Numerical Investigation of GasâLiquid Flow in a Newly Developed

Article Cite This: Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

pubs.acs.org/IECR

Numerical Investigation of Gas−Liquid Flow in a Newly Developed Carbonation Reactor Ruibing Li,†,‡ Shibo Kuang,*,† Tingan Zhang,*,‡ Yan Liu,‡ and Aibing Yu† †

ARC Research Hub for Computational Particle Technology, Department of Chemical Engineering, Monash University, Clayton, Victoria 3800, Australia ‡ School of Metallurgy, Northeastern University, Shenyang 110819, China ABSTRACT: This paper presents a numerical study of the gas−liquid flow inside a novel Venturi carbonation reactor for red mud processing. The model is based on the Eulerian− Eulerian model, with population balance method being used to describe bubble size distribution. The validity of the model is confirmed through different applications. It is then used to analyze the flow and gas dispersion inside the reactor at different liquid flow rates. The numerical results reveal that the new reactor can produce periodic variations of fluid pressure and gas holdup with time. Correspondingly, the ascending liquid flow presents a vortex column, swinging periodically in the radial direction. This flow oscillation becomes more obvious at an increased liquid flow rate, promoting bubble refining and uniform distribution. The results of this study should be useful not only for better understanding the gas−liquid flow but also for designing and controlling this new reactor.

1. INTRODUCTION Red mud is a residue of the Bayer process, which is the main method for extracting alumina from bauxite. Generally speaking, up to 2.5 tons of red mud per ton of alumina is generated in the Bayer process, depending on the type of bauxite and operating conditions.1 Over 120 million tons of red mud with high alkalinity is estimated to be generated per year globally, and the present worldwide accumulation is considered to be up to 2.7 billion tons,2 posing a significant environmental issue in terms of the air, soil, and groundwater pollution. In recent years, some efforts have been made to either decrease the amount of bauxite residues or utilize red mud by recovering alumina, soda, ferric, or titanium oxide, leading to the implementation of a few industrial processes despite their high costs and low yields.3,4 More recently, a novel approach, namely, the calcification−carbonation method, was proposed with the potential of combining red mud treatment with cement production.5−7 In this process, a new Venturi carbonation reactor was used for carbonation, where the hydrogarnet is expected to be efficiently decomposed into calcium silicate, calcium carbonate, and aluminum hydroxide.8 Therefore, a better understanding of this new reactor, especially its inner multiphase flow, is necessary to ensure the successful running of the entire calcification−carbonation process. The Venturi carbonation reactor is one type of self-stirring reactor with a cylindrical vertical cross section and a conical bottom part equipped with a Venturi tube at the bottom (Figure 1). The ascending CO2 gas, which is laterally introduced near the bottom, disperses into bubbles within the reactor. The efficiency of the carbonate reaction is governed by © XXXX American Chemical Society

the contact between bubbles and liquid. Generally speaking, in gas−liquid flow systems, this contact mainly depends on several factors: the bubble sizes and their distribution,9,10 global gas holdup,11 local gas holdup,12 and bubble rising velocity.13,14 Quantifying the characteristics of these parameters under different conditions is therefore very useful for achieving a reliable design, control, and optimization of the involved flow system as well as its scale-up.15 This is particularly true for the new reactor considered in this study, where the gas−liquid flow behaviors are not yet clear, especially at a quantitative level. In the past decades, various measuring techniques such as pressure difference techniques,8,16 high-speed camera,17 double optical probes,18,19 particle image velocimetry (PIV) technology,20 and tomography techniques21,22 have been proposed to study the hydrodynamic behaviors of gas−liquid flows. These techniques provide useful information to better understand the gas−liquid flows under different conditions; however, they may have certain limitations. For example, the full measurement of the transient flow properties related to fluid velocities and gas dispersion inside an entire flow system is generally difficult and in many cases involves high costs. However, such detailed information is highly desirable for the present reactor. Numerical modeling and simulations provide promising alternatives. For example, the multiple-relaxation-time−lattice Boltzmann method (MRT-LBM) has been developed to study Received: Revised: Accepted: Published: A

September 27, 2017 December 6, 2017 December 8, 2017 December 8, 2017 DOI: 10.1021/acs.iecr.7b04026 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

Figure 1. Geometry and representative CFD mesh of the Venturi carbonation reactor.

2. MATHEMATICAL MODEL 2.1. Model Description. The present mathematical model is a transient three-dimensional Eulerian−Eulerian model. Therefore, each phase is described by separate conservation equations of mass and momentum. In the model, the k−ω based shear stress transport (SST) model is used to describe liquid turbulence, as this model provides a more realistic prediction of the void fraction close to the wall.40 An algebraic or zero-equation turbulence model is used to consider gas turbulence. This gas turbulence model can decrease the computer load significantly and at the same time give a good prediction on fluid flow pattern and velocity profiles, as suggested by the work of Chen et al.41 To describe the size distribution of bubbles, the MUSIG population balance model is used, which employs multiple discrete bubble size groups to represent the population balance of bubbles. The interactions between the gas and liquid phases include the drag force, lift force, turbulent dispersion force, and wall lubrication force. Table 1 summarizes the equations of the model, which is in principle similar to the multiphase flow models reported elsewhere,41−48 where the model details can be found and thus are not included here for brevity. 2.2. Experimental and Simulation Conditions. Figure 1 shows the geometry of the carbonation reactor, and its dimensions are listed in Table 2. The main feature of the reactor is the Venturi tube, which is used as a liquid inlet at the bottom. The gas is laterally introduced into the reactor near the bottom and mainly escapes from the outlet at the top, whereas liquid and bubbles are removed from the right side of the outlet. To perform experiments, a full-scale water-model experimental system was established. In the experiment, water was used as the liquid phase, and CO2 as the gas phase. The volume flow rate of gas was fixed at 4 m3/h, and that of the liquid (Ql) was varied from 2 to 5.38 m3/h. For model validation, an electrical conductivity probe was used to measure bubble diameters. The probe was located axially, 0.115 m away from the top of the reactor (Figure 1). The simulation conditions follow those of the experiments. However, the liquid flow rate in the simulations is increased to 7.8 m3/h to examine its effect on the gas dispersion properties

the dynamics of a single bubble, a bubble pair, and bubble swarm.23 In recent years, the volume-of-fluid (VOF) method, which traces the gas−liquid interface, was used to predict the bubble sliding velocity, bubble diameter, and motion of different sized bubbles in an air−water system.24,25 Such a model was also applied to the highly dynamic gas−metal−slag system where the intensive interactions between gas and liquids occur due to the presence of supersonic jets.26 Besides, the Eulerian−Eulerian model with a uniform bubble size has been successfully developed to predict the complicated gas−liquid flows inside different metallurgical reactors.27,28 A similar model has also been used to describe gas−liquid−solid flows.29 On the other hand, the dual-bubble-size (DBS) model, which couples the Eulerian−Eulerian model with the energy-minimization multiscale (EMMS) method for the consideration of stability condition, has also been developed to predict the radial distribution of gas holdup, global gas holdup, and two-phase flow field.30−33 Such a model has also been used to formulate a new drag force correlation of bubbles,34 as well as combined with population balance model to predict the behaviors of different sized bubbles in an internal-loop airlift reactor.35 In addition, the inhomogeneous multiple size group (MUSIG) model36 has been applied to investigate the behaviors of different sized bubbles and related gas and liquid flow dynamics under different flow systems.27,37,38 In essence, this MUSIG model is an Eulerian−Eulerian model that takes into account the effects of bubble breakup and coalescence. These complicated bubble behaviors can also be modeled by the Euler−Lagrange framework, where all individual bubbles are traced.39 In this study, the gas−liquid flow inside the novel carbonation reactor is studied by means of the MUSIG model. The applicability of this model is first confirmed, following which the model is used to characterize the flow and gas dispersion, especially bubble sizes that are of main interest in practice. Also, the effect of liquid flow rate is quantified to identify the flow-rate range that benefits the performance of the novel reactor. B

DOI: 10.1021/acs.iecr.7b04026 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research Table 1. Governing Equations of the Present Model item

formula

mass equation liquid

∂(α lρ l ) ∂t

gas

+ ∇·(αlρl ul) = 0

∂(αgρg fi ) ∂t

+ ∇·(αgρg ugfi ) = Sdi

Sdi = BC + BB − DC − DC momentum equation liquid ∂(α lρ l ul)

+ ∇·(αlρl ulul) = − αl∇P + αlρl g + ∇·[αlτl] + Flg

∂t

gas ∂(αgρg ug) ∂t

liquid turbulence model k-equation

+ ∇·(αgρg ugug) = − αg∇P + αgρg g + ∇·[αgτg] + Fgl

⎡ + ∇·(αlρl ulk) = ∇·⎢ μ l + ⎣

∂(α lρ l k)

(

∂t

ω-equation ∂(α lρ l ω) ∂t

⎡ + ∇·(αlρl ulω) = ∇·⎢ μ l + ⎣

(

μtl σk

)∇k⎤⎦⎥ + P − β′α ρ kω + P

μtl σω

k

)∇ω⎤⎥⎦ + α

gas turbulence model41

MUSIG breakup rate

ω l k Pk

μtg =

bubble population balance model42

∂ni ∂t

43

kb

l l

− βαlρl ω2 + Pωb

ρg μ tl ρ l σpra

+ ∇(ugni) = BC + BB − DC − DB N

BB = ∑ j = i + 1 Ω(vj:vi)nj and DB = Ωini ⎛ ε ⎞1/3 where Ω(vj:vi) = 0.923FB(1 − αg)nj⎜ 2 ⎟ ⎝ db , j ⎠ 1

∫ξ

(1 + ξ)2

11/3 min ξ

⎛ 12(f 2/3 + (1 − f 2/3 ) − 1)σ ⎞ ⎟ dξ exp⎜ BV 2/3 5/3BV11/3 2ρl ε db , j ξ ⎝ ⎠

MUSIG coalescence rate44

BC =

1 2

i

i

N

∑ j = 1 ∑k = 1 ηjkixijninj and DC = ∑ j = 1 xijninj

⎧ (vj + vk) − vi − 1 ⎪ vi − 1 < vj + vk < vi vi − vi − 1 ⎪ where ηjki = ⎨ vi + 1 − (vj + vk) ⎪ vi < vj + vk < vi + 1 vi + 1 − vi ⎪ ⎪ ⎩ 0 else

⎛ tij ⎞ π xij = FC 4 [di + dj]2 (|u ti|2 + |u tj|2 )0.5 exp⎜− τ ⎟ ⎝ ij ⎠ drag force45

FD = − 4 αgρl dD |ug − ul|(ug − ul)

lift force46

FL = αgρl C L(ug − ul) × (∇ × ul)

3

C

b

⎧ ⎪ min[0.288 tanh(0.121Rep f (Eo′))] Eo′ ≤ 4 ′ C L = ⎨ f (Eo′) 4 < Eo′ ≤ 10 ⎪ ⎩− 0.27 10 < Eo′ wall lubrication force47

FWL = −

αgρ l (ug − ul) DS

⎛ D ⎞ max⎜0, C W1 + C W2 y S ⎟n w and DS = 1 ⎝ w⎠ vt,g ⎛ ∇ α l

turbulent dispersion force48

⎜ t,g ⎝ α l

FTD = C TDC D σ

fully. The reactor is meshed with hexahedral grids. To obtain grid-independence numerical solution, tests are conducted at the liquid flow rate of 5.38 m3/h to select suitable grid sizes referring to bubble size as it is of great importance to reactor performance. For this purpose, the grid schemes of 100 050, 168 135 and 202 252 hexahedra are considered at the initial stage of this study. These simulations respectively predict the time-averaged bubble size of 3.65 mm, 3.86 mm, and 3.88 mm against the experimental value of 4 mm at the measuring point

−

∇ αg ⎞ αg

⎟

⎠

and C TD = 1

of the probe. Clearly, the moderate grid number (168 135) is adequate to ensure grid-independence results and thus selected in simulating the Venturi carbonation reactor. In the simulations, a “velocity inlet” condition is chosen for both the gas and liquid inlets. A pressure boundary condition is applied to the right side of the outlet, and a degassing boundary condition to the top side of the outlet. The pressure at the pressure boundary is set to the ambient atmospheric pressure. The wall boundaries are set to a no-slip condition for water C


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position at the height of 36 tube diameters from the bottom. Note that the radial position shown is normalized by the tube diameter. Figure 2a shows that the void fraction or gas holdup is maximum near the wall rather than at the center of the tube. Both the gas and liquid velocities show a plateau at the center but a sharp decline near the wall (Figure 2c and Figure 2d). It is the decreased rising velocity of the bubbles accumulating near the wall that increases the gas holdup there. Here, the numerical and experimental results are in reasonable agreement with each other. The same can be stated for the Sauter mean diameter (Figure 2b). Overall, the prediction errors are in the range of 1.7−52.5%, 0.35−14.6%, 2.2−9.1%, and 0.7−13.7%, respectively, for the gas holdup, bubble diameter, gas velocity, and liquid velocity. It is of interest to note that both the experiment and simulation show that bubble diameter is nearly uniform in the radial direction; however, it increases first and then decreases near the wall. This result can be explained as follows. On the one hand, driven by lift forces, small bubbles migrate toward the wall, enhancing the coalescence of bubbles, as suggested by Cheung et al.51 On the other hand, the turbulence dissipation rate (ε), calculated by turbulence eddy frequency (ω) and turbulence kinetic energy (k) by the expression of ε = β′ωk, contributes to the behaviors of bubbles near the wall. It was found that the increase in the dissipation rate promotes the bubble breakup.52,53 As such, the radial profile of turbulence dissipation rate is also examined, and the results are included in Figure 2b. As seen from this figure, the turbulence dissipation rate is nearly uniform in the radial direction but drastically increases near the wall, leading to the generation of smaller bubbles there. Therefore, it is the opposite effects of lift force and turbulence dissipation rate that lead to the appearance of bubble diameter peak near the wall. Figure 3 compares the predicted air plumes and liquid velocities with the experimental data obtained on the middepth plane by Sokolichin et al.,50 using laser Doppler anemometry (LDA) for the gas−liquid flow within a flat column airlift loop reactor. To highlight the importance of the MUSIG model in the current modeling, the simulation was performed with and without the MUSIG model. Clearly, when the MUSIG model is omitted, the bubbles do not disperse to the right of the central wall (Figure 3c) unlike in the case of the experiment (Figure 3a). Conversely, when the MUSIG model

Table 2. Dimensions of Venturi Carbonation Reactor components geometrical parameter

symbol

value (mm)

diameter of cylindrical section diameter of liquid outlet diameter of carbonation reactor throat diameter of liquid inlet throat diameter of liquid inlet diameter of gas inlet length of cylindrical section length of conical section length of carbonation reactor

D1 D2 D3 D4 D5 D6 H1 H2 H3

240 100 30 14.7 42 10 675 240 1183

while free slip condition for gas. The automatic near-wall treatment is adopted for the liquid phase, which allows for a smooth shift from a low-Re near wall formulation to a standard wall function formulation depending on the grid resolution near the wall. Note that our tests suggest that the Venturi tube of the reactor always breaks up the continuous gas into small bubbles less than 0.5 mm, and the use of any bubble sizes larger than 0.5 at the inlet produces nearly the same results. To cover a wide range of flow conditions and at the same time facilitate the Venturi tube to generate bubble fines from continuous gas to gain efficient calculations, the bubble size is set to 2.5 mm at the inlet. All the simulations are conducted using the transient solver in ANSYS CFX V16 with a time step of 0.0005 s. The physical time considered is 58 s for each simulation. Within this period, the flow can be established.

3. RESULTS AND DISCUSSION 3.1. Model Applicability. Confirming the validity of a numerical model before applying it to numerical experiments is necessary. For this purpose, the gas−liquid flows within three systems are simulated and compared against the measurements, which include a vertical round tube,49 a flat column airlift loop reactor,50 and the present carbonation reactor. Figure 2 compares the simulation results with the experimental ones obtained by Hibiki et al.49 in the case of the bubbly flow through the vertical tube with the internal diameter of 50.8 mm. Here, the gas holdup, bubble diameter, and gas and liquid velocities are shown as a function of radial

Figure 2. Comparison of simulated and measured time-averaged results when gas and liquid inlet superficial velocities are 0.0473 and 0.986 m/s, respectively: (a) gas holdup, (b) bubble diameter, (c) gas velocity, and (d) liquid velocity. D


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Figure 3. Comparison of the experimental and numerical results when the gas flow rate is 4 L/min in the column airlift loop reactor: (a) measured air plume photograph, (b) measured liquid velocity vectors, (c) calculated air holdup without using the MUSIG model, (d) calculated air holdup using the MUSIG model, as well as calculated liquid velocity vectors (e) at six heights and (f) within the axial plane using the MUSIG model.

Figure 4. Comparison between the calculated and measured time-averaged liquid velocities, corresponding to the sampling positions in Figure 3e in the case of column airlift loop reactor.

heights corresponding to Figure 3e are considered, and the results are shown in Figure 4. Generally, the trends of the velocity profiles at different heights can be well predicted. The prediction errors range from 0.1% to 80%. The large errors come from a few data points near the top of the reactor (lines 1 and 2), where a strong free-surface flow exists but is not modeled in this study. Figure 5 shows the comparison of the predicted bubble sizes with the measurements by the electrical probe for the Venturi carbonation reactor at four different liquid flow rates (2, 3, 4, and 5.38 m3/h). In this figure, the results are averaged over the period after the flow is established. The bubble size decreases with increasing flow rate, and the simulation results agree well with the experimental results, with the prediction errors being less than 3.5%. Overall, all the results obtained in this study suggest that the present model can satisfactorily predict the behaviors of different gas−liquid flows, as well as the distribution of bubble sizes which is a key parameter needed for the design and control of the present reactor. 3.2. Flow Characteristics of the Carbonation Reactor. The gas holdup is associated with the coalescence and breakage of bubbles and thus the variation in the bubble sizes, which in

Figure 5. Time-averaged bubble diameter as a function of liquid flow rate in the case of Venturi carbonation reactor.

is taken into account, the numerical results (Figure 3d) match much better with the experimental observation (Figure 3a). In further support of the model, nearly the same liquid flow pattern can be observed from both the simulation (Figure 3e and Figure 3f) and experiment (Figure 3b). To make a quantitative comparison, the liquid velocities at different E


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Figure 8. Temporal variations of pressure at different heights.

Figure 6. Temporal variations of the gas holdup, bubble diameter, as well as gas velocity and pressure at z = −0.745 m when the liquid flow rate is 6 m3/h.

turn affects the performance of the present reactor. Figure 6 shows how the CO2 gas holdup typically changes with time at

Figure 7. Snapshots showing representative (a) liquid flow fields and (b) gas holdup distributions during one period of flow oscillations, corresponding to Figure 6. F


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Figure 9. Snapshots of the pressure distributions at different times, corresponding to Figure 6.

the cross-sectional plane z = −0.745 m. This figure also includes the temporal variations of bubble size, as well as gas velocity and pressure. Here, the results are the average over the cross-sectional area. Only a representative case is analyzed; however, the main findings can apply to other conditions. It is of great interest to note that the gas holdup varies periodically with time after 5 s. Within one period, a large peak appears first, followed by several much smaller waves. Corresponding to this variation of the gas holdup, the bubble size and gas velocity and pressure all oscillate periodically, although their oscillation patterns are different from each other. These oscillations of flow properties are related to each other and should be mainly attributed to the use of Venturi tube in the reactor design. To confirm this understanding, the spatial variations of the gas holdup together with the liquid flow are examined at several representative times within one period, namely, at the points A, B, C, D, E, and F shown in Figure 6, and the results are given in Figure 7. Figure 7 shows that the liquid flow presents a vortex column or large eddy inside the reactor, which swings periodically in the radial direction as liquid ascends from the bottom to the top of the reactor. The gas holdup in the vortex column is generally higher than that outside the column. Notably, the ascending vortex is pushed by the replenishing fluid from the reactor bottom. Most of the fluid is spilled out from the overflow outlet on the right, whereas some of the fluid rises to the top of reactor and generates a downward reflux under the effect of gravity. The downward reflux affects the upward flux and generates an extrusion force, leading to a skewing, rotation, and swing of fluid. The reflux can increase the contact area and contact time between gas and liquid phases and thus will favor the carbonation reaction ultimately. Some gas does not escape from the outlet at the top of the reactor and returns with the reflux, thus increasing the gas holdup. As such, the swinging vortex is beneficial for mixing gas with liquid and dispersing gas from the center to the outside, which in turn drags liquid from the bottom to the top of the reactor. Figure 8 shows the temporal variations of pressure at different heights along the reactor axis. Expectedly, the pressures at different heights all fluctuate with time periodically. It is of interest to note that in the Venturi part, the pressure is over 57 kPa at z = −1.26 m, but it decreases sharply to less than −1.7 kPa at z = −1.21 m. This result well supports the design principle of the new reactor, where gas is required to be sucked into the device from the gas inlet, while the liquid is being

pumped from the bottom. Notably, the magnitude of the pressure fluctuation gradually decreases from the bottom to the top of the reactor, which reflects the extents of the interaction between the gas and liquid at different height levels. Generally, a higher liquid velocity increases the negative pressure at the gas inlet, which causes a greater amount of gas to be sucked in, blocking the liquid flow, and vice versa. Such gas−liquid interactions should account for the swinging flow inside the reactor. Figure 9 shows typical pressure distributions within the reactor during one period of the flow oscillations. As seen from this figure, the pressure distribution in the bottom half of the reactor (the green region) varies with time. However, in the upper half of the reactor (yellow/red regions), only slight pressure changes with time are observed. Moreover, the pressure variations in the lower part take place in the radial and axial directions; conversely, it takes place only in the axial direction in the upper part of the reactor. This result indicates that the phenomenon of flow swinging may be controlled by the gas−liquid interaction near the bottom part of the reactor. 3.3. Effect of Liquid Flow Rate. The liquid flow rate may have a significant effect on the gas−liquid contact and thus the carbonation reactions in the present reactor. A better understanding of the role of liquid flow rate is useful for achieving the optimum design and control of the reactor. For this reason, the influences of liquid flow rate on the flow properties such as gas bubble size, gas holdup, as well as gas and liquid velocities are investigated. The results are shown in Figures 10−15. Figure 10 shows how liquid flow rate affects the timeaveraged number and volumetric percentage of different sized bubbles in the Venturi, conical, and cylindrical parts of the reactor. Here, the number of jth group of bubbles in ith reactor ⎛ ∑nsi εckεck ,j) ⎞ ⎟, where n section (Nbj,si) is determined by Nbj , si = ⎜ k =0V si ⎝ ⎠ bj is the number of CFD cells in section i, εck is the gas hold of kth CFD cell, εck,j the volumetric percentage of jth group of bubbles among all the bubbles in kth CFD cell, and Vbj is the volume of a single bubble of jth group. For a given liquid flow rate, the number of bubbles largely increases with the decrease of bubble diameter in all the sections, which is favorable for reactions. Notably, the volumetric percentage of a bubble group with a uniform diameter presents peaks within the Venturi and cylindrical parts; however, it increases drastically with the G


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Figure 11. Average bubble diameter as a function of liquid flow rate at different heights.

Figure 12. Comparison of the pressure fluctuations at the liquid flow rates of 4 and 6 m3/h at z = −1.21 m.

Figure 10. Bubble size distributions at different liquid flow rates within the section of (a) cylinder, (b) cone, and (c) Venturi tube.

decrease of bubble diameter. This is because the continuous gas tends to be fully broken up into very fine bubbles in the conical section due to the intensive interactions between the gas and liquid phases resulting from the use of the Venturi tube; while rising up toward the top, these fine bubbles may somewhat become larger. Notably, within the cylindrical part where the reactions are to take place mainly, either the number or volumetric percentage of the finest (0.5 mm) bubbles increases with the increase of liquid flow rate. This result suggests that an increased liquid flow rate helps promote bubble refining. Figure 11 shows the variation of bubble size with the liquid flow rate at different axial positions in the cylindrical part. Here, the results are the averaged values over the cross-sectional area. As seen from Figure 11, for a given liquid flow rate, the bubble

Figure 13. Average gas holdup as a function of liquid flow rate at different heights.

size increases from the bottom to the top. At a lower position, the flow oscillation is stronger as reflected from Figure 8, which results in the mixing between the liquid and gas phases and breaking up of bubbles into smaller ones. Although the oscillation amplitude reduces at higher positions, the increased bubble size along the axial position enhances the possibility of coalescence of bubbles, thus further increasing the bubble size at higher positions. H


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heterogeneous (Figure 7), particularly when the fluid flow rate is low (e.g., 2 and 3m3/h). Under such a condition, with the increase of the fluid flow rate, the chance for gas bubbles to come in contact with each other for coalescence is enhanced by the intensified flow oscillation, increasing bubble sizes. Figure 13 shows the variation of the time and cross-section averaged gas holdup at different heights as a function of the liquid flow rate. As seen from the figure, the variation of the gas holdup along the axial direction is larger at lower liquid flow rates; it indicates that the gas distribution is less uniform along the axial direction at these low flow rates. This figure also shows that the effect of liquid flow rate on the gas holdup has become less significant in the upper part of the cylinder than in the lower part. When the liquid flow rate is increased, the gas holdup in the lower part of the cylinder (z ≤ −0.545) first increases to a peak value and then decreases gradually. Conversely, the gas holdup in the upper part (z ≥ −0.445) shows a monotonic decrease as the liquid flow rate is increased. These different trends can be explained as follows. Generally, the gas distribution is highly heterogeneous over the crosssectional area in the lower part of the cylinder. A larger liquid flow intensifies the flow oscillation (as seen from Figure 12). This reduces the heterogeneity in the gas distribution and promotes the mixing of gas and liquid phases, increasing the gas holdup in the lower part of the cylinder. Conversely, the increase in the liquid flow rate enhances the entrapment of gas in the liquid flow toward the outlet, which reduces the gas holdup in the liquid phase along the reactor axis. These two opposite effects change the gas holdup nonmonotonically in the lower part of the cylinder as the liquid flow rate varies. Differently, in the upper part of the cylinder, the gas distribution is relatively uniform, and only the capacity of liquid in entraining gas dominates the behavior of gas holdup at different liquid flow rates. Thus, a monotonic change is observed when liquid flow rate is varied. Figures 14 and 15 show the axial profiles of liquid and gas velocities, respectively, at different fluid flow rates. The results in Figure 14 reveal that for a given the liquid flow rate, the liquid velocity in the axial direction sharply decreases in the lower part but reaches a uniform value in the upper part. This sharp decrease can be due to the presence of the conical section and the Venturi tube. When the liquid flow rate is increased, the liquid velocity at a given axial position generally increases to a maximum and then decreases when z < −0.65 but increases monotonically when z > −0.55. Figure 15 shows that the gas velocities vary in similar trends to those of the liquid velocities. An exception is that when the liquid flow rate is 2 m3/h, the change in the gas velocity in the axial direction is largely negligible compared to that of liquid velocity. Another difference is that the gas velocity presents the maximum near the outlet and largely remains constant at the upper part.

Figure 14. Axial variations of the average liquid velocity at different liquid flow rates.

Figure 15. Axial variations in the average gas velocity at different liquid flow rates.

The results shown in Figure 11 also reveal that the bubble sizes at a given height in the cylindrical section do not change significantly at liquid flow rates higher than 5.38 m3/h. In other words, the bubble sizes are more uniform at relatively large liquid flow rates. In addition, it is of great interest to note that the changes in the bubble size have three types of trends when the liquid flow rate is increased: (a) the bubble size increases first to a maximum (Ql = 4 m3/h) and then decreases to a constant at the lower part of the cylinder (z = −0.81 m in Figure 11); (b) the bubble size initially decreases and then becomes constant at the middle part (z = −0.745, −0.645, −0.545, and −0.445 m in Figure 11); and (c) the bubble size initially does not change much, then decreases, finally becoming constant at the upper part (z = −0.345 and −0.245 m in Figure 11). All these results suggest that the increase in the liquid flow rate is useful for bubble refining, which is effective when the flow rate is in the range from 3 to 7 m3/h under the conditions considered. The complicated relationship between the bubble size and liquid flow rate can be explained as follows. As the liquid flow rate increases, the amplitude of the pressure fluctuations becomes much larger, although the fluctuation frequency itself is smaller (Figure 12). Accordingly, the flow oscillation is intensified, enhancing the self-stirring and bubble refining. However, this effect is weakened at lower positions in the cylindrical part where the gas distribution is highly

4. CONCLUSIONS The gas−liquid flows and gas dispersion inside a novel carbonation reactor have been studied by the Eulerian− Eulerian model facilitated with the population balance model. The major findings of this study are as follows: 1. The mathematical model offers an effective method to study the gas−liquid flow in the new carbonation reactor for red mud processing. The applicability of the model can be confirmed by the satisfactory agreement between I


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Industrial & Engineering Chemistry Research fi f BV FB Flg, Fgl FC FD FL FWL FTD g h0 hf k N Nbj,si n ni nsi nj nw P Pεb Pk Pkb Ql Sdi

numerical and experimental results in terms of gas and liquid velocities, bubble size, and gas holdup under different conditions. 2. The Venturi tube of the reactor generates a significant negative pressure which helps readily suck in the gas from the lateral side. The pressure and gas holdup periodically varies with time, inducing an oscillating gas− liquid flow. Due to these variations, a gas column swings in the radial direction when gas and liquid flow from the bottom to the top of the reactor. These flow characteristics play an important role in self-stirring and bubble refining. They also favor the uniform distribution of gas bubbles in the axial direction and hence help promote the efficiency of the carbonation reactor. 3. An increase in the liquid flow rate promotes the bubble refining and gaining a uniform distribution. The result is true only within a certain range of liquid flow rates due to the presence of the significant heterogeneous gas−liquid flow region in the lower cylinder part of the reactor as well as the weakened flow oscillation at a lower liquid flow rate. Finally, it should be pointed out that the gas−liquid flow within the carbonation reactor is affected by many pertinent variables related to operational conditions and reactor geometries. The present study considers only liquid flow rate. In order to fully optimize the reactor, a systematic study is needed to investigate the effects of all the important variables and their interplays. Some work has been planned in this direction, with the findings reported in the future.

■

t tij u ut xij yw

AUTHOR INFORMATION

Corresponding Authors

*S.K.: e-mail, [email protected]. *T.Z.: e-mail, [email protected].

scalar variable of the dispersed phase breakage volume fraction breakage calibration factor total interfacial forces (N) coalescence calibration factor drag force (N) lift force (N) wall lubrication force (N) turbulent dispersion force (N) gravitational vector (m·s−2) unitial film thickness (m) critical film thickness (m) turbulence kinetic energy (m2·t−2) number of bubble groups Number of jth group of bubbles average number density of gas phase number density of ith group of bubbles number of CFD cells in ith reactor section number density of jth group of bubbles outward vector normal to the wall surface pressure (Pa) influence of the buoyancy forces production rate of turbulence influence of the buoyancy forces Liquid volume flow rate (m3·h−1) net change in the number density distribution due to coalescence and breakage processes time (s) time required for two bubbles to coalescence (s) velocity vector (m·s−1) turbulent velocity (m·s−1) coalescence rate of ith and jth groups of bubbles Adjacent point normal to the wall surface

Greek

α β, β′ ε εck εck,j

ORCID

Shibo Kuang: 0000-0002-2969-9420 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to the National Natural Science Foundation of China (NSFC) (Grants U1202274, U1402271, 51274064, and 51422403), Fundamental Research Funds for the Central Universities (Grants N130102002 and N140204013), China Scholarship Council (Grant 201306080062), and the Australian Research Council (ARC) (IH140100035) for financial support.

ηjki μ μt vi vj vk νt,g ξ

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LIST OF SYMBOLS BB birth rate due to breakup BC birth rate due to coalescence CD drag coefficient CL lift force coefficient CTD turbulent dispersion coefficient Cw1, Cw2 wall lubrication constants Cμ,BI model constant d diameter (m) db,i diameter of ith group of bubbles (m) DB death rate due to breakup DC death rate due to coalescence DS Sauter mean bubble diameter (m) db,j Bubble diameter (m)

ρ σ σk σpra σt,g τ τij ω Ωi

volume fraction mModel constants turbulent dissipation rate gas hold of kth CFD cell volumetric percentage of jth group of bubbles among all bubbles of kth CFD cell transfer coefficient between bubble groups arising from bubble breakup molecular viscosity (kg·m−1·s−1) turbulent viscosity (kg·m−1·s−1) volume corresponding to ith group of bubbles volume corresponding to jth group of bubbles volume corresponding to kth group of bubbles turbulent kinematic viscosity (m2·s−1) size ratio between an eddy and a bubble in the inertial subrange density (kg·m−3) surface tension turbulence model constant of k equation turbulent Prandtl number turbulent Schmidt number shear stress (Pa) time constant for two bubbles turbulence eddy frequency breakup rate of ith group of bubbles

Subscripts

l liquid phase g gas phase J


Article


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stress with the coaxial mixers composed of two different central impellers and an anchor. Chem. Eng. Process. 2017, 111, 101. (22) Assima, G. P.; Hamitouche, A.; Schubert, M.; Larachi, F. Liquid drainage in inclined packed beds-accelerating liquid draining time via column tilt. Chem. Eng. Process. 2015, 95, 249. (23) Shu, S. L.; Yang, N. Direct numerical simulation of bubble dynamics using phase-field model and lattice Boltzmann method. Ind. Eng. Chem. Res. 2013, 52, 11391. (24) Zhang, K. Y.; Feng, Y. Q.; Schwarz, P.; Wang, Z. W.; Cooksey, M. Computational fluid dynamics (CFD) modeling of bubble dynamics in the aluminum smelting process. Ind. Eng. Chem. Res. 2013, 52, 11378. (25) Zhao, Z. B.; Feng, Y. Q.; Schwarz, P.; Witt, P.; Wang, Z. W.; Cooksey, M. Numerical modeling of flow dynamics in the aluminum smelting process: comparison between air−water and CO2−cryolite systems. Metall. Mater. Trans. B 2017, 48, 1200. (26) Li, M. M.; Li, Q.; Kuang, S. B.; Zou, Z. S. Computational investigation of the splashing phenomenon induced by the impingement of multiple supersonic jets onto a molten slag−metal bath. Ind. Eng. Chem. Res. 2016, 55, 3630. (27) Song, T.; Jiang, K. X.; Zhou, J. W.; Wang, D. Y.; Xu, N.; Feng, Y. Q. CFD modelling of gas−liquid flow in an industrial scale gas-stirred leaching tank. Int. J. Miner. Process. 2015, 142, 63. (28) Feng, Y. Q.; Yang, W.; Cooksey, M.; Schwarz, M. Development of bubble driven flow CFD model applied for aluminium smelting cells. J. Comput. Multiphase Flows 2010, 2, 179. (29) Ghodrat, M.; Qi, Z.; Kuang, S. B.; Ji, L.; Yu, A. B. Computational investigation of the effect of particle density on the multiphase flows and performance of hydrocyclone. Miner. Eng. 2016, 90, 55. (30) Chen, J.; Yang, N.; Ge, W.; Li, J. Modeling of regime transition in bubble columns with stability condition. Ind. Eng. Chem. Res. 2009, 48, 290. (31) Yang, N.; Wang, W.; Zhao, H.; Ge, W.; Li, J. H. Structureoriented multi-scale simulation of two-phase flowsmethodology and application. Presented at the 15th International Conference on CFD in the Process Industries, CSIRO, Melbourne, Australia, December 13− 15, 2006. (32) Yang, N.; Wu, Z. Y.; Chen, J. H.; Wang, Y. H.; Li, J. H. Multiscale analysis of gas-liquid interaction and CFD simulation of gasliquid flow in bubble columns. Chem. Eng. Sci. 2011, 66, 3212. (33) Zhou, R.; Yang, N.; Li, J. H. CFD simulation of gas-liquid-solid flow in slurry bubble columns with EMMS drag model. Powder Technol. 2017, 314, 466. (34) Xu, T. T.; Jiang, X. D.; Yang, N.; Zhu, J. H. CFD simulation of internal-loop airlift reactor using EMMS drag model. Particuology 2015, 19, 124. (35) Yang, N.; Xiao, Q. A mesoscale approach for population balance modeling of bubble size distribution in bubble column reactors. Chem. Eng. Sci. 2017, 170, 241. (36) Yuan, Y.; Li, X. D.; Tu, J. Y. Numerical modelling of air− nanofluid bubbly flows in a vertical tube using the multiple-size-group (MUSIG) Model. Int. J. Heat Mass Transfer 2016, 102, 856. (37) Liu, Z. Q.; Qi, F. S.; Li, B. K.; Cheung, S. C. P. Modeling of bubble behaviors and size distribution in a slab continuous casting mold. Int. J. Multiphase Flow 2016, 79, 190. (38) Song, T.; Lane, G.; Feng, Y. Q.; Jiang, K. X.; Zhou, J. W.; Shen, Z. C. CFD simulation of bubble recirculation regimes in an internal loop airlift reactor. Presented at the 27th International Mineral Processing Congress (IMPC 2014), Santiago, Chile, October 20−24, 2014. (39) Lau, Y. M.; Bai, W.; Deen, N. G.; Kuipers, J. A. M. Numerical study of bubble break-up in bubbly flows using a deterministic Euler− Lagrange framework. Chem. Eng. Sci. 2014, 108, 9. (40) Menter, F. R. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 1994, 32, 1598. (41) Chen, Q. Y.; Xu, W. R. A zero-equation turbulence model for indoor airflow simulation. Energy Build. 1998, 28, 137.

REFERENCES

(1) Liu, W. C.; Yang, J. K.; Xiao, B. Review on treatment and utilization of bauxite residues in china. Int. J. Miner. Process. 2009, 93, 220. (2) Klauber, C.; Gräfe, M.; Power, G. Bauxite residue issues: ii. options for residue utilization. Hydrometallurgy 2011, 108, 11. (3) Liu, W. C.; Sun, S. Y.; Zhang, L.; Jahanshahi, S.; Yang, J. K. Experimental and simulative study on phase transformation in Bayer red mud soda-lime roasting system and recovery of Al, Na and Fe. Miner. Eng. 2012, 39, 213. (4) Agatzini-Leonardou, S.; Oustadakis, P.; Tsakiridis, P. E.; Markopoulos, C. Titanium leaching from red mud by diluted sulfuric acid at atmospheric pressure. J. Hazard. Mater. 2008, 157, 579. (5) Lu, G. Z.; Zhang, T. A.; Zhu, X. F.; Liu, Y.; Wang, Y. X.; Guo, F. F.; Zhao, Q. Y.; Zheng, C. Z. Calcification−carbonation method for cleaner alumina production and CO2 utilization. JOM 2014, 66, 1616. (6) Lv, G. Z.; Zhu, X. F.; Zhang, T. A.; Guo, F. F.; Pan, L.; Liu, Y.; Zhao, Q. Y.; Li, Y.; Jiang, X. L.; He, J. C. Multi-steps carbonation treatment of calcified slag of red mud. Light Met. 2014, 2, 91. (7) Lv, G. Z.; Zhang, T. A.; Zhu, X. F.; Pan, L.; Qin, M. X.; Liu, Y.; Zhao, Q. Y.; Jiang, X. L. Research on the phase transformation and separation performance in calcification−carbonation method for alumina production. Light Met. 2013, 245. (8) Li, R. B.; Zhang, T. A.; Liu, Y.; Zhou, J. P.; Zou, R. P.; Kuang, S. B. Characteristics of red mud slurry flow in carbonation reactor. Powder Technol. 2017, 311, 66. (9) Raghunathan, K.; Kumar, S.; Fan, L.-S. Pressure distribution and vortical structure in the wake behind gas bubbles in liquid and liquidsolid systems. Int. J. Multiphase Flow 1992, 18, 41. (10) Gordiychuk, A.; Svanera, M.; Benini, S.; Poesio, P. Size distribution and sauter mean diameter of micro bubbles for a Venturi type bubble generator. Exp. Therm. Fluid Sci. 2016, 70, 51. (11) Warmoeskerken, M. M. C. G.; Smith, J. M. Flooding of disc turbines in gas-liquid dispersions: a new description of the phenomenon. Chem. Eng. Sci. 1985, 40, 2063. (12) Chen, M. N.; Wang, J. J.; Zhao, S. W.; Xu, C. Z.; Feng, L. F. Optimization of dual-impeller configurations in a gas-liquid stirred tank based on computational fluid dynamics and multiobjective evolutionary algorithm. Ind. Eng. Chem. Res. 2016, 55, 9054. (13) Maurer, S.; Rüdisüli, M.; Teske, S. L.; Schildhauer, T. J.; van Ommen, J. R.; Biollaz, S. M. A.; Wokaun, A. Transformation of local bubble rise velocity measurements to global results: shown by a Monte Carlo simulation of a fluidized bed. Int. J. Multiphase Flow 2015, 70, 89. (14) Abdulrahman, M. W. Experimental studies of the transition velocity in a slurry bubble column at high gas temperature of a heliumwater-alumina system. Exp. Therm. Fluid Sci. 2016, 74, 404. (15) Fan, L.-S.; Bavarian, F.; Gorowara, R. L.; Kreischer, B. E.; Buttke, R. D.; Peck, L. B. Hydrodynamics of gas-liquid-solid fluidization under high gas hold-up conditions. Powder Technol. 1987, 53, 285. (16) Tan, Y. H.; Rafiei, A. A.; Elmahdy, A.; Finch, J. A. Bubble size, gas holdup and bubble velocity profile of some alcohols and commercial frothers. Int. J. Miner. Process. 2013, 119, 1. (17) Fang, C. C.; Xu, J. L.; Zhao, H.; Li, W. F.; Liu, H. F. Influences of the cross angle on the dispersion characteristics in a dense gasparticle coaxial jet. Ind. Eng. Chem. Res. 2016, 55, 11160. (18) Tyagi, P.; Buwa, V. V. Experimental characterization of dense gas−liquid flow in a bubble column using voidage probes. Chem. Eng. J. 2017, 308, 912. (19) Besagni, G.; Inzoli, F. Comprehensive experimental investigation of counter-current bubble column hydrodynamics: holdup, flow regime transition, bubble size distributions and local flow properties. Chem. Eng. Sci. 2016, 146, 259. (20) Du, W.; Sun, Z.; Lu, G. M.; Yu, J. G. The two-phase high-speed stream at the centerline of a hollow-cone spray produced by a pressure-swirl nozzle. Ind. Eng. Chem. Res. 2017, 56, 359. (21) Kazemzadeh, A.; Ein-Mozaffari, F.; Lohi, A.; Pakzad, L. Intensification of mixing of shear-thinning fluids possessing yield K


Article

Industrial & Engineering Chemistry Research (42) Kumar, S.; Ramkrishna, D. On the solution of population balance equations by discretizationI. a fixed pivot technique. Chem. Eng. Sci. 1996, 51, 1311. (43) Luo, H.; Svendsen, H. F. Theoretical model for drop and bubble breakup in turbulent dispersions. AIChE J. 1996, 42, 1225. (44) Prince, M. J.; Blanch, H. W. Bubble coalescence and break-up in air-sparged bubble columns. AIChE J. 1990, 36, 1485. (45) Ishii, M.; Zuber, N. Drag coefficient and relative velocity in bubbly, droplet or particulate flows. AIChE J. 1979, 25, 843. (46) Tomiyama, A. Struggle with computational bubble dynamics. Multiphase Sci. Technol. 1998, 10, 369. (47) Antal, S. P.; Lahey, R. T.; Flaherty, J. E. Analysis of phase distribution in fully developed laminar bubbly two-phase flow. Int. J. Multiphase Flow 1991, 17, 635. (48) Burns, A. D.; Frank, T.; Hamill, I.; Shi, J. M. The Favre averaged drag model for turbulent dispersion in Eulerian multi-phase flows. Presented at the 5th International Conference on Multiphase Flow, (ICMF ’04), Yokohama, Japan, May 30−June 4,2004. (49) Hibiki, T.; Ishii, M.; Xiao, Z. Axial interfacial area transport of vertical bubbly flows. Int. J. Heat Mass Transfer 2001, 44, 1869. (50) Sokolichin, A.; Eigenberger, G.; Lapin, A. Simulation of buoyancy driven bubbly flow: established simplifications and open questions. AIChE J. 2004, 50, 24. (51) Cheung, S. C. P.; Yeoh, G. H.; Tu, J. Y. On the numerical study of isothermal vertical bubbly flow using two population balance approaches. Chem. Eng. Sci. 2007, 62, 4659. (52) Qin, C. P.; Chen, C.; Xiao, Q.; Yang, N.; Yuan, C. S.; Kunkelmann, C.; Cetinkaya, M.; Mülheims, K. CFD-PBM simulation of droplets size distribution in rotor-stator mixing devices. Chem. Eng. Sci. 2016, 155, 16. (53) Liu, Y. F.; Hinrichsen, O. Study on CFD−PBM turbulence closures based on k−ε and Reynolds stress models for heterogeneous bubble column flows. Comput. Fluids 2014, 105, 91.

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