CFD Simulation of GasâLiquidâLiquid Three-Phase Flow in an

Article pubs.acs.org/IECR

CFD Simulation of Gas−Liquid−Liquid Three-Phase Flow in an Annular Centrifugal Contactor Shaowei Li,*,† Wuhua Duan,† Jing Chen,† and Jianchen Wang† †

Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China ABSTRACT: A computational fluid dynamics (CFD) simulation of gas−liquid−liquid three-phase flow was carried out on an annular centrifugal contactor. An Euler−Euler, volume-of-fluid, multiphase-flow model was used for the three-phase flow simulation. The three-phase flow behaviors in the open and sealed inlet operation modes were investigated under various operating conditions. The location and morphology of the aqueous/organic interface were discussed in detail in light of the simulated pressure distribution. An interesting bistability phenomenon was observed in the simulation. The throughput of the annular centrifugal contactor was obtained from the simulation under various phase ratios and compared with experimental results. Excellent agreement was obtained, supporting the validity of the simulation method. tional fluid dynamics (CFD) provides a useful tool for solving the above problems. It can be used for the design of new ACCs, to evaluate a current design, support deployment of the contactors, and optimize the operating conditions. CFD can partly substitute for experiments in these situations and can reveal the detailed flow field and concentration profile in the device, which significantly contributes to the in-depth study of flow and mass transfer mechanics. Several reports have been published on CFD studies of ACCs,22−29 and these can be classified into two types. In the first type, a single-phase or free-surface flow in the annular mixing zone of the contactor was simulated.22−27 In the second type, two-phase separation in the rotor zone was simulated.28,29 To the authors’ knowledge, CFD simulation of the whole ACC, including both the annular and the rotor zones, is little reported to date. The entire ACC must be studied because the flow conditions in the annular zone and the rotor zone interact with one another. The fluid in the annular zone and the rotor zone are connected by a hole at the bottom of the rotor and the pressure in the rotor zone affects the flow in the annular zone through the hole, while the flow field in the rotor zone is affected by the fluid injected through the hole. The mixing condition of the fluid passing through the hole also affects the phase separation behavior in the rotor zone. Furthermore, there is gas−liquid−liquid, three-phase flow in the ACC. Aqueous phase and organic phase are introduced from the inlets and are mixed in the annular zone. The annular zone is not completely filled with the two liquids, and the air in the upper part will be entrained into the liquids when the rotor is rotating at high speed. The three-phase flow passes into the rotor zone through the hole and phase separation is achieved by the centrifugal field. Simulation of three-phase flow in the ACC is little reported in the literature to date. A recent work by Wardle is the only article that reports the simulation of three-phase flow

1. INTRODUCTION The centrifugal contactor was devised at the Savannah River Laboratory more than four decades ago. The first centrifugal contractor was a paddle type, and it was modified to the annular type at Argonne National Laboratory in the late 1960s.1 The annular centrifugal contactor (ACC) is an efficient liquid− liquid extraction system and is now used in the chemical, nuclear, and biotechnology industries. In particular, in the nuclear industry, the ACC has the advantages of higher mass transfer efficiency, higher separation performance, smaller holdup volume, compactness, a less solvent degradation, and shorter start-up time than conventional contactors such as mixersettlers or pulse columns. Moreover, compact contactors can readily meet the criticality requirements.2−4 Because of the above advantages, much experimental work on ACCs has been performed over the past four decades.5−16 We have studied ACCs for more than thirty years at the Institute of Nuclear and New Energy Technology (INET), Tsinghua University, China. INET developed its own ACCs in the late 1970s, and a series of ACCs with rotor diameters from 10 to 230 mm have been developed since then. These ACCs have been successfully used in the fields of hydrometallurgy, wastewater treatment, biotechnology, the pharmaceutical industry, and partition of high level liquid wastes.8−16 Although extensive experimental work has been carried out and reported in the literature, more theoretical work using these data is required for further study. An analytical approach to determining the proper dimensions of ACC weirs has been demonstrated based on experimental correlations and hydrostatic balance arguments.17,18 Some prediction and analysis of the experimental results has been made by treating the contactor device as a black box.19−21 Despite the experimental and analytical research that has been carried out on ACCs, procedures for their reliable design and scale-up are yet to be developed, and the flow and mass transfer details in the device are not yet clear. Existing modeling methods are based on either experimental data correlation or mass and species conservation.17−21 Therefore, these are of limited help to either physical design and scale-up of the device or the elucidation of flow and mass transfer details. Computa© 2012 American Chemical Society

Received: Revised: Accepted: Published: 11245

March 27, 2012 July 14, 2012 August 9, 2012 August 9, 2012 dx.doi.org/10.1021/ie300821t | Ind. Eng. Chem. Res. 2012, 51, 11245−11253

Industrial & Engineering Chemistry Research

Article

in the entire ACC.30 Volume of Fluid model in the OpenFOAM-based solvers was used for the simulation. However, more research is required for the simulation technique of three-phase flow in the entire ACC, to provide visualization of the actual behavior and therefore directly aid device design, optimization of operating conditions, and provide insights into various aspects of the contactor problem. Two main challenges must be overcome for the simulation of three-phase flow in the entire ACC. The first is the connection of the static frame (the annular zone) and the high speed rotating frame (the rotor zone). The second is the selection of an appropriate multiphase-flow model for the three-phase simulation. In this work, the first problem was solved via a frame-changing model when setting the interface connection, while the second was addressed by using an Euler−Euler multiphase-flow model for the three-phase flow simulation. Thus, simulation of three-phase flow in the ACC was finally realized. The throughput of the ACC was obtained from the simulation under a range of phase ratios and compared with experimental results. Excellent agreement was obtained, indicating the validity of the simulation method.

Both methods can be used for the three-phase flow simulation in ACC, but the latter is more accurate. The PBM method is a more accurate Eulerian-Eulerian method, which treats droplets (or bubbles) of one class (with size in a range) as a separate phase. Coalescence and breakup of droplets (or bubbles) are considered in this method, and droplet (or bubble) size distribution can be finally obtained. It is of great significance to introduce the PBM model into the simulation of ACC in future work. The Eulerian-Eulerian method is used in this work because it is more accurate than ASMM but not as complex as PBM. In the Eulerian-Eulerian multiphase model, the governing equations of continuity and the momentum conservation for the ‘kth’ phase are given by the following equations

2. SIMULATION METHOD 2.1. Multiphase Model. Existing numerical methods used to solve multiphase flow problems include the front-tracking method,31 the boundary integral method,32,33 the level set method,34,35 the volume of fluid (VOF) method,36,37 the phase field method,38,39 the Lattice Boltzmann method (LBM),40,41 the Eulerian-Lagrangian method,42 the algebraic slip mixture model (ASMM),43 the Eulerian-Eulerian method,42 and the population balance model (PBM).44−46 All of the above methods have their advantages and disadvantages. The first five methods are mainly used for tracking a free surface. For example, the level set method is a powerful technique to determine implicit surfaces within a fixed grid system. It can accurately compute two-phase flows with complex topological changes, especially for problems with surface tension. The VOF method can simulate free surfaces without special procedures to model topological changes of the front. However a high-order scheme needs to be introduced for reconstructing highly curved surface. The LBM is not a traditional CFD method based on Navier−Stokes equations. This method has experienced a rapid expanding and evolving in recent years and provides a powerful method for multiphase simulation. It is anticipated that future research can introduce this method to the simulation of ACC. The Eulerian-Lagrangian approach solves the continuous phase through governing equations that consider the interphase interaction effects of the particulates (particles, drops, or bubbles) in an Eulerian frame and solves the dispersed phase by tracking the individual particulates (particles, drops, or bubbles) through a trajectory or Lagrangian model within the flow field of the continuous phase. This approach is usually used when one phase is continuous and the other phases are dispersed as particulates, especially when the phase ratio of the dispersed phases is sufficiently low such that droplet−droplet interactions are minimized. Similar to the VOF method, volume fractions of different phases are calculated in the ASMM and in the Eulerian-Eulerian method. The difference between the two methods is that the ASMM solves only one set of momentum equations and calculates relative velocities of the dispersed and continuous phases via an algebraic slip velocity formulation, while the Eulerian-Eulerian method solves separate sets of momentum and continuity equations for each of the phases.

All phases are assumed to be present at each grid of the flow domain in these equations. The volume fraction αk is computed at each cell. Γk describes the mass transfer between phases and is assumed to be zero in this work because mass transfer is not ⎯⇀ ⎯ τ k is the stress tensor of the ‘kth’ phase, including considered. ⇀

∂(αkρk ) ∂t

+ ∇·(αkρk ⇀ uk) = Γk

uk) ∂(αkρk ⇀ ∂t

(1)

uk uk) + ∇·(αkρk ⇀⇀

⎯⇀ ⎯ ⎯ g + ⎯⇀ M = −αk∇pk + ∇·(αk⇀ τk ) + αkρk⇀ k

(2)

⎯⎯⎯⇀

the viscous stress tensor and Reynolds stress tensor. Mk describes the interfacial forces acting on the ‘kth’ phase due to the presence of the other phases, including the effects of drag, lift, and virtual mass forces. Only the drag effect is taken into account in this work, because other effects are small in the liquid−liquid dominated flow in the ACC. The drag effect of both drops and bubbles must be considered in the three-phase flow of the ACC. The Ishii-Zuber drag model was used to evaluate drag force because this model is applicable to general fluid particles (drops and bubbles).47 Moreover, this model takes into account both spherical and spherical cap limits and dense fluid particle effects and is therefore suitable for modeling flows containing a high fluid volume fraction within the ACC. The mean diameter for the organic phase and the gas phase were set as 1 mm and 5 mm, respectively. There were secondary flows at the bottom of the annular zone and in the rotor cells because of the high speed rotation of the rotor and the impediment of the vanes. Therefore, the Reynolds Stress turbulence model was selected because it is suitable for the simulation of complex flow conditions containing secondary flows. 2.2. Geometry and Modeling Method. The CFD simulation was carried out for a ϕ70 mm ACC developed in our previous work, for which extensive experimental data have been obtained.9,11,14,15 A cross-section of the ACC is shown in Figure 1. The rotor is placed in the annular zone to form the complete ACC. Correspondingly, the geometry of the flow domain in the ACC is shown in Figure 2. Two tangential inlets were located on opposite sides of the annular zone (indicated by 1 in Figure 2), one for the aqueous phase and the other for the organic phase. Because the rotor was in high speed rotation, there was a big shear effect in the annular zone. The two liquids were mixed by the shear effect to form a dispersion after being pumped into the annular zone. Four (or sometimes six or other numbers) radial vanes (3) were located on the bottom of the 11246

dx.doi.org/10.1021/ie300821t | Ind. Eng. Chem. Res. 2012, 51, 11245−11253


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between the two liquids relatively static. The separated liquids exited the rotor zone from the heavy phase outlet (5) and the light phase outlets (8) separately. Before exit, the two liquids first passed through the heavy phase (7) and light phase channels (10). The heavy phase (6) and light phase (9) weirs were used to adjust the operating range of the ACC. The CFD simulation in this work was carried out using the geometry shown in Figure 2, i.e. the whole fluid domain of the ϕ70 mm ACC, including both the annular and the rotor zones. The mesh for the geometry shown in Figure 2 was created by CFX Build. As shown in Figure.3, the mesh was consisted of 1.61 M unstructured, tetrahedral cells. The mesh sizing was 2.0 mm in the rotor zone and on the rotor surface and expanding to 4.5 mm in the rest of the annular zone. The cell size in the rotor is small so that the behavior of the air−liquid and organicaqueous interfaces can be simulated clearly. A steady-state simulation was carried out by using the commercial software CFX 5.6, and the parameters used in the simulation were listed in Table 1. CFX’s high resolution discretization for both the

Figure 1. The inner structure of the annular centrifugal contactor.

Table 1. Parameters Used in the Simulation (Operated at 25 °C) parameter

19.2

radius of the light phase weir inner radius of the rotor zone outer radius of the rotor zone inner radius of the outer housing density of the aqueous phase (water)

R (mm) R′(mm) Ro (mm) ρa (kg/m3)

33 35 50 997

density of the organic phase (kerosene)

ρo (kg/m3)

780

density of the gas phase (air)

ρg (kg/m3)

1.185

γao (mN/ m) surface tension between the aqueous and the gas γag (mN/ phase m) ω (rad/s) rotation speed flow rate of the aqueous phase Fa (cm3/s) flow rate of the organic phase Fo (cm3/s)

interfacial tension between the aqueous and the organic phase

annular zone, enhancing the mixing of the two liquids. The mixed liquids passed through the connecting hole into the rotor zone and were separated by the centrifugal field. Six rotary vanes were located in the rotor zone (4) to hold the interface

value

ra*(mm) ro*(mm)

radius of the heavy phase weir

Figure 2. Geometry of the ACC for CFD simulation: a) the phase separation and outlet regions for the heavy phase and b) the outlet region for the light phase.

symbol (unit)

17.0

8.0 72.7 154 2.8−55.6 2.8−55.6

Figure 3. Tetrahedral mesh used for CFX simulation. 11247



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which is a distinctive feature of the flow in the rotor zone of the ACC. By comparing the two operating modes at condition of Fa = Fo = 20.8 cm3/s, we can see that there were three main differences between the two modes: First, the lower part of the rotor was filled with liquids in the open inlet mode, while the air core occupied the center of the rotor bottom in the sealed inlet mode, as shown in Figure 4. This distinction was caused by the difference in gas pressure in the annular zone. In the open inlet mode, the gas pressure in the annular zone was equal to atmospheric pressure, while the pressure of the air core in the rotor zone was lower than atmospheric pressure because of the pumping effect of the light phase outlets. To balance this pressure difference, the liquid level in the rotor was higher than that in the annular zone, and the bottom of the rotor was filled. In the sealed inlet mode, the pressure at the top of the annular zone was lower than that of the air core because of the pumping effect, and the liquid level in the rotor was lower than that in the annular zone. The pressure distribution in the ACC is discussed in detail in the next section. Second, the aqueous−organic interface at Position 1 (Figure 4) of the open inlet mode was closer to the light phase weir than that of the sealed inlet mode when the other operating conditions were the same. If we ignore the effect of the flow field, then the location of the aqueous−organic interface at the top of the phase separation region can be expressed by eq 3, which is derived based on the pressure balance.48

advection and turbulence terms were used for the calculation. The convergence criterion is set as that the normalized rootmean-square of the equation residuals reaches 0.00001. Both inlets were defined by normal speed calculated from flow rate. Both the outlets of the organic and aqueous phases were set as opening boundaries with 1 atm pressure. The rotor and housing walls were set as no-slip conditions, and the rotor wall was given a rotation velocity. The top of the annular zone was set as opening boundary or wall to simulate two different operation models, i.e., the open inlet mode and the sealed inlet mode.

3. RESULTS AND DISCUSSION 3.1. Three-Phase Flow Behavior. Two different operating modes for the ACC were simulated in this work, one with open inlets and the other with sealed inlets. In the former mode, the two inlets were open to atmosphere, which maintained atmospheric pressure at the top of the annular zone. In the latter mode, the two inlets were isolated from the atmosphere, and a micronegative pressure was formed at the top of the annular zone because of the pumping effect of the rotor. Figure 4 shows a vertical-section view of the simulated gas (blue)-

ri =

ρ

2g Δh

a

ω2

ra2 − ρo ro2 −

1−

−

2(Pa − Po) ρa ω2

ρo ρa

(3)

In eq 3, ra is the location of the aqueous free surface on the heavy phase weir, and ro is the location of the organic free surface on the light phase weir. ra and ro can be replaced by r*a and r*o when the flow rates of both aqueous and organic phases are low. Δh is the height from the top of the phase separation region to the heavy phase weir. Pa and Po are the gas pressure at the heavy phase and light phase weirs, respectively. Substituting the values of these parameters into eq 3 (Pa and Po were obtained from the simulation results, as will be described in the next section), we have ri ≈ 21 mm. We carried out the simulation in Figure 4 and found that the results at conditions Fa = Fo = 6.9 cm3/s and Fa = Fo = 20.8 cm3/s in the open inlet mode coincided with the result of eq 3 well. In contrast, the simulation results in the sealed inlet mode did not match the result from eq 3, indicating that the assumption of eq 3 (ignoring the effect of the flow field) was not true when the air core penetrates the rotor zone. The flow field has an obvious effect on the location of the aqueous−organic interface in this condition. Third, the aqueous−organic interface of the open inlet mode was approximately cylindrical, while that of the sealed mode was parabolic. The reason for this is discussed in detail in the next section. Another phenomenon that can be observed in Figure 4 is that the aqueous−organic interface moved centrifugally when the flow rate of the organic phase increased but moved centripetally when the flow rate of the aqueous phase increased. When Fo increased, the organic phase on the light phase weir became thicker, thus ro became smaller. We know from eq 3 that ri increases in this case, i.e., the aqueous−organic interface

Figure 4. Vertical section of the simulated three-phase flow.

organic (green)-aqueous (red) three-phase flow in the ACC under the two operating modes. Comparing with Wardle’s work,30 we can see that the organic-aqueous interface here is smoother. This is probably because the mesh used in this work is tetrahedral, while that is polyhedral in Wardle’s work. Another probable reason is the model difference. The Euler− Euler model is used here, and the Volume of Fluid model is used by Wardle. We can see from Figure 4 that the phase separation process was completed immediately after the mixed liquid was injected into the rotor zone. This is probably because the set dispersion diameter of the organic phase is too large. In both operating modes, there was an air core formed in the center of the rotor zone. The air/kerosene free surface is part of a parabolic surface (or approximately a conical surface when the centrifugal acceleration is much higher than the gravitational acceleration), 11248



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moves centrifugally. Similarly, when Fa increased, ri became smaller because ra becomes smaller. Thus, the interface moved centripetally. In fact, Fa affects the interface location not only through this mechanism but also by another. The aqueous phase flows from the phase separation region to the heavy phase weir through six channels. The resistance of the channels causes an additional pressure difference between the top of the phase separation region and the heavy phase weir. When Fa increases, this pressure difference increases and pushes the interface centripetally. The location of the aqueous−organic interface also affects the operating range of the ACC. The operating range of the ACC is defined as all operating conditions at which the aqueous−organic interface is located between the light phase weir and the inner wall of the heavy phase channel. The aqueous−organic interface of the open inlet mode was closer to the light phase weir. Therefore this mode is more applicable for a higher organic phase flow rate. On the other hand, the sealed inlet mode is more applicable for a higher aqueous phase flow rate. To investigate the morphology of the interfaces more in more detail, the cross-sectional views at Positions 1 and 2 marked in Figure 4 are plotted in Figures 5 and 6. The interface

Figure 7. Water velocity distribution on the cross sections at Positions 1 and 2 of the two operation modes.

Meanwhile, the vortex also causes the deformation of the aqueous−organic interface and a convex surface occurs. The cross-sectional views at Position 2 show how the liquid flows into the phase separation region. As shown in Figure 6, the liquid flows along the clockwise wall of each cell into the cell under the effect of centrifugal force. When the rotor bottom is filled (Figure 6 (a)), the organic phase extends along the clockwise wall of each cell because a clockwise vortex (relative to the rotor) is formed at the center of the rotor (see Figure 7 (c)). In this case, a fan-shaped organic phase pattern is created. When the rotor bottom is not filled (Figure 6 (b)), the organic phase forms a convex surface in the middle of each cell because of the tendency to form an anticlockwise vortex in the cell (as described above and shown in Figure 7(d)). In this case, a flower-shaped organic phase pattern is formed. 3.2. Pressure Distribution. Pressure distribution in the ACC is important because it determines the flow conditions of the three-phase flow within it. In fact, some researchers have controlled the operating range of the ACC by adjusting the pressure of the aqueous phase and/or organic phase outlet.1,5,6 Figure 8 shows the simulated pressure distribution on a vertical section of the ACC. Figure 8 (a) corresponds to the open inlet mode and (b) to the sealed inlet mode. In both modes, the lefthand graph covers the whole range of the pressure, while the right-hand graph covers a narrow range of pressures to distinguish the pressure difference of some specified area (the air core and the top of the annular zone). We can see from the right-hand graph of Figure 8 (a) that the pressures at the top of the annular zone and at the aqueous outlet are equal to atmospheric pressure, as expected. We can also see that the pressure at the air core is approximately −100 Pa. This negative pressure is caused by the flow of the organic phase in the light phase channels under centrifugal force and liquid is drawn into the rotor zone by this negative pressure. We can see from the right-hand graph of Figure 8 (b) that the pressure at the top of the annular zone is about −400 Pa and in the air core is about −100 Pa. These simulation data can be substituted into eq 3 to calculate the interface location. It can

Figure 5. Cross section of the simulated three-phase flow at the top of the phase separation region (marked as Position 1 in Figure 4).

Figure 6. Cross-section of the simulated three-phase flow at the bottom of the rotor (marked as Position 2 in Figure 4).

at the cross-section at Position 1 is not circular because of the barrier effect of the rotary vanes. The organic phase tends to move clockwise, while the aqueous phase tends to move anticlockwise between the two vanes in each cell, as shown in Figure 7. When the rotor moves anticlockwise, the liquid in each cell has a tendency to form a single anticlockwise vortex (relative to the rotor). However, the vortex is separated to two because of the restriction of the organic-aqueous interface. 11249



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rotor. The aqueous/organic interface in the open inlet mode can be divided into three sections: an upper, a lower, and a middle section. As shown in Figure 9, the upper section obeys

Figure 9. Sketch to aid analysis of the aqueous/organic interface in the open inlet mode.

eq 4, while the lower section obeys eq 6. The surface defined by eq 6 is parallel to but lower than the surface defined by eq 4. The middle section obeys neither eq 4 nor eq 6, but it connects the two sections to form the whole interface. Because of the sectional structure, the aqueous/organic interface in the open inlet mode does not appear to be parabolic but somewhat cylindrical. This also explains why the isobaric surfaces in the left-hand graph of Figure 8 (a) are not parabolic. 3. 3. Bistability. An interesting phenomenon occurred in the simulation results for the open inlet mode. As shown in Figure 10, bistability was observed, i.e., two steady states occur

Figure 8. Simulation results for the pressure distribution.

be concluded from the calculation results of eq 3 that the pressure difference between locations at the heavy phase and the light phase weirs has little effect on the interface location if it is no higher than 200 Pa. The isobaric surface can be seen from the left-hand graph of Figure 8 (a) and (b). For the sealed inlet mode, the isobaric surface was parabolic. Because the aqueous/organic interface and the organic free surface are isobaric surfaces, they are also parabolic, as discussed above. We can obtain the equation for the interface and the free surface based on pressure balance, as expressed by eqs 4 and 5 z=

ω 2 2 Pab − Pi ω 2R2 − rif + ρa g 2g 2g 2

z=

(4)

2 2

P − Pi P − Pc ω 2 ωR − + i r fs + ab ρa g ρo g 2g 2g

Figure 10. Bistability of the ACC in the open inlet mode, Fa = Fo = 6.9 cm3/s.

(5)

In these equations, z is the height from the rotor bottom, and rif and rfs are the radii of the interface and the free surface, respectively. The constants Pab, Pi, and Pc are the pressures at the rotor bottom corner, on the interface, and in the air core, respectively. Equations 4 and 5 are right parabolic. The difference between eqs 4 and 5 is a constant, which indicates that the interface and the free surface are parallel, which can also be observed in Figure 4 (b). The analysis described in the above paragraph is not applicable to the open inlet mode. Because the lower part of the rotor is filled, the equation for the aqueous/organic interface in this region is expressed by eq 6

at the same operating conditions, depending on different initial conditions. If the ACC is empty of liquids in the initial condition, then the state shown in the left-hand graph occurs in simulation, but if it is filled with liquids in the initial condition, then the state shown in the right-hand graph occurs in simulation. Note that the left-hand state is different from the steady state in the sealed inlet mode shown in Figure 4 (b), although they look similar. The liquid level in the annular zone of the former was much lower than that of the latter. Each of the two states can switch to the other under some specific conditions. For example, filling the ACC with a large quantity of liquids causes the left-hand state to switch to the right-hand state. Nevertheless, both states can be stable after sufficient iterations, even if there is no feed of liquids, because the pressure is balanced in both states. In the left-hand state, the centrifugal force can hold the two liquids in the rotor, even

2 2

z=

ρa ω R P − Po ω2 2 rif + ab − 2g (ρa − ρm )g 2(ρa − ρm )g

(6)

In eq 6, ρm is the density of the mixture in the lower central part of the rotor. Po is the central pressure in the lower part of the 11250



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parabolic and parallel to the organic free surface, while the interface of the open inlet mode is somewhat cylindrical because of its three-section structure. The pressure distribution supported the interface location and morphology analysis. A bistability phenomenon was observed in the simulation results for the open inlet mode of operation. The throughput of the ACC was obtained by simulation under different phase ratios and compared with experimental results. The close agreement obtained indicates the validity of the simulation method.

if the bottom of the annular zone is empty. The liquid level in the annular zone should not be higher than the rotor base in this state. In the right-hand state, the pressure is balanced in both the radial direction and the vertical direction. In the radial direction, the centrifugal force holds the liquids in the rotor. In the vertical direction, the pressure of the liquids in the annular zone is balanced with that in the rotor zone, and thus the liquid level in the annular zone is higher than the rotor bottom but a little lower than the base of the air core. Although both states are steady, only the right-hand state is used in actual operation because the liquids in the annular zone can be sufficiently stirred up by the rotor in this state. The bistability phenomenon occurs only at low flow rate. At the normal operation conditions of an ACC, the flow rate is usually high enough that only the right-hand state is stable. The bistability described here is only a simulation result, and experimental verification is needed in the future work. 3.4. Throughput. Though two different operating modes for the ACC were simulated, only the open inlet mode was used in our previous experiments. The throughput of the ACC was measured under different phase ratios in the experimental work operated in the open inlet mode. The throughput during experiments was defined as the total flow rate of the two phases for a given flow ratio, below which the end stream entrainment was below 0.5%.9 In the simulation, the throughput could be determined by the ultimate location of the aqueous/organic interface. The aqueous/organic interface should be located between the light phase weir and the inner wall of the heavy phase channels under normal operating conditions. To obtain the throughput, we iteratively changed the total flow rate of the two phases at each phase ratio. When the interface reached its ultimate location (the light phase weir or the inner wall of the heavy phase channel), the throughput was identified. The simulated throughput is compared with experimental measurements (see Figure 6 of ref 10 at 1470 rpm condition) in Figure 11, showing excellent agreement between simulation and experiment. The comparison supports validity of the simulation method.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS

We gratefully acknowledge support from the National High Technology Research and Development Program of China (2009AA050703), the National Natural Science Foundation of China (21106077) and Beijing Natural Science Foundation (2113047).

■

NOTATION Fa = flow rate of the aqueous phase (L/h) Fo = flow rate of the organic phase (L/h) ⎯⎯⎯⇀

Mk = interfacial forces acting on the ‘kth’ phase (N/m3) Pa = pressure at the heavy phase (Pa) Pab = pressure at the rotor bottom corner (Pa) Pc = pressure in the air core (Pa) Pi = pressure on the interface (Pa) Po = pressure at the light phase weir (Pa) ra = location of the aqueous free surface on the heavy phase weir (mm) ro = location of the organic free surface on the light phase weir (mm) r*a = radius of the heavy phase weir (mm) ro* = radius of the light phase weir (mm) ri = location of the aqueous−organic interface (mm) rif = radius of the aqueous/organic interface (mm) rfs = radius of the free surface (mm) R = radius of the rotor zone (mm) ⇀ uk = velocity vector of the ‘kth’ phase (m/s) z = height from the rotor bottom (m) αk = volume fraction of the ‘kth’ phase γag = interfacial tension between the aqueous and the gas phase (mN/m) γao = interfacial tension between the aqueous and the organic phase(mN/m) Γk = mass transfer speed between phases (kg/(m3·s)) ρk = density of the ‘kth’ phase (kg/m3) ⎯⇀ ⎯ ⇀ τ k = stress tensor of the ‘kth’ phase (Pa) ω = rotation speed (rad/s)

Figure 11. Comparison of simulated throughputs with experimental results under the open inlet condition.

4. CONCLUSIONS The CFD simulation of gas−liquid−liquid three-phase flow was realized in the ACC by using an Euler−Euler, volume-of-fluid, multiphase-flow model. The three-phase flow behavior under two operating modes (open inlet and sealed inlet modes) was simulated under various operating conditions. The air core at the center of the rotor was a common feature of the two modes, and the organic free surface in both modes was parabolic. The location and morphology of the aqueous/organic interface were discussed in detail. The interface of the sealed inlet mode is

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REFERENCES

(1) Bernstein, G.; Grosvenor, D.; Lenc, J.; Levitz, N. A High-Capacity Annular Centrifugal Contactor. Nucl. Technol. 1973, 20, 200. (2) Leonard, R. A. Recent Advances in Centrifugal Contactor Design. Sep. Sci. Technol. 1988, 23, 1473.

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