Experimental and numerical investigations of scale-up effects on the hydrodynamics of slurry bubble columns

Experimental and numerical investigations of scale-up effects on the hydrodynamics of slurry bubble columns

    Experimental and numerical investigations of scale-up effects on the hydrodynamics of slurry bubble columns Zhaoqi Li, Xiaoping Guan,...

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    Experimental and numerical investigations of scale-up effects on the hydrodynamics of slurry bubble columns Zhaoqi Li, Xiaoping Guan, Lijun Wang, Youwei Cheng, Xi Li PII: DOI: Reference:

S1004-9541(16)30436-0 doi: 10.1016/j.cjche.2016.05.009 CJCHE 562

To appear in: Received date: Revised date: Accepted date:

4 June 2015 15 November 2015 23 February 2016

Please cite this article as: Zhaoqi Li, Xiaoping Guan, Lijun Wang, Youwei Cheng, Xi Li, Experimental and numerical investigations of scale-up effects on the hydrodynamics of slurry bubble columns, (2016), doi: 10.1016/j.cjche.2016.05.009

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2015-0276

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Graphic Abstract

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Fluid Dynamics and Transport Phenomena

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Experimental and numerical investigations of scale-up effects on the hydrodynamics of slurry bubble columns*

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Zhaoqi Li(李兆奇), Xiaoping Guan(管小平), Lijun Wang(王丽军)**, Youwei Cheng(成有为), and Xi Li(李希)

Article history:

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Received 4 June 2015

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Department of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, China

Received in revised form 15 November 2015 Accepted 23 February 2016 

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Supported by the National High Technology Research and Development Program of China (2011AA05A205) and the National Natural Science Foundation of China (U1162125,U1361112). ** Corresponding author. E-mail address: [email protected]

Abstract: Experiments and simulations were conducted for bubble columns with diameter of 0.2 m (180 mm i.d.), 0.5 m (476 mm i.d.) and 0.8 m (760 mm i.d.) at high superficial gas velocities (0.12-0.62 ms-1) and high solid concentrations (0-30 vol.%). Radial profiles of time-averaged gas holdup, axial liquid velocity, and turbulent kinetic energy were measured by using in-house developed conductivity probes and Pavlov tubes. Effects of column diameter, superficial gas velocity, and solid concentration were investigated in a wide range of operating conditions. Experimental results indicated that the average gas holdup remarkably increases with superficial gas velocity, and the radial profiles of investigated flow properties become steeper at high superficial gas velocities. The axial liquid velocities significantly increase with the growth of the column size, whereas the gas holdup was slightly affected. The presence of solid in bubble columns would inhibit the breakage of bubbles, which results in an increase in bubble rise velocity and a decrease in gas holdup, but time-averaged axial liquid velocities maintain almost the same as that of the hollow column. Furthermore, a 2-D axisymmetric k- model was used to simulate heterogeneous bubbly flow using commercial code FLUENT 6.2. The lateral lift force and the turbulent diffusion force were introduced for the determination of gas holdup profiles and the effects of solid concentration were

ACCEPTED MANUSCRIPT considered as the variation of average bubble diameter in the model. Results predicted by the CFD simulation showed good agreement with experimental data. Keywords: Bubble column, CFD, Hydrodynamics, Multiphase flow, Scaling-up, Solid concentration

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1. Introduction

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Bubble columns are widely used for a variety of gas–liquid or gas–liquid–solid reactions, including oxidation, hydrogenation, carbonylation, and Fischer-Tropsch synthesis etc. With the

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expansion of industrial processes, the largest diameter of commercial bubble columns has constantly grown up to 10 m diameter. There is considerable interest, both within academia and industry, on scaling-up of bubbly reactors. During the past decades, numerous studies have been conducted for measurement and simulation of hydrodynamic behaviors of bubble column [1-13].

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But these investigations were restricted to low superficial gas velocity (VG < 0.3 ms-1), small column size (D < 0.5 m), and no solid presence. In order to study the scale-up rules of bubble column, experimental and numerical investigations were futher conducted in bubble columns of

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large diameter in the open literature. Tsutsumi et al. [14,15] used hot-wire probe to detect the bubble behaviors and heat-transfer rate in bubble columns with diameters of 0.2, 0.4 and 0.8 m, and set up an artificial neural network (ANN) model to predict the scale-up effect. Nottenkamper

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et al.[16] and Forett et al.[17,18] respectively used wheel anemometer and Pavlov tube to detect

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liquid velocities in bubble columns with diameter up to 1.0 m to highlight the scale effect in slurry bubble columns. However, experimental data were still inadequate in large diameter columns

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(D>0.5 m), and only the normalized profiles of liquid velocity were listed in most works. Simulation of bubble column operated in the heterogeneous or churn-turbulent regime was much difficult due to significant coalescence and breakage of bubbles. Joshi and coworkers [19-24] adopted drift flux theory to model the profile of gas holdup in bubble column by CFD solution of

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model equations. But some empirical parameters had to be determined in advance, including gas-liquid slip velocity VS and others. Krishna and coworkers [25-28] developed a two-class bubble model, in which bubble breakup and coalescence was expressed as the change of proportion of large and small bubbles. Olmos et al. [29], Chen et al. [30], Jokobeson et al. [31] and Bhole et al. [32]made use of the population balance model (PBM) to simulate the distribution of bubble size. The population balance model was more reasonable for understanding of some special phenomena of bubble movements and formations, but it is too difficult to be solved so that it is still impractical for the scale-up of commercial bubble columns under the current computing power. In most CFD simulation works on gas-liquid and gas-liquid-solid flows in the literature, a constant bubble size was used in homogeneous regime. For churn-turbulent flow regime, most attention has been drawn to coupling the PBM into the CFD framework. Due to the high computational cost and difficulties in considering bubble deformation, breakup, and coalescence, the PBM-CFD model is difficult to be solved for commercial scale bubble columns. In this work a 2-D axisymmetric k~ model simulation was conducted, in which an average bubble size was

ACCEPTED MANUSCRIPT assumed in churn turbulent multi-phase flow. In the simulation, bubble size was determined by force balance between buoyance and drag force, and gas holdup profiles were determined by the balance between the lateral lift force and the turbulent diffusion force. In addition, liquid-solid system was regarded as pseudo-homogeneous mixture, and effects of solid concentration were

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considered as the variation of average bubble size. In order to verify the capability of the model in

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predicting the effects of scale, superficial gas velocity and solid concentration, plenty of experiments in a wide range of superficial gas velocities (0.12-0.62 ms-1) and solid concentrations

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(0-30 vol.%) were conducted in bubble columns of 0.2 m, 0.5 m, and 0.8 m diameter.

2. Experimental section

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2.1 Experimental setup

To determine the sensitivity of hydrodynamic characteristics to column diameter and to be able to predict their quantitative extent, measurements were performed in different columns with

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the column diameter as large as possible. In the present work, we used three columns with internal diameter D = 0.2 m, 0.5 m and 0.8 m (Fig. 1).

Experiments were conducted at ambient temperature and atmospheric pressure with the

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air/water system. A 30 mm thick perforated-plate distributor with 2.5 mm holes uniformly distributed was placed at the bottom of the column. The percentages of open area of the distributor

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are controlled within 1% for each bubble column in order that air could be bubble into the columns continuously and uniformly. Provision was made on the column wall for mounting the

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conductivity probe and Pavlov tube at two different positions above the distributor. The gas flow-rates were measured and controlled using a set of pre-calibrated rotameters and needle valves. Superficial gas velocities were regulated in the range of 0.12 - 0.62 ms-1. Tap water and glass

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beads were added into columns in advance. The average particle size of solid particles is 100 m, and solid concentrations were regulated from 0% to 30% by weight. The dispersed slurry height was measured by a ruler, and the clear slurry height was obtained using a side tube.

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(a)

(b)

(c)

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Fig. 1. Schematic views of the bubble column of (a)0.8 m, (b)0.5m and (c)0.2m i.d.

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2.2 Measurement of local gas holdup.

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Voltage /

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An electrical resistivity probe (conductivity probe) was used to measure local gas holdup in bubble column. It was made of IC Ni-Cr alloy wire (diameter of 0.15 mm) and coated with insulating material to the tip. The probe was fixed to a stainless steel support tube elbow as shown in Fig. 2. The data were acquired by a computer with a 16-bit A/D converter card. The data was acquired at a sampling frequency of 2000 Hz for 60 s. The acquired conductivity data time series were subjected to noise removal and phase discrimination, using Labview. A typical signal obtained was shown in Fig. 3, in which high voltage was detected when the probe submerged in liquid but low voltage when the probe contacted with bubbles. A phase discrimination threshold was set to filter the bubble signals, and the threshold magnitude of 10% of the max voltage was set from the comparison of the signal achieved using the probe with the average gas holdup estimated from bed expansion.

Time / s

ACCEPTED MANUSCRIPT Fig. 2 Structure of the conductivity probe

Fig. 3 typical conductive signal for the measurement of local gas holdup

2.3 Measurement of local liquid velocity.

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Local liquid velocities are measured by a modified Pavlov tube (o.d. 6 mm, openings 1 mm)

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based on the literature works [33,34,18]. The structure of the modified Pavlov tube is shown in Fig. 4. The P measuring time for each acquisition is 3 min with a frequency of 135 Hz. The

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instantaneous liquid velocity ui and the time-averaged velocity Vl were calculated in line with a revised formulation considering the influence of gas hold-up [35,36]:

VL  r  

 ui i 1

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 2Pi  K    g g  J  l l   with ui   2Pi    K    J   g g l l 

if Pi  0

(1)

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N

if Pi  0

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in which K, called the momentum conversion factor, can be regressed by calibration experiment as K  1.56/(1  0.5 S ) , and J=1+εG is the momentum exchange factor [34]. Furthermore, the root

mean square (r.m.s.) velocity uσ were calculated as N

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i 1

2

(2)

N

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u 

  ui  VL 

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Bubble column

Pavlov tube

Pressure transducer

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Fig. 4 Structure of the Pavlov tube

3. CFD model for heterogeneous bubbly flow In bubble column, gas bubbles appear to move towards the column centric region while rising upwards. The determination of the gas holdup profile is a key difficulty for the simulation of heterogeneous bubbly flow. Besides the drag force, other two forces, namely lateral lift force and turbulent dispersion force, have great influence on the radial profiles of gas holdup in heterogeneous flow [24]. Therefore, they were introduced for the computation of gas-liquid equations of motion in the CFD model, in spite that there was a dispute regarding the magnitude and even the sign of them [37]. The influence of solid concentration was considered as follows. Firstly, in the range of

ACCEPTED MANUSCRIPT experimental conditions investigated in this work, spatial profiles of the solid concentration are much

uniform.

The

liquid-solid

system

in

bubble

column

could

be

treated

as

pseudo-homogeneous mixture [ 38 - 40 ]. Secondly, many experiments indicated that solid concentration mainly influencees on the gas holdup. Some authors [41-44] believed that the

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addition of solid concentration lead to an increasing bubble size, which is attributed to an increase

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in the apparent suspension viscosity. However, predicting the effect of apparent viscosity on the bubble size is much difficult in CFD simulations, unless bubble coalescence/breakage is

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considered. In view of the complexity of the description of bubble coalescence/breakage, a simpler method was adopted for the consideration of the effect of solid concentration in the work: An average bubble size was assumed and estimated according to experimentally observed average

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gas holdup, and then the effect of solid concentration was equivalent to the variation of the average bubble diameter.



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3.1. Interface force terms

Drag force: Schiller and Naumann’s formula was used in the work [45]

 3 FD =  gl l CD ul  ug (ul  ug ) 4 dB

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(3)

 24(1  0.15Re0.687 ) / Re Re  1000 CD    0.44Re  1000

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(4)



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where Reynolds’ number is defined as Re  d B ul  ug l / l , and dB is the bubble size. Lift force: The radial force depends upon bubble rotation around its own axis, relative

gas–liquid velocity and a liquid velocity gradient, viscous and turbulent shear gradients, radial pressure gradients, bubble shape changes, wake phenomena and the coalescence tendency etc. The

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lateral lift force may be expressed as [19] FL  CL g  lVS  ( ul )

(5)

where CL is the lift coefficient. Joshi [19] recommended that the lift coefficient should be regarded as an adjustable parameter to match experimental results. In order to match the experimentally observed gas holdup profile at superficial gas velocity ranging from 0.12 to 0.62 ms-1 in the bubble columns of 0.2-0.8 m diameter, we regarded the lift coefficient as a function of local phase holdup, and expressed as CL  0.5 



 l2 l

(6)

Turbulent dispersion force: The turbulent dispersion force is also important for the

determination of radial profiles of gas holdup. The turbulent dispersion force was proposed by Lopez [46] based on analogy to molecular dynamics: FTD  CTD l kl   ln l 

(7)

where CTD is the force coefficient, and k is the liquid turbulent kinetic energy per unit of mass.

ACCEPTED MANUSCRIPT CTD was determined as a constant value 2.2 resulted from a good fitting for the present experimental data of overall gas holdup at superficial gas velocity ranging from 0.12 to 0.62 ms-1.

3.2. Governing equations

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In this work, a 2-D axisymmetric two-fluid Euler k-ε model is used. According to the

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literature works [47-49,19], the equations of continuity and motion for the r-z cylindrical coordinate system are summarized in Table 1.

Continuity equation :

(i i)    (i i ui )  0 t

(i i ui )    (i i ui ui )  i p    (i τ i )  i i g  FD,i  FL,i  FTD,i t

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Momentum equation:

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Table 1 Governing equations of axisymmetric k ~ ε model for bubbly flows

(9)

( m k )     ( m um k )    ( eff k )  G  m t k

(10)

 (  m )   2    ( m um )    ( eff  )  C 1 G  C 2 m t  k k

(11)

k2



(12)

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Turbulent viscosity equation: t  C

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k –ε equation:

(8)

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The value of parameters C, k,  , C,1, and C,2 came from the standard k- equations, which are respectively 0.09, 1.0, 1.3, 1.44 and 1.92. In the model, bubble size is assumed as

dB 

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uniform which is determined by force balance between buoyance and drag force 3CD lVs 2 4  l   g  g

(13)

Slip velocity is assumed by average gas holdup

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VS  VG /  g

(14)

While average gas holdup is computed by the correlation given by Wang et al. [13]  g l 2  g  0.186  L B  1 g  L 

0.16

 g  L 2l B 3    2  L 

0.04

 G   0  G 

0.26

 VG   glB

  

0.675

   D  0.95  1  2.03 1  exp     S   0.32    

(15)

3.3. Simulation strategy and conditions The above given conservation equations were solved by a finite volume method by commercial CFD code, FLUENT 6.2.16 (Ansys Inc., US), in double precision mode. The pressure-velocity coupling was resolved using the SIMPLE algorithm. The grids are created by GAMBIT 2.2.30 and exported into FLUENT. To get rid of dependence of discretization resolution, different sets of grids were tried. Fig. 5 shows the radial profiles of time-averaged axial liquid velocities computed with different numbers of grids at superficial gas velocity 0.31 ms-1 in 0.8 m diameter column. Eventually, it was determined that about 1001000 cells were sufficient and effective in all of the investigated situations.

ACCEPTED MANUSCRIPT 1.2 50*500 100*1000 400*4000

0.9

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0.3 0.0

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ul / ms-1

0.6

-0.6 0.0

0.2

0.4

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-0.3

0.6

r/R

0.8

1.0

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Fig. 5. Radial profiles of time-averaged axial liquid velocities computed with different sets of grids

The initial and boundary conditions were set as follows. For the gas phase at the inlet the

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velocity-inlet boundary condition was used, while the pressure-outlet boundary condition was applied on the outlet. Initially the column was filled with liquid up to the level that matches the static liquid height measured in the experiment. To prevent liquid escape from the column the

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computational domain in the axial direction was about 50%-80 % higher than the static liquid height. The additional terms of lift force, turbulent dispersion force were imbedded in FLUENT

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code with user-defined subroutines (UDFs). Transient CFD simulations were carried out using a time step of 1×10-3 s. Generally it took about half an hour in a 64 core work station to reach the

with time.

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quasi-steady state (1×105-2×105 time steps) when almost all physical parameters didn’t change

4. Results and Dicussion

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The experimental findings and their comparison with the CFD simulation were discussed in this section. All measurements are performed in fully developing region to get rid of influence of the gas distributor, about 1 times diameter at least above the gas distributor and 1 times diameter below the free surface. The simulations were performed for all experimental conditions. Hydrodynamic rules on the scaling-up and effects of superficial gas velocity and solid concentration were revealed.

4.1. Flow field The most important characteristics of the flow field in bubble columns are the radial gas holdup profile and the intense liquid circulation. Fig. 6(a) presented a liquid velocity vector graph obtained from the CFD simulations in a 2D axisymmetric coordination at superficial gas velocity of 0.31 ms-1 in the column of 0.8 m i.d. Although, the instantaneous liquid recirculation in a bubble column is very complex and visually seems to be quite chaotic, the time-averaged liquid flow seemed to be quite regular: an upward flow in the centre of the column and a downward flow

ACCEPTED MANUSCRIPT near the wall. In addition, the gas velocity vector graph was presented in Fig. 6(b). It can be found that, there is almost no downward gas flow in the column even near the wall. The profiles of time-averaged gas holdup obtained from the CFD simulations are shown in Fig. 6(c). Higher gas holdups occur in the centre of the column, but lower near the wall. At the

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vicinities of gas spager and free surface, a complex graphic is shown owing to the recirculating

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flow in these areas. In bubble column, fluid is driven by density difference induced by radial non-uniform profiles of gas holdup, and proper prediction of gas holdup profiles is the key point

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for obtaining a stable solution of CFD model. The lift force makes bubbles gathered at the centre of the column; otherwise the turbulent dispersion homogenizes the gas holdup gradient. Simulations indicated that gas holdup profile is sensitive to the selection of force coefficients CL and CTD.

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Furthermore, Figs. 6(d) and (e) provided typical profiles of k and t in the column, which are related with fluid mixing. In fully-developing region, turbulent viscosity maximizes at the centre

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of the column, and then gradually decreases toward the wall, finally quickly falls near the wall. Correspondingly, turbulent kinetic energy presents a dual-peek distribution, whose maximum value occurs at a point (r/R = 0.7) which is close to the inversion point of liquid recirculation

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velocity, where the maximum turbulent shear stress appears. Because the k - ε model is based on isotropic assumption, turbulent kinetic energy in the figures is constructed with a limitation that all

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the normal components of stresses are equal to each other. As a result, there may be some degree of deviations for the calculation of turbulent flow at anisotropic turbulent regions, such as the

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vicinities of gas spager, free surface, and the wall.

(a)

(b)

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(c)

(d)

(e)

Fig. 6. Distributions of flow properties at superficial gas velocity of 0.31 ms-1 in the column of 0.8 m i.d. (a)

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Vector-graph of liquid velocity (ms-1); (b) Vector-graph of gas velocity (ms-1); (c) Contours of gas holdup;

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(d) Contours of turbulent kinetic energy (m2s-2); (e) Contours of turbulent viscosity (Pas)

4.2. Effect of superficial gas velocity

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The superficial gas velocity is a dominant factor that affects hydrodynamic behaviors of bubble column. As shown in Fig. 7, the average gas holdup increases with the increase of the superficial gas velocity while profiles of gas holdup become steeper at high superficial gas velocity than low one. The change of gas holdup profile could be explained by the radial force

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balance of the lift force and the turbulent dispersion force in fully-developing region. As stated in Eq. (5), the lift force is related with the relative slip velocity VS. The appearance of large bubbles at high gas velocity results in the rising of VS between gas-liquid phases. Thus, the increase of the lift force drives more gas bubbles towards the centre of the column. 0.90

-1

VG= 0.12 ms by exp. -1

VG= 0.19 ms by CFD

-1

VG= 0.31 ms by CFD

-1

VG= 0.47 ms by CFD

-1

VG= 0.62ms by CFD

VG= 0.31 ms by exp.

0.75

-1

VG= 0.12 ms by CFD -1

VG= 0.19ms by exp. VG= 0.47 ms by exp. VG= 0.62 ms by exp.

-1 -1

-1

g

0.60 0.45

0.30

0.15 0.0

0.2

0.4

0.6

0.8

1.0

r/R Fig. 7. Radial profiles of gas holdup at different superficial gas velocities in the column of 0.8 m i.d.

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The centre-line liquid velocity ul(0) is a key parameter in describing the liquid circulation of bubble columns. Fig. 8(a) shows that ul(0) increases strongly with superficial gas velocity. It is noted that ul(0) is higher than 1.3 ms-1 in the column of 0.8 m diameter at VG = 0.62 ms-1, more

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than twice the value of superficial gas velocity. Fig. 8(a) also shows the comparisons of the

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hydrodynamic parameter in large diameter column with literature results. The computational values of ul(0) in the column if 1 m diameter is in agreement with experimental data in [16] but

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about 20% lower than measurements in [17]. In addition, liquid velocity profiles also become steeper with the increase of superficial gas velocities (Fig. 8(b)). The flow reversal occurs at the dimensionless radial coordinate of about 0.7 under all investigated conditions. This result is in

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agreement with numerous authors [1,16,25].

2.1

-1

ul / m  s

0.6 0.0

0.2

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0.9

0.4

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VG /ms

-1

0.6

-1

VG= 0.19 ms by CFD

-1

VG= 0.31 ms by CFD

-1

-1

VG= 0.47 ms by CFD

-1

VG= 0.62ms by CFD

VG= 0.31 ms by exp.

1.6

1.2

-1

VG= 0.12 ms by CFD

-1

VG= 0.19ms by exp.

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1.5

-1

VG= 0.12 ms by exp.

2.0

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ul(0) / ms

-1

1.8

2.4

exp. (D = 0.8 m) by CFD model (D = 0.8 m) Forret exp. (D = 1 m) Nottenkmper exp. (D = 1 m) by CFD model (D = 1 m)

-1

VG= 0.47 ms by exp.

-1

VG= 0.62 ms by exp.

1.2 0.8 0.4 0.0

-0.4 -0.8

0.8

0.0

0.2

(a)

0.4

0.6

0.8

1.0

r/R (b)

Fig. 8. Effects of superficial gas velocities on time-averaged axial liquid velocities in the column of 0.8 m i.d. (a) Variation of the centre-line liquid velocities at different superficial gas velocities; (b) Radial profiles of

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time-averaged axial liquid velocities at different superficial gas velocities

Fig. 9(a) provided computational profiles of k at superficial gas velocities of 0.62 ms-1 in the column of 0.8 m i.d. by using different turbulent model. It could be seen that the average error is within 10% among them. Therefore, the commonly used standard k-ε model was chosen to investigate influences of operating conditions on hydrodynamics of bubble columns. The measurements of r.m.s. fluctuation velocities in three coordinate directions were carried out in the work. Turbulent kinetic energy k was calculated in line with the summation of them. Fig. 9(b) provided profiles of k at five superficial gas velocities of 0.12, 0.19, 0.31, 0.47, and 0.62 ms-1 in the column of 0.8 m i.d. As shown in the figure, turbulent kinetic energy is lowest at the wall, and then rises rapidly inwards the column. At the inversion of liquid velocity, a maximum value is reached, then k gradually falls and flattens at the column axis. As shown in the figure, k increases with superficial gas velocities. The centric value of k reaches 0.5 m2s-2 at the superficial gas velocity of 0.62 ms-1, while it is only 0.16 m2s-2 for the superficial gas velocity of 0.12 ms-1.

ACCEPTED MANUSCRIPT 0.8

1.2 -1

-1

VG= 0.12 ms by exp.

VG= 0.12 ms by CFD

-1

-1

VG= 0.19ms by exp.

VG= 0.19 ms by CFD

-1

VG= 0.31 ms by CFD

-1

-1

VG= 0.47 ms by CFD

-1

VG= 0.62ms by CFD

VG= 0.31 ms by exp.

0.9

-1

VG= 0.47 ms by exp.

-1

-2

VG= 0.62 ms by exp.

2

k / m s

0.4 Standard k-e model RNG k-e model Realizable k-e model

0.0

0.2

0.4

0.6

0.8

0.0

1.0

r/R (a)

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2

k / m s

-2

0.6

0.0

0.2

0.4

0.6

0.8

1.0

r/R (b)

Fig. 9. Radial profiles of turbulent kinetic energies in the column of 0.8 m i.d. (a) Comparisons of different

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turbulent models at superficial gas velocity of 0.62 ms-1; (b) Comparisons between standard k-ε model and experimental results at different superficial gas velocities

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4.3 Effect of column diameter

To investigate the scaling effect of bubble column, experiments were conducted in three different columns with diameters of 0.2 m, 0.5m and 0.8 m i.d. Fig. 10(a) shows that average gas

D

holdups are very close in all columns, that is, the averaged gas holdup is slightly affected by

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column size. The curve plotted in the figure seems to be an appropriate correlation for fitting experimental data, which was obtained by Wang et al. [13]. Profiles of gas holdup at superficial gas velocity of 0.62 ms-1 in three columns were showed in Fig. 10(b), in which the profiles of gas

CE P

holdup in the columns of 0.5 m and 0.8 m i.d. are quite similar, but different with the column of 0.2 m i.d. Profile of gas holdup in the smallest column is steeper than others, perhaps due to the wall effect. This trend follows the same similar profile found early by Forret et al. [17] based on

0.5

AC

experiments performed on three columns of 0.15 m, 0.4 m, and 1 m i.d.

0.75

0.60

0.4 0.3

g

g

D=0.2 m D=0.5 m D=0.8 m by CFD model

D =0.2 m D =0.5 m D =0.8 m by Wang (2008)

0.2

0.45

0.30

0.1 0.15

0.0 0.0

0.2

0.4

0.6

VG / ms

-1

(a)

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

r/R (b)

Fig. 10 Effects of column scales on gas holdups (a) Variation of average gas holdup with superficial gas velocities in columns of different sizes; (b) Radial profiles of gas holdups in columns of different sizes at superficial gas velocities of 0.62 ms-1.

ACCEPTED MANUSCRIPT Comparing the centre-line liquid velocities in columns of different sizes (Fig. 11(a)), it could be found that the liquid recirculation velocities enhanced with the growth of column size. For example, the centric liquid velocity reached 1.3 ms-1 in the column of 0.8 m i.d. at superficial gas velocity of 0.62 ms-1, but only 1.0 ms-1 in the column of 0.2 m i.d. Zehner’s [2] and

T

Nottenkamper’s [16] correlation and the CFD of our work provided a good agreement with

IP

experimental results than Riquarts’ [50]. The axial force balance of liquid phase in bubble column

SC R

sheds more light on the understanding of scaling-up effect of bubble column. In the fully-developing region, the axial momentum conservation equation of liquid phase could be simplified as [51] 1   t ul  dP   l l g  l 2     dz R

  

(14)

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where =r/R is the non-dimensional radius. In Eq. (14), the influence of column sizes on the axial liquid velocity is mainly reflected in the term, t/R2. Fig. 11(b) provided simulation results of

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turbulent viscosity t in columns of different scales, which showed that t is approximately proportional to R1.5. Therefore, it wasn’t hard to conclude that unless the change of gas holdup was considered, the radial profile of time-averaged axial liquid velocity was about 0.5 powers

D

dependent on the column scale.

2.5 2.0 1.5

0.0 0.0

AC

1.0

0.5

1.0

Riquarts (1981) Zehner (1986) Nottenkaemper (1983) by CFD model Experimental data

1.5

D / m (a)

2.0

D = 0.2 m D = 0.5 m D = 0.8 m

16

CE P

ul(0)  / ms

-1

3.0

t / Pas

3.5

0.5

20

TE

4.0

2.5

12

8

4

3.0

0 0.0

0.2

0.4

0.6

0.8

1.0

r/R (b)

Fig. 11. Effects of column scales on time-averaged axial liquid velocities and turbulent viscosities at superficial gas velocities of 0.62 ms-1 (a) Prediction and comparison of the centre-line liquid velocities between various publish models; (b) simulation results of turbulent viscosities in three columns

Figure 12 provided profiles of turbulent kinetic energies at the superficial gas velocities of 0.62 ms-1 in three columns. It can be seen that k increases with the growth of column scales. When variations of kinetic turbulent energy were correlated with column diameters, a power-law relation k  R0.5 was obtained. According to Eq. (7), the increase of turbulent kinetic energy with the growth of column scale homogenizes the gas holdup gradient. On the contrary, in view of Fig. 11 and Eq. (5), the large gradient of liquid velocity with the growth of column scale enhances the lateral lift force, which results in the steep trend of gas holdup profile. Combination of the two

ACCEPTED MANUSCRIPT factors leads to the insignificant dependence of gas holdup on column diameters. 0.8 D = 0.2 m D = 0.5 m D = 0.8 m by CFD model

0.7

T IP

0.5

2

k / m s

-2

0.6

0.3 0.2 0.1 0.0

0.0

0.2

0.4

SC R

0.4

0.6

0.8

1.0

NU

r/R

Fig. 12. Effects of column scales on turbulent kinetic energies at superficial gas velocities of 0.62 ms-1 in

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three columns

4.4 Effect of solid concentration

Experiments showed that the main influence of the solid concentration lies in the change of

D

gas holdup. Fig. 13 provided radial profiles of gas holdup at four different solid concentrations in

TE

the column of 0.5 m i.d. It can be seen that averaged gas holdup decreases apparently with the increase of solid concentration. The reason for the decrease of gas holdup is that the addition of

CE P

solid concentration expands the bubble size, which results in an increase in the bubble rise velocity. In addition, the curve shape of gas holdup profiles maintain similar.

0.4

0.3

g

AC

0.5

0.2

0.1

0.0 0.0

S = 0% by exp.

S = 0% by CFD

S = 10% by exp.

S = 10% by CFD

S = 20% by exp.

S = 20% by CFD

S = 30% by exp.

S = 30% by CFD

0.2

0.4

0.6

0.8

1.0

r/R Fig. 13. Effects of solid concentrations on radial profiles of gas holdup under conditions of superficial gas velocities of 0.62 ms-1, four solid concentrations in the column of 0.5 m i.d.

Differencing from gas holdup, time-averaged axial liquid velocities remained almost unchanged with the increase of solid concentration (Fig. 14). The reason for this discrepancy is that the driven force of liquid circulation, namely density difference of fluid, maintains the same due to parallel shift of gas holdup profile. CFD simulations also indicated that the density of solid

ACCEPTED MANUSCRIPT particles and the apparent viscosity of liquid-solid mixture have only slight effect on the time-averaged axial liquid velocity.

1.0

T

0.8

IP

0.4 0.2

SC R

ul / m  s

-1

0.6

0.0 -0.2 -0.4

S = 0% by exp.

S = 0% by CFD

S = 10% by exp.

S = 10% by CFD

S = 20% by exp.

S = 20% by CFD

S = 30% by exp.

S = 30% by CFD

0.0

0.2

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-0.6 0.4

r/R

0.6

0.8

1.0

Fig. 14. Effects of solid concentrations on radial profiles of time-averaged axial liquid velocities under

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conditions of superficial gas velocities of 0.62 ms-1, four solid concentrations in the column of 0.5 m i.d.

5. Conclusions

D

Experiments and simulations were conducted for bubble columns with diameter of 0.2, 0.5

TE

and 0.8 m at high superficial gas velocities (0.12-0.62 ms-1) and high solid concentrations (0-30 vol.%). Some important findings and conclusions were obtained. 

The average gas holdup increase with the increase of the superficial gas velocity. Profiles of

CE P

gas holdup become steep at high superficial gas velocity. Similarly, an identical trend was shown for time-averaged liquid velocity and turbulent kinetic energy. 

The presence of solid in bubble column would apparently inhibit the breakage of bubbles,

AC

which results in an increase in the bubble rise velocity and a decrease in the gas holdup. The curve shape of radial gas holdup profiles maintain similar, and time-averaged axial liquid velocities were slightly affected by solid concentration. 

Scale-up rules of bubble column are mainly due to variation of hydrodynamic parameters with column diameters. The axial liquid velocity remarkably increases in the core of columns with the larger column diameter, whereas the gas holdup is slightly affected. Turbulent kinetic energy increases with column scales. Our study reveals the scale-up rules on the hydrodynamics of bubble columns and shows the

scale-up trends at high superficial gas velocities up to 0.62 ms-1. However, due to the assumption of average bubble size in the CFD model, it is short of research and discussion when referring to bubble behaviors.

Nomenclature CD

drag coefficient

ACCEPTED MANUSCRIPT CL

lift coefficient

CTD dispersion force coefficient C, k,  ,C,1 ,C,2 ,C,3 D

parameters in standard k~ model

column diameter, m drag force, N·m-3

FL

lift force, N·m-3 turbulent dispersion force, N·m-3

g

gravity accelaration, m·s-2

k

turbulent kinetic energy, m2·s-2

N

number of experimental data

p

pressure, Pa

u

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t

Reynolds number (= ρl| ug – ul |dB/μl) flow time, s velocity, m·s-1 superficial gas velocity, m·s-1

Vs

slip velocity of gas-liquid phases, m·s-1

αg

volume fraction of gas phase

αl

volume fraction of liquid phase

αs ε

mass concentration of solid

turbulent kinetic energy dissipation rate, m2·s-3 mixing turbulent viscosity, Pa·s

ρ

density, kg·m-3

g

gas phase

k

phase index

l

liquid phase

mixture of gas-liquid phases

AC

s

CE P

Subscripts

TE

μt

m

D

VG

MA

Re

SC R

FTD

IP

FD

T

dB bubble diameter, m

solid phase

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