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Numerical simulation of bubble characteristics in bubble columns with different liquid viscosities and surface tensions using a CFD-PBM coupled model
Journal Pre-proof Numerical simulation of bubble characteristics in bubble columns with different liquid viscosities and surface tensions using a CFD-PBM coupled model Peng Yan, Haibo Jin, Guangxiang He, Xiaoyan Guo, Lei Ma, Suohe Yang, Rongyue Zhang
PII:
S0263-8762(19)30559-3
DOI:
https://doi.org/10.1016/j.cherd.2019.11.030
Reference:
CHERD 3915
To appear in:
Chemical Engineering Research and Design
Received Date:
16 August 2019
Revised Date:
31 October 2019
Accepted Date:
22 November 2019
Please cite this article as: Yan P, Jin H, He G, Guo X, Ma L, Yang S, Zhang R, Numerical simulation of bubble characteristics in bubble columns with different liquid viscosities and surface tensions using a CFD-PBM coupled model, Chemical Engineering Research and Design (2019), doi: https://doi.org/10.1016/j.cherd.2019.11.030
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Numerical simulation of bubble characteristics in bubble columns with different liquid viscosities and surface tensions using a CFD-PBM coupled model
Peng Yan, Haibo Jin*, Guangxiang He, Xiaoyan Guo, Lei Ma, Suohe
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Yang, Rongyue Zhang Key Laboratory of Fuel Cleanliness and Efficient Catalytic Emission Reduction Technology,
Department of Chemical Engineering, Beijing Institute of Petrochemical Technology, Beijing Beijing 102617)
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Graphical Abstract
Highlight CFD-PBM model was well validated in a bubble column with different physical properties of liquids. The influence of the liquid viscosity and the liquid surface tension on the hydrodynamic parameters was simulated. The influence of the liquid viscosity and the surface tension on the bubble size distribution was presented.
Abstract Most liquids in gas–liquid phase reactions are organic solvents; hence, it is particularly important to study the effect of liquid properties on fluid dynamic parameters in bubble columns. In this study, the correction of surface tension and viscosity were used to determine the influence of different liquid properties on the hydrodynamic parameters of bubble columns. These were implemented based on the minimum energy model proposed by Li (Li et al., 1999; Li and Kwauk, 2003; Xu and Li, 1998), our previous work (Zhang et al., 2018), the drag model of atmospheric pressure from Xiao et al. (2017) and that from Yan et al. (2019). According to previous studies (Syed et al., 2017), because liquid properties significantly influence
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the bubble size distribution in a bubble column, the density correction term and gas holdup of large bubbles were utilized to optimize the coalescence coefficient (Ce).
Computational fluid dynamics coupled with the population balance model were used to simulate the effects of liquid viscosities and liquid surface tensions on the
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hydrodynamic parameters of the bubble column. The simulation results showed that
when the liquid viscosity or surface tension increases, there is a higher probability of
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coalescence between two bubbles, resulting in the formation of a large bubble. The collision of large bubbles with turbulent eddies can increase the energy required to break up large bubbles into small ones; large bubbles in a bubble column are more
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stable, and the gas holdup of large bubbles increase. Moreover, the gas holdup of small bubbles, total gas holdup in the bubble column, and contact area between gas and liquid in the bubble column decrease, which leads to the decrease of the mass and
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heat transfers between the two phases.
Keywords: bubble column; CFD–PBM; viscosity; surface tension; gas holdup; large
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bubbles
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Nomenclature
g
volume fraction of the gas phase, dimensionless
g ,small
volume fraction of small bubbles, dimensionless
g ,l arg e
volume fraction of large bubbles, dimensionless
g ,min , g ,max
restriction constant of the turbulent diffusion force
A
area, m2
b fv , d
bubble breakup rate
b( d )
bubble breakup probability
c di , d j
bubble coalescence rate
C 1 , C 2 , C
turbulence equation coefficient effective drag coefficient for a bubble around a
CD
swarm, dimensionless lift coefficient
CTD
turbulent dispersion coefficient
CW
wall lubrication coefficient
CVM
virtual mass coefficient
Ce
coalescence coefficient
d
bubble diameter, m
e
turbulent eddy kinetic energy
Eo
Eötvos number, dimensionless
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CL
fv
bubble breakup ratio
f v ,min
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minimum bubble breakup ratio
FD
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FL
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f v ,max
maximum bubble breakup ratio drag force, N transverse lift force, N
FT
turbulent dispersion force, N
FW
wall lubrication force, N
FV
virtual mass force, N
g
gravitational acceleration, m/s2
H
bubble column height, m
height of static liquid, m
k
kinetic energy of a turbulent flow, m2/s2
P
system pressure, MPa
Pc di , d j
bubble coalescence efficiency
Pb f v d ,
bubble breakup probability
r
radial distance, m
R
radius of a bubble column, m
Re
Reynolds number
T
temperature,℃
Ug
superficial gas velocity, m/s
ug
gas velocity, m/s
ul
liquid phase velocity, m/s
uslip
slip velocity, m/s
u
average velocity of turbulent eddies
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H0
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c di , d j
collision rate
We z
Weber number
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measuring point height, m
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turbulent dissipation rate, m2/s2 viscosity, mPa·s surface tension, N/m density, kg/m3 turbulent eddy size stress tensor
Abbreviations CFD
computational fluid dynamics
EMMS
energy minimization multi-scale
Subscripts b
bubble
g
gas phase
l
liquid phase
small
small bubble
large
large bubble
eff
effective
1. Introduction Bubble columns are widely used in the petrochemical, pharmaceutical, and environmental fields (Rollbusch et al., 2015b; Duduković et al., 2002; Jhawar and Prakash, 2012) because of their advantages of good mass and heat transfers, the large phase area between the liquid and gas, easy operation, and so on (Anastasiou et al.,
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2013; Li et al., 2003; Wang et al., 2007). For example, bubble columns are utilized in the Fischer–Tropsch synthesis (Ge and Li, 2003), methanol synthesis (Wu and
Gidaspow, 2000), and wastewater treatment (Smith and Valsaraj, 1997). Several studies have focused on the air–water system to investigate the hydrodynamic
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behavior of bubble columns (Monahan, 2007; Monahan and Fox, 2007). However, in industry processes, bubble columns are used with organic solvents. Therefore, it is
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particularly important to establish experimental and simulation methods and study the influence of liquid properties on the hydrodynamic characteristics of bubble columns. The results can significantly aid in the operation, design optimization, and scale-up of
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bubble column reactors (Krishna and Sie, 2000; Rollbusch et al., 2015b). One important factor that affects the gas holdup and bubble size distribution in a bubble column is the liquid properties, which include the liquid density, viscosity,
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surface tension, specific heat capacity, and electrical conductivity. Additionally, liquid viscosity and surface tension are two key parameters that affect the fluid dynamics of
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bubble columns (Xing et al., 2013; Chaumat et al., 2007; Elgozali et al., 2002). Several experimental studies have reported the effect of liquid viscosity and surface tension on the hydrodynamics of bubble columns. For example, Franz et al.(1980)
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used the combination of glycerin and Carboxy methyl cellulose solution to study the effect of viscosity on the gas holdup and bubble size distribution. Takagi and Matsumoto (2011) investigated the effect of different surface tensions on the flow structure and bubble size distribution by adding a small amount of surfactant to water. Ruzicka et al. (2003) studied the effect of liquid viscosity on the homogeneous– heterogeneous regime transition and reported that a moderate viscosity (3–22 mPa·s) destabilizes the homogeneous regime and advances the transition; however, a low viscosity (1–3 mPa·s) can stabilize the homogeneous regime. Krishna et al. (2000)
developed a bubble column with an air–water system to which ethanol on a 0.03 to 1 v% concentrations was added. The addition of alcohol resulted in a significant gas holdup increase, which was attributed to the delay at the transition point from the homogeneous to the heterogeneous flow regime. In this study, we investigated the effects of liquid viscosity and surface tension on the flow parameters of a bubble column using a combination of two systems. In the medium to high liquid viscosity range, bubble breakup is significantly inhibited; in the low viscosity range, bubble coalescence is enhanced. Generally, organic liquids have a considerably lower surface tension than water. As surface tension decreases, bubble breakup is enhanced, which results in smaller and more uniform bubble sizes and an increase in the total gas
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holdup in the bubble column. In industrial processes, the liquid phases in many
reaction processes are typically organic fluids (Ruzicka et al., 2003; Mouza et al.,
2005), such as in toluene oxidation and ethylene chlorination (Lemoine et al., 2004).
The viscosity and surface tension of organic liquids considerably differ from those of
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water. Furthermore, some researchers have studied bubble columns with pure acetone and cumene (Rollbusch et al., 2015a), cyclohexane (Upkare et al., 2010), organic
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mixtures of toluene and petroleum (Grund et al., 1992), and C9+ isoparaffins (Godbole et al., 2010) . They concluded that the gas holdup was higher and the bubble
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size was smaller in organic liquids than in water. However, research on the influence of liquid surface tension and viscosity on the flow parameters of bubble columns is relatively limited. For example, studies on the effect of liquid properties on bubble
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size distribution, bubble rise velocity and bubble radial size distribution are insufficient. Therefore, it is necessary to investigate further the effects of liquid properties on the hydrodynamic parameters and bubble size distribution in bubble
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columns using both numerical simulation and experimental techniques. Computational fluid dynamics (CFD) (Al-Baali and Farid, 2006; Alobaid, 2018)
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is an important tool used for studying fluid dynamics in bubble columns. Several studies have used CFD simulations to investigate the bubble column of air and water systems. Through model optimization, a good prediction of the fluid dynamics and mass transfer behavior in the bubble column has been obtained (Xiao et al., 2013). Although a CFD simulation can predict the hydrodynamic parameters in several bubble columns, it cannot predict the changes in bubble size. Therefore, it is necessary to couple the population balance model (PBM) (Marchisio et al., 2003) with CFD to predict this size change. Several studies have used the CFD-PBM coupled
model to simulate the bubble column of an air-water system with good predictability (Wang and Wang, 2007; Liu and Hinrichsen, 2014). However, because the liquid properties of organic solutions considerably differ compared to those of water, organic solvents are typically used in many industrial applications. The change in liquid properties has a significant function in the coalescence and breakup of bubbles. Therefore, to better predict the influence of different organic solvents on the hydrodynamic parameters of bubble columns, further investigations on mathematical models are necessary. This study focused on organic solvents employed in industrial applications. A mixture of SEBS-1650 and cyclohexane solvent (20% n-hexane and 80% cyclohexane)
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and a mixture of oleic acid and water were used as liquid phases; air was the gas
phase. Based on the drag models of Xiao et al. (2017) and Yan et al. (2019), surface
tension and viscosity corrections were further incorporated in this study. Moreover, to predict the influence of different liquid properties on the hydrodynamic parameters of
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the bubble column, the coalescence model of Luo et al. (1993) was used for
optimization. The optimized CFD–PBM coupled model is used to simulate the
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complex multiphase behavior caused by the changes in liquid viscosity (21.0–75.2 mPa·s) and surface tension (0.053–0.072 N/m) in the bubble column. The variation in
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bubble size distribution, gas holdup, and rising velocity of the bubble swarm with liquid viscosity and surface tension are presented. 2. Mathematical model In this study, the Euler-Euler model was used, and the two-equation
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standard k-ε turbulence model was used in the closed equation. The k-ω model has good performance for predicting the flow and separation of the boundary
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layer of the adverse pressure gradient. The standard k-ε turbulence model is converges easily and has higher accuracy for simulating churn-turbulence in bubble column (Bhole et al ,2008; M. Elena Díaz et al ,2008; Ekambara et al ,2010).
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Therefore, the standard k-ε turbulence model was chosen in this study. The main mathematical models used in this study are summarized in Table 1. This section presents the preliminary work of the research group that has achieved excellent prediction results (Yan et al., 2019; Zhang et al., 2018). 2.1. Drag force The energy minimization multi-scale concept of Li is based on the double bubble size model (Yang et al., 2007; Yang et al., 2011; Zhou et al., 2017). The closed model
of the relationship between the drag coefficient and bubble diameter proposed by Xiao et al.(2013) is expressed as follows. U g ,small CD g , small CD ,small g ,small db d small
2
g ,l arg e U g .l arg e CD ,l arg e g ,l arg e dl arg e
2
g2 Ug
(1)
The double-scale bubble model for the energy minimization multi-scale concept is a simplified model of the air–water system. However, the liquid properties significantly influence the drag force on the bubble. Therefore, to improve the applicability of the drag model, this study proposes the introduction of liquid viscosity
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and surface tension into the double-scale simplified drag model of the minimum energy model to further modify it.
The drag model under atmospheric pressure adopts the double-scale simplified
model of the energy minimization multi-scale concept that was proposed by Xiao et al. (2013). Accordingly, the viscosity correction term is introduced to optimize it. The
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pressurized drag model is based on the optimized model C proposed by Yan et al. (2019), which is premised on the study by Xiao et al. (2017); the surface tension
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correction term is introduced to optimize it. The drag model is specifically expressed as shown below.
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Atmospheric system
0.22 431.14 6729.02U g 35092.2U g2 CD 0 db 0.15 56 0
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U g 0.101
(2) U g 0.101
Pressurized system CD f l db 0 0
4.7 8U
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1.28
g
69.47U g2
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f l 5 l 7.1 l 1.1 0 0 0
(3)
2
(4)
2.2. PBM
The bubble size distribution is an important factor for the design and scale-up of bubble columns; the PBM used herein is typically used for the simulation of the bubble size distribution. In this study, the PBM is coupled with the CFD. The specific expressions of this model are summarized in Table 2.
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Fig. 1 - Sketch of the effect of different liquid properties on the bubble size distribution in the bubble column
According to the research results of Besagnia et al.(2016), when the viscosity or
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surface tension of the liquid changes in a bubble column, the shape and size of the bubble formation in the bubble column will change, and the probabilities of the
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formed large and small bubbles will change, making the gas holdups of large bubbles and small bubbles change in the bubble column. Guédon et al (2017) showed that when the viscosity of the liquid phase increases, the large bubbles, which tend to
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generate a negative lift coefficient moves toward the center of the bubble column, and the acceleration effect of large bubbles is the key to the coalescence coefficient. Hence, the gas holdup of large bubbles and the density correction term based on the
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bubble coalescence model of Luo (1993) were used to optimize the coalescence
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coefficient, Ce, as follows. g Ce 0.92 g ,0
l arg e
0.28
g 0.82 g ,0
1 1.2 l arg e
0.17
Ug U0
0.67
(5) l 0
0.05
l 0
0.2
(6)
3. Simulation details The bubble column size and operating conditions used herein are summarized in Table 3, and the liquid phase properties are listed in Table 4.
In the ANSYS FLUENT 15.0 software platform, based on the pressure solver, the discretization in space is in the bounded center differential (BCD) format. A two-dimensional structure grid was used and the working conditions were simulated by the finite volume method. The boundary conditions included the velocity inlet, pressure outlet, and the initial conditions of turbulence at the inlet and outlet according to the “intensity and hydraulic diameter” method. The turbulent intensity was set at 5%, and the hydraulic diameter involved the inner diameter of the bubble column. The simulation time was 90 s and the time step size was 0.001. The Courant
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number was lower than 1 according to the maximum gas or liquid phase velocity in
the X and Y axes of the bubble column. When the calculation completed, the residual curve values were all less than 10-3. The experimental method involved the
differential pressure method and the bed collapse method. The experimental data were
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an average value measured over a period of time in a steady-state. The gas holdups of the large and small bubbles were obtained by the bed collapse method, and the total
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gas holdup was obtained by the differential pressure method and is consistent with the
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results obtained by the bed collapse method. 4.Results and discussion 4.1 Grid independence verification
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Fig. 2 - Effect of the grid on the simulation
Bubble columns 1 and 2 were simulated with four different sizes of grids. From the grid size and simulation results shown in Fig. 2, when the number of grids
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increased, there was no influence on the simulation accuracy, but the calculation amount increased. Therefore, the subsequent simulation comprehensively considered the calculation accuracy and the calculation efficiency, and the second grid size was
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selected. 4.2 Flow regime analysis
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Fig. 3 - Flow regime of bubble column
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As shown in Fig. 3, the operating conditions of the two systems are in a
transitional flow range and churn-turbulent regime in an air-water system. Compared with the air-water system, using the mixed SEBS-1650 and cyclohexane solvent
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system (SEBS solvent system) with increased viscosity and the oleic acid system with an approximate constant viscosity, The operating conditions under the SEBS solvent
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system was approximated in transitional range, and the operating conditions for the oleic acid system was in the churn-turbulent regime. In the churn-turbulent regime or transitional range, the influence of the bubble size distribution involved the
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coalescence and breakup of bubbles. The churn-turbulent regime is mainly a dynamic equilibrium process in which small bubbles coalesce into large bubbles, and large bubbles break up into small bubbles due to surface instability. Because the application
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of bubble columns in industry is mostly in the churn-turbulent regime, the operating state of my research is also in the churn-turbulent regime(the SEBS solvent system is
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considered approximately to be a churn-turbulent regime). Therefore, this study focused on the influence of the liquid phase properties of the churn-turbulent regime on the bubble size in the bubble column. Numerous studies have shown that the differences in the properties of large and small bubbles in the bubble column have led many scholars to use the gas holdup of large bubbles or small bubbles to optimize the model further. Therefore, this study utilized the gas holdup of large bubbles to further improve the bubble coalescence model under the influence of liquid phase properties. This will be of great significance for the study of different liquid bubble columns in
the future.
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4.3 Average gas holdup
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Fig. 4 - Effect of liquid viscosity on large/small bubble gas holdup at different superficial gas velocities
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Fig. 5 - Effect of liquid viscosity on large/small bubble gas holdup at different superficial gas velocities The mixed SEBS-1650 and cyclohexane solvent (20% n-hexane, 80% cyclohexane) was used as the liquid phase. The gas holdup with superficial gas
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velocity under different viscosity conditions was investigated. According to the dual role of the viscosity proposed by Besagni et al (2017), a low-viscosity liquid is less prone to large bubbles than a high-viscosity liquid. At a higher superficial gas velocity,
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the breaking probability of a large bubble in a low-viscosity liquid into a small bubble is higher than that of a high-viscosity liquid. This results in an increase in the number
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of small bubbles and an increase in the overall gas holdup. In a moderate/high viscosity liquid, when there is a transition of the homogeneous flow regime to the churn-turbulent flow regime, the large bubbles, which tend to generate a negative lift coefficient moves toward the center of the bubble column, thus promoting “coalescence-induced” bubbles and the flow regime transition. Therefore, under the same operating conditions, there are more large bubbles in the moderate/high viscosity column than in the low-viscosity liquid column; thus, the overall gas holdup in the moderate/high viscosity liquid column is lower than that of the low-viscosity
liquid column. This also indicates that the moderate/high viscosity liquid makes it possible to accumulate small bubbles in the bubble column, which become a large bubble. As shown in Fig. 4 (a,c,d), the average gas holdup increases with increasing superficial gas velocity; as the viscosity of the liquid phase increases, the total gas holdup and the gas holdup of small bubbles decrease, and the gas holdup of large bubbles increases. This phenomenon occurs because a large liquid phase viscosity increases the probability of small bubbles to coalesce into large bubbles. Fig. 4(b) shows the trend of the average gas holdup at different liquid surface tensions. The decrease in liquid surface tension increases the average gas holdup in the bubble column. The model simulation results are basically consistent with
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experimental results.
As shown in Fig. 5, the simulation results of the model are basically consistent with the experimental results, and it can be seen from the Fig. 5 that the increase of
liquid viscosity leads to an increase in gas holdup of large bubbles, a decrease in gas
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holdup of small bubbles, and a decrease in total gas holdup in bubble column. 4.4 Radial gas holdup
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Fig. 6 - Effect of liquid viscosity on the radial gas holdup distribution (H=0.85 m) Fig. 6 (a-c) shows the effect of liquid viscosity on the radial gas holdup. As the
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liquid viscosity increased, the gas holdup in the radial direction close to the wall surface significantly decreased. Because the area was closer to the wall, the number of small bubbles that occupied this section was larger, the liquid viscosity increased, and the number of small bubbles in the bubble column decreased; consequently, the overall gas holdup decreased. Fig. 6 (d-f) illustrates the effect of the liquid surface tension on the radial gas holdup. The increase in the surface tension of the liquid caused the radial gas holdup in the bubble column to decrease. This is primarily because the smaller the surface
tension, the greater the number of small bubbles in the column; however, when the surface tension was high, large bubbles easily formed. Because the rising velocity of large bubbles was higher than that of small bubbles, the residence time of the former in the bubble column was lower than that of the latter. Therefore, an increase in liquid surface tension increased the probability of large bubbles forming; consequently, the
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gas holdup in the bubble column decreased. 4.5 Radial bubble diameter
Fig. 7 - Effect of liquid viscosity on the radial bubble size distribution (H=0.85 m) Fig. 7 (a-c) shows the effect of the liquid viscosity on radial bubble diameter. As the liquid viscosity increased, the radial bubble diameter in the bubble column
increased; this resulted in an increase in the number of large bubbles and a decrease in small bubbles. Moreover, the probability of bubble coalescence and generation of large bubbles increased. Consequently, the total contact area between the gas and liquid phases in the bubble column reduced, which was not conducive to mass and heat transfers between these two phases. Fig. 7 (d-f) illustrates the effect of liquid surface tension on the radial bubble diameter. As the surface tension of the liquid increased, the radial bubble diameter in the column similarly increased. The additional pressure required to break up the bubble became larger because of the increase in the surface tension of the liquid. Consequently, the additional pressure caused by the surface tension of the bubble
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increased, and the probability of bubble breakup decreases. Thereafter, the number of large bubbles in the tower increased, the number of small bubbles decreased, and the total gas holdup decreased.
According to simulation results, the liquid viscosity or the surface tension of the
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liquid increases, the number of large bubbles in the bubble column increased. Because the large bubbles in the bubble column had a shorter residence time than small
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bubbles, the rising velocity of bubbles was higher. The liquid rise velocity in the bubble column did not change significantly at different liquid viscosities and different
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liquid surface tensions; this was attributed to the liquid density being very large relative to gas. The main factor that affects the change in the liquid velocity is the superficial gas velocity; on the other hand, liquid viscosity, surface tension, and
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bubble size only have a slight influence on the liquid rise velocity. Therefore, the change in liquid viscosity and the change in liquid surface tension did not affect the liquid rise velocity in the bubble column.
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4.6 Radial bubble swarm rising velocity
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Fig.8 Radial bubble swarm rising velocity
Fig. 8(a) shows the effect of different viscosities on the radial gas holdup in the
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bubble column. As the viscosity of the liquid increased, the velocity of the radial bubble swarm in the bubble column increased. The increase in the bubble swarm velocity in the center of the bubble column was caused by the increase in the viscosity
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of the liquid, which was caused by the increase in the large bubble in the bubble column, which is consistent with the dual effect of viscosity proposed by Besagni et al. (2017). This phenomenon led to an increase in the gas holdup of large bubbles in the
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bubble column; additionally, the gas holdup of small bubbles and the total gas holdup became smaller, and the contact area between the gas and liquid phases became
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smaller, which was not conducive to mass transfer or heat transfer. Fig. 8(c) shows the effect of the surface tension on the distribution of the radial
gas holdup in the bubble column. The increase in the surface tension of the liquid caused the probability of bubble coalescence to increase, resulting in an increase in the number of large bubbles in the bubble column. Because the residence time of the large bubbles was short and the rising velocity was fast, the viscosity increase caused the bubble swarm to rise at the center of the bubble column. This phenomenon led to a
smaller contact area between the gas and liquid phases, which was not conducive to mass transfer or heat transfer. Fig. 8 (b, d) shows the effect of the superficial gas velocity on the rising velocity of the radial bubble swarm. As shown in Fig.8, the superficial gas velocity increased, resulting in an increase in the rising velocity of the bubble swarm in the bubble column. The increase in the rising velocity of the center bubble swarm was caused by large bubbles in bubble column. This also comfirmed that the increase in the superficial gas velocity led to a higher probability of bubble coalescence in the bubble column, and the total gas holdup became larger.
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4.7 Bubble size distribution
Fig. 9 - Effect of the liquid properties on the bubble size distribution Fig. 9 (a) shows the effect of liquid viscosity on bubble size distribution. The
increase in the liquid viscosity resulted in more stable large bubbles, and the energy required for the breakup of large bubbles into small bubbles was greater. The probability of bubble collisions to form large bubbles became high. Therefore, the number of large bubbles slightly increased, whereas that of small bubbles significantly decreased. Hence, there was a decrease in the overall gas holdup in the
bubble column, and the contact area between the two phases became small. Fig. 9 (c) demonstrates the effect of the liquid surface tension on the bubble size distribution as a function of frequency. The surface tension of the liquid decreased, and the stability of the large bubble decreased; consequently, large bubbles tended to break up and generate small bubbles. The probability of bubble collision to form large bubbles became low. As a result, the number of small bubbles in the column increased, and that of the large bubbles decreased. Because the small bubbles in the bubble column had a longer residence time than large bubbles, the total gas holdup in the column increased, and the contact area of the gas–liquid phases became larger; this was conducive for the mass and heat transfers between the two phases.
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Fig.9 (b,d) shows the effect of superficial gas velocity on the bubble size
distribution with frequency in the bubble column. It can be seen from Fig. 9(b) that When the viscosity of the liquid becomes larger, the increase of the superficial gas
velocity will result in an increase in the gas holdup in the bubble column. The number
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of large bubbles increases, and the number of small bubbles decreases. However, the number of smaller bubbles increases and is stable in the bubble column. As can be
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seen in Fig. 9(d), when the surface tension of the liquid is small, an increase in the superficial gas velocity causes a widening of the bubble size distribution in the bubble
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column, and an increase in the proportion of the large bubbles.
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4.8 Bubble size distribution at different axial positions
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Fig. 10 - Effect of the axial position on the bubble size distribution
Fig. 10 shows the effect of axial position on the number density of the bubble
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size distribution at different superficial gas velocities and liquid viscosities. We found the closer the bubble to the center of the column, the larger the bubble size; the closer it is to the column wall, the smaller the bubble diameter. These simulation results are
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consistent with the experimental results. 5. Conclusion
In this study, an optimized drag model of bubble swarms was coupled with the
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PBM (optimized bubble coalescence model and Luo’s bubble breakup model). The effects of liquid viscosity (SEBS-1650 and cyclohexane mixed solvent (20% n-hexane, 80% cyclohexane)) and liquid surface tension (Oleic acid and water mixed system) on
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the hydrodynamic parameters in the bubble column were investigated. The detailed conclusions are as follows. An increase in the liquid viscosity or surface tension resulted in a wider bubble
size distribution range and a decrease in the number of bubbles and total gas holdup, an increase in the gas holdup of large bubbles, a decrease in the gas holdup of small bubbles, which were not conducive to mass and heat transfer. The main effect of the increase in liquid viscosity is that the gas holdup near the
bubble column wall decreased, whereas that near the center did not change significantly. Moreover, the bubble size near the column wall became smaller, the increase in liquid viscosity led to a widening bubble distribution, and the number of bubbles decreased. Finally, the increase in the liquid’s surface tension caused a decrease in the overall radial gas holdup. Declaration of interests
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☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
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Financial supported by the National Natural Science Foundation of China
(91634101) and The Project of Construction of Innovative Teams and Teacher Career
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Development for Universities and Colleges under Beijing Municipality
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(IDHT20180508).
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Takagi, S., Matsumoto, Y., 2011. Surfactant Effects on Bubble Motion and Bubbly Flows. Annu. Rev. Fluid Mech. 43, 615-636. https://doi.org/10.1146/annurev-fluid-122109-160756 Tomiyama, A., 1998. Struggle with computational bubble dynamics. Multiph. Sci. Technol. 10, 369-405. https://doi.org/10.1615/MultScienTechn.v10.i4.40 Upkare, M.M., Rajurkar, K.B., Gupta, P.R., Jaganathan, R., 2010. Mathematical modeling and simulation of bubble column reactor for aerial liquid phase cyclohexane oxidation, in: AIP Conference Proceedings. https://doi.org/10.1063/1.3516293 Wang, T., Wang, J., 2007. Numerical simulations of gas-liquid mass transfer in bubble columns with a CFD-PBM coupled model. Chem. Eng. Sci. 62, 7107-7118. https://doi.org/10.1016/j.ces.2007.08.033 Wang, T., Wang, J., Jin, Y., 2007. Slurry reactors for gas-to-liquid processes: A review. Ind. Eng. Chem. Res. 46, 5824-5847. https://doi.org/10.1021/ie070330t Wu, Y., Gidaspow, D., 2000. Hydrodynamic simulation of methanol synthesis in gas-liquid slurry bubble column reactors. Chem. Eng. Sci. 55, 573-587. https://doi.org/10.1016/S0009-2509(99)00313-9 Xiao, Q., Wang, J., Yang, N., Li, J., 2017. Simulation of the multiphase flow in bubble columns with stability-constrained multi-fluid CFD models. Chem. Eng. J. 329, 88-99. https://doi.org/10.1016/j.cej.2017.06.008 Xiao, Q., Yang, N., Li, J., 2013. Stability-constrained multi-fluid CFD models for gas-liquid flow in bubble columns. Chem. Eng. Sci. 100, 279-292. https://doi.org/10.1016/j.ces.2013.02.027 Xing, C., Wang, T., Wang, J., 2013. Experimental study and numerical simulation with a coupled CFD-PBM model of the effect of liquid viscosity in a bubble column. Chem. Eng. Sci. 95, 313-322. https://doi.org/10.1016/j.ces.2013.03.022 Xu, G., Li, J., 1998. Analytical solution of the energy-minimization multi-scale model for gas-solid two-phase flow. Chem. Eng. Sci. 53, 1349-1366. https://doi.org/10.1016/S0009-2509(97)00424-7 Yan, P., Jin, H., He, G., Guo, X., Ma, L., Yang, S., Zhang, R., 2019. CFD simulation of hydrodynamics in a high-pressure bubble column using three optimized drag models of bubble swarm. Chem. Eng. Sci. 199, 137-155. https://doi.org/10.1016/j.ces.2019.01.019 Yang, N., Chen, J., Zhao, H., Ge, W., Li, J., 2007. Explorations on the multi-scale flow structure and stability condition in bubble columns. Chem. Eng. Sci. 62, 6978-6991. https://doi.org/10.1016/j.ces.2007.08.034 Yang, N., Wu, Z., Chen, J., Wang, Y., Li, J., 2011. Multi-scale analysis of gas-liquid interaction and CFD simulation of gas-liquid flow in bubble columns. Chem. Eng. Sci. 66, 3212-3222. https://doi.org/10.1016/j.ces.2011.02.029 Zhang, B., Kong, L., Jin, H., He, G., Yang, S., Guo, X., 2018. CFD simulation of gas– liquid flow in a high-pressure bubble column with a modified population balance model. Chinese J. Chem. Eng. 26, 1350–1358. https://doi.org/10.1016/j.cjche.2018.01.003 Zhou, R., Yang, N., Li, J., 2017. CFD simulation of gas-liquid-solid flow in slurry bubble columns with EMMS drag model. Powder Technol. 314, 466-479. https://doi.org/10.1016/j.powtec.2016.09.083
f
Equations Continuity equation
i, j
i i g, i g , l
P' P
k Equation
i i ui ui l lam,l t ,l t ,b k kl l Gk ,l l l
eff ,l lam,l t ,l b,l ,
e-
2 2 eff ,l ul l kl , 3 3
i i uiui l lam,l t ,l t ,b l l
na l
Turbulence equations ε Equation
Gk ,l eff ,l ul ul ul
t , g t ,l g l
T
23 u l
eff ,l
b,l Cb l g db ug ul ,
l C1Gk ,l C 2 l l kl
ul l kl
t ,l C l kl2 l
1 kl ,t kl kl , g , l ,t l l , g , kl , g g Cvmuslip , l , g g guslip 2
Drag force (Xiao et al., 2013)
3 FD g CD l ug ul ug ul 4 db
Virtue mass force (Milne, 1968)
FVM CVM g l ug ul
Transverse lift force (Liu et al., 2017)
FL CL g l ug ul ul
Jo ur
Interphase forces
F
Momentum conservation equation
Pr
Governing equations
i i i iui 0, i g , l t i iui i iuiui iP' i eff u uT t
pr
Model
oo
Table 1 - Governing equations of gas–liquid phases
CVM 0 d du CL g us l k g CTD dr dr
CL 0.2CTD
l 2 l
eff , g
g b,l l t ,l
f
oo
g ,max g g ,max g ,min
pr
na l Jo ur
CTD
2 1 2 2 FW CW g db R r R r l ug ul 2
Pr
Wall lubrication force (Tomiyama, 1998)
FTD, L FTD,G CTD l kl g
e-
Turbulent dispersion force (Lahey et al., 1993)
0.47 0.933 Eo 0.179 e CW 0.00599 Eo 0.0187 0.179
Eo 1 1
f
Equations
Daughter bubble size distribution
b fv , d
d
min
Pb fv d , d d
pr
Breakup rate (Hean Luo and Svendsen, 1996; Prince and Blanch, 1990; H. Luo and Svendsen, 1996)
fv , d
e-
Bubble breakup caused by turbulent eddies
2
1
min
1
2 1 11 3 exp c d
1 1
Pr
Items
oo
Table 2 - Models of bubble breakup and coalescence
2
0 min
d
4
na l
Collision frequency (Prince and Blanch, 1990)
n
Jo ur
Breakup probability
d
0.822 1 g
4
2
u n n
min
11 3 exp c d
min d 2
u n l 3 d E k l 1 g dk 6 2
u 2
13
4 3 3 1 2 2 exp 2
d 0.923 1 g n
Pb fv d , Pb fv d , e , Pe e de 0
1 f Pb f v d , e , v ,max f v ,min 0
Pe e
f v ,max f v ,min , f v ,min f v f v ,max other
13
1
e
d
2
11 3
exp e e
2
u e 3 l 6 2
f
Coalescence efficiency (Prince and Blanch, 1990)
12 2 2 1 3 di d j di2 3 d 2j 3 4
tij Pc di , d j exp ij
di dj
na l Jo ur
0.75 1 2 1 3 1 2 ij ij 12 Weij exp Ce 3 C 1 g l vm ij
Weij l di u ij
Pr
ij
oo
cu c Pc
c di , d j
pr
Collision rate (H. Luo and Svendsen, 1996; Lee et al., 1987; Chesters, 1991)
e-
Coalescence rate caused by different rising velocities
2
2 12
u ij u i u j
Table 3 - Operating conditions Operating conditions
1
2
Column diameter (m)
0.165
0.3
Column height (m)
2.0
6.6
Plexiglas
Stainless steel
Superficial gas velocity, ug (m/s)
0.03–0.25
0.120–0.25
Operating pressure, P (MPa)
0.1
0.5
Initial liquid level, H0(m)
1.1
2.1
Material
Opening rate (%)
3.56 25
25
Jo
ur
na
lP
re
-p
ro of
Operating temperature (℃)
Table 4 - Liquid properties Viscosity (mPa·s)
Density (kg/m3)
Surface tension (N/m)
log10(Mo)
Device
V1
21.0
766.9
0.0145
-3.08903
1
V2
31.7
768.3
0.0148
-2.40114
1
V3
37.7
769.2
0.0153
-2.14381
1
V4
75.2
772.5
0.0153
-0.94616
1
S1
1.0
998.2
0.0530
-10.1809
2
S2
1.0
998.2
0.0590
-10.3207
2
S3
1.0
998.2
0.0640
-10.4267
2
S4
1.0
998.2
0.0720
-10.5801
2
Jo
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na
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No
PII:
S0263-8762(19)30559-3
DOI:
https://doi.org/10.1016/j.cherd.2019.11.030
Reference:
CHERD 3915
To appear in:
Chemical Engineering Research and Design
Received Date:
16 August 2019
Revised Date:
31 October 2019
Accepted Date:
22 November 2019
Please cite this article as: Yan P, Jin H, He G, Guo X, Ma L, Yang S, Zhang R, Numerical simulation of bubble characteristics in bubble columns with different liquid viscosities and surface tensions using a CFD-PBM coupled model, Chemical Engineering Research and Design (2019), doi: https://doi.org/10.1016/j.cherd.2019.11.030
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Numerical simulation of bubble characteristics in bubble columns with different liquid viscosities and surface tensions using a CFD-PBM coupled model
Peng Yan, Haibo Jin*, Guangxiang He, Xiaoyan Guo, Lei Ma, Suohe
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Yang, Rongyue Zhang Key Laboratory of Fuel Cleanliness and Efficient Catalytic Emission Reduction Technology,
Department of Chemical Engineering, Beijing Institute of Petrochemical Technology, Beijing Beijing 102617)
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Graphical Abstract
Highlight CFD-PBM model was well validated in a bubble column with different physical properties of liquids. The influence of the liquid viscosity and the liquid surface tension on the hydrodynamic parameters was simulated. The influence of the liquid viscosity and the surface tension on the bubble size distribution was presented.
Abstract Most liquids in gas–liquid phase reactions are organic solvents; hence, it is particularly important to study the effect of liquid properties on fluid dynamic parameters in bubble columns. In this study, the correction of surface tension and viscosity were used to determine the influence of different liquid properties on the hydrodynamic parameters of bubble columns. These were implemented based on the minimum energy model proposed by Li (Li et al., 1999; Li and Kwauk, 2003; Xu and Li, 1998), our previous work (Zhang et al., 2018), the drag model of atmospheric pressure from Xiao et al. (2017) and that from Yan et al. (2019). According to previous studies (Syed et al., 2017), because liquid properties significantly influence
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the bubble size distribution in a bubble column, the density correction term and gas holdup of large bubbles were utilized to optimize the coalescence coefficient (Ce).
Computational fluid dynamics coupled with the population balance model were used to simulate the effects of liquid viscosities and liquid surface tensions on the
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hydrodynamic parameters of the bubble column. The simulation results showed that
when the liquid viscosity or surface tension increases, there is a higher probability of
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coalescence between two bubbles, resulting in the formation of a large bubble. The collision of large bubbles with turbulent eddies can increase the energy required to break up large bubbles into small ones; large bubbles in a bubble column are more
lP
stable, and the gas holdup of large bubbles increase. Moreover, the gas holdup of small bubbles, total gas holdup in the bubble column, and contact area between gas and liquid in the bubble column decrease, which leads to the decrease of the mass and
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heat transfers between the two phases.
Keywords: bubble column; CFD–PBM; viscosity; surface tension; gas holdup; large
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bubbles
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Nomenclature
g
volume fraction of the gas phase, dimensionless
g ,small
volume fraction of small bubbles, dimensionless
g ,l arg e
volume fraction of large bubbles, dimensionless
g ,min , g ,max
restriction constant of the turbulent diffusion force
A
area, m2
b fv , d
bubble breakup rate
b( d )
bubble breakup probability
c di , d j
bubble coalescence rate
C 1 , C 2 , C
turbulence equation coefficient effective drag coefficient for a bubble around a
CD
swarm, dimensionless lift coefficient
CTD
turbulent dispersion coefficient
CW
wall lubrication coefficient
CVM
virtual mass coefficient
Ce
coalescence coefficient
d
bubble diameter, m
e
turbulent eddy kinetic energy
Eo
Eötvos number, dimensionless
lP
re
-p
ro of
CL
fv
bubble breakup ratio
f v ,min
na
minimum bubble breakup ratio
FD
Jo
FL
ur
f v ,max
maximum bubble breakup ratio drag force, N transverse lift force, N
FT
turbulent dispersion force, N
FW
wall lubrication force, N
FV
virtual mass force, N
g
gravitational acceleration, m/s2
H
bubble column height, m
height of static liquid, m
k
kinetic energy of a turbulent flow, m2/s2
P
system pressure, MPa
Pc di , d j
bubble coalescence efficiency
Pb f v d ,
bubble breakup probability
r
radial distance, m
R
radius of a bubble column, m
Re
Reynolds number
T
temperature,℃
Ug
superficial gas velocity, m/s
ug
gas velocity, m/s
ul
liquid phase velocity, m/s
uslip
slip velocity, m/s
u
average velocity of turbulent eddies
re
-p
ro of
H0
lP
c di , d j
collision rate
We z
Weber number
na
measuring point height, m
ur
Jo
turbulent dissipation rate, m2/s2 viscosity, mPa·s surface tension, N/m density, kg/m3 turbulent eddy size stress tensor
Abbreviations CFD
computational fluid dynamics
EMMS
energy minimization multi-scale
Subscripts b
bubble
g
gas phase
l
liquid phase
small
small bubble
large
large bubble
eff
effective
1. Introduction Bubble columns are widely used in the petrochemical, pharmaceutical, and environmental fields (Rollbusch et al., 2015b; Duduković et al., 2002; Jhawar and Prakash, 2012) because of their advantages of good mass and heat transfers, the large phase area between the liquid and gas, easy operation, and so on (Anastasiou et al.,
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2013; Li et al., 2003; Wang et al., 2007). For example, bubble columns are utilized in the Fischer–Tropsch synthesis (Ge and Li, 2003), methanol synthesis (Wu and
Gidaspow, 2000), and wastewater treatment (Smith and Valsaraj, 1997). Several studies have focused on the air–water system to investigate the hydrodynamic
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behavior of bubble columns (Monahan, 2007; Monahan and Fox, 2007). However, in industry processes, bubble columns are used with organic solvents. Therefore, it is
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particularly important to establish experimental and simulation methods and study the influence of liquid properties on the hydrodynamic characteristics of bubble columns. The results can significantly aid in the operation, design optimization, and scale-up of
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bubble column reactors (Krishna and Sie, 2000; Rollbusch et al., 2015b). One important factor that affects the gas holdup and bubble size distribution in a bubble column is the liquid properties, which include the liquid density, viscosity,
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surface tension, specific heat capacity, and electrical conductivity. Additionally, liquid viscosity and surface tension are two key parameters that affect the fluid dynamics of
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bubble columns (Xing et al., 2013; Chaumat et al., 2007; Elgozali et al., 2002). Several experimental studies have reported the effect of liquid viscosity and surface tension on the hydrodynamics of bubble columns. For example, Franz et al.(1980)
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used the combination of glycerin and Carboxy methyl cellulose solution to study the effect of viscosity on the gas holdup and bubble size distribution. Takagi and Matsumoto (2011) investigated the effect of different surface tensions on the flow structure and bubble size distribution by adding a small amount of surfactant to water. Ruzicka et al. (2003) studied the effect of liquid viscosity on the homogeneous– heterogeneous regime transition and reported that a moderate viscosity (3–22 mPa·s) destabilizes the homogeneous regime and advances the transition; however, a low viscosity (1–3 mPa·s) can stabilize the homogeneous regime. Krishna et al. (2000)
developed a bubble column with an air–water system to which ethanol on a 0.03 to 1 v% concentrations was added. The addition of alcohol resulted in a significant gas holdup increase, which was attributed to the delay at the transition point from the homogeneous to the heterogeneous flow regime. In this study, we investigated the effects of liquid viscosity and surface tension on the flow parameters of a bubble column using a combination of two systems. In the medium to high liquid viscosity range, bubble breakup is significantly inhibited; in the low viscosity range, bubble coalescence is enhanced. Generally, organic liquids have a considerably lower surface tension than water. As surface tension decreases, bubble breakup is enhanced, which results in smaller and more uniform bubble sizes and an increase in the total gas
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holdup in the bubble column. In industrial processes, the liquid phases in many
reaction processes are typically organic fluids (Ruzicka et al., 2003; Mouza et al.,
2005), such as in toluene oxidation and ethylene chlorination (Lemoine et al., 2004).
The viscosity and surface tension of organic liquids considerably differ from those of
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water. Furthermore, some researchers have studied bubble columns with pure acetone and cumene (Rollbusch et al., 2015a), cyclohexane (Upkare et al., 2010), organic
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mixtures of toluene and petroleum (Grund et al., 1992), and C9+ isoparaffins (Godbole et al., 2010) . They concluded that the gas holdup was higher and the bubble
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size was smaller in organic liquids than in water. However, research on the influence of liquid surface tension and viscosity on the flow parameters of bubble columns is relatively limited. For example, studies on the effect of liquid properties on bubble
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size distribution, bubble rise velocity and bubble radial size distribution are insufficient. Therefore, it is necessary to investigate further the effects of liquid properties on the hydrodynamic parameters and bubble size distribution in bubble
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columns using both numerical simulation and experimental techniques. Computational fluid dynamics (CFD) (Al-Baali and Farid, 2006; Alobaid, 2018)
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is an important tool used for studying fluid dynamics in bubble columns. Several studies have used CFD simulations to investigate the bubble column of air and water systems. Through model optimization, a good prediction of the fluid dynamics and mass transfer behavior in the bubble column has been obtained (Xiao et al., 2013). Although a CFD simulation can predict the hydrodynamic parameters in several bubble columns, it cannot predict the changes in bubble size. Therefore, it is necessary to couple the population balance model (PBM) (Marchisio et al., 2003) with CFD to predict this size change. Several studies have used the CFD-PBM coupled
model to simulate the bubble column of an air-water system with good predictability (Wang and Wang, 2007; Liu and Hinrichsen, 2014). However, because the liquid properties of organic solutions considerably differ compared to those of water, organic solvents are typically used in many industrial applications. The change in liquid properties has a significant function in the coalescence and breakup of bubbles. Therefore, to better predict the influence of different organic solvents on the hydrodynamic parameters of bubble columns, further investigations on mathematical models are necessary. This study focused on organic solvents employed in industrial applications. A mixture of SEBS-1650 and cyclohexane solvent (20% n-hexane and 80% cyclohexane)
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and a mixture of oleic acid and water were used as liquid phases; air was the gas
phase. Based on the drag models of Xiao et al. (2017) and Yan et al. (2019), surface
tension and viscosity corrections were further incorporated in this study. Moreover, to predict the influence of different liquid properties on the hydrodynamic parameters of
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the bubble column, the coalescence model of Luo et al. (1993) was used for
optimization. The optimized CFD–PBM coupled model is used to simulate the
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complex multiphase behavior caused by the changes in liquid viscosity (21.0–75.2 mPa·s) and surface tension (0.053–0.072 N/m) in the bubble column. The variation in
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bubble size distribution, gas holdup, and rising velocity of the bubble swarm with liquid viscosity and surface tension are presented. 2. Mathematical model In this study, the Euler-Euler model was used, and the two-equation
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standard k-ε turbulence model was used in the closed equation. The k-ω model has good performance for predicting the flow and separation of the boundary
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layer of the adverse pressure gradient. The standard k-ε turbulence model is converges easily and has higher accuracy for simulating churn-turbulence in bubble column (Bhole et al ,2008; M. Elena Díaz et al ,2008; Ekambara et al ,2010).
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Therefore, the standard k-ε turbulence model was chosen in this study. The main mathematical models used in this study are summarized in Table 1. This section presents the preliminary work of the research group that has achieved excellent prediction results (Yan et al., 2019; Zhang et al., 2018). 2.1. Drag force The energy minimization multi-scale concept of Li is based on the double bubble size model (Yang et al., 2007; Yang et al., 2011; Zhou et al., 2017). The closed model
of the relationship between the drag coefficient and bubble diameter proposed by Xiao et al.(2013) is expressed as follows. U g ,small CD g , small CD ,small g ,small db d small
2
g ,l arg e U g .l arg e CD ,l arg e g ,l arg e dl arg e
2
g2 Ug
(1)
The double-scale bubble model for the energy minimization multi-scale concept is a simplified model of the air–water system. However, the liquid properties significantly influence the drag force on the bubble. Therefore, to improve the applicability of the drag model, this study proposes the introduction of liquid viscosity
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and surface tension into the double-scale simplified drag model of the minimum energy model to further modify it.
The drag model under atmospheric pressure adopts the double-scale simplified
model of the energy minimization multi-scale concept that was proposed by Xiao et al. (2013). Accordingly, the viscosity correction term is introduced to optimize it. The
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pressurized drag model is based on the optimized model C proposed by Yan et al. (2019), which is premised on the study by Xiao et al. (2017); the surface tension
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correction term is introduced to optimize it. The drag model is specifically expressed as shown below.
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Atmospheric system
0.22 431.14 6729.02U g 35092.2U g2 CD 0 db 0.15 56 0
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U g 0.101
(2) U g 0.101
Pressurized system CD f l db 0 0
4.7 8U
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1.28
g
69.47U g2
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f l 5 l 7.1 l 1.1 0 0 0
(3)
2
(4)
2.2. PBM
The bubble size distribution is an important factor for the design and scale-up of bubble columns; the PBM used herein is typically used for the simulation of the bubble size distribution. In this study, the PBM is coupled with the CFD. The specific expressions of this model are summarized in Table 2.
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Fig. 1 - Sketch of the effect of different liquid properties on the bubble size distribution in the bubble column
According to the research results of Besagnia et al.(2016), when the viscosity or
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surface tension of the liquid changes in a bubble column, the shape and size of the bubble formation in the bubble column will change, and the probabilities of the
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formed large and small bubbles will change, making the gas holdups of large bubbles and small bubbles change in the bubble column. Guédon et al (2017) showed that when the viscosity of the liquid phase increases, the large bubbles, which tend to
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generate a negative lift coefficient moves toward the center of the bubble column, and the acceleration effect of large bubbles is the key to the coalescence coefficient. Hence, the gas holdup of large bubbles and the density correction term based on the
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bubble coalescence model of Luo (1993) were used to optimize the coalescence
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coefficient, Ce, as follows. g Ce 0.92 g ,0
l arg e
0.28
g 0.82 g ,0
1 1.2 l arg e
0.17
Ug U0
0.67
(5) l 0
0.05
l 0
0.2
(6)
3. Simulation details The bubble column size and operating conditions used herein are summarized in Table 3, and the liquid phase properties are listed in Table 4.
In the ANSYS FLUENT 15.0 software platform, based on the pressure solver, the discretization in space is in the bounded center differential (BCD) format. A two-dimensional structure grid was used and the working conditions were simulated by the finite volume method. The boundary conditions included the velocity inlet, pressure outlet, and the initial conditions of turbulence at the inlet and outlet according to the “intensity and hydraulic diameter” method. The turbulent intensity was set at 5%, and the hydraulic diameter involved the inner diameter of the bubble column. The simulation time was 90 s and the time step size was 0.001. The Courant
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number was lower than 1 according to the maximum gas or liquid phase velocity in
the X and Y axes of the bubble column. When the calculation completed, the residual curve values were all less than 10-3. The experimental method involved the
differential pressure method and the bed collapse method. The experimental data were
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an average value measured over a period of time in a steady-state. The gas holdups of the large and small bubbles were obtained by the bed collapse method, and the total
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gas holdup was obtained by the differential pressure method and is consistent with the
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results obtained by the bed collapse method. 4.Results and discussion 4.1 Grid independence verification
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Fig. 2 - Effect of the grid on the simulation
Bubble columns 1 and 2 were simulated with four different sizes of grids. From the grid size and simulation results shown in Fig. 2, when the number of grids
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increased, there was no influence on the simulation accuracy, but the calculation amount increased. Therefore, the subsequent simulation comprehensively considered the calculation accuracy and the calculation efficiency, and the second grid size was
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selected. 4.2 Flow regime analysis
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Fig. 3 - Flow regime of bubble column
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As shown in Fig. 3, the operating conditions of the two systems are in a
transitional flow range and churn-turbulent regime in an air-water system. Compared with the air-water system, using the mixed SEBS-1650 and cyclohexane solvent
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system (SEBS solvent system) with increased viscosity and the oleic acid system with an approximate constant viscosity, The operating conditions under the SEBS solvent
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system was approximated in transitional range, and the operating conditions for the oleic acid system was in the churn-turbulent regime. In the churn-turbulent regime or transitional range, the influence of the bubble size distribution involved the
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coalescence and breakup of bubbles. The churn-turbulent regime is mainly a dynamic equilibrium process in which small bubbles coalesce into large bubbles, and large bubbles break up into small bubbles due to surface instability. Because the application
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of bubble columns in industry is mostly in the churn-turbulent regime, the operating state of my research is also in the churn-turbulent regime(the SEBS solvent system is
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considered approximately to be a churn-turbulent regime). Therefore, this study focused on the influence of the liquid phase properties of the churn-turbulent regime on the bubble size in the bubble column. Numerous studies have shown that the differences in the properties of large and small bubbles in the bubble column have led many scholars to use the gas holdup of large bubbles or small bubbles to optimize the model further. Therefore, this study utilized the gas holdup of large bubbles to further improve the bubble coalescence model under the influence of liquid phase properties. This will be of great significance for the study of different liquid bubble columns in
the future.
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4.3 Average gas holdup
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Fig. 4 - Effect of liquid viscosity on large/small bubble gas holdup at different superficial gas velocities
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Fig. 5 - Effect of liquid viscosity on large/small bubble gas holdup at different superficial gas velocities The mixed SEBS-1650 and cyclohexane solvent (20% n-hexane, 80% cyclohexane) was used as the liquid phase. The gas holdup with superficial gas
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velocity under different viscosity conditions was investigated. According to the dual role of the viscosity proposed by Besagni et al (2017), a low-viscosity liquid is less prone to large bubbles than a high-viscosity liquid. At a higher superficial gas velocity,
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the breaking probability of a large bubble in a low-viscosity liquid into a small bubble is higher than that of a high-viscosity liquid. This results in an increase in the number
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of small bubbles and an increase in the overall gas holdup. In a moderate/high viscosity liquid, when there is a transition of the homogeneous flow regime to the churn-turbulent flow regime, the large bubbles, which tend to generate a negative lift coefficient moves toward the center of the bubble column, thus promoting “coalescence-induced” bubbles and the flow regime transition. Therefore, under the same operating conditions, there are more large bubbles in the moderate/high viscosity column than in the low-viscosity liquid column; thus, the overall gas holdup in the moderate/high viscosity liquid column is lower than that of the low-viscosity
liquid column. This also indicates that the moderate/high viscosity liquid makes it possible to accumulate small bubbles in the bubble column, which become a large bubble. As shown in Fig. 4 (a,c,d), the average gas holdup increases with increasing superficial gas velocity; as the viscosity of the liquid phase increases, the total gas holdup and the gas holdup of small bubbles decrease, and the gas holdup of large bubbles increases. This phenomenon occurs because a large liquid phase viscosity increases the probability of small bubbles to coalesce into large bubbles. Fig. 4(b) shows the trend of the average gas holdup at different liquid surface tensions. The decrease in liquid surface tension increases the average gas holdup in the bubble column. The model simulation results are basically consistent with
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experimental results.
As shown in Fig. 5, the simulation results of the model are basically consistent with the experimental results, and it can be seen from the Fig. 5 that the increase of
liquid viscosity leads to an increase in gas holdup of large bubbles, a decrease in gas
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holdup of small bubbles, and a decrease in total gas holdup in bubble column. 4.4 Radial gas holdup
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Fig. 6 - Effect of liquid viscosity on the radial gas holdup distribution (H=0.85 m) Fig. 6 (a-c) shows the effect of liquid viscosity on the radial gas holdup. As the
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liquid viscosity increased, the gas holdup in the radial direction close to the wall surface significantly decreased. Because the area was closer to the wall, the number of small bubbles that occupied this section was larger, the liquid viscosity increased, and the number of small bubbles in the bubble column decreased; consequently, the overall gas holdup decreased. Fig. 6 (d-f) illustrates the effect of the liquid surface tension on the radial gas holdup. The increase in the surface tension of the liquid caused the radial gas holdup in the bubble column to decrease. This is primarily because the smaller the surface
tension, the greater the number of small bubbles in the column; however, when the surface tension was high, large bubbles easily formed. Because the rising velocity of large bubbles was higher than that of small bubbles, the residence time of the former in the bubble column was lower than that of the latter. Therefore, an increase in liquid surface tension increased the probability of large bubbles forming; consequently, the
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gas holdup in the bubble column decreased. 4.5 Radial bubble diameter
Fig. 7 - Effect of liquid viscosity on the radial bubble size distribution (H=0.85 m) Fig. 7 (a-c) shows the effect of the liquid viscosity on radial bubble diameter. As the liquid viscosity increased, the radial bubble diameter in the bubble column
increased; this resulted in an increase in the number of large bubbles and a decrease in small bubbles. Moreover, the probability of bubble coalescence and generation of large bubbles increased. Consequently, the total contact area between the gas and liquid phases in the bubble column reduced, which was not conducive to mass and heat transfers between these two phases. Fig. 7 (d-f) illustrates the effect of liquid surface tension on the radial bubble diameter. As the surface tension of the liquid increased, the radial bubble diameter in the column similarly increased. The additional pressure required to break up the bubble became larger because of the increase in the surface tension of the liquid. Consequently, the additional pressure caused by the surface tension of the bubble
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increased, and the probability of bubble breakup decreases. Thereafter, the number of large bubbles in the tower increased, the number of small bubbles decreased, and the total gas holdup decreased.
According to simulation results, the liquid viscosity or the surface tension of the
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liquid increases, the number of large bubbles in the bubble column increased. Because the large bubbles in the bubble column had a shorter residence time than small
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bubbles, the rising velocity of bubbles was higher. The liquid rise velocity in the bubble column did not change significantly at different liquid viscosities and different
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liquid surface tensions; this was attributed to the liquid density being very large relative to gas. The main factor that affects the change in the liquid velocity is the superficial gas velocity; on the other hand, liquid viscosity, surface tension, and
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bubble size only have a slight influence on the liquid rise velocity. Therefore, the change in liquid viscosity and the change in liquid surface tension did not affect the liquid rise velocity in the bubble column.
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4.6 Radial bubble swarm rising velocity
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Fig.8 Radial bubble swarm rising velocity
Fig. 8(a) shows the effect of different viscosities on the radial gas holdup in the
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bubble column. As the viscosity of the liquid increased, the velocity of the radial bubble swarm in the bubble column increased. The increase in the bubble swarm velocity in the center of the bubble column was caused by the increase in the viscosity
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of the liquid, which was caused by the increase in the large bubble in the bubble column, which is consistent with the dual effect of viscosity proposed by Besagni et al. (2017). This phenomenon led to an increase in the gas holdup of large bubbles in the
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bubble column; additionally, the gas holdup of small bubbles and the total gas holdup became smaller, and the contact area between the gas and liquid phases became
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smaller, which was not conducive to mass transfer or heat transfer. Fig. 8(c) shows the effect of the surface tension on the distribution of the radial
gas holdup in the bubble column. The increase in the surface tension of the liquid caused the probability of bubble coalescence to increase, resulting in an increase in the number of large bubbles in the bubble column. Because the residence time of the large bubbles was short and the rising velocity was fast, the viscosity increase caused the bubble swarm to rise at the center of the bubble column. This phenomenon led to a
smaller contact area between the gas and liquid phases, which was not conducive to mass transfer or heat transfer. Fig. 8 (b, d) shows the effect of the superficial gas velocity on the rising velocity of the radial bubble swarm. As shown in Fig.8, the superficial gas velocity increased, resulting in an increase in the rising velocity of the bubble swarm in the bubble column. The increase in the rising velocity of the center bubble swarm was caused by large bubbles in bubble column. This also comfirmed that the increase in the superficial gas velocity led to a higher probability of bubble coalescence in the bubble column, and the total gas holdup became larger.
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4.7 Bubble size distribution
Fig. 9 - Effect of the liquid properties on the bubble size distribution Fig. 9 (a) shows the effect of liquid viscosity on bubble size distribution. The
increase in the liquid viscosity resulted in more stable large bubbles, and the energy required for the breakup of large bubbles into small bubbles was greater. The probability of bubble collisions to form large bubbles became high. Therefore, the number of large bubbles slightly increased, whereas that of small bubbles significantly decreased. Hence, there was a decrease in the overall gas holdup in the
bubble column, and the contact area between the two phases became small. Fig. 9 (c) demonstrates the effect of the liquid surface tension on the bubble size distribution as a function of frequency. The surface tension of the liquid decreased, and the stability of the large bubble decreased; consequently, large bubbles tended to break up and generate small bubbles. The probability of bubble collision to form large bubbles became low. As a result, the number of small bubbles in the column increased, and that of the large bubbles decreased. Because the small bubbles in the bubble column had a longer residence time than large bubbles, the total gas holdup in the column increased, and the contact area of the gas–liquid phases became larger; this was conducive for the mass and heat transfers between the two phases.
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Fig.9 (b,d) shows the effect of superficial gas velocity on the bubble size
distribution with frequency in the bubble column. It can be seen from Fig. 9(b) that When the viscosity of the liquid becomes larger, the increase of the superficial gas
velocity will result in an increase in the gas holdup in the bubble column. The number
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of large bubbles increases, and the number of small bubbles decreases. However, the number of smaller bubbles increases and is stable in the bubble column. As can be
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seen in Fig. 9(d), when the surface tension of the liquid is small, an increase in the superficial gas velocity causes a widening of the bubble size distribution in the bubble
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column, and an increase in the proportion of the large bubbles.
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4.8 Bubble size distribution at different axial positions
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Fig. 10 - Effect of the axial position on the bubble size distribution
Fig. 10 shows the effect of axial position on the number density of the bubble
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size distribution at different superficial gas velocities and liquid viscosities. We found the closer the bubble to the center of the column, the larger the bubble size; the closer it is to the column wall, the smaller the bubble diameter. These simulation results are
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consistent with the experimental results. 5. Conclusion
In this study, an optimized drag model of bubble swarms was coupled with the
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PBM (optimized bubble coalescence model and Luo’s bubble breakup model). The effects of liquid viscosity (SEBS-1650 and cyclohexane mixed solvent (20% n-hexane, 80% cyclohexane)) and liquid surface tension (Oleic acid and water mixed system) on
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the hydrodynamic parameters in the bubble column were investigated. The detailed conclusions are as follows. An increase in the liquid viscosity or surface tension resulted in a wider bubble
size distribution range and a decrease in the number of bubbles and total gas holdup, an increase in the gas holdup of large bubbles, a decrease in the gas holdup of small bubbles, which were not conducive to mass and heat transfer. The main effect of the increase in liquid viscosity is that the gas holdup near the
bubble column wall decreased, whereas that near the center did not change significantly. Moreover, the bubble size near the column wall became smaller, the increase in liquid viscosity led to a widening bubble distribution, and the number of bubbles decreased. Finally, the increase in the liquid’s surface tension caused a decrease in the overall radial gas holdup. Declaration of interests
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☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
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Financial supported by the National Natural Science Foundation of China
(91634101) and The Project of Construction of Innovative Teams and Teacher Career
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Development for Universities and Colleges under Beijing Municipality
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(IDHT20180508).
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f
Equations Continuity equation
i, j
i i g, i g , l
P' P
k Equation
i i ui ui l lam,l t ,l t ,b k kl l Gk ,l l l
eff ,l lam,l t ,l b,l ,
e-
2 2 eff ,l ul l kl , 3 3
i i uiui l lam,l t ,l t ,b l l
na l
Turbulence equations ε Equation
Gk ,l eff ,l ul ul ul
t , g t ,l g l
T
23 u l
eff ,l
b,l Cb l g db ug ul ,
l C1Gk ,l C 2 l l kl
ul l kl
t ,l C l kl2 l
1 kl ,t kl kl , g , l ,t l l , g , kl , g g Cvmuslip , l , g g guslip 2
Drag force (Xiao et al., 2013)
3 FD g CD l ug ul ug ul 4 db
Virtue mass force (Milne, 1968)
FVM CVM g l ug ul
Transverse lift force (Liu et al., 2017)
FL CL g l ug ul ul
Jo ur
Interphase forces
F
Momentum conservation equation
Pr
Governing equations
i i i iui 0, i g , l t i iui i iuiui iP' i eff u uT t
pr
Model
oo
Table 1 - Governing equations of gas–liquid phases
CVM 0 d du CL g us l k g CTD dr dr
CL 0.2CTD
l 2 l
eff , g
g b,l l t ,l
f
oo
g ,max g g ,max g ,min
pr
na l Jo ur
CTD
2 1 2 2 FW CW g db R r R r l ug ul 2
Pr
Wall lubrication force (Tomiyama, 1998)
FTD, L FTD,G CTD l kl g
e-
Turbulent dispersion force (Lahey et al., 1993)
0.47 0.933 Eo 0.179 e CW 0.00599 Eo 0.0187 0.179
Eo 1 1
f
Equations
Daughter bubble size distribution
b fv , d
d
min
Pb fv d , d d
pr
Breakup rate (Hean Luo and Svendsen, 1996; Prince and Blanch, 1990; H. Luo and Svendsen, 1996)
fv , d
e-
Bubble breakup caused by turbulent eddies
2
1
min
1
2 1 11 3 exp c d
1 1
Pr
Items
oo
Table 2 - Models of bubble breakup and coalescence
2
0 min
d
4
na l
Collision frequency (Prince and Blanch, 1990)
n
Jo ur
Breakup probability
d
0.822 1 g
4
2
u n n
min
11 3 exp c d
min d 2
u n l 3 d E k l 1 g dk 6 2
u 2
13
4 3 3 1 2 2 exp 2
d 0.923 1 g n
Pb fv d , Pb fv d , e , Pe e de 0
1 f Pb f v d , e , v ,max f v ,min 0
Pe e
f v ,max f v ,min , f v ,min f v f v ,max other
13
1
e
d
2
11 3
exp e e
2
u e 3 l 6 2
f
Coalescence efficiency (Prince and Blanch, 1990)
12 2 2 1 3 di d j di2 3 d 2j 3 4
tij Pc di , d j exp ij
di dj
na l Jo ur
0.75 1 2 1 3 1 2 ij ij 12 Weij exp Ce 3 C 1 g l vm ij
Weij l di u ij
Pr
ij
oo
cu c Pc
c di , d j
pr
Collision rate (H. Luo and Svendsen, 1996; Lee et al., 1987; Chesters, 1991)
e-
Coalescence rate caused by different rising velocities
2
2 12
u ij u i u j
Table 3 - Operating conditions Operating conditions
1
2
Column diameter (m)
0.165
0.3
Column height (m)
2.0
6.6
Plexiglas
Stainless steel
Superficial gas velocity, ug (m/s)
0.03–0.25
0.120–0.25
Operating pressure, P (MPa)
0.1
0.5
Initial liquid level, H0(m)
1.1
2.1
Material
Opening rate (%)
3.56 25
25
Jo
ur
na
lP
re
-p
ro of
Operating temperature (℃)
Table 4 - Liquid properties Viscosity (mPa·s)
Density (kg/m3)
Surface tension (N/m)
log10(Mo)
Device
V1
21.0
766.9
0.0145
-3.08903
1
V2
31.7
768.3
0.0148
-2.40114
1
V3
37.7
769.2
0.0153
-2.14381
1
V4
75.2
772.5
0.0153
-0.94616
1
S1
1.0
998.2
0.0530
-10.1809
2
S2
1.0
998.2
0.0590
-10.3207
2
S3
1.0
998.2
0.0640
-10.4267
2
S4
1.0
998.2
0.0720
-10.5801
2
Jo
ur
na
lP
re
-p
ro of
No