscillations 4. In terms of the ratio of the total AMS force to the sum of the averaged drag, lift, and added mass forces, the magnitude of the ratio can also reach 9 % in the lower part of the bubble column but follows the same trend as the ratio of SGS‐TDF to the sum of the drag, lift, and added mass forces, as shown in Fig.…”

Bubble motion and reaction in different viscous liquids

“…The EL simulation was superior concerning computational time to the EE simulation up to a critical bubble number of 40,000 in the investigated case of a pseudo two dimensional bubble column. Recently, Sommerfeld et al (2018) highlighted the influence of tumpling bubble motion and concluded its relevance to mass transfer, while a direct comparision to mass transfer experiments was not presented. However, in the simulation of bubble columns, many of these models do not describe in detail the motion of individual bubbles, e.g., oscillating or tumbling motion of the bubbles (Fig.…”

Influence of Wettability on Bubble Formation from Submerged Orifices

“…Other approaches to the simulation of multiphase flows such as the k-ε model or large-eddy simulation , have also been developed. Some features of multiphase flows such as bubble coalescence and breakup have been challenging to represent accurately using fixed grids .…”