Bubble column turbulence modeling

Ekambra etal. [21] compared the results from ID, 2D, and 3D simulations of a bubble column with experimental results. They obtained similar results for holdup and axial velocity, while eddy viscosity, Reynolds stresses, and energy dissipation were very different in the three simulations as shown in Figure 15.7. This example also illustrates the importance of selecting the right variables for model vahdation. A 2D model will yield good results for velocity but will predict all variables based on turbulent characteristics poorly. 

In system 1, the 3-D dynamic bubbling phenomena in a gas liquid bubble column and a gas liquid solid fluidized bed are simulated using the level-set method coupled with an SGS model for liquid turbulence. The computational scheme in this study captures the complex topological changes related to the bubble deformation, coalescence, and breakup in bubbling flows. In system 2, the hydrodynamics and heat-transfer phenomena of liquid droplets impacting upon a hot flat surface and particle are analyzed based on 3-D level-set method and IBM with consideration of the film-boiling behavior. The heat transfers in... 

A Two-Bubble Class Model for Churn Turbulent Bubble Column Slurry Reactor... 

The two bubble class model is applied here to the absorption of CO2 in NaOH, which conforms to a fast pseudo-first order reaction under certain operating conditions (15). In the data reported by Schumpe et al. ( 7 ), COo was absorbed during cocurrent flow in NaOH solution in a 0.102 m diameter bubble column. The gas phase consisted of approximately 10 vol % of CO2 in N2. The gas velocities ranged from 0.025 to 0.15 m/s. Since the churn turbulent regime prevailed for gas velocities greater than approximately 0.07 m/s, only the data in the range 0.07 m/s to 0.15 m/s were considered. 

In the previous section, stability criteria were obtained for gas-hquid bubble columns, gas-solid fluidized beds, liquid-sohd fluidized beds, and three-phase fluidized beds. Before we begin the review of previous work, let us summarize the parameters that are important for the fluid mechanical description of multiphase systems. The first and foremost is the dispersion coefficient. During the derivation of equations of continuity and motion for multiphase turbulent dispersions, correlation terms such as esv appeared [Eqs. (3) and (10)]. These terms were modeled according to the Boussinesq hypothesis [Eq. (4)], and thus the dispersion coefficients for the sohd phase and hquid phase appear in the final forms of equation of continuity and motion [Eqs. (5), (6), (14), and (15)]. However, for the creeping flow regime, the dispersion term is obviously not important. 

Bubble columns Loop reactors Stirred tanks Hydrocyclones Reasonable Reasonable Reasonable Reasonable Modeling of chum-turbulent flow regime Modeling of chum-turbulent flow regime Improved geometrical representation of impeller and baffles Improved geometrical representation of system... 

The recent progress in experimental techniques and applications of DNS and LES for turbulent multiphase flows may lead to new insights necessary to develop better computational models to simulate dispersed multiphase flows with wide particle size distribution in turbulent regimes. Until then, the simulations of such complex turbulent multiphase flow processes have to be accompanied by careful validation (to assess errors due to modeling) and error estimation (due to numerical issues) exercise. Applications of these models to simulate multiphase stirred reactors, bubble column reactors and fluidized bed reactors, are discussed in Part IV of this book. 

Ranade, V.V. (1997b), Modeling of turbulent flow in a bubble column reactor, Chem. Eng. Res. Des., 75, 14. 

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. 

Sokolichin, A. and Eigenberger, G. (1999), Applicability of standard k-e turbulence model to the dynamic simulation of bubble columns, Chem. Eng. Sci., 54, 2273-2284. 

The given k — e turbulence model formulation has been used to determine the turbulence of the continuous phase in two-phase bubbly flow by several investigators on bubble columns (e.g., [65, 127]) and on stirred tank reactors (e.g., [49]). 

Based on these observations [93] proposed a modified model containing two time constants, one for the liquid shear induced turbulence and a second one for the bubble induced turbulence. The basic assumption made in this model development is that the shear-induced turbulent kinetic energy and the bubble-induced turbulent kinetic energy may be linearly superposed in accordance with the hypothesis of [128, 129]. Note, however, that [82] observed experimentally that this assumption is only valid for void fractions less than 1 %, whereas for higher values there is an amplification in the turbulence attributed to the interactions between the bubbles. The application of this model to the high void fraction flows occurring in operating multiphase chemical reactors like stirred tanks and bubble columns is thus questionable. 

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