- Email: [email protected]
Measurement and CFD simulation of single-phase flow in solvent extraction pulsed column
Chemical Engineering Science 61 (2006) 2930 – 2938 www.elsevier.com/locate/ces
Measurement and CFD simulation of single-phase flow in solvent extraction pulsed column J.M. Bujalski, W. Yang, J. Nikolov, C.B. Solnordal, M.P. Schwarz∗ CSIRO MINERALS, Box 312, Clayton South, Victoria 3169, Australia Received 5 July 2005; received in revised form 5 October 2005; accepted 10 October 2005 Available online 15 December 2005
Abstract A CFD (computational fluid dynamics) model of a solvent extraction pulsed column has been developed and run with a single water phase. The results are compared with experimental measurements taken on a pilot scale column using PIV (particle image velocimetry). The pulsed column investigated had disk–doughnut internals and was operated under pulsing intensities ranging from 10 to 32.5 mm/s. PIV measurements of velocity were used to validate the CFD model and to characterise the pulsing flow of a single phase through the column. The CFD modelling was performed for the same geometry and operating conditions using a 2D computational grid and a low Reynolds Number k– turbulence model. An improved velocity prediction was achieved by adding a gap between the doughnut internal and the pulsed column wall. The combined measurements and predictions give insight into the effect of the geometry internals on the flow hydrodynamics in the pulsed column. 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Fluid mechanics; Simulation; Pulsed column; CFD; PIV
1. Introduction Solvent extraction is a technique for separating components in solution by distribution between two immiscible liquid phases. Over the years different types of solvent extraction contactors have been developed for use in the minerals processing industry. The most common type is the mixer settler arrangement but more recently pulsed columns have been employed. In recent years they have started gaining acceptance by the minerals industry as an alternative to the mixer/settler configuration used in solvent extraction. The pulsed column’s major advantage over conventional solvent extraction systems is a small footprint for multistage extraction systems. Also the possibility of reduction in organic losses and organic inventory, and lower sensitivity to solids loading and crud make the process attractive (Fox et al., 1998). A more detailed analysis of the relative merits of pulsed columns and mixer/settlers is ∗ Corresponding author. Tel.: +61 3 9545 8568; fax: +61 3 9562 8919.
E-mail address: [email protected] (M.P. Schwarz). 0009-2509/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2005.10.057
presented by Vancas and Buchalter (2003). Nitsch and Schuster (1983) stated that due to the complex nature of pulsed columns, they had to be designed empirically and that more fundamental research into the local flow structures, hydrodynamics and mass transfer was therefore needed. Hydrodynamics in different pulsed extraction columns have been investigated using indirect experimental methods (Dimitrova Al Khani et al., 1988; Camurdan et al., 1989; Lorenz et al., 1990). The reported experimental work has focused on the mass transfer aspect of the operation (droplet size distribution and hold-up). By analysing the extraction efficiency data, conclusions have been drawn about the hydrodynamics in the pulsed columns. Direct investigation of pulsed column hydrodynamics has been reported by Angelov et al. (1990). The authors measured the axial velocity component at different Reynolds numbers and positions in a pulsed column using LDA (laser doppler anemometry) in a non-pulsating flow. The measured inlet and outlet velocity profiles were used by the authors as boundary conditions for CFD simulations whilst the results in the centre of the column were used to validate their simulations. The work
J.M. Bujalski et al. / Chemical Engineering Science 61 (2006) 2930 – 2938
of Ni et al. (2002) measured the velocity field in an oscillatory baffled reactor by PIV but, to the knowledge of the authors, no previous work on PIV measurements in disk doughnut pulsed columns has been reported. Angelov et al. (1998) investigated the energy dissipation maps between the disk doughnut cells and concluded that there were moving energy dissipation zones above and below the plates in addition to the high shear rate zones near the doughnut edges leading to additional droplet break-up zones. Angelov and Gourdon (2002) linked the turbulent macroscale to the height between the disk doughnut internals and found that the turbulence energy in the pulsed column is linked to the size of the generated vortices. This implies a strong dependence of the pulsed column performance on internals. CFD simulation of the disk doughnut geometry under pulsed flow has been reported by Aoun Nabli et al. (1998). In this work authors modelled the single phase hydrodynamics and axial dispersion coefficient of an injected tracer but did not validate their velocity field results. In later work Aoun Nabli et al. (1998) used CFD to investigate the level of turbulence of different disk doughnut geometries and Reynolds numbers. The authors concluded that “more precise experimental knowledge of the hydrodynamics within these columns is necessary to improve the simulations” and suggested PIV as the best method to achieve this. In most studies, the authors have assumed that the internals fit the column walls. In test scale columns there is a possibility of a gap between the doughnut internal and the column wall. In the literature there is no mention of any special treatment of such gaps but discrepancies between the predicted and measured axial dispersion have been observed (Aoun Nabli et al., 1997) which could be explained by a gap. The effect of this geometry imperfection on the hydrodynamics should be investigated. In the literature the pulsed column hydrodynamics in single phase and non-oscillating flow conditions have been experimentally investigated with the LDA measurement technique, but there have been no reported results of the velocity profile when a column is under pulsation operation or with the measurement of the velocity field using the PIV technique. The work presented in this paper fills in some of the gaps in the knowledge of pulsed column hydrodynamics by using experimental and modelling tools to investigate pulsation flow in a single phase pulsed column. This work is the first stage of a research program on pulsed column hydrodynamics; the second stage investigates two-phase flow and will be reported separately.
2931
Fig. 1. Schematic diagram of PIV set-up for the pulsed column.
were held by three metal rods of 50 mm height. At the top of the pulsed column was a settler, see Fig. 1. The pulsation amplitude and frequency was controlled by a variable speed motor and in the upward through-flow experiments additional fluid was added at the bottom of the column whilst for the downward through flow experiment the additional fluid was added at the top of the column. 2.2. PIV (particle image velocimetry)
2. Methods 2.1. Experimental pulsed column A one meter section of a 0.1 m internal diameter pulsed column with disk doughnut metal internals was used as a basis for the set of experiments. The spacing between disk and doughnut was set to half the internal diameter of the column and the free flow area of the two types of internals was 23%. The internal disks were held by a central shaft whilst the doughnuts
The single-phase fluid flow field within a pulsed column was measured using 2D particle image velocimetry (PIV). The ILA 2D PIV system consists of a 1.3 Megapixel (1280 × 1024 pixels) 12-bit digital CCD camera which was synchronised with a New Wave 120 mJ double-cavity Nd:YAG laser. The laser beam was expanded by a cylindrical lens to form a 2 mm thick plane vertical light sheet that was directed horizontally through the centre of the pulsed column. As shown in Fig. 1, a square Perspex box filled with water was placed
2932
J.M. Bujalski et al. / Chemical Engineering Science 61 (2006) 2930 – 2938
Table 1 Operating conditions of single-phase pulsed column for PIV measurements Trial number
Throughflow condition
Pulsing amplitude (mm)
Pulsing frequency (Hz)
Pulsation intensity (mm/s)
Flux (m3 /m2 /hr)
No-flow
10
2
20
—
2 3 4
20
0.5 0.75 1
10 15 20
5 6 7 8 9
26
0.25 0.5 0.75 1 1.25
6.5 13 19.5 26 32.5
10 11 12 13
30 20 20 20
0.67 1 1 1
20 20 20 20
1
Down-flow (2 L/min) Up-flow (2 L/min)
outside the cylindrical glass column to minimise the effect of optical distortion at the curved surface. The positions of tracer particles illuminated by the light sheet were recorded at a frame rate that was a multiple of the pulsation frequency of the liquid. An electrical encoder was installed on the crank of the pulsator to allow selection of the single crank angle trigger for the PIV synchronisation system. This ensured that images could be taken repetitively in a sequence to a known pulsator crank angle. The field of view of the CCD camera was 80 × 64 mm2 using 1280 × 1028 pixels of CCD array. The smallest resolvable length scale of the PIV set-up, which is the real length of each pixel, equals 62.5 m. The interrogation windows were 64 × 64 pixels (4 × 4 mm2 ), with a 50% overlapping between consecutive interrogation cells providing a velocity vector spacing of 32 pixels (2 mm). Each instantaneous 2D velocity measurement contained a total of 1209 vectors. The seeding particles used were TSI silver-coated hollow glass beads with mean diameter of 14 m and relative density of 1.65. The relaxation time of the particles was 18 s, which is negligible compared to the separation time of 1–3 ms between pairs of images used for computation of particle displacements. The uncertainty of pixel displacement in the measurement was about 0.2 pixel within the interrogation window of 64 × 64 pixels. Therefore the error of PIV measurements is about 0.31%. Measurements were taken over a period of approximately 100 cycles, and the flow fields averaged for each of 8 phases within a cycle. In this way the effects of turbulence, which mean that the detailed flow at each cycle is different, were averaged out. For the preliminary single-phase flow field investigation, the PIV measurements were carried out under the experimental operating conditions in Table 1. These conditions correspond to the range of pulsation intensity for which the column can be operated in the mixer-settler or emulsion mode according to the experimentally determined regime map and flooding curve (Logsdail and Slater, 1991). Most of the measurements have
— 15.3 15.3
been made in the absence of through-flow, with one up-flow and one down-flow case also studied (see Trial 12 and 13 in Table 1). The LDV (laser doppler velocimetry) measurements were used as a crosscheck of the PIV results and the CFD simulations for Trial 4. LDV has been reported extensively in literature for other systems (Fei et al., 2000) and is an extremely robust technique requiring no calibration. It is most suitable as a method for accurately determining turbulence characteristics (such as Reynolds stresses) of steady flows but is used here to cross-check against the PIV. LDV is slow compared to PIV for velocity measurement which is why the PIV was the preferred method for investigating the velocity field.
2.3. Computational method The experimental pulsed column geometry has been modelled using an axi-symmetric 2D geometry. This should be an excellent approximation particularly away from the upper and lower ends of the column. The axi-symmetric modelling assumption of the flow field is valid since the large number of axisymmetric internal plates present in the column means that any variations in velocity with angular position around the column present at the top and bottom of the column will be damped out for sections away from the top and bottom. Furthermore, the tangential component of flow is negligible when compared to the radial and axial components (Aoun Nabli et al., 1998). The model computational domain extends over three disk–doughnut sections in which the single-phase flow is considered to be typical of the flow over most of the column height. Although there will be entrance regions at the top and bottom of the column, it is expected that the flow will be the same in most of the sections of the column. The computational domain was terminated at top and bottom by a 1 mm thick section of a disk, and the associated flow
J.M. Bujalski et al. / Chemical Engineering Science 61 (2006) 2930 – 2938
2933
Navier–Stokes Eqs. (2) and (3) (AEA Technology, 2002). j + ∇ · (U) = 0, jt j U + ∇ · (U ⊗ U) − ∇ · (eff ∇U) jt = −∇p + ∇ · (eff (∇U)T ) + B,
(2)
(3)
In Eq. (3), eff is the effective viscosity and calculated in Eq. (4): eff = + T .
(4)
The Reynolds number in the simulations is around 2000 and so the standard k– turbulence model is not appropriate. The low Reynolds number k– turbulence model was used instead (AEA Technology, 2002). This turbulence model differs from the standard k– model in that in the low Reynolds number k– model the turbulence properties are damped and directly calculated on the walls, without the use of wall functions. Additionally the turbulent viscosity is modified as shown in Eq. (5): k2 , (5) where C is a fitting constant set to 0.09 and f is a function calculated in Eq. (6): −3.4 . (6) f = exp (1 + (k 2 /50))2
T = C f
Fig. 2. Axi-symmetric computational geometry used in the CFD simulations.
passage between the disk and the wall, at which inlet/outlet flow boundary conditions must be defined. The height of the computational domain was 156 mm whilst its radius was 50 mm. To model the pulsed column an axi-symmetric uniform grid of 1 mm cell edge length was used with 7800 computational cells as shown in Fig. 2. To simulate the disks and doughnut internal plates, 2 mm thick walls were inserted in the geometry at correct heights. In the simulation only half the 6 mm diameter shaft holding the disks was modelled, as it was positioned on the axis of symmetry, running from the bottom to the top of the simulated geometry. The properties of the single phase were those of water with a density of 1000 kg/m3 and viscosity 0.001 kg/ms. The Reynolds number for the pulsating flow, ReP , can be defined as (Ni et al., 2003): ReP =
D(f A) .
(1)
The required boundary conditions for the system are complex, given the time dependent sinusoidal behaviour of the inlet/outlet boundaries. The velocity pulsation magnitude at the boundary condition was defined by Eq. (7): U = Af sin(2f t).
(7)
At the top boundary (the “outlet”) pressure was set to be uniform, with zero normal gradients for the other variables (i.e., Dirichlet condition) whereas, when the flow was entering the computational domain, the velocity was set to be uniform and equal to Eq. (7). The lower boundary (the “inlet”), velocity was set to be uniform and equal to Eq. (7) at all times. The wall boundary conditions for the low Reynolds number k– turbulence model were set to no-slip with the kinetic energy and energy dissipation set to 0. The oscillation in the flow boundary condition required the use of a transient simulation. The number of time steps used for each pulsation period was from 25 to 80 and the number of iterations per time step was from 35 and 100, respectively. No difference was found in the results in the two different simulation procedures. The time for the simulations to reach periodic steady state was 15 oscillation periods. 3. Results and discussion
For the case with frequency, f, equal to 1 Hz and peak-to-peak amplitude, A, equal to 20 mm, ReP = 2000. The general purpose CFD code, CFX 4, was used as the basis for the model development. The conservation of mass and momentum were determined using the Reynolds averaged
3.1. PIV validation LDV was used to verify the PIV results at a selected measurement point A over the period of a whole oscillation. The
2934
J.M. Bujalski et al. / Chemical Engineering Science 61 (2006) 2930 – 2938
Velocity, [m/s]
0.2
0.0
LDV - Axial velocity PIV - Axial velocity CFD - Axial velocity
-0.2
-0.4 0.0
0.2
0.4
0.6
0.8
1.0
Time, [s]
Fig. 3. Comparison between LDV, PIV measurements and CFD predictions of axial velocity component for point A (20 mm amplitude, 1 Hz frequency).
axial velocity data taken using LDV and PIV at point A (14 mm from the centreline and 7 mm under the doughnut internal, see Fig. 2) are shown in Fig. 3, and compared with velocity data from CFD. Fig. 3 shows the time variation of the axial velocity component over one 1 Hz and 20 mm amplitude oscillation (Trial 4). This comparison provides evidence that the PIV measurements are accurate and can be used for comparison with the CFD model. 3.2. PIV and CFD velocity maps An example of a set of PIV and CFD results are given in Figs. 4 and 5. The eight images show the time variation of the flow field as the pulsing progresses through one full cycle, with the interval between images corresponding to an increment of 45◦ crank angle. Fig. 4 shows the velocity field over the first half of the pulsation cycle and Fig. 5 over the second half. The flow predicted by CFD is shown on the left side and the corresponding PIV measured flow on the right. The PIV velocity measurements near the doughnuts could be prone to error as there is a possibility of laser light scatter from the doughnut surface. On the downstroke the flow impacts upon and sweeps across the tops of the disks and doughnuts, while the undersides of both disks and doughnuts is stagnant. On the upstrokes, flow impacts on and sweeps across the undersides of the internals, and the top surfaces are stagnant. This behaviour is important for surface regeneration of dispersed phase in solvent extraction. The most important feature in the pulsed column is the formation of the vortex between the disk and doughnut internals and in most images the generated vortices are not uniformly distributed. Furthermore, the vortices move substantially with time over a cycle. So for example there is a large vortex present at the angles 0◦ and 45◦ between the doughnut and disk but almost nothing in the next stage below. A reverse vortex is observed between the angles 180◦ and 225◦ . At the angles 90◦ and 270◦ , although there is no net flow, remnant vortices exist
in the compartments in both the CFD predictions and measurements which contribute to the mixing, break-up and residence time in each compartment. The predicted flow in Figs. 4 and 5 agrees well with the measurements in both shape and magnitude of the vortices. With the additional quantitative comparison of PIV and CFD results over a single phase shown in Fig. 3, the agreement is sufficiently good for there to be a large degree of confidence in the use of the computational model for design purposes. Some of the vortices are of slightly different strength in the measured flow compared with the predictions, and these slight discrepancies are probably due to the difference in the geometry between the experiment set-up (gap between the column wall and doughnut edge) and the CFD model (no gap between the doughnut edge and the column wall). 3.3. Axial velocity radial profile The pulsed column in solvent extraction operation is not a closed system but operates as a counter-current system with throughflow of organic downwards and aqueous upwards. To gauge the effect of the throughflow on the combined flow field within the column, two trials were carried out in the single phase apparatus, one with upward throughflow and the other with downward throughflow superimposed on the pulsation (trials 12 and 13). In each case the additional flow was 2 L/min which corresponds to a superficial velocity of 0.008 m/s. The effect of throughflow is shown in Fig. 6 which plots the axial velocity profile on a horizontal line across the column at the height of point A when the pulsator position is set to phase 0◦ . The additional throughflow in cases 12 and 13 has very little effect on the velocity profile when compared to the nothroughflow case, consistent with the small throughflow superficial velocity. At this angle of the pulsator (maximum downflow) the axial flow close to the centre of the column is mostly downwards through the doughnut opening above point A as expected. The change of direction to up-flow closer to the wall indicates a creation of the vortex. Surprisingly, the flow reverses yet again very close to the wall to down-flow. This can also be seen in the top right-hand plot of Fig. 4, as a pronounced downflow along the entire outer wall of the column. This secondary reversal is not captured in the CFD simulation without gap. In Fig. 7 the axial component of the flow is presented for the three different flow configurations when the pulsator is at the position of 180◦ (maximum up-flow). The flow underneath the doughnut is relatively stationary whilst there is a large upward flow component near the column wall. Once again the cases with additional throughflow up and down are quite similar, although unexpectedly the measured upward flow near the wall for no throughflow is somewhat different, in fact even lower than the down throughflow case, whereas the two throughflow cases would be expected to bracket the no throughflow measurements. We will see below that the gap between the doughnut and the wall affects the velocity significantly in this region, and it is possible that due to re-installation of the internals
J.M. Bujalski et al. / Chemical Engineering Science 61 (2006) 2930 – 2938
Mean Velocity Vectors at Time Phase - 45 Degree
Mean Velocity Vectors at Time Phase - 0 Degree 1m/s CFD Prediction
1m/s
0° PIV Measurement
CFD Prediction
Mean Velocity Vectors at Time Phase - 90 Degree 1m/s CFD Prediction
2935
90°
PIV Measurement
45°
PIV Measurement
Mean Velocity Vectors at Time Phase - 135 Degree 135° 1m/s CFD Prediction
PIV Measurement
Fig. 4. Flow field comparison between PIV measurement and CFD predictions at pulsator phases 0◦ –135◦ .
in the middle of the campaign, the gap was slightly different for the throughflow cases. Closer to centreline all sets of measurements are quite similar as the flow is mostly radial in this region, as shown also in Fig. 5.
circuiting and possibly the creation of a fast ‘jet’ flow along the column wall. This additional vertical flow will reduce size of the generated vortex, thus changing the local flow and shear rate in the column.
3.4. Effect of the gap between doughnut edge and column wall
3.5. Pulsation intensity
In Figs. 6 and 7 the main discrepancy between the PIV and the CFD is in the flow near the column wall. It was observed that in the experimental set-up the doughnut rings did not fit tightly against the column wall and a gap of varying size was present in individual doughnut configurations. The CFD geometry was modified to include a gap of 2 mm between the column wall and the doughnut edge. The CFD results for the modified geometry in Figs. 6 and 7 give a better prediction of the axial velocity than the original CFD results without the 2 mm gap. The gap between the wall and the doughnut could become significant in the scale-up of the pulsed column, leading to short
Fig. 8 shows the comparison of the maximum velocity (upward and downward) at point A as a function of pulsation intensity for trials 1 to 11. The results show the close agreement between the PIV and the CFD results for the downward velocity in the pulsation cycle, but there is an over prediction of the upward velocity component at this point. This discrepancy could be attributed to the turbulence model used as supported by similar work of Fei et al. (2000) who found a similar discrepancy between their CFD modelling using the k– turbulence model with their LDV measurements. The results indicate that the velocity component of the pulsed column can be scaled up with
2936
J.M. Bujalski et al. / Chemical Engineering Science 61 (2006) 2930 – 2938
Mean Velocity Vectors at Time Phase - 180 Degree 180°
Mean Velocity Vectors at Time Phase - 225 Degree 225° 1m/s
1m/s CFD Prediction
PIV Measurement
Mean Velocity Vectors at Time Phase - 270 Degree 270° 1m/s CFD Prediction
PIV Measurement
CFD Prediction
PIV Measurement
Mean Velocity Vectors at Time Phase - 315 Degree 1m/s CFD Prediction
315° PIV Measurement
Fig. 5. Flow field comparison between PIV measurement and CFD predictions at pulsator phases 180◦ –315◦ .
the pulsation intensity and that there is reliability in extrapolating the CFD simulation results in single phase flow to higher pulsation intensities.
and oscillation period T:
3.6. Energy dissipation
The value of the average energy dissipation for the system of 1 Hz and 20 mm amplitude by Eq. (8) is 0.044 m2 /s3 whilst the CFD predicted value of was 0.025 m2 /s3 (k– turbulence models are known to underpredict the turbulent properties in stirred tanks by a similar amount). The average energy dissipation in the pulsed column might not be representative of the average level of turbulence and mixing in the operation, and may only be a crude estimate in the analysis of the column operation. For example in the analysed system the maximum value of at a given time, ranged from 0.0446 m2 /s3 to 0.698 m2 /s3 , but the question remains whether the generated maximum occurs at the point in the pulsation cycle and at a location in the
As shown in Figs. 4 and 5 the pulsed flow generates vortices in the flow field which in turn generate the shear rate necessary for the dispersed phase break-up and coalescence needed for mass transfer. In turbulent flow the value of shear is linked to the turbulent energy dissipation, . Previously in the literature (Milot et al., 1990; Aoun Nabli et al., 1998) only average values of the kinetic energy dissipation over a pulsation cycle have been reported. Eq. (8) is a correlation proposed by Milot et al. (1990) to estimate the average energy dissipation in a pulsed column as a function of peak-to-peak amplitude, A,
= 778
3 A . T
(8)
J.M. Bujalski et al. / Chemical Engineering Science 61 (2006) 2930 – 2938
0.2
0.3
0.1
CFD - No through flow (no gap) Exp. - No through flow (Trial 4) Exp. - Up through flow (Trial 13) Exp. - Down through flow (Trial 12) CFD - No through flow (2mm gap)
0.1 0.0 0 Velocity, [m/s]
Vertical velocity, [m/s]
0.2
0.0 -0.1 0°
-0.2
0.01
0.02 0.03 Radial distance, [m]
0.04
35
-0.3 Maximum velocity Down (CFD) Regression for Down Maximum velocity Up (CFD) Regression for Up Maximum velocity Down (PIV) Maximum velocity Up (PIV)
-0.6
0.05
Fig. 6. Comparison of the PIV measurements and CFD simulation of axial velocity component at a line positioned 7 mm under the doughnut at a pulsation phase set at 0◦ (20 mm amplitude, 1 Hz frequency).
10 15 20 25 30 Intensity (Frequency x Amplitude), [mm/s]
-0.2
-0.5
Point A
5
-0.1
-0.4
-0.3 -0.4 0.00
2937
Fig. 8. Point A maximum and minimum velocity at different pulsation intensities: PIV measurement and CFD simulation comparison.
4. Conclusions 0.30
Vertical velocity, [m/s]
0.25 0.20
CFD- No through flow (no gap) Exp. - No through flow (Trial 4) Exp. - Up through flow (Trial 13) Exp. - Down through flow (Trial 12) CFD - No through flow(2mm gap) 180°
0.15 0.10 Point A
0.05 0.00 -0.05 0.00
0.01
0.02
0.03
0.04
0.05
Radial distance, [m] Fig. 7. Comparison of the PIV measurements and CFD prediction of axial velocity component at a line positioned 7 mm under the doughnut at a pulsation phase set at 180◦ (20 mm amplitude, 1 Hz frequency).
column where the energy can be used effectively for phase dispersion. The maximum for the pulsed column is lower than the predicted maximum values in stirred tanks under fully turbulent conditions. Zhou and Kresta (1998) found the values for Rushton turbines to be in a range of 85.2–528 m2 /s3 , but these are localised values inside the impeller generated vortex which is comparatively small in volume, whilst 57% of occurs at a lower value over majority of vessel volume (Ng and Yianneskis, 2000). Stirred vessels have a large difference between maximum and minimum energy dissipation—ranging by at least two orders of magnitude (Ng and Yianneskis, 2000) which generates a larger number of fine droplets and a broader size distribution. The range of in the pulsed column is smaller (maximum value ranged from 0.0446 to 0.698 m2 /s3 ) generating a narrower droplet size distribution.
The pulsed column operation in single phase flow was investigated with PIV and LDV experimental techniques. Extensive sets of PIV measurements have been taken of the unsteady flow within the column for a range of operating conditions and accurate point measurements taken with LDV have confirmed the PIV data. The PIV velocity measurements were taken at seven different phases in the pulsation cycle. The system was modelled with CFD and the simulations were validated by comparing with the measurements at various phases in the pulsation cycle: the flow field was well matched by the CFD simulation. The comparison of the CFD and PIV results showed that the flow field in certain regions of the pulsed column can depend sensitively on the positioning of the doughnut internal relative to the column wall if a small gap exists between the two. PIV measurements and CFD model predictions for the pulsed column operating in single phase mode show an oscillating sinuous flow through the column, with significant regions of low velocity and hence low shear. The range of in the pulsed column is narrower than in a stirred tank which would lead to different performance e.g. narrower droplet size distribution.
Notation A B C D f f k p Re t T U
amplitude of oscillation, m body force, N constant in low Re k– turbulence model pulsed column diameter, m frequency of oscillation, s−1 function to determine the turbulent viscosity turbulent kinetic energy, m2 /s2 pressure, Pa Reynolds number, dimensionless time, s oscillation period, s velocity, m/s
2938
J.M. Bujalski et al. / Chemical Engineering Science 61 (2006) 2930 – 2938
Greek letters
energy dissipation, m2 /s3
viscosity, Pa s density of phase, kg/m3
Subscripts eff P T
effective pulsation turbulent
Acknowledgements The authors would like to acknowledge the financial support for this work from Anglo Platinum, Bateman Solvent Extraction, BHP Billiton, Cognis Australia Pty Ltd, Kvaerner E&C Australia Pty Ltd, Minara Resources Ltd, Phelps Dodge Mining Company and WMC Resources Ltd, through the AMIRA International Project P706 “Improving Solvent Extraction Technology”. References AEA Technology, 2002. CFX 4.4 Flow Solver User Guide. AEA Technology, Harwell, Oxfordshire, UK. Angelov, G., Gourdon, C., 2002. Study on the turbulence in pulsed stagewise extraction columns: turbulent macroscale. Hungarian Journal of Industrial Chemistry 30, 137–142. Angelov, G., Journe, E., Liné, A., Gourdon, C., 1990. Simulation of the flow patterns in a disc and doughnut column. Chemical Engineering Journal 45, 87–97. Angelov, G., Gourdon, C., Liné, A., 1998. Simulation of flow hydrodynamics in a pulsed solvent extraction column under turbulent regimes. Chemical Engineering Journal 71, 1–9. Aoun Nabli, M., Guiraud, P., Gourdon, C., 1997. Numerical experimentation: a tool to calculate the axial dispersion coefficient in discs and doughnuts pulsed solvent extraction columns. Chemical Engineering Science 52 (14), 2353–2368. Aoun Nabli, M., Guiraud, P., Gourdon, C., 1998. CFD contribution to a design procedure for discs and doughnuts extraction column. Chemical
Engineering Research & Design Part A: Transactions of Institution of Chemical Engineers 76, 951–960. Camurdan, M.C., Baird, M.H.I., Taylor, P.A., 1989. Steady state hydrodynamics and mass transfer characteristics of a Karr extraction column. Canadian Journal of Chemical Engineering 67, 554–559. Dimitrova Al Khani, S., Gourdon, C., Casamatta, G., 1988. Simulation of hydrodynamics and mass transfer of a disk and rings pulsed column. Industrial Engineering Chemical Research 27 (2), 329–333. Fei, W.Y., Wang, Y.D., Wan, Y.K., 2000. Physical modelling and numerical simulation of velocity fields in rotating disc contactor via CFD simulation and LDV measurements. Chemical Engineering Journal 78, 131–139. Fox, M.H., Ralph, S.J., Sithebe, N.P., Buchalter, E.M., Riordan, J.J., 1998. Comparison of some aspects of the performance of a Bateman pulsed column and conventional box-type mixer/settlers. ALTA 1998 Nickel/cobalt pressure leaching and hydrometallurgy forum, Perth, Australia. Logsdail, D.H., Slater, M.J., 1991. Pulsed perforated-plate columns. In: Lo, T.C., Baird, H.I., Hanson, C. (Eds.), Handbook of Solvent Extraction. Krieger Publishing Company, pp. 355–372. Lorenz, M., Haverland, H., Vogelpohl, A., 1990. Calculation of the dynamic pressure drop in pulsed disk-plate columns. Extraction 1990: A Five-Day Symposium, IChemE Symposium Series, vol. 119, pp. 249–266. Milot, J.F., Duhamet, J., Gourdon, C., Casamatta, G., 1990. Simulation of a pneumatically pulsed liquid–liquid extraction column. Chemical Engineering Journal 45, 111–122. Ng, K., Yianneskis, M., 2000. Observations on the distribution of energy dissipation in stirred vessels. Chemical Engineering Research & Design Part A: Transactions of Institution of Chemical Engineers 78, 334–341. Ni, X., Jian, H., Fitch, A.W., 2002. Computational fluid dynamic modelling of flow patterns in an oscillatory baffled column. Chemical Engineering Science 57, 2849–2862. Ni, X., Jian, H., Fitch, A., 2003. Evaluation of turbulent integral length scale in an oscillatory baffled column using large eddy simulation and digital particle image velocimetry. Chemical Engineering Research & Design Part A: Transactions of Institution of Chemical Engineers 81, 842–853. Nitsch, W., Schuster, U., 1983. Liquid/liquid-mass transfer at swarms of droplets: kinetics of mass transfer in the system uranylnitrate, nitric acid, tributylphosphate. Separation Science and Technology 18, 1509–1533. Vancas, M.F., Buchalter, E., 2003. Mixer-settlers and pulsed columns: where are we now and where are we going? ALTA 2003 SX/IX World Summit, Perth, Australia ALTA, Castlemaine, Victoria, Australia, pp. 1–7. Zhou, G., Kresta, S.M., 1998. Correlation of mean drop size and minimum drop size with turbulence energy dissipation and the flow in an agitated tank. Chemical Engineering Science 53, 2063–2079.
Measurement and CFD simulation of single-phase flow in solvent extraction pulsed column J.M. Bujalski, W. Yang, J. Nikolov, C.B. Solnordal, M.P. Schwarz∗ CSIRO MINERALS, Box 312, Clayton South, Victoria 3169, Australia Received 5 July 2005; received in revised form 5 October 2005; accepted 10 October 2005 Available online 15 December 2005
Abstract A CFD (computational fluid dynamics) model of a solvent extraction pulsed column has been developed and run with a single water phase. The results are compared with experimental measurements taken on a pilot scale column using PIV (particle image velocimetry). The pulsed column investigated had disk–doughnut internals and was operated under pulsing intensities ranging from 10 to 32.5 mm/s. PIV measurements of velocity were used to validate the CFD model and to characterise the pulsing flow of a single phase through the column. The CFD modelling was performed for the same geometry and operating conditions using a 2D computational grid and a low Reynolds Number k– turbulence model. An improved velocity prediction was achieved by adding a gap between the doughnut internal and the pulsed column wall. The combined measurements and predictions give insight into the effect of the geometry internals on the flow hydrodynamics in the pulsed column. 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Fluid mechanics; Simulation; Pulsed column; CFD; PIV
1. Introduction Solvent extraction is a technique for separating components in solution by distribution between two immiscible liquid phases. Over the years different types of solvent extraction contactors have been developed for use in the minerals processing industry. The most common type is the mixer settler arrangement but more recently pulsed columns have been employed. In recent years they have started gaining acceptance by the minerals industry as an alternative to the mixer/settler configuration used in solvent extraction. The pulsed column’s major advantage over conventional solvent extraction systems is a small footprint for multistage extraction systems. Also the possibility of reduction in organic losses and organic inventory, and lower sensitivity to solids loading and crud make the process attractive (Fox et al., 1998). A more detailed analysis of the relative merits of pulsed columns and mixer/settlers is ∗ Corresponding author. Tel.: +61 3 9545 8568; fax: +61 3 9562 8919.
E-mail address: [email protected] (M.P. Schwarz). 0009-2509/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2005.10.057
presented by Vancas and Buchalter (2003). Nitsch and Schuster (1983) stated that due to the complex nature of pulsed columns, they had to be designed empirically and that more fundamental research into the local flow structures, hydrodynamics and mass transfer was therefore needed. Hydrodynamics in different pulsed extraction columns have been investigated using indirect experimental methods (Dimitrova Al Khani et al., 1988; Camurdan et al., 1989; Lorenz et al., 1990). The reported experimental work has focused on the mass transfer aspect of the operation (droplet size distribution and hold-up). By analysing the extraction efficiency data, conclusions have been drawn about the hydrodynamics in the pulsed columns. Direct investigation of pulsed column hydrodynamics has been reported by Angelov et al. (1990). The authors measured the axial velocity component at different Reynolds numbers and positions in a pulsed column using LDA (laser doppler anemometry) in a non-pulsating flow. The measured inlet and outlet velocity profiles were used by the authors as boundary conditions for CFD simulations whilst the results in the centre of the column were used to validate their simulations. The work
J.M. Bujalski et al. / Chemical Engineering Science 61 (2006) 2930 – 2938
of Ni et al. (2002) measured the velocity field in an oscillatory baffled reactor by PIV but, to the knowledge of the authors, no previous work on PIV measurements in disk doughnut pulsed columns has been reported. Angelov et al. (1998) investigated the energy dissipation maps between the disk doughnut cells and concluded that there were moving energy dissipation zones above and below the plates in addition to the high shear rate zones near the doughnut edges leading to additional droplet break-up zones. Angelov and Gourdon (2002) linked the turbulent macroscale to the height between the disk doughnut internals and found that the turbulence energy in the pulsed column is linked to the size of the generated vortices. This implies a strong dependence of the pulsed column performance on internals. CFD simulation of the disk doughnut geometry under pulsed flow has been reported by Aoun Nabli et al. (1998). In this work authors modelled the single phase hydrodynamics and axial dispersion coefficient of an injected tracer but did not validate their velocity field results. In later work Aoun Nabli et al. (1998) used CFD to investigate the level of turbulence of different disk doughnut geometries and Reynolds numbers. The authors concluded that “more precise experimental knowledge of the hydrodynamics within these columns is necessary to improve the simulations” and suggested PIV as the best method to achieve this. In most studies, the authors have assumed that the internals fit the column walls. In test scale columns there is a possibility of a gap between the doughnut internal and the column wall. In the literature there is no mention of any special treatment of such gaps but discrepancies between the predicted and measured axial dispersion have been observed (Aoun Nabli et al., 1997) which could be explained by a gap. The effect of this geometry imperfection on the hydrodynamics should be investigated. In the literature the pulsed column hydrodynamics in single phase and non-oscillating flow conditions have been experimentally investigated with the LDA measurement technique, but there have been no reported results of the velocity profile when a column is under pulsation operation or with the measurement of the velocity field using the PIV technique. The work presented in this paper fills in some of the gaps in the knowledge of pulsed column hydrodynamics by using experimental and modelling tools to investigate pulsation flow in a single phase pulsed column. This work is the first stage of a research program on pulsed column hydrodynamics; the second stage investigates two-phase flow and will be reported separately.
2931
Fig. 1. Schematic diagram of PIV set-up for the pulsed column.
were held by three metal rods of 50 mm height. At the top of the pulsed column was a settler, see Fig. 1. The pulsation amplitude and frequency was controlled by a variable speed motor and in the upward through-flow experiments additional fluid was added at the bottom of the column whilst for the downward through flow experiment the additional fluid was added at the top of the column. 2.2. PIV (particle image velocimetry)
2. Methods 2.1. Experimental pulsed column A one meter section of a 0.1 m internal diameter pulsed column with disk doughnut metal internals was used as a basis for the set of experiments. The spacing between disk and doughnut was set to half the internal diameter of the column and the free flow area of the two types of internals was 23%. The internal disks were held by a central shaft whilst the doughnuts
The single-phase fluid flow field within a pulsed column was measured using 2D particle image velocimetry (PIV). The ILA 2D PIV system consists of a 1.3 Megapixel (1280 × 1024 pixels) 12-bit digital CCD camera which was synchronised with a New Wave 120 mJ double-cavity Nd:YAG laser. The laser beam was expanded by a cylindrical lens to form a 2 mm thick plane vertical light sheet that was directed horizontally through the centre of the pulsed column. As shown in Fig. 1, a square Perspex box filled with water was placed
2932
J.M. Bujalski et al. / Chemical Engineering Science 61 (2006) 2930 – 2938
Table 1 Operating conditions of single-phase pulsed column for PIV measurements Trial number
Throughflow condition
Pulsing amplitude (mm)
Pulsing frequency (Hz)
Pulsation intensity (mm/s)
Flux (m3 /m2 /hr)
No-flow
10
2
20
—
2 3 4
20
0.5 0.75 1
10 15 20
5 6 7 8 9
26
0.25 0.5 0.75 1 1.25
6.5 13 19.5 26 32.5
10 11 12 13
30 20 20 20
0.67 1 1 1
20 20 20 20
1
Down-flow (2 L/min) Up-flow (2 L/min)
outside the cylindrical glass column to minimise the effect of optical distortion at the curved surface. The positions of tracer particles illuminated by the light sheet were recorded at a frame rate that was a multiple of the pulsation frequency of the liquid. An electrical encoder was installed on the crank of the pulsator to allow selection of the single crank angle trigger for the PIV synchronisation system. This ensured that images could be taken repetitively in a sequence to a known pulsator crank angle. The field of view of the CCD camera was 80 × 64 mm2 using 1280 × 1028 pixels of CCD array. The smallest resolvable length scale of the PIV set-up, which is the real length of each pixel, equals 62.5 m. The interrogation windows were 64 × 64 pixels (4 × 4 mm2 ), with a 50% overlapping between consecutive interrogation cells providing a velocity vector spacing of 32 pixels (2 mm). Each instantaneous 2D velocity measurement contained a total of 1209 vectors. The seeding particles used were TSI silver-coated hollow glass beads with mean diameter of 14 m and relative density of 1.65. The relaxation time of the particles was 18 s, which is negligible compared to the separation time of 1–3 ms between pairs of images used for computation of particle displacements. The uncertainty of pixel displacement in the measurement was about 0.2 pixel within the interrogation window of 64 × 64 pixels. Therefore the error of PIV measurements is about 0.31%. Measurements were taken over a period of approximately 100 cycles, and the flow fields averaged for each of 8 phases within a cycle. In this way the effects of turbulence, which mean that the detailed flow at each cycle is different, were averaged out. For the preliminary single-phase flow field investigation, the PIV measurements were carried out under the experimental operating conditions in Table 1. These conditions correspond to the range of pulsation intensity for which the column can be operated in the mixer-settler or emulsion mode according to the experimentally determined regime map and flooding curve (Logsdail and Slater, 1991). Most of the measurements have
— 15.3 15.3
been made in the absence of through-flow, with one up-flow and one down-flow case also studied (see Trial 12 and 13 in Table 1). The LDV (laser doppler velocimetry) measurements were used as a crosscheck of the PIV results and the CFD simulations for Trial 4. LDV has been reported extensively in literature for other systems (Fei et al., 2000) and is an extremely robust technique requiring no calibration. It is most suitable as a method for accurately determining turbulence characteristics (such as Reynolds stresses) of steady flows but is used here to cross-check against the PIV. LDV is slow compared to PIV for velocity measurement which is why the PIV was the preferred method for investigating the velocity field.
2.3. Computational method The experimental pulsed column geometry has been modelled using an axi-symmetric 2D geometry. This should be an excellent approximation particularly away from the upper and lower ends of the column. The axi-symmetric modelling assumption of the flow field is valid since the large number of axisymmetric internal plates present in the column means that any variations in velocity with angular position around the column present at the top and bottom of the column will be damped out for sections away from the top and bottom. Furthermore, the tangential component of flow is negligible when compared to the radial and axial components (Aoun Nabli et al., 1998). The model computational domain extends over three disk–doughnut sections in which the single-phase flow is considered to be typical of the flow over most of the column height. Although there will be entrance regions at the top and bottom of the column, it is expected that the flow will be the same in most of the sections of the column. The computational domain was terminated at top and bottom by a 1 mm thick section of a disk, and the associated flow
J.M. Bujalski et al. / Chemical Engineering Science 61 (2006) 2930 – 2938
2933
Navier–Stokes Eqs. (2) and (3) (AEA Technology, 2002). j + ∇ · (U) = 0, jt j U + ∇ · (U ⊗ U) − ∇ · (eff ∇U) jt = −∇p + ∇ · (eff (∇U)T ) + B,
(2)
(3)
In Eq. (3), eff is the effective viscosity and calculated in Eq. (4): eff = + T .
(4)
The Reynolds number in the simulations is around 2000 and so the standard k– turbulence model is not appropriate. The low Reynolds number k– turbulence model was used instead (AEA Technology, 2002). This turbulence model differs from the standard k– model in that in the low Reynolds number k– model the turbulence properties are damped and directly calculated on the walls, without the use of wall functions. Additionally the turbulent viscosity is modified as shown in Eq. (5): k2 , (5) where C is a fitting constant set to 0.09 and f is a function calculated in Eq. (6): −3.4 . (6) f = exp (1 + (k 2 /50))2
T = C f
Fig. 2. Axi-symmetric computational geometry used in the CFD simulations.
passage between the disk and the wall, at which inlet/outlet flow boundary conditions must be defined. The height of the computational domain was 156 mm whilst its radius was 50 mm. To model the pulsed column an axi-symmetric uniform grid of 1 mm cell edge length was used with 7800 computational cells as shown in Fig. 2. To simulate the disks and doughnut internal plates, 2 mm thick walls were inserted in the geometry at correct heights. In the simulation only half the 6 mm diameter shaft holding the disks was modelled, as it was positioned on the axis of symmetry, running from the bottom to the top of the simulated geometry. The properties of the single phase were those of water with a density of 1000 kg/m3 and viscosity 0.001 kg/ms. The Reynolds number for the pulsating flow, ReP , can be defined as (Ni et al., 2003): ReP =
D(f A) .
(1)
The required boundary conditions for the system are complex, given the time dependent sinusoidal behaviour of the inlet/outlet boundaries. The velocity pulsation magnitude at the boundary condition was defined by Eq. (7): U = Af sin(2f t).
(7)
At the top boundary (the “outlet”) pressure was set to be uniform, with zero normal gradients for the other variables (i.e., Dirichlet condition) whereas, when the flow was entering the computational domain, the velocity was set to be uniform and equal to Eq. (7). The lower boundary (the “inlet”), velocity was set to be uniform and equal to Eq. (7) at all times. The wall boundary conditions for the low Reynolds number k– turbulence model were set to no-slip with the kinetic energy and energy dissipation set to 0. The oscillation in the flow boundary condition required the use of a transient simulation. The number of time steps used for each pulsation period was from 25 to 80 and the number of iterations per time step was from 35 and 100, respectively. No difference was found in the results in the two different simulation procedures. The time for the simulations to reach periodic steady state was 15 oscillation periods. 3. Results and discussion
For the case with frequency, f, equal to 1 Hz and peak-to-peak amplitude, A, equal to 20 mm, ReP = 2000. The general purpose CFD code, CFX 4, was used as the basis for the model development. The conservation of mass and momentum were determined using the Reynolds averaged
3.1. PIV validation LDV was used to verify the PIV results at a selected measurement point A over the period of a whole oscillation. The
2934
J.M. Bujalski et al. / Chemical Engineering Science 61 (2006) 2930 – 2938
Velocity, [m/s]
0.2
0.0
LDV - Axial velocity PIV - Axial velocity CFD - Axial velocity
-0.2
-0.4 0.0
0.2
0.4
0.6
0.8
1.0
Time, [s]
Fig. 3. Comparison between LDV, PIV measurements and CFD predictions of axial velocity component for point A (20 mm amplitude, 1 Hz frequency).
axial velocity data taken using LDV and PIV at point A (14 mm from the centreline and 7 mm under the doughnut internal, see Fig. 2) are shown in Fig. 3, and compared with velocity data from CFD. Fig. 3 shows the time variation of the axial velocity component over one 1 Hz and 20 mm amplitude oscillation (Trial 4). This comparison provides evidence that the PIV measurements are accurate and can be used for comparison with the CFD model. 3.2. PIV and CFD velocity maps An example of a set of PIV and CFD results are given in Figs. 4 and 5. The eight images show the time variation of the flow field as the pulsing progresses through one full cycle, with the interval between images corresponding to an increment of 45◦ crank angle. Fig. 4 shows the velocity field over the first half of the pulsation cycle and Fig. 5 over the second half. The flow predicted by CFD is shown on the left side and the corresponding PIV measured flow on the right. The PIV velocity measurements near the doughnuts could be prone to error as there is a possibility of laser light scatter from the doughnut surface. On the downstroke the flow impacts upon and sweeps across the tops of the disks and doughnuts, while the undersides of both disks and doughnuts is stagnant. On the upstrokes, flow impacts on and sweeps across the undersides of the internals, and the top surfaces are stagnant. This behaviour is important for surface regeneration of dispersed phase in solvent extraction. The most important feature in the pulsed column is the formation of the vortex between the disk and doughnut internals and in most images the generated vortices are not uniformly distributed. Furthermore, the vortices move substantially with time over a cycle. So for example there is a large vortex present at the angles 0◦ and 45◦ between the doughnut and disk but almost nothing in the next stage below. A reverse vortex is observed between the angles 180◦ and 225◦ . At the angles 90◦ and 270◦ , although there is no net flow, remnant vortices exist
in the compartments in both the CFD predictions and measurements which contribute to the mixing, break-up and residence time in each compartment. The predicted flow in Figs. 4 and 5 agrees well with the measurements in both shape and magnitude of the vortices. With the additional quantitative comparison of PIV and CFD results over a single phase shown in Fig. 3, the agreement is sufficiently good for there to be a large degree of confidence in the use of the computational model for design purposes. Some of the vortices are of slightly different strength in the measured flow compared with the predictions, and these slight discrepancies are probably due to the difference in the geometry between the experiment set-up (gap between the column wall and doughnut edge) and the CFD model (no gap between the doughnut edge and the column wall). 3.3. Axial velocity radial profile The pulsed column in solvent extraction operation is not a closed system but operates as a counter-current system with throughflow of organic downwards and aqueous upwards. To gauge the effect of the throughflow on the combined flow field within the column, two trials were carried out in the single phase apparatus, one with upward throughflow and the other with downward throughflow superimposed on the pulsation (trials 12 and 13). In each case the additional flow was 2 L/min which corresponds to a superficial velocity of 0.008 m/s. The effect of throughflow is shown in Fig. 6 which plots the axial velocity profile on a horizontal line across the column at the height of point A when the pulsator position is set to phase 0◦ . The additional throughflow in cases 12 and 13 has very little effect on the velocity profile when compared to the nothroughflow case, consistent with the small throughflow superficial velocity. At this angle of the pulsator (maximum downflow) the axial flow close to the centre of the column is mostly downwards through the doughnut opening above point A as expected. The change of direction to up-flow closer to the wall indicates a creation of the vortex. Surprisingly, the flow reverses yet again very close to the wall to down-flow. This can also be seen in the top right-hand plot of Fig. 4, as a pronounced downflow along the entire outer wall of the column. This secondary reversal is not captured in the CFD simulation without gap. In Fig. 7 the axial component of the flow is presented for the three different flow configurations when the pulsator is at the position of 180◦ (maximum up-flow). The flow underneath the doughnut is relatively stationary whilst there is a large upward flow component near the column wall. Once again the cases with additional throughflow up and down are quite similar, although unexpectedly the measured upward flow near the wall for no throughflow is somewhat different, in fact even lower than the down throughflow case, whereas the two throughflow cases would be expected to bracket the no throughflow measurements. We will see below that the gap between the doughnut and the wall affects the velocity significantly in this region, and it is possible that due to re-installation of the internals
J.M. Bujalski et al. / Chemical Engineering Science 61 (2006) 2930 – 2938
Mean Velocity Vectors at Time Phase - 45 Degree
Mean Velocity Vectors at Time Phase - 0 Degree 1m/s CFD Prediction
1m/s
0° PIV Measurement
CFD Prediction
Mean Velocity Vectors at Time Phase - 90 Degree 1m/s CFD Prediction
2935
90°
PIV Measurement
45°
PIV Measurement
Mean Velocity Vectors at Time Phase - 135 Degree 135° 1m/s CFD Prediction
PIV Measurement
Fig. 4. Flow field comparison between PIV measurement and CFD predictions at pulsator phases 0◦ –135◦ .
in the middle of the campaign, the gap was slightly different for the throughflow cases. Closer to centreline all sets of measurements are quite similar as the flow is mostly radial in this region, as shown also in Fig. 5.
circuiting and possibly the creation of a fast ‘jet’ flow along the column wall. This additional vertical flow will reduce size of the generated vortex, thus changing the local flow and shear rate in the column.
3.4. Effect of the gap between doughnut edge and column wall
3.5. Pulsation intensity
In Figs. 6 and 7 the main discrepancy between the PIV and the CFD is in the flow near the column wall. It was observed that in the experimental set-up the doughnut rings did not fit tightly against the column wall and a gap of varying size was present in individual doughnut configurations. The CFD geometry was modified to include a gap of 2 mm between the column wall and the doughnut edge. The CFD results for the modified geometry in Figs. 6 and 7 give a better prediction of the axial velocity than the original CFD results without the 2 mm gap. The gap between the wall and the doughnut could become significant in the scale-up of the pulsed column, leading to short
Fig. 8 shows the comparison of the maximum velocity (upward and downward) at point A as a function of pulsation intensity for trials 1 to 11. The results show the close agreement between the PIV and the CFD results for the downward velocity in the pulsation cycle, but there is an over prediction of the upward velocity component at this point. This discrepancy could be attributed to the turbulence model used as supported by similar work of Fei et al. (2000) who found a similar discrepancy between their CFD modelling using the k– turbulence model with their LDV measurements. The results indicate that the velocity component of the pulsed column can be scaled up with
2936
J.M. Bujalski et al. / Chemical Engineering Science 61 (2006) 2930 – 2938
Mean Velocity Vectors at Time Phase - 180 Degree 180°
Mean Velocity Vectors at Time Phase - 225 Degree 225° 1m/s
1m/s CFD Prediction
PIV Measurement
Mean Velocity Vectors at Time Phase - 270 Degree 270° 1m/s CFD Prediction
PIV Measurement
CFD Prediction
PIV Measurement
Mean Velocity Vectors at Time Phase - 315 Degree 1m/s CFD Prediction
315° PIV Measurement
Fig. 5. Flow field comparison between PIV measurement and CFD predictions at pulsator phases 180◦ –315◦ .
the pulsation intensity and that there is reliability in extrapolating the CFD simulation results in single phase flow to higher pulsation intensities.
and oscillation period T:
3.6. Energy dissipation
The value of the average energy dissipation for the system of 1 Hz and 20 mm amplitude by Eq. (8) is 0.044 m2 /s3 whilst the CFD predicted value of was 0.025 m2 /s3 (k– turbulence models are known to underpredict the turbulent properties in stirred tanks by a similar amount). The average energy dissipation in the pulsed column might not be representative of the average level of turbulence and mixing in the operation, and may only be a crude estimate in the analysis of the column operation. For example in the analysed system the maximum value of at a given time, ranged from 0.0446 m2 /s3 to 0.698 m2 /s3 , but the question remains whether the generated maximum occurs at the point in the pulsation cycle and at a location in the
As shown in Figs. 4 and 5 the pulsed flow generates vortices in the flow field which in turn generate the shear rate necessary for the dispersed phase break-up and coalescence needed for mass transfer. In turbulent flow the value of shear is linked to the turbulent energy dissipation, . Previously in the literature (Milot et al., 1990; Aoun Nabli et al., 1998) only average values of the kinetic energy dissipation over a pulsation cycle have been reported. Eq. (8) is a correlation proposed by Milot et al. (1990) to estimate the average energy dissipation in a pulsed column as a function of peak-to-peak amplitude, A,
= 778
3 A . T
(8)
J.M. Bujalski et al. / Chemical Engineering Science 61 (2006) 2930 – 2938
0.2
0.3
0.1
CFD - No through flow (no gap) Exp. - No through flow (Trial 4) Exp. - Up through flow (Trial 13) Exp. - Down through flow (Trial 12) CFD - No through flow (2mm gap)
0.1 0.0 0 Velocity, [m/s]
Vertical velocity, [m/s]
0.2
0.0 -0.1 0°
-0.2
0.01
0.02 0.03 Radial distance, [m]
0.04
35
-0.3 Maximum velocity Down (CFD) Regression for Down Maximum velocity Up (CFD) Regression for Up Maximum velocity Down (PIV) Maximum velocity Up (PIV)
-0.6
0.05
Fig. 6. Comparison of the PIV measurements and CFD simulation of axial velocity component at a line positioned 7 mm under the doughnut at a pulsation phase set at 0◦ (20 mm amplitude, 1 Hz frequency).
10 15 20 25 30 Intensity (Frequency x Amplitude), [mm/s]
-0.2
-0.5
Point A
5
-0.1
-0.4
-0.3 -0.4 0.00
2937
Fig. 8. Point A maximum and minimum velocity at different pulsation intensities: PIV measurement and CFD simulation comparison.
4. Conclusions 0.30
Vertical velocity, [m/s]
0.25 0.20
CFD- No through flow (no gap) Exp. - No through flow (Trial 4) Exp. - Up through flow (Trial 13) Exp. - Down through flow (Trial 12) CFD - No through flow(2mm gap) 180°
0.15 0.10 Point A
0.05 0.00 -0.05 0.00
0.01
0.02
0.03
0.04
0.05
Radial distance, [m] Fig. 7. Comparison of the PIV measurements and CFD prediction of axial velocity component at a line positioned 7 mm under the doughnut at a pulsation phase set at 180◦ (20 mm amplitude, 1 Hz frequency).
column where the energy can be used effectively for phase dispersion. The maximum for the pulsed column is lower than the predicted maximum values in stirred tanks under fully turbulent conditions. Zhou and Kresta (1998) found the values for Rushton turbines to be in a range of 85.2–528 m2 /s3 , but these are localised values inside the impeller generated vortex which is comparatively small in volume, whilst 57% of occurs at a lower value over majority of vessel volume (Ng and Yianneskis, 2000). Stirred vessels have a large difference between maximum and minimum energy dissipation—ranging by at least two orders of magnitude (Ng and Yianneskis, 2000) which generates a larger number of fine droplets and a broader size distribution. The range of in the pulsed column is smaller (maximum value ranged from 0.0446 to 0.698 m2 /s3 ) generating a narrower droplet size distribution.
The pulsed column operation in single phase flow was investigated with PIV and LDV experimental techniques. Extensive sets of PIV measurements have been taken of the unsteady flow within the column for a range of operating conditions and accurate point measurements taken with LDV have confirmed the PIV data. The PIV velocity measurements were taken at seven different phases in the pulsation cycle. The system was modelled with CFD and the simulations were validated by comparing with the measurements at various phases in the pulsation cycle: the flow field was well matched by the CFD simulation. The comparison of the CFD and PIV results showed that the flow field in certain regions of the pulsed column can depend sensitively on the positioning of the doughnut internal relative to the column wall if a small gap exists between the two. PIV measurements and CFD model predictions for the pulsed column operating in single phase mode show an oscillating sinuous flow through the column, with significant regions of low velocity and hence low shear. The range of in the pulsed column is narrower than in a stirred tank which would lead to different performance e.g. narrower droplet size distribution.
Notation A B C D f f k p Re t T U
amplitude of oscillation, m body force, N constant in low Re k– turbulence model pulsed column diameter, m frequency of oscillation, s−1 function to determine the turbulent viscosity turbulent kinetic energy, m2 /s2 pressure, Pa Reynolds number, dimensionless time, s oscillation period, s velocity, m/s
2938
J.M. Bujalski et al. / Chemical Engineering Science 61 (2006) 2930 – 2938
Greek letters
energy dissipation, m2 /s3
viscosity, Pa s density of phase, kg/m3
Subscripts eff P T
effective pulsation turbulent
Acknowledgements The authors would like to acknowledge the financial support for this work from Anglo Platinum, Bateman Solvent Extraction, BHP Billiton, Cognis Australia Pty Ltd, Kvaerner E&C Australia Pty Ltd, Minara Resources Ltd, Phelps Dodge Mining Company and WMC Resources Ltd, through the AMIRA International Project P706 “Improving Solvent Extraction Technology”. References AEA Technology, 2002. CFX 4.4 Flow Solver User Guide. AEA Technology, Harwell, Oxfordshire, UK. Angelov, G., Gourdon, C., 2002. Study on the turbulence in pulsed stagewise extraction columns: turbulent macroscale. Hungarian Journal of Industrial Chemistry 30, 137–142. Angelov, G., Journe, E., Liné, A., Gourdon, C., 1990. Simulation of the flow patterns in a disc and doughnut column. Chemical Engineering Journal 45, 87–97. Angelov, G., Gourdon, C., Liné, A., 1998. Simulation of flow hydrodynamics in a pulsed solvent extraction column under turbulent regimes. Chemical Engineering Journal 71, 1–9. Aoun Nabli, M., Guiraud, P., Gourdon, C., 1997. Numerical experimentation: a tool to calculate the axial dispersion coefficient in discs and doughnuts pulsed solvent extraction columns. Chemical Engineering Science 52 (14), 2353–2368. Aoun Nabli, M., Guiraud, P., Gourdon, C., 1998. CFD contribution to a design procedure for discs and doughnuts extraction column. Chemical
Engineering Research & Design Part A: Transactions of Institution of Chemical Engineers 76, 951–960. Camurdan, M.C., Baird, M.H.I., Taylor, P.A., 1989. Steady state hydrodynamics and mass transfer characteristics of a Karr extraction column. Canadian Journal of Chemical Engineering 67, 554–559. Dimitrova Al Khani, S., Gourdon, C., Casamatta, G., 1988. Simulation of hydrodynamics and mass transfer of a disk and rings pulsed column. Industrial Engineering Chemical Research 27 (2), 329–333. Fei, W.Y., Wang, Y.D., Wan, Y.K., 2000. Physical modelling and numerical simulation of velocity fields in rotating disc contactor via CFD simulation and LDV measurements. Chemical Engineering Journal 78, 131–139. Fox, M.H., Ralph, S.J., Sithebe, N.P., Buchalter, E.M., Riordan, J.J., 1998. Comparison of some aspects of the performance of a Bateman pulsed column and conventional box-type mixer/settlers. ALTA 1998 Nickel/cobalt pressure leaching and hydrometallurgy forum, Perth, Australia. Logsdail, D.H., Slater, M.J., 1991. Pulsed perforated-plate columns. In: Lo, T.C., Baird, H.I., Hanson, C. (Eds.), Handbook of Solvent Extraction. Krieger Publishing Company, pp. 355–372. Lorenz, M., Haverland, H., Vogelpohl, A., 1990. Calculation of the dynamic pressure drop in pulsed disk-plate columns. Extraction 1990: A Five-Day Symposium, IChemE Symposium Series, vol. 119, pp. 249–266. Milot, J.F., Duhamet, J., Gourdon, C., Casamatta, G., 1990. Simulation of a pneumatically pulsed liquid–liquid extraction column. Chemical Engineering Journal 45, 111–122. Ng, K., Yianneskis, M., 2000. Observations on the distribution of energy dissipation in stirred vessels. Chemical Engineering Research & Design Part A: Transactions of Institution of Chemical Engineers 78, 334–341. Ni, X., Jian, H., Fitch, A.W., 2002. Computational fluid dynamic modelling of flow patterns in an oscillatory baffled column. Chemical Engineering Science 57, 2849–2862. Ni, X., Jian, H., Fitch, A., 2003. Evaluation of turbulent integral length scale in an oscillatory baffled column using large eddy simulation and digital particle image velocimetry. Chemical Engineering Research & Design Part A: Transactions of Institution of Chemical Engineers 81, 842–853. Nitsch, W., Schuster, U., 1983. Liquid/liquid-mass transfer at swarms of droplets: kinetics of mass transfer in the system uranylnitrate, nitric acid, tributylphosphate. Separation Science and Technology 18, 1509–1533. Vancas, M.F., Buchalter, E., 2003. Mixer-settlers and pulsed columns: where are we now and where are we going? ALTA 2003 SX/IX World Summit, Perth, Australia ALTA, Castlemaine, Victoria, Australia, pp. 1–7. Zhou, G., Kresta, S.M., 1998. Correlation of mean drop size and minimum drop size with turbulence energy dissipation and the flow in an agitated tank. Chemical Engineering Science 53, 2063–2079.