Flow in bubble columns

Schematic representation of a bubble column with cocunent How of gas and liquid 

In bubble columns the static head of the fluid is the dominant component of the pressure drop and consequendy it is important to determine the void fraction of the dispersion. All quantities will be measured as positive in the upward direction, this being the direction of flow of the dispersed phase. Assuming that the gas bubbles are of uniform size and are uniformly distributed over any cross section of the column, the gas and liquid velocities relative to the column are 

The relative velocity of the gas with respect to the liquid is known as the slip velocity. 

For counter-current flow the value of Ql must be taken as negative. 

For many dispersed systems (gas bubbles in liquids, liquid droplets in another liquid, solid particles in a liquid), it has been found that the slip velocity is related to the terminal velocity u, of a single bubble, droplet or particle by the equation 

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Owing to the high computational load, it is tempting to assume rotational symmetry to reduce to 2D simulations. However, the symmetrical axis is a wall in the simulations that allows slip but no transport across it. The flow in bubble columns or bubbling fluidized beds is never steady, but instead oscillates everywhere, including across the center of the reactor. Consequently, a 2D rotational symmetry representation is never accurate for these reactors. A second problem with axis symmetry is that the bubbles formed in a bubbling fluidized bed are simulated as toroids and the mass balance for the bubble will be problematic when the bubble moves in a radial direction. It is also problematic to calculate the void fraction with these models. 

Pareek, V., M.P. Brungs, and A.A. Adesina, Photocausticization of Spent Bayer liquor A Pilot-Scale Study. Advances in Environmental Research, 2003. 7(2) p. 411-420. Bertola, F., M. Vanni, and G. Baldi, Application of Computational Fluid Dynamics to Multiphase Flow in Bubble Columns. International journal of Chemical Reactor Engineering, 2003. 1 p. A3. 

S. Becker, A. Sokolichin, G. Eigenberger, Gas-liquid flow in bubble column and loop reactors. Part II. Comparison of detailed experiments and flow simulations, Chem. Eng. Sci. 49 (1994) 5747-5762. 

Lapin A, Lubbert A. Numerical simulation of the dynamics of two-phase gas-liquid flows in bubble columns. Chem Eng Sci 1994 49 3661-3674. 

Sokolichin A, Eigenberger G. Gas-liquid flow in bubble columns and loop reactors. Part I. Detailed modelling and numerical simulation. Chem Eng Sci 1994 49 5735-5746. 

Albeit originally proposed for gas-solid fluidization, the concepts of structure resolution and compromise between dominant mechanisms embodied in the EMMS model can be generalized into the so-called variational multi-scale methodology (Li and Kwauk, 2003) and extended to other complex systems (Ge et al., 2007). One typical example out of these extensions is the Dual-Bubble-Size (DBS) model for gas-liquid two-phase flow in bubble columns (Yang et al., 2007, 2010). 

Kumar et al. (1995) used the CFDLIB code developed at Los Alamos Scientific Laboratory to simulate the gas-liquid flow in bubble columns. Their model, which is based on the Eulerian approach, could successfully predict the experimentally observed von Karman vortices (Chen et al., 1989) in a 2D bubble colunm with large aspect ratio (i.e., ratio of colunm height and colunm diameter). 

Fig. 11. Typical computational results obtained by Lapin and Liibbert (1994) with a mixed Eulerian-Lagrangian approach. Liquid phase velocity pattern (left) and the bubble positions (right) in a wafer column (diameter, 1.0 m height, 1.5 m) where the bubbles are generated uniformly over its entire bottom. (Reprinted from Chemical Engineering Science, Volume 49, Lapin, A. and Liibbert, A., Numerical simulations of the dynamics of two-phase gas-liquid flows in bubble columns, p. 3661, copyright 1994 with permission from Elsevier Science.)...

Bubble columns find frequent application in the process industries due to their relatively simple construction and advantageous properties such as excellent heat transfer characteristics to immersed surfaces. Despite their frequent use in a variety of industrial processes, many important fluid dynamical aspects of the prevailing gas-liquid two-phase flow in bubble columns are unfortunately poorly un-... 

For integrating Eq. (4-9), vji= ei Er) should be known as a function of and operating variables. However, the momentum diffusivity is the only term we know, with essentially no systematic data for In the case of free turbulence of a homogeneous fluid, the diffusivity of a scalar quantity like heat and mass is estimated to be about two times that of momentum (S4) and the two diffusivities are not far apart for turbulent pipe flow (S8). However, such a relation is not available yet for gas-liquid bubble flow in bubble columns. Generally the local radial mass diffusivity may be expressed by a, with a being a numerical coefficient of order unity. 

Ranade, VV. (1992), Flow in bubble column some numerical experiments, Chem. Eng. Sci., 47, 1857. 

The fluid dynamics of bubble column reactors is very complex and several different CFD models may have to be used to address critical reactor engineering issues. The application of various approaches to modeling dispersed multiphase flows, namely, Eulerian-Eulerian, Eulerian-Lagrangian and VOF approaches to simulate flow in a loop reactor, is discussed in Chapter 9 (Section 9.4). In this chapter, some examples of the application of these three approaches to simulating gas-liquid flow bubble columns are discussed. Before that, basic equations and boundary conditions used to simulate flow in bubble columns are briefly discussed. 

Application of model equations to simulate flow in bubble columns... 

Instead of arbitrarily considering two bubble classes, it may be useful to incorporate a coalescence break-up model based on the population balance framework in the CFD model (see for example, Carrica et al., 1999). Such a model will simulate the evolution of bubble size distribution within the column and will be a logical extension of previously discussed models to simulate flow in bubble columns with wide bubble size distribution. Incorporation of coalescence break-up models, however, increases computational requirements by an order of magnitude. For example, a two-fluid model with a single bubble size generally requires solution of ten equations (six momentum, pressure, dispersed phase continuity and two turbulence characteristics). A ten-bubble class model requires solution of 46 (33 momentum, pressure. 

Ranade, V.V. (1993b), Numerical simulation of turbulent flow in bubble column reactors, AIChE Symposium Series no. 293, 89, 61-71. 

Ranade, V.V. (1998), Modeling of flow in bubble columns. NCL internal report. 

Ranade, V.V. and Utikar, R.P. (1999), Dynamics of gas-liquid flows in bubble column reactors, Chem. 

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