Flow Visualization and Three-Dimensional CFD Simulation of the

Dec 11, 2007 - (PIV) and laser Doppler velocimetry (LDV) to understand the flow patterns and velocity profiles in both the presence and the absence of...
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Ind. Eng. Chem. Res. 2008, 47, 3677-3686

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Flow Visualization and Three-Dimensional CFD Simulation of the Annular Region of an Annular Centrifugal Extractor Sandesh S. Deshmukh and Jyeshtharaj B. Joshi* Institute of Chemical Technology, UniVersity of Mumbai, Matunga, Mumbai 400 019, India

Sudhir B. Koganti Indira Gandhi Centre for Atomic Research, Kalpakkam, TN 603 102, India

The single phase flow patterns in the annular region of an annular centrifugal extractor (ACE) have been studied both experimentally and computationally. Experiments were conducted using particle image velocimetry (PIV) and laser Doppler velocimetry (LDV) to understand the flow patterns and velocity profiles in both the presence and the absence of the net flow through the annulus. The data obtained in these experiments have been used for the validation of the computational fluid dynamics (CFD) simulations. Further, complete energy balance has been established. The CFD simulations were performed over a wide range of operating conditions. In contrast with the Taylor annular region (having no end effects), the ACE was found to exhibit markedly different cell patterns. The number of cells was found to be strongly dependent on the Taylor number. The effect of the internals such as radial baffles in the annulus, as well as vanes on the bottom plate, on the flow patterns has been investigated. From the simulations it was revealed that the flow patterns in ACE were also dependent on the start-up procedure of the equipment. 1. Introduction The flow in the annular region between two cylinders, when inner one is rotating and outer one stationary, is known as Taylor-Couette flow. When rotational speed is sufficient (Ta > 1000Tacr), the flow becomes turbulent and can be used to disperse one liquid into another. This type of mixing is used as an integral part of the annular centrifugal extractor (ACE) for solvent extraction which was developed, among others, by Argonne National Laboratory.1 In the ACE, mixing (liquidliquid dispersion and mass transfer) takes place in the annular space, stratification occurs inside the inner cylinder (rotor), and separation takes place in the weir system, as shown in Figure 1. ACE is a vertical, liquid-liquid extractor capable of both mixing and separation in a single unit. Two-fluid Taylor vortex ACE offers several advantages in liquid-liquid extraction processes because of centrifugally accelerated settling, short residence times, low hold-up volumes, and flexible phase ratios. These features are desirable in applications where high throughput (petroleum industry), safety (nuclear fuel processing), or facilitated settling (biological separations) is required. Owing to the advantages offered by the ACE as well as the commercial success of the equipment, this equipment has been investigated over the past three decades.1-3 Although substantial work has been carried out to operate it successfully, procedures for the reliable design and scale-up are yet to be developed; hence the study of the flow patterns in the reactor becomes important to be investigated. Advanced experimental techniques (such as particle image velocimetry (PIV) and laser Doppler velocimetry (LDV)) and computational fluid dynamics (CFD) are the key tools in evaluating the extractor design and the operational changes. Recently, Vedantam et al.4,5 demonstrated the usefulness of CFD in such an extractor. They used CFD simulations for understanding mixing and residence time distribution in a Taylor-Couette contactor4 and the radial stratification in two* To whom correspondence should be addressed. Tel.: 00-91-222414 0865. Fax: 00-91-22-2414 5614. E-mail: [email protected].

Figure 1. Schematic of annular centrifugal extractor (ACE).

fluid Taylor-Couette flow.5 Vedantam and Joshi6 presented a state-of-the-art review for the design of the ACE. They brought out the usefulness of CFD for efficient design of the ACE by providing detailed information about (i) the flow patterns for a wide range of geometric and operational conditions and (ii) the end effects of the vanes on axial as well as radial mixing. Wardle et al.7 simulated single-phase flow in the annular region of the contactor, and the turbulence has been modeled using the k- model. The results obtained were qualitative and needed validation with experimental measurements. Deshmukh et al.8 compared the CFD predictions and the experimental data for all the flow regimes in Taylor-Couette flow. From the previous work, it is clear that the CFD simulation of the actual annular region of the ACE has not been systematically investigated. Further, the bottom region below the rotor consists of vanes and hence three-dimensional (3D) simulations are needed for

10.1021/ie070959w CCC: $40.75 © 2008 American Chemical Society Published on Web 12/11/2007

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Figure 3. Schematic of the computational grid used.

Figure 2. (A) Details of experimental geometry investigated: (1) rotor; (2) annular space; (3) stator; (4) inlets; (5) outlet; (6) radial baffles in annulus; and (7) top ring to avoid air entrapment. (B) Provision of radial baffles in annulus. All dimensions are given in millimeters.

the annular as well as the bottom gap. In addition, the earlier work4-8 has shown that the k- turbulence model has limitations for simulating the ACEs. Therefore, for modeling the turbulence, the Reynolds stress model (RSM) has been used. To validate the model, flow visualization experiments have been carried out using particle image velocimetry (PIV) and laser Doppler velocimetry (LDV). The comparison between the two different measurements assures the accuracy in the measurements. The presence of vanes on the stationary bottom plate (Figure 2A) directs the liquid to the separator and prevents the dispersed phase from being separated before it enters the separator. The effect of vanes has been investigated by comparing the flow patterns in the absence and presence of vanes. It was found that the presence of vanes on the bottom plate reduces the number of vortices in the annulus, and contributes to enhanced back-mixing and turbulence in the annulus. The extent of back-mixing can be reduced by providing radial baffles (Figure 2B) in the annulus. Therefore, the quantitative effect of radial baffles has also been investigated. 2. Experimental Section The geometry of the ACE used in this work has been shown schematically in Figure 2. The rotor inside diameter, the stator inside diameter, and the bottom clearance were 39, 52, and 8 mm, respectively. Figure 2A shows the details of vanes fixed on the bottom plate. The six vanes had a height of 5 mm each and a thickness of 3 mm. Each vane had a length of 20 mm, and the gap between the inside diameter of the outer cylinder and the outer edge of a vane was 1.5 mm. This means, at the center, that a circular portion of 9 mm diameter was vane free and the clearance in this region was 8 mm. The clearance between the top edge of the vane and the bottom face of the

rotor was 3 mm. The shaded portion in Figure 2A shows the measurement region for flow visualization and velocimetry experiments. The rotor and outer vessel were made of acrylic (refractive index of 1.49). The difficulties arising in the measurements near the wall due to curvature effects have been resolved by a refractive index matching technique, which was previously used by Parker and Merati.9 For this purpose a solution of sodium iodide in water was used. The kinematic viscosity and the density of the solution were found to be 1.523 cS and 1837 kg/m3 at 24 °C, respectively, and the refractive index of the solution was 1.48 ( 0.05. It can be noted that the rotor was a solid cylinder of acrylic. The present study is focused on the flow patterns in the annular region. The difficulty in the experimental measurements with LDV as well as PIV was air induction, and in the presence of air measurements were not possible. Hence, care was taken to avoid air entrapment by providing a radial solid ring at the top of the liquid surface as shown in the revised equipment (indicated by label 7 in Figure 2A). In other words, no free surface existed and the entire volume was full of liquid. The measurements were reported at the two rotational speeds, viz., 10 and 20 r/s (rotations per second), for which no air was entrapped in the flow domain and reliable data could be obtained. Measurements were made in a batch as well as a continuous mode of operation. For batch mode the liquid volume was 74.6 mL and the liquid height was 72 mm. For continuous mode two inlets were provided at the top which were located diametrically opposite to each other and the outlet was at the center of the bottom plate. The two inlets and the outlet tubes had 5 mm diameter. The fluid was pumped using two peristaltic pumps with each giving a flow rate around 2 mL/s so that the average velocity from each inlet was found to be around 0.106 m/s. In order to avoid pulsations, gravity flow through a constant head tank connected to the inlet was used. The flow visualization experiments were performed using particle image velocimetry (TSI, Inc.) and laser Doppler velocimetry (Dantec Dynamic). The details of these experiments are given below. 2.1. PIV Measurements. In the PIV measurements, the laser source was a pulsed Nd:YAG laser having a pulse duration of 6 ns and which was synchronized with the camera using a synchronizer. The optics included a combination of cylindrical and spherical lenses, attached in view of creating a thin laser

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Figure 4. Comparison between mean radial and axial velocities measured by LDV and PIV at 10 r/s: (9) radial velocity (LDV), (0) radial velocity (PIV), (2) axial velocity (LDV), and (4) axial velocity (PIV).

Figure 5. Comparison between mean radial and axial velocities measured by LDV and PIV at 20 r/s: (9) radial velocity (LDV), (0) radial velocity (PIV), (2) axial velocity (LDV), and (4) axial velocity (PIV).

sheet of 1 mm thickness. The images were captured using a high-resolution 4M CCD camera (of 15 Hz frequency), placed perpendicular to the laser sheet, with 2048 × 2048 pixels. The liquid was seeded with silver-coated hollow glass particles of 20 µm mean diameter. The interrogation area was set at 64 × 64 pixels with a 50% overlap, resulting in approximately 1500 vectors for the images. The time difference between the two laser pulses was optimized based on Nyquest criterion. The PC functioned as a central data acquisition and processing unit. The processing of a PIV vector field contains following steps: grid generation, spot masking, correlation, peak location, and validation. The GridEngine breaks the input images into smaller spots for processing and initializes the vector field. For each grid point the process manager copies the pixels from the input images into the spots and passes the spots to the SpotMaskEngine, which modifies or conditions image spots before processing, helping the signal-to-noise ratio. The images are then passed to the Correlation Engine, which computes correlation functions and returns the correlation map to the PeakEngine for locating the peaks. The calculated velocity field is then stored and passed through validation, which removes bad vectors, fills the hole with interpolated vectors, and smoothes the vector field before saving the final vector file. Image processing of vectors extracted from PIV images was done by using the Nyquest grid, passing the signal-to-noise ratio

using a threshold value of 4 so that most of the bad vectors are eliminated. The post-processing was then done, where vectors were compared with neighboring vectors. The vectors which vary by more than the validation tolerance from the neighborhood average were removed. After the vectors were validated the missing points were filled in, and the properties of the flow were computed. 2.2. LDV Measurements. A three-beam LDV was used to measure the two velocity components (axial-radial and axialtangential) simultaneously. The LDV setup comprised Dantec 55 X modular series optics along with electronic instrumentation and a personal computer (PC). A 5 W Ar ion laser from Spectra Physics was used as a source. To identify the flow direction, a frequency shift of 40 MHz is given to one laser beam. All the optics are from Dantec Dynamics, including the cover and retarder plates (to adjust the beam polarization), beam splitters, Bragg cell, beam expander, and 600 mm front lens for focusing. The measurement volume is formed by three mutually perpendicular laser beams, viz., blue (588 nm), green (614 nm), and cyan (combination of blue and green) beams. The scattered laser light from the measurement volume is captured by photomultiplier tubes in a forward scatter mode. It can be noted that NaI solution in water has been used as working fluid. It already contains some impurities (may be called “dirt”). The use of this solution gives a sufficient data rate with LDV; hence no additional seeding was used during the measurements. In the case of PIV this type of seeding was insufficient to scatter light so as to provide a good image for obtaining cross-correlation. Data validation and signal processing (on-line fast Fourier transform) were performed by a Burst Spectrum Analyzer (62N40 BSA F60 processor) from Dantec Dynamics which consists of two velocity channels. The average data rate was around 700 Hz with validity above 90%. The entire operation of data acquisition including the high voltage to photomultiplier tubes and the record length selection for the burst detection were controlled by a personal computer using BSA Flow software, version 4.0. Additional experimental details have been provided by Ranade et al.10 3. Mathematical Modeling 3.1. Model Formulation. For a swirling flow between two concentric cylinders, the governing equations for continuity and motion are given by

∂ui ∂ui )0 + ∂t ∂xi

(1)

( )

∂ui ∂uiuj 1 ∂Pi ∂ ∂ui + )+ ν ∂t ∂xj F ∂xi ∂xj ∂xj

(2)

Equations 1 and 2 on Reynolds averaging reduce to the following forms:

∂〈ui〉 ∂〈ui〉 )0 + ∂t ∂xi

(3)

(

)

∂〈ui〉 ∂〈ui〉 ∂〈ui〉 1 ∂〈Pi〉 1 ∂ + 〈uj〉 )+ µ + τij ∂t ∂xj F ∂xi F ∂xj ∂xj

(4)

The modeling of τij can be done by various turbulent models. It has been observed that the k- model was not appropriate for modeling highly turbulent Taylor vortex flow.8 The largeEddy-simulation (LES) model is definitely more promising for

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predicting turbulent quantities and local flow structures. The objective of this work is to develop a CFD model for understanding the performance of the ACE and using it for commercial-size equipment. In such a type of equipment where energy dissipation is very high (around 500 W/kg near the walls to 20 W/kg in the bulk region), the total grid size required for studies of commercial sizes using the LES model is on the order of 6 × 108, leading to expensive and time-consuming simulations. Henceforth, for turbulence modeling, the Reynolds stress model (RSM) has been employed. In this model, individual Reynolds stresses τij are computed using following equation:

(

)

∂τij ∂τij ∂〈uj〉 ∂〈ui〉 + 〈uk〉 ) - τik + τjk ∂t ∂xk ∂xk ∂xk ∂ C + Πij - ij + ν∇2τij (5) ∂xk ijk Figure 6. Energy balance.

where

Πij )

〈[

]〉

P′ ∂u′j ∂u′i + ) pressure-strain correlation F ∂xi ∂xj

ij ) 2ν

〈 〉

∂u′i ∂u′j ) dissipation rate correlation ∂xk ∂xk

1 Cijk ) 〈u′i u′j u′k〉 + (〈P′u′i〉δjk + 〈P′u′j〉δik) ) F turbulent diffusive transport The second term on the right-hand side of eq 5 represents turbulent diffusive transport. It has been simplified in FLUENT11 to use a scalar turbulent diffusivity as ∂/∂xk[(νt/σk)(∂τij/∂xk)] (Launder et al.12) with σk ) 0.82. In this term νt is unknown; therefore, it is calculated as follows:

k2 ν t ) Cµ 

(6)

The turbulence kinetic energy was obtained from normal Reynolds stresses (eq 7), and  is computed from eq 8.

1 k ) (τii + τjj + τkk) 2

(7)

The third term of eq 5, the linear pressure-strain (Πij) model, is explained in FLUENT,11 while the fourth term (ij dissipation rate of turbulent stresses) is modeled as (2/3)δij. Here  is computed with the following transport equation:

[( ) ]

νt ∂  2 ∂ ∂ ∂ + 〈uj〉 ) C1 P - C2 + ν+ ∂t ∂xj k k ∂xj σ ∂xj

(8)

In these equations, P represents the generation of turbulent kinetic energy due to the mean velocity gradients, defined as

P ) τij

∂〈ui〉 ∂xj

(9)

The turbulent viscosity (νt) is computed using eq 6, and the model constants are C1 ) 1.44, C2 ) 1.92, and Cµ ) 0.09. 3.2. Boundary Conditions. The rotational velocities of the walls were specified. The inner cylinder rotation varied from 10 to 35 r/s. It has been specified that no-slip condition holds

at all the walls. The results were obtained for two cases: (a) sudden start of the rotor and (b) gradual increase of speed from zero to the desired value. In the former (case a), angular velocity was specified for a rotating boundary and transient simulations were carried out. In the latter (case b), the simulations were started at a lower angular velocity (1.67 r/s) and after the steady state was attained this solution was used as an initial condition for the next higher rotational speed. This was followed until the final desired speed was achieved. For investigating the effect of axial flow using CFD, the two inlets located at geometrically opposite ends at the top were specified as velocity inlets with the desired velocity magnitude (0.1 m/s, in terms of flat velocity profiles) and the outlet located at the center of the bottom (see Figure 2A, label 5) was specified as outflow. 3.3. Boundary Conditions for Reynolds Stresses. Whenever flow enters the domain, it is required to specify the values for individual Reynolds stresses and for the turbulence dissipation rate. FLUENT11 uses the specified turbulence quantities at the inlets to derive the Reynolds stresses from the assumption of isotropy of turbulence. At the wall, the values of the Reynolds stresses and  were computed from Launder and Spalding13 wall functions. The explicit wall boundary conditions were applied for Reynolds stresses by using logarithm law and the assumption of equilibrium, thus disregarding convection and diffusion in the transport equations for stresses. 4. Numerical Framework 4.1. Method of Solution. With the finite volume formulation, all the simulations were carried out using 3D grids. The commercial software FLUENT (version 6.2.16) has been used in all the studies, using ∼600 000 nonuniform hex grids (Figure 3).The grids have been selected on the basis of establishment of energy balance. At higher rotational speed the grids near the walls are refined further to satisfy energy balance. A segregated implicit solver method was used for the momentum equations. The equations were discretized with the QUICK upwind scheme, and for the pressure-velocity coupling, the PISO scheme has been used, which is recommended for transient simulations.11 The time step used was 1 × 10-4 s. The convergence criteria used to terminate the simulations were 1 × 10-4 for continuity and 1 × 10-5 for all velocity components and turbulent quantities. For the pressure equation, the PRESTO scheme was used. Eccentricity (ratio of offset distance of the cylinder axis to the average gap width) was assumed to be zero.

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Figure 7. Comparison between CFD predictions and experimental measurements for mean axial and radial velocity profiles at 10 r/s at (A) z/H ) 0.055 and (B) z/H ) 0.72: (9) axial velocity (experimental), (0) radial velocity (experimental), (s) axial velocity (CFD), and (- - -) radial velocity (CFD).

Figure 8. Comparison between CFD predictions and experimental measurements for mean axial and radial velocity profiles at 20 r/s at (A) z/H ) 0.055 and (B) z/H ) 0.72: (9) axial velocity (experimental), (0) radial velocity (experimental), (s) axial velocity (CFD), and (- - -) radial velocity (CFD).

Data were collected at specified points to track the development of the flow and confirm that the asymptotic solution was reached. The start-up effect has also been studied by considering different simulations. For sudden start the boundary conditions at the rotating walls were specified equal to the desired speed, while to study the effect of gradual speed increase simulations were started at a lower rotational speed (1.67 r/s) and, after assuring the steady state, the speed was further increased at intervals of 1.67 r/s. In the cases of continuous operation with net axial flow, the simulations were initially carried out for the specified axial flow without the rotation of the inner cylinder. After the steady state was attained, the rotational speed of the rotor was specified and the transient simulations were then performed. 5. Results and Discussion 5.1. Comparison between PIV and LDV Measurement. The flow visualization experiments have been carried out to obtain the flow patterns and velocity profiles in the annulus of ACE of specified dimensions, which could be used for the validation of the CFD model. During the experiments by Parker and Merati,9 symmetry was observed for turbulent Taylor-Couette flow. Hence the flow has been assumed to be axisymmetric around the plane passing through the axis of rotation. The PIV measurements give radial and axial velocity

Figure 9. Comparison between CFD predictions and experimental measurements for mean tangential velocity profiles at z/H ) 0.055: (0) 10 r/s (experimental), (2) 20 r/s (experimental), (- - -) 10 r/s (CFD), and (s) 20 r/s (CFD).

components in the annulus plane which can also be obtained by LDV. The time averaged axial and radial velocities have been calculated from both PIV and LDV. The LDV measure-

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Figure 10. Vector plot representing flow patterns at different rotational speeds predicted by (A, left) CFD and (B, right) PIV.

Figure 11. Comparison between CFD predictions and experimental measurements for the turbulent kinetic energy: (9) 10 r/s (experimental), (0) 20 r/s (experimental), (s) 10 r/s (CFD), and (- - -) 20 r/s (CFD).

ments have been carried out at the interval of 4 mm in the axial direction and 1 mm in the radial direction. LDV gives a very good data rate because the measurements are recorded only at a single point. Data rate obtained is a function of the seeding particle concentration and the velocity at the measurement point. The typical data rate obtained in the current work was ∼700 Hz. In the case of PIV, two images per measurement frame were recorded and needed to be transferred to the computer in order to process it. As the resolution of the image increases, the spatial resolution of the measurement increases. However, the image data that needed to be transferred also increase and the bus speed becomes the limitation. Thus, the data rate of the high-resolution PIV system (with 4 megapixel cameras) remained limited to 7 Hz for stereoscopic arrangement.

Figure 12. Vector plot of representing flow patterns obtained by CFD at 20 r/s, when vanes would not protrude beyond rotor circumference: (A) schematic of geometry; (B) vector plot.

Considering the availability of velocity data acquired simultaneously over a plane, PIV data seem sufficient to describe the flow field. However, in order to check the statistics (mean and fluctuating velocity field) obtained with the PIV, comparison with same statistics (mean and fluctuating field) was thought desirable. The error in the mean velocity of a set of flow velocity measurements is given by Bevington14 as

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σµ

σTI2 + σM2 x )

xN

(10)

where σTI is the flow turbulence intensity, σM is the inherent measurement error, and N is the number of measurements. This equation demonstrates the effect of sample size and inherent measurement technique errors on the estimated statistics (mean value). Provided the measurement error is insignificant (σM < 1%), first-order statistics can be derived from a relatively small sample population (N ) 100). However, in order to reduce the ambiguity about the reliability of the mean velocity fields obtained, it was thought desirable to carry out measurements with both LDA and PIV, and to make the comparison. Figures 4 and 5 show the mean axial and radial velocity profiles obtained using LDV and PIV measurements at 10 and 20 r/s, respectively, at z/H ) 0.88. The velocities have been made nondimensional using the speed at the surface of rotating cylinder while the radial distance has been normalized with the gap between the stationary and rotating cylinders. A very good agreement between LDV and PIV measurement confirms the reliability of both experimental measurements. The positive and negative axial velocities indicate the presence of the vortices, which would be clear by observing the complete velocity profiles obtained by PIV. 5.2. Validation of CFD Model Using Energy Balance. An important criterion for the validation of CFD simulation is the establishment of the energy balance. This means that the energy input rate (by the rotation of cylinder) and the energy dissipation rate (both by the viscous and turbulent modes of dissipation) need to be equal. Input energy was computed from the moment about a specified center. FLUENT calculates this moment vector by summing the product of the force vectors for each face with the moment vector, i.e., summing the forces on each face about the moment center,11 while output energy was found as

energy output ) F

∫02π∫0z∫rr (v + t)r dr dz dθ o

(11)

i

where the viscous energy dissipation rate, v, is given by

()

v ) ν

∂ui ∂xj

2

(12)

The turbulent energy dissipation rate, t, is given by

( )

t ) ν

∂u′i ∂u′i ∂xj ∂xj

(13)

Thus, the dissipation rates have been predicted from the CFD simulations. Figure 6 shows fairly good agreement between these two, which validates the simulations. The difference between the input energy and the dissipated energy can be seen to be increasing with an increase in the rotational speed. This may be attributed to the grid size. For resolving the turbulence at higher rotational speeds, finer and larger numbers of grids are required; however, we were constrained by the computational power. 5.3. Comparison between the CFD Predictions and the Flow Visualization. A comparison has been made between the predicted velocity profiles and those measured using LDV for the same geometry as used in experiments. Figures 7 and 8 show the CFD predictions and the experimental measurements for mean axial and radial velocities at two different locations for

Table 1. Effect of the Start-Up Procedure on the Number of Vortices at Various Speeds no.

rotational speed (r/s)

sudden start

gradual speed increase

1 2 3 4 5 6 8 9 10 11 12

1.67 6.67 10 15 18.33 20 25 30 35 40 45

10 8 6 6 6 4 4 4 4 4 2

10 10 6 6 4 4 4 2

rotational speeds of 10 and 20 r/s, respectively. The comparison of between measured and predicted mean tangential velocity profiles for 10 and 20 r/s is shown in Figure 9. A very close agreement can be seen for the mean velocity profiles. The velocity vectors obtained using CFD data comprising axial and radial components for velocity in the plane bisecting vanes and passing through the axis of rotation are shown in Figure 10A. The flow patterns in the entire annulus, obtained using PIV at 10 and 20 r/s, are shown in Figure 10B. The figure shows formation of six vortices at the rotational speed of 10 r/s and four vortices at the rotational speed of 20 r/s. This can be seen to be in complete agreement with the experimental observations using PIV. Thus the flow patterns have been correctly simulated using the CFD model. To have an insight of the flow below the rotor in the measurement plane, the experimental and predicted flow patterns are shown magnified in Figure 10, where a clear circulation has been observed in this region. The flow pattern in ACEs shows existence of toroidal vortices in the annular region and circulation below the rotor region due to the presence of vanes. Further, fairly good agreement has been observed between the measured and predicted turbulent kinetic energies (at z/H ) 0.16), which is shown in Figure 11. 5.4. Effect of the Presence of Vanes below the Rotor. The flow patterns in a absence of bottom vanes of ACE have been reported in earlier studies by Deshmukh et al.8 In this work the effect of the presence of vanes has been studied. When the flow is characterized by well-defined vortices, each vortex can be treated as a well-mixed reactor.15,16 Thus it is possible to get the idea about the back-mixing depending upon the number of vortices in the flow domain. It may be pointed out that when the rotor speed was increased from 10 to 20 r/s, the number of vortices reduced from eight to six in the absence of bottom vanes. However, in the presence of vanes the number of vortices were six and four at the respective speeds. Further, in the presence of vanes, purely tangential flow below the rotor region was found to be completely absent and vortices were observed in this region (axial-radial plane) (Figure 10). The presence of vanes below the rotor region creates turbulence. This is perceptible by comparing the turbulence intensities in the absence and presence of vanes under otherwise identical conditions. The volume average turbulent intensities obtained using CFD, at 20 r/s, were 5 and 9.5% in the absence and presence of vanes, respectively. Thus vanes enhance the turbulence and the back-mixing in the annulus. To reduce the vane effect on the flow patterns in the annulus, it was thought desirable to carry out a simulation keeping the length of vane below the rotor equal to 14.5 mm (instead of 20 mm), so that vanes would not protrude beyond the rotor circumference (Figure 12A). The CFD result predictions in terms of vector plot for this case are shown in Figure 12B, showing

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Figure 13. Vector plot representing the flow patterns below the rotor at 20 r/s: (A) in the absence of vanes; (B) 20 mm vanes; (C) 14.5 mm vanes.

Figure 15. Contour stream function depicting the flow patterns in the absence and presence of radial baffles in the annulus at 50 r/s.

Figure 14. Comparison between CFD predictions and experimental measurements for mean axial and radial velocity profiles at z/H ) 0.055 at (A) 10 and (B) 20 r/s: (9) axial velocity (experimental), (0) radial velocity (experimental), (s) axial velocity (CFD), and (- - -) radial velocity (CFD).

an increase in the number of vortices; however, weak circulation was observed below the rotor (axial-radial plane). Parts A, B, and C of Figure 13 show the flow patterns in the radial tangential

plane below the rotor in the absence of vanes, with 20 mm vanes, and with 14.5 mm vanes, respectively. It can be seen that the region between neighboring vanes contains a circulation cell and the length of vanes decides its size. The volume average turbulent intensity in the case of 14.5 mm vanes was found to be 8.15%. 5.5. Effect of the Start-Up Procedure and Rotational Speed. The validated CFD model has been used to study the effects of operational parameters. One of them is the effect of the start-up procedure. It should be noted that all the experimental measurements reported in this work have been carried out for the sudden start of the rotor at the specified speed. However, the gradual increase of speed can also be followed. For Taylor vortex type flow, the flow patterns strongly depend on the start-up procedure.17 In this work the CFD has been used to investigate this effect. The simulations have been performed for various rotational speeds starting from 1.67 to 45 r/s. As mentioned earlier, in case of sudden start of rotation of the rotor, the initial rotor boundary condition was specified at that particular speed. For the case of gradual increase of speed, the rotor was started at 1.67 r/s rotational speed and the mean velocity magnitude at three different locations in the system was monitored to ensure the steady state at starting speed. The simulations were then continued with higher rotational speed until a new steady state was attained at higher rotational speed and this stepwise procedure was continued and results were obtained.

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When the rotation speed was increased gradually, the vortices present at the ends elongated, which compressed the vortices present away from the ends. When this compression exceeded a certain value, new state was found to be reached with the disappearance of a pair of vortices. This behavior continued to happen until the entire annulus was occupied by only two counter-rotating vortices. The results in terms of number of vortices are summarized in Table 1. In the sudden start procedure different equilibrium states were found at the same rotational speeds and the final state of two counterrotating vortices appeared at a much higher rotational speed (45 r/s) than in the case of gradual increase of speed (30 r/s). 5.6. Flow Patterns in the Presence of Axial Flow. From the stability studies of Taylor-Couette flow it has been revealed that incorporation of a small amount of axial flow delays the instability.15 A similar consequence has been thought in the case of ACE. The axial flow has been incorporated in the simulations as mentioned earlier, so the axial Reynolds number (Rez ) 2FUd/µ) was 465. Two rotational speeds, viz., 10 and 20 r/s, have been selected. The comparison for mean axial and radial velocities predicted using CFD and measured experimentally using PIV is shown in Figure 14. It was observed that the number of vortices were the same in the presence and absence of axial flow. Thus a small amount of axial flow does not show significant difference in the flow patterns. However, at higher Rez values the flow patterns may be affected. 5.7. Effect of Radial Baffles in the Annulus on the Flow Patterns. As discussed, increase in rotational speed leads to back-mixing in the ACE. In ACE, the back-mixing can be reduced by modifying the annulus. One of the options available is to provide radial baffles and divide the annulus into compartments. The entire annulus has been divided into four compartments providing three equally spaced radial baffles. The width of the baffles was picked equal to half of the annular gap. The simulations have been carried out for a very high rotational speed (50 r/s), for which two counter-rotating vortices in the entire annulus could be obtained. It should be noted that vanes below the rotor were not considered in the simulation. Under these conditions, the geometry is axisymmetric and can be modeled as axisymmetric swirl which is capable of predicting the circumferential velocity; the advantages were lower computational efforts and time saving.8,11 The predicted flow pattern in terms of stream functions in the absence and presence of radial baffles is shown in Figure 15. It can be seen that each compartment has been acquired with two counter-rotating vortices and the entire annulus contained eight vortices. The back-mixing can be thus reduced by providing radial baffles in the annulus. 6. Conclusions The CFD model has been developed to study the flow patterns in the annular region of ACE. To validate the model, flow visualization experiments have been carried out using PIV and LDV. A very good comparison has been found between CFD predictions and experimental measurements for the average velocity profiles and flow patterns in the annulus in both the presence and absence of axial flow. Further, the compete energy balance has been established, which is one of the criteria for validating the simulations. The effect of the start-up procedure on the flow pattern has been studied for different rotational speeds using CFD. As the rotational speed increases, backmixing becomes dominant. The presence of vanes on the bottom plate, below the rotor, essential to direct the flow inside the

rotor, enhances the back-mixing and turbulence. The CFD results show that providing suitable internals such as radial baffles as well as the length of vanes on the bottom plate can reduce backmixing in the annulus. Acknowledgment This work has been part of the project program supported by the Board of Research in Nuclear Sciences (BRNS), Sanction No. 2006/34/24-BRNS/2803. The authors also acknowledge Dr. L. M. Gantayet for the discussions provided during this study. Nomenclature C1, C2, Cµ ) turbulent parameters d ) annular gap (m) Di ) inner diameter of stator (m) Do ) outer diameter of rotor (m) H ) annulus height (m) k ) turbulent kinetic energy (m2/s2) N ) number of measurements P ) pressure (Pa) P′ ) fluctuating pressure (Pa) P ) generation of turbulent kinetic energy due to mean velocity gradients (kg m-1 s3) r ) radial distance (m) ri ) radius of inner cylinder (m) ro ) radius of outer cylinder (m) Rez ) axial Reynolds number; Rez ) 2FUd/µ t ) time (s) Ta ) Taylor number Tacr ) critical Taylor number u ) velocity component (m/s) u′ ) fluctuating velocity component (m/s) 〈u〉 ) time average velocity (m/s) U ) mean axial velocity (m/s) V ) velocity (m/s) x ) directional coordinate (m) z ) axial distance (m) Greek Symbols δ ) Kronecker delta Ω ) angular velocity (rad/s) F ) density (kg/m3) µ ) molecular viscosity (Pa‚s) νt ) turbulent viscosity (m2/s) ν ) kinematic viscosity (m2/s) σTI ) flow turbulence intensity (%) σM ) inherent measurement error (%) σµ ) error in the mean velocity (%) σ, σk ) turbulent parameters  ) turbulent energy dissipation rate (m2/s3) θ ) azimuthal coordinate τij ) Reynolds stresses (N/m2) Subscripts i, j, k ) Cartesian coordinate components Literature Cited (1) Bernstein, G. J.; Grodsvenor, D. E.; Lenc, J. F.; Levitz, N. M. Development and performance of a high-speed annular centrifugal contactor. Argonne National Laboratory Report; ANL-7968, Argonne National Laboratory, Argonne, IL, 1973. (2) Leonard, R. A.; Bernstein, G. J.; Pelto, R. H. Liquid-liquid dispersion in turbulent Couette flow. AIChE J. 1981, 27, 495.

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(3) Leonard, R. A. Recent advances in centrifugal contactor design. Sep. Sci. Technol. 1988, 23, 1473. (4) Vedantam, S.; Joshi, J. B.; Koganti, S. B. CFD simulation of RTD and mixing in the annular region of a Taylor-Couette Contactor. Ind. Eng. Chem. Res. 2006, 45, 6360. (5) Vedantam, S.; Joshi, J. B.; Koganti, S. B. Three dimensional CFD simulation of stratified two-fluid Taylor-Couette flow. Can. J. Chem. Eng. 2006, 84, 279. (6) Vedantam, S.; Joshi, J. B. Annular centrifugal Contactors: A review. Chem. Eng. Res. Des. 2006, 84 (A5), 522. (7) Wardle, K.; Allen, T.; Swaney, R. Computational Fluid Dynamics (CFD) study of the flow in an annular centrifugal contactor. Sep. Sci. Technol. 2006, 41, 2225. (8) Deshmukh, S. S.; Vedantam, S.; Joshi, J. B. Computational flow modeling and visualization in the annular region of annular centrifugal extractor. Ind. Eng. Chem. Res. 2007, published online June 29, 2007 (http:// dx.doi.org/10.1021/ie061587e). (9) Parker, J.; Merati, P. An investigation of turbulent Taylor-Couette flow using Laser Doppler Velocimetry in a refractive index matched facility. Trans. ASME 1996, 118, 810. (10) Ranade, V. V.; Mishra, V. P.; Saraph, V. S.; Deshpande, G. B.; Joshi, J. B. Comparison of axial flow impellers using LDA. Ind. Eng. Chem. Res. 1992, 31, 2370.

(11) FLUENT 6.0 User Guide; FLUENT: Lebanon, NH, 2002. (12) Launder, B. E.; Reece, G. J.; Rodi, W. Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 1975, 68, 537. (13) Launder, B. E.; Spalding, D. B. The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Eng. 1974, 3, 269. (14) Bevington, P. R. Data Reduction and Error Analysis for the Physical Sciences; McGraw-Hill: New York, 1969. (15) Kataoka, K.; Doi, H.; Hongo, T.; Fugatawa, M. Ideal plug-flow properties of Taylor-vortex flow. J. Chem. Eng. Jpn. 1975, 8, 472. (16) Pudijiono, P. I.; Tavare, N. S.; Garside, J.; Nigam, K. D. P. Residence time distribution from a continuous Couette flow device. Chem. Eng. J. 1992, 48, 101. (17) Koschmieder, E. L. Benard Cells and Taylor Vortices; Cambridge University Press: New York, 1993.

ReceiVed for reView July 15, 2007 ReVised manuscript receiVed October 8, 2007 Accepted October 10, 2007 IE070959W