numerical simulation of bubble breakup and...

Dessislava Moutafchieva, Veselin Iliev

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NUMERICAL SIMULATION OF BUBBLE BREAKUP AND COALESCENCE IN BUBBLING TWO-PHASE FLOW


ABSTRACT

The aim of the present work is to study the behavior of gas-liquid bubbly flow by means of Computational Fluid Dynamics (CFX ANSYS). The population balance approach taking into account the bubble coalescence and breakup in turbulent gas-liquid dispersion is included.The Euler-Euler approach and the standard k-ε mixture turbulence model in three-dimensional computational domains accounting the effect of turbulence are used to simulate the two phase flows of the bubble column.The bubble size distribution along the column height, the gas volume fraction and liquid velocity have been predicted for the two-phase systems and for liquids different from water(ethanol, glycerol). The results of nonuniform bubbles size distribution in dispersed flow are presented grouped into individual size fractions at varying initial conditions and density of the elementary mesh.

Keywords: bubble breakup, CFD modeling, two-phase flow.

Received 05 October 2017Accepted 10 January 2018

Journal of Chemical Technology and Metallurgy, 53, 3, 2018, 511-517

University of Chemical Technology and Metallurgy8 Kliment Ohridsky, 1756 Sofia, BulgariaE-mail: [email protected]

INTRODUCTION

The two-phase flows are widely used in many in-dustrial processes, such as absorption, fermentation and wastewater treatment. One of the determining factors for the successful operation of bubble columns is mass transfer in gas-liquid system. For example, the effective-ness of the fermentation process needs to ensure a high transfer speed and maintain a constant concentration of dissolved oxygen in liquid phase [1, 2]. The dispersion of gas in bubble columns provides employment in large phase transfer surface.

The gas volume fraction, interfacial area concentra-tion and bubble size distribution characterize the internal flow structure of two-phase flow in gas-liquid system [3, 4]. The accurate prediction of these parameters is im-portant for modeling of the interfacial transfer processes and for the design of a bubble column.

The achievement of the optimal process parameters of the bubble column in a production installation is ac-complished in the process of operation by significant financial and time resources. One way to reduce this

resource is to include a preliminary computer simulation stage in which the approximate process values are set. This has encouraged the development of gas-liquid CFD analyses in recent years. A particularly important part in these analyses is the numerical modeling of bubble breakup and coalescence.

Wang et al. [5] applied a population balance model to determine successfully bubble size distribution account-ing the breakage and coalescence effects in bubbly flows. The population balance model is based on the number density ni, which represents the number of bubbles per unit volume Vi in the range V to V+dV and is used to define how the population of bubbles develops over time.

An accurate knowledge of physical mechanisms determining bubble size requires to provide models for bubble breakup and coalescence processes. The reviews and analysis of these models are given by Liao and Lucas [6]. The breakup and coalescence kernels are functions of the turbulent dissipation energy. Various mechanisms of bubble breakup can be found in the literature: tur-bulence fluctuation, viscous shear stress, shearing off and surface instability [7]. The breakup of bubbles in

Journal of Chemical Technology and Metallurgy, 53, 3, 2018

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turbulent dispersions employs the model developed by Luo and Svendsen [8]. This bubble breakup model is based on the theory of isotropic turbulence, assuming the turbulent kinetic energy of eddy is greater than a critical value and binary breakup of bubbles.

One of the most widely used coalescence models is described by Prince and Blanch [9]. Bubble coalescence is modeled by considering bubble collisions due to tur-bulence, buoyancy, and laminar shear, and by analysis of the coalescence efficiency of collisions [9, 10]. Only the first cause of collision (turbulence) is considered in the presented model. The model of Prince and Blanch proposed the coalescence approach for deformable parti-cles with fully mobile interfaces, where the coalescence of two bubbles is assumed to occur in three steps. In the first step, the bubbles surfaces capture a small amount of liquid between them. This liquid film drains until it reaches a critical thickness and finally the liquid film disappears and the bubbles join together.

The motion of an eddy of the same length scale with the bubble diameter is responsible for the relative motion between bubbles. Collision is also induced by the dif-ference in rise velocities of bubbles with different sizes.

A good presentation of the current state of this problem is made by Mouza K. et al. [11].

A general form of the population balance equation is:

(1)

where ug is the gas velocity, ni represents the number density of size group i and the terms on the right-hand side Bb, Bc, express the ‘birth’ rates due to break-up and coalescence of bubbles and respectively Db, Dc are ‘death’ rates.

The bubble number density ni is related to the gas holdup εg by relationship:

(2)

where fi is the volume fraction of bubbles of group i and Vi is the corresponding volume of a bubble of group i.

The birth rate of group i due to coalescence of group j and group k bubbles is:

(3)

The death rate of group i due to coalescence with other bubbles is:

(4)

where Q is the collision frequency.The birth rate of group i bubbles due to breakup of

larger bubbles is:

(5)

where g is gravitational force, Vj and Vi are the corre-sponding volumes of a bubble of group j and i.

The death rate of group i bubbles due to breakup into smaller bubbles is:

(6)The possibility of combining Population balance

model with the implemented in Ansys Fluent bubbles breakup and coalescence models to predict the bubble size distribution in gas-liquid flow is demonstrated in this study. This approach refers to the recording of the initial number of bubbles and the tracking of their evolution in the space of two-phase dispersed flow over time. The size range of the bubbles is split into several groups with, for example, bands of equal diameter or equal volume. The gas volume fraction and axial liquid velocity have beenpredicted depending on the gas flow rate and liquid flow parameters.

EXPERIMENTAL

The numerical calculations were achieved through the use of the CFD code Ansys Fluent [12] and the stand-ard Euler-Euler two-fluid flow approach. For turbulent contribution in a continuous phase is used the k-ε turbu-lent model and zero equation model for dispersed phase.

The simulation was carried out in a bubble column shown in Fig. 1, which represents a vertical cylindrical column with heights h1 = 1.3 m, h2 = 3 m and a diameter D = 1 m. The sparger, located at the bottom of the column has a toroidal shape with a ring radius d1 = 0.145 m and a tube diameter d2 = 0.120 m. The top side of the tube is perforated with round holes, that determine the intensity of the gas flow and the initial diameter of the bubbles.


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The hydrodynamic behavior of two-phase system with air as gas phase and water, alcohol and glycerol as liquid phase at the homogeneous regime were studied computationally.

The complete modeling of the two-phase flow in the ANSYS environment was carried out according to the methodology for geometry, mesh and setup verifica-tion, described in previous papers [13, 14]. Due to axial symmetry of the object and the operation with volume elements only the 30°sector of the column is simulated, which reduces the calculation time. The main calculation area (the area over the sparger) is meshed by regular hexagonal dominated mesh (Fig. 2).

For the computer simulation, the several size ranges of the bubbles are split into groups with bands of equal diameter. Nine bins are set in bubble breakup and coa-lescence model with sizes listed in Table 1.

For bubbles breakup the model of Luo and Svendsen [8] has been applied for all computations.

The aggregation and breakage kernel of the model are based on the Luo-model implemented inAnsys Flu-ent [12] with Hageshaether formulation for breakage rate.The model proposed by Hageshaether et al. [15] for binary breakup of dispersed bubbles is most suitable for the implementation in CFD code.

The „ degassing“ boundary condition was applied at the top of the column, which permits only the dispersed bubbles to escape and not the liquid phase. The walls were treated as non-slip boundaries with standard wall function.

For monitoring of the bubble size distribution along the column height, seven horizontal planes are defined from bottom to top by 50 cm, such as the first plane is localized on 5 cm above the sparger.

Two series of air bubbles with initial diameter of 3 mm (all bubbles initially in bin 6) and 12 mm (all bubbles ini-tially in bin 3) were examined in water. For each series, air

Fig. 1. Geometric model of the bubble column.

Table 1. Bubble diameter distribution in bins.

Fig. 2. Mesh.

Bin number Bubble diameter [mm]

0 48,0 1 30,2 2 19,0 3 12,0 4 7,5 5 4,7 6 3,0 7 1,9 8 1,2


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distribution and bubble diameters were monitored along the column height in the defined seven horizontal planes. The simulation was carried out at two superficial gas ve-locity 1 m/s and 3 m/s. In addition, the bubble diameter distribution was investigated in two-phase systems with different liquid phase (ethanol 100 %, ethanol 40 % and glycerol) with transport properties according Ansys Flu-ent data base materials and Bibble [12], listed in Table 2.

RESULTS AND DISCUSSION

The simulation predictions of the overall gas volume fraction distribution along the column height is shown in Fig. 3. One of the important process parameters, monitored during the simulations is the distribution of the bubble diameters along the column height. The graphic in Fig. 4 shows bubble size distribution for two

Table 2. Properties of the fluids used at 20°C.

Fluid Density [kg/m3] Dynamic viscosity [kg/m.s]

Air 1,225 1,7894 10-5

Water 998 100,3.10-5

Ethanol 100% 790 120. 10-5

Ethano 40% 920 209.10-5

Glycerol 1270 1480.10-3

Fig. 3. Gas holdup in bubble column for numerical solution with superficial gas velocity 3 m/s: a) glycerol, b) ethanol 40%, c) ethanol 100%, d) water.

a) b) c) d)


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sets of bins with diameters between 1,2 and 48 mm for three different gas-liquid systems, i.e. air-water, air-ethanol 100 % and air-ethanol 40 % for superficial gas velocity 3 m/s.

A general tendency to unify the results along the height can be noted. Another trend observed in these results is the effect of viscosity on bubble break-up in the initial stage of motion - the first 50 cm above the sparger. In the air- water system the bubble break-up process is not intense and the number of bubbles of the initial diameter gradually decreases as they move up the column. In the other two systems with higher viscosity, the number of bubbles of initial diameter decreases in the initial stage and then is increased by coalescence of smaller diameter bubbles.

The graphics in Fig. 4 show that the increase in viscosity of liquid phase (alcohol) leads to a decrease in bubbles breakup and the coalescence of the bubbles oc-curres more easily. Thus viscosity has a dampening effect on the stress transmitted to bubble surface, which in turn

hinders bubble breakage. Another way of presenting the results obtained is shown in Fig. 5. Each line shows the volume distribution of bubbles of a specified diameter in one of the horizontal planes. There is some difference in the behavior of the bubbles in the air-water system for an initial diameter of 12 mm (bin 3) and for 3 mm (bin 6). For a large initial diameter (Fig. 5a), the bubble concentration is kept in one diameter along the height and only transfers from the initial diameter in the bottom of the column (bin 3 in plane 1) to another diameter at the upper end of the column (bin 4 in plane 6). For a small initial diameter (Fig. 5b), the bubble concentration is dissipates from the initial diameter at the bottom of the column (bin 6 in plane 1) evenly distributed over the other diameters in the upper part (plane 6).

CONCLUSIONSThis work presents the possibility of combining

Population balance approach with the implemented in CFX bubbles breakup and coalescence models to predict

Fig. 4. Bin distribution in height for a solution with initial bubble diameter 12 mm for Bin 3 - bubble diameter 12 mm (a) and Bin 6 - bubble diameter 3 mm (b).

Fig. 5. Average bin volume fraction in horisontal planes for air-water system with initial bubble diameter 12 mm (a) and with initial bubble diameter 3 mm (b).


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the bubble size distribution in gas-liquid flow in a bubble column. Computational data were obtained in a bubble column for two different superficial gas velocities at seven height positions with four air-liquid systems the liquids having viscosity, different from this of water. Computational results show that bubble size distribution and gas holdup can be well predicted in the homogene-ous regime for systems with various physical properties.

The effect of liquid viscosity on the hydrodynamic behavior in a bubble column was investigated by numeri-cal simulation with ANSYS CFX code. The viscosity of the liquid phase is also found to play an important role in bubble stability. In the high viscosity range, an increased viscosity led to a decrease in the total gas holdup and volume fraction of small bubbles and an increase in the volume fraction of the large bubbles. Therefore the increase in viscosity leads to a decrease in gas-liquid interfacial area.

The simulation performed provides information on these process characteristics and shows that, when the viscosity of the liquid is below 1 mPa s, it does not have a significant effect on the bubbles break up rate and the distribution of the secondary bubbles, whereas the increase in fluid viscosity significantly reduces the rate of bubble break up. The viscosity has a significant effect on the bubble break up, and hence on hydrody-namic behavior, while the bubble coalescence effect is less pronounced.

With the use of break up and coalescence models and the bubble size distribution, the combined CFD-PBM model is suitable for describing the influence of viscos-ity on the overall gas content and volume fractions of the bubbles with different size. The CFD code permits the successful prediction of hydrodynamic behavior of bubbly two-phase flow and can be regarded as an effec-tive method to design of bubble columns.

AcknowledgementsThe financial support by National Scientific Fund of

Bulgaria, project DN 07/11 “Method for assessment the transfer efficiency of integrated processes in bioreactor with membrane separation” and the Research Sector of the University of Chemical Technology and Metallurgy, Sofia, contract № 11690 “Numerical simulation of bub-bling two-phase flow considering bubble breakup and coalescence”, are gratefully acknowledged.

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