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A Systematic Study of the Effect of Geometrical Parameters on Mixing Time in Oscillatory Baffled Columns
0263±8762/98/$10.00+0.00 Institution of Chemical Engineers Trans IChemE, Vol. 76, Part A, July 1998
A SYSTEMATIC STUDY OF THE EFFECT OF GEOMETRICAL PARAMETERS ON MIXING TIME IN OSCILLATORY BAFFLED COLUMNS X. NI (MEMBER), G. BROGAN*, A. STRUTHERS*, D. C. BENNETT* and S. F. WILSON* Department of Mechanical and Chemical Engineering, Heriot-Watt University, Edinburgh, UK *Department of Chemical and Process Engineering, University of Strathclyde, Glasgow, UK
T
he systematic experimental investigation on the effect of baf¯ e free area, baf¯ e spacing and baf¯ e thickness on mixing time in batch oscillatory baf¯ ed columns is reported where the form of oscillation can be achieved by either pulsing the ¯ uid from the base of the column or oscillating the baf¯ es at the top. Local concentration pro® les are measured using conductivity probes at two locations along each column. The mixing time was determined based on the equilibrium concentration format. The experimental results have identi® ed the optimal geometrical parameters for obtaining the lowest mixing times in such columns. Keywords: mixing time; oscillatory baf¯ ed column; free baf¯ e area; baf¯ e spacing; baf¯ e thickness
INTRODUCTION
baf¯ ed reactor, and a single parameter, namely the axial dispersion coef® cient, was evaluated from the RTD curves and used to quantify characteristics of mixing in the system. For batch processes, however, the characteristics of mixing in oscillatory baf¯ ed columns (OBCs) are less well studied with no previous reports on mixing time in particular, although the batch OBCs have been used extensively for mass transfer212 23 , particle mixing and separation24 , reaction25 and scale-up studies26 . In this paper, the research efforts are concentrated on a systematic investigation of geometrical parameters on mixing time in batch OBCs where the form of oscillation can be achieved by either pulsing the ¯ uid from the base of the column or oscillating the baf¯ es at the top. The mixing times evaluated are based on the equilibrium concentration method27 , i.e. when the concentration differences measured by probes are brought into closer physical proximity with the equilibrium concentration. The aim of this paper is to examine the effect of baf¯ e free area, baf¯ e spacing and baf¯ e thickness on mixing time in OBCs with a view to identifying optimal parameters systematically which could be used for scale up purposes.
Oscillatory ¯ ow has been around for a long time, applications in pulsed packed columns and reciprocating plate solvent extraction are the earliest examples12 9 . In packed columns10 the mixing energy is transmitted hydraulically to ® xed plates or packings. Their principal advantage is that no mechanical moving parts come in contact with the process ¯ uid11 . In reciprocating plate columns, oscillatory ¯ ow is produced by the displacement of liquid through the plate perforations while oscillation is not present in regions of the ¯ uid remote from the plates. The resulting enhancement in mixing is due to the superimposition of an unsteady oscillatory ¯ ow component to the system12 11 . Further developments have been reported in the biomedical ® eld where oscillatory ¯ ow in furrowed channels has been the subject of interest for both ¯ ow visualization12 and numerical studies13 . More recently, the studies on oscillatory ¯ ow in an ori® ce baf¯ ed tube, or oscillatory baf¯ ed ¯ ow, have extended the previous investigations and shown that the vortex mixing mechanism is the key factor responsible for the signi® cant enhancement of mixing achieved in the systems142 18 . The mixing mechanism in question breaks down into two halves of a cycle, i.e. the formation of vortices behind baf¯ es, drawing ¯ uid and substance from the walls, and their subsequent ejection at ¯ ow reversal, moving ¯ uid and substance from walls to the centre. In this way, radial mixing is signi® cantly increased in the cells. This mechanism has also been reported to be present in wavy-walled19 and baf¯ e channels20 . The characteristics of mixing in oscillatory baf¯ ed ¯ ow have been studied previously152 18 from the residence time distribution (RTD) perspective, i.e. the changes of concentration are measured as a function of time as the mixing takes place, in a continuous oscillatory
EXPERIMENTAL FACILITIES AND PROCEDURE Three oscillatory baf¯ ed columns were used in this work; two of the three employed a mechanism of oscillatingbaf¯ es as the means of achieving oscillation while one pulsed the ¯ uid. A schematic diagram of the experimental apparatus and facilities is given in Figure 1. The OBCs are made of Perspex columns of two diameters and their dimensions are listed in Table 1. A number of sets of ori® ce baf¯ es, made of polyethylene plates, were used in the experiments, with baf¯ e free areas ranging from 11 to 51%, baf¯ e spacing from 1 to 2.5 times 635
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Figure 1. Schematic diagram of the oscillatory baf¯ ed columns. (a) Pulsing ¯ uid mechanism. (b) Oscillating baf¯ e mechanism.
the tube diameter used, and baf¯ e thickness from 1 to 48 mm. For the OBC (1) where oscillation was located at the base of the column, a 50 mm diameter stainless steel bellows was used to achieve the pulsation, and for the OBC (2&3) where oscillation was initiated at the top of the columns, the motion of baf¯ es was powered by a motor with a linking cam. Oscillation frequencies from 1 to 10 Hz and oscillation amplitudes from 1 to 20 mm centre-to-peak can be obtained in the OBCs. Two Vernier conductivity probes were used to monitor the changes of concentration of NaCl against time along the height of each column. The probes are automatically temperature compensated between temperatures of 5 and 35°C. Prior to the start of the experiments, the conductivity probes were calibrated using the standard two-point method at 0 mg l2 1 (using deionized water) and 500 mg l2 1 concentration of NaCl. The probes, of 10 mm in diameter and 100 mm in length, were placed so that the tips of the probes are located in the centre of the column at a 45 degree angle. The sensors were connected to a Multi Purpose Lab Interface (MPLI) and the signals are shown in real-time graphic mode as well as in a tabulated form.
The rate of data gathering was set at 3 readings per second for both sensors simultaneously for a typical period of 3 minutes. The upper probe was labelled A and the lower probe B. The experiments started by applying oscillation to the columns ® lled with water at pre-set oscillation amplitude and frequency, and then initiating the MPLI program. After a known delay, say 10 seconds, the NaCl tracer was injected via either the top or bottom port, and the data recording in this way contains both the pre and in situ events of concentration vs. time in the columns. For the top injection port, 4 ml of 40 g l2 1 NaCl tracer was used, while for the bottom part, 6 ml was added due to the construction of the port channel where an estimated 2 ml of tracer was contained by the channel itself. The MPLI program stops automatically when the duration of the pre-set experimental time is reached. The columns were then drained and washed with water before a new experiment was initiated. A large number, 351 in total, of experiments were carried out, covering all the pre-described parameters and conditions. In addition, approximately ® ve percent of the experiments were repeated for consistency.
Table 1. Detail speci® cation of OBCs. OBC (1) Oscillating mechanism Parameter investigated Tube diameter (D) Overall height (H ) Operational height Location of top injection port Location of bottom injection port No. of conductivity probes used Location of probe A (HA ) Location of probe A (HB ) No. of baf¯ es
pulsing ¯ uid from the base baf¯ e free area (11, 20, 28, 35, 40, 45, 51%) 50 mm 950 mm 865 mm 900 mm 50 mm Two 530 mm 240 mm 9
OBC (2) oscillating baf¯ es at the top baf¯ e thickness (1, 3, 6, 12, 24, 48 mm) 50 mm 990 mm 750 mm 850 mm 50 mm One/Two 570 mm 200 mm 9 to 5 depending on thickness
OBC (3) oscillating baf¯ es at the top baf¯ e spacing (1, 1.25, 1.5, 1.75, 2, 2.5 D) 90 mm 730 mm 500 mm 700 mm 25 mm Two 410 mm 125 mm 9 to 6 depending on spacing
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CHARACTERIZATION OF MIXING Axial Dispersion Coef® cient In a manner analogous to Fick’ s law of molecular diffusion28 , the contributions due to eddy mixing in oscillatory baf¯ ed ¯ ow can be described by a quantitative parameter, E, the axial dispersion coef® cient. The governing equation for a continuous mode is 2 ¶C ¶ C ¶C = E U (1) 2 2 ¶t ¶Z ¶Z where U is the mean axial velocity of the ¯ ow (m s2 1 ). For a batch operation it becomes
¶C ¶ C = E (2) 2 t ¶ ¶Z where Z is the axial direction of ¯ ow (m). An exact analytical solution of the partial differential equations is dif® cult to obtain, however, approximate mathematical solutions or numerical results are widely used. The numerical solutions usually require a minimization procedure, i.e. E is estimated (and U for the open one) and C calculated, then the values of E (and U ) are adjusted in such a way that the sum of the squared difference between the measured concentrations and the calculated ones is a minimum. The degree of the minimization gives the con® dence level, which in turn measures the error in the evaluation of E. For the case of a net ¯ ow in a baf¯ ed tube superimposed by an oscillatory motion, the residence time distributions (RTDs) have displayed a nearly perfect form of a Gaussian curve172 18 . In those circumstances, the minimization process was quick and the E values obtained are of very high levels of con® dence, from 95% to 100%. However, when the RTDs are not in the form of the Gaussian distribution, such as the RTDs obtained in a smooth tube in a laminar ¯ ow with or without oscillation where the concentration pro® les have a long tail after a sharp break through, the E values can only be obtained at much reduced con® dence levels, e.g. less than 60% depending on operational conditions172 18 . For a batch OBC, a known volume of NaCl tracer, of a similar viscosity to the bulk liquid, is added to the column containing water and by means of two conductivity probes located along each OBC, as shown in Figure 1, the tracer concentrations are measured as a function of time. The typical pro® les are illustrated in Figures 2 and 3. It can be 2
Figure 3. Concentration vs. time. Oscillation frequency = 1.7 Hz, Oscillation amplitude = 20 mm, Baf¯ e spacing = 1 D, Injection location = bottom. Oscillation mechanism = Oscillating baf¯ es, Rig used = OBC (3).
seen that the change of concentrations is instantly detected by the top probe for the top injection (Figure 2). The change registered by the bottom probe was smaller and slightly later than that by the top probe. Both concentration curves quickly converged to an equilibrium concentration. For the bottom injection (Figure 3), a similar pro® le but with the reverse probe order can clearly be noticed as compared to that shown in Figure 2. In this case, it was the bottom probe that responded ® rst for the bottom injection, and the top probe that followed. The responses from the upper probe for the top injection (or the lower probe for the bottom injection) can be approximated to a Gaussian form, although the ® nal concentration is higher than the initial one, but the pro® les from the lower probe (or the upper probe for the bottom injection) are not at all in the form of a Gaussian distribution. For those cases, the errors in evaluating E are as high as 70%. It was considered that one error code could not be applied to all the E evaluated from the experimental data. As a consequence of this, the axial dispersion coef® cient was not applied in this paper. Mixing Time `Mixing time’ should be the time measured from the instant of tracer addition until the column contents have reached a speci® ed degree of uniformity 27 . As the volume of the tracer added is known in these experiments, the equilibrium concentration, C¥ , can be calculated via Vinitial Cinitial 1
Figure 2. Concentration vs. time. Oscillation frequency = 1.7 Hz, Oscillation amplitude = 20 mm, Baf¯ e spacing = 1 D, Injection location = top. Oscillation mechanism = Oscillating baf¯ es, Rig used = OBC (3).
Trans IChemE, Vol 76, Part A, July 1998
Vinjection Cinjection = Vfinal C¥
(3)
where V and C stand for volume (m 3 ) and concentration (g l2 1 ) respectively. The mixing time can now be de® ned as the time required from the instant of NaCl addition for the concentrations at the two locations of A and B to reach the equilibrium value, C¥ 27 . Taking the pro® les shown in Figure 2 for example, the mixing time equals (t2 2 t1 ), where t1 and t2 are the times denoting the instant of tracer injection and when it reaches the equilibrium value. For the majority of the experiments carried out, the concentration-time data obtained have displayed a similar format to those shown in Figures 2 and 3, i.e. the degree of convergence of the two curves to the equilibrium value is very high, consequently the determination of the mixing
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time is a straightforward process and independent of the injection locations. For the extreme geometrical parameters investigated in this study, such as the largest free baf¯ e area and the thickest baf¯ es at the lowest oscillation intensity, however, the concentrations measured at two locations approached C¥ in an asymptotic manner and it was dif® cult to detect the end point of the experiment with precision. In those circumstances, either the experiment has to be prolonged or the percentage of deviation from the ® nal equilibrium value has to be reduced. By trial and error, a 6 5% of deviation from C¥ can be regarded as the end point for 98% of the experiments carried out, irrespective of injecting locations and experimental durations, and was subsequently used in all the following presentations. By doing this, it was considered that the results are consistent and the presentation uni® ed. In order to ensure that the starting point at which the tracer was added is the same for each type of experiment, a row number in the tabulated form of the MPLI program was identi® ed as the precise time that the tracer was injected, usually about 10 seconds after the MPLI program had been initiated. The determination of the mixing time also depends on the way in which the tracer is added. For all the parameters investigated in this study, 20 ml syringes were used for the purpose of tracer injection, and the tracer was added in a one shot manner. The time of the injection was kept as constant as possible, generally within 1 second. For the top injection, 4 ml of 40 g l2 1 NaCl tracer was added to the surface of the liquid, while for the bottom injection, the tracer was added through a channel perpendicularly situated at a short distance above the base (Table 1). The opening/closing of the port was controlled by a one-way valve, which was connected to the syringe. This design also allows a one shot injection, similar to the top port. An extra 2 ml of tracer was used for the bottom injection since about 2 ml tracer was contained by the channel itself. In this way, the total volume of tracer injection at the bottom is the same as that at the top. In summary, the application of a mixing time to the characterization of mixing in the batch OBCs gave more consistent results with higher levels of con® dence than when using the axial dispersion coef® cient; mixing time has therefore been used throughout this work. RESULTS AND DISCUSSIONS The Effect of Tracer Concentration The effect of the tracer concentration on dispersion in continuous oscillatory baf¯ ed reactors was investigated172 18 . The results showed that when there were neither baf¯ es nor ¯ uid oscillation present in the ¯ ow, such an effect is signi® cant. The velocity pro® les skewed to the bottom for the horizontal tubes and ¯ atted for the vertical tubes. In some experiments, sugar was used to neutralize such an effect in order to obtain the appropriate pro® les. However, when both baf¯ es and oscillation were applied to the system, the effect in question was found to be insigni® cant172 18 . For batch operations, however, there is no net ¯ ow and a density gradient between the tracer and the bulk ¯ uid could have a signi® cant effect on mixing and dispersion, specially in vertical columns. Taking the pro® les shown in Figures 2 and 3 for example, the difference in
mixing time between the top and bottom injections is clearly noticeable. As a result of the concentration gradient of the denser tracer, the mixing time evaluated from Figure 2 for the top injection was 34% shorter than that derived from Figure 3 for the bottom injection. All the differences in mixing time between the two injection modes were calculated for all the experiments carried out, and the results show that the enhancements due to the sinking of the denser tracer decreased with the increase in oscillation intensity in terms of oscillation frequency, amplitude and baf¯ e geometrical design. Such enhancements ranged from 74% for the lowest level of oscillation used combined with the extreme baf¯ e geometrical parameters, e.g. the largest free area with the largest baf¯ e thickness and baf¯ e spacing, to merely 0.7% for the strongest oscillation intensity and the optimal baf¯ e geometry. The average enhancement in mixing time was around 32%. Although there are few data on mixing time reported in relation to oscillatory baf¯ ed ¯ ow, these results have found a common ground with many of the previous studies on the effect of the concentration gradient on dispersion, e.g. Emin Erdogan and Chatwin29 in 1967 investigated and modelled the effect of buoyancy on the laminar dispersion of solute in a horizontal tube and reported that buoyancy should have a noticeable effect on dispersion only when the effects of gravity and lateral mixing are not in balance. Holmes, Kar and Baird 30 found that axial dispersion coef® cients were 10 to 20 times higher than the values in reciprocating plate liquid±liquid extraction systems with uniform densities. More recently, Aravamudan and Baird 31 have reported that even under well-agitated conditions, the dispersion can be increased by as much as 25% in the presence of an unstable density gradient. Although no direct comparison could be made here, the similar effect on mixing time was indeed observed. It should be noted that since the bottom-injection results are not affected by the density gradient, they should be taken as more reliable than the top-injection results which are also presented in this paper. The Effect of Free Baf¯ e Area The ratio of the free baf¯ e area, a, is de® ned as the ratio of the free baf¯ e area to the tube area, i.e. pD 2o /4/pD 2 /4 = (Do /D)2 , where Do and D are the diameter of the hole of ori® ce plates (m), and the diameter of the tube (m) respectively. The free baf¯ e area controls the width of vortices within each baf¯ ed cell in an OBC. The larger the free baf¯ e area, the shallower the width of the eddies, consequently the poorer the mixing within the OBC. An alternative term of baf¯ e restriction ratio is de® ned as (1 2 a). A restriction ratio of 66%, a = 34%, was evaluated in ¯ ow visualization studies15 as the optimal value for effective mixing and has since been used in the oscillatory baf¯ ed ¯ ow research. In this study, seven ratios of the free baf¯ e area ranging from 11% to 51% were examined with a view to assessing the effect of such ratios on mixing time in OBC and verifying the optimal value. Figures 4 to 7 show the mixing time as a function of a with both top and bottom injections. It can be seen that the mixing time decreased as the oscillation frequency or amplitude increased. This is expected; as the intensity of mixing, in terms of the product of the oscillation frequency and amplitude, increases, it Trans IChemE, Vol 76, Part A, July 1998
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Figure 4. Mixing time vs. free baf¯ e area. Oscillation amplitude = 5 mm, Injection location = top.
Figure 6. Mixing time vs. free baf¯ e area. Oscillation amplitude = 5 mm, Injection location = bottom.
leads to better mixing and consequently shorter mixing time. However, the degree of the decrease in mixing time was found to be less for higher products of oscillation frequency and amplitude than for the lower ones. This could suggest that a threshold in the uniformity of mixing in OBC exists, once the column has reached such a uniformity; further increase in either oscillation frequency or amplitude would lead to a much smaller improvement in mixing time. In addition, it can also be noted that the degree of the decrease in mixing time was generally small for the free baf¯ e ratios from 11% to about 35% and increased for the larger ratios. To explain this, the following equation is introduced evaluating the power density for OBCs23 as
of oscillatory frequency and amplitude. As for the optimal ratios of the free baf¯ e area, 20 to 22% is recommended, at which the shortest mixing times were obtained irrespective of injection locations. In addition, the difference in mixing time between the top and bottom injections at 20% free baf¯ e area was found to be small, ranging from 1% to 14%. Although a free baf¯ e area of 34% has widely been used in the past, it should be pointed out that it is not the optimal one. It is also envisaged that such optimal ratios could be used for the scale up of OBCs using either oscillation mechanism without any modi® cations.
P 2 rN 1 2 a 2 3 3 = x ov V 3pC 2D a 2
(W/m3 )
(4)
where N is the number of baf¯ es per unit length (m2 1 ), r the density of ¯ uid (kg m2 3 ), xo the oscillation amplitude (m), v the angular oscillation frequency (rad s2 1 ) and CD the ori® ce discharge coef® cient (usually 0.7). It can be seen that the smaller a, the larger the term of (1 2 a 2 )/a 2 in equation (4), suggesting that the large is the mixing intensity and the shorter the mixing time. This again re¯ ects the suggestion of the existence of a threshold in the uniformity of mixing in OBCs. The decrease in the free baf¯ e area ratio would have a similar effect on mixing time as the increase of the product
Figure 5. Mixing time vs. free baf¯ e area. Oscillation frequency = 3 Hz, Injection location = top.
Trans IChemE, Vol 76, Part A, July 1998
The Effect of Baf¯ e Spacing Baf¯ e spacing is a key design parameter in OBC since it in¯ uences the shape/length of the eddies within each baf¯ e cavity for a given oscillation amplitude. The optimal baf¯ e spacing in any OBC should ensure a full expansion of eddies generated behind baf¯ es so that the vortices will spread effectively throughout the entire interbaf¯ e region. In the previous studies, 1.5 times the tube diameter was reported as the optimal baf¯ e spacing by Brunold et al.15 from ¯ ow visualization studies, and 1.8 times the tube diameter was suggested by Ni and Gao32 in their mass transfer studies. It should be noted, however, that all the previous investigations on baf¯ e spacing were based on the mechanism of pulsing ¯ uid at the base of OBCs. In this work, the systematic examination of the effect of baf¯ e spacing on mixing time was carried out in an OBC employing
Figure 7. Mixing time vs. free baf¯ e area. Oscillation frequency = 3 Hz, Injection location = bottom.
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Figure 8. Mixing time vs. baf¯ e spacing. Oscillation frequency = 2.8 Hz, Injection location = top.
Figure 10. Mixing time vs baf¯ e spacing. Oscillation frequency = 2.8 Hz, Injection location = bottom.
the mechanism of oscillating baf¯ es, and the results can serve as a comparison with those from the pulsing ¯ uid OBCs. Figures 8±11 show the pro® les of mixing time vs. the ratio of the baf¯ e spacing to the column diameter for both top and bottom injections and for a range of oscillation frequencies and amplitudes tested. The general conclusions made from all the graphs shown here are similar to those described earlier, i.e. the increase in oscillation frequency/ amplitude led to the decrease in mixing time, and the degree of the decrease in mixingtime was much less for high products ofoscillationfrequencyandamplitudethanfor lowones. As to the identi® cation of the optimal baf¯ e spacing, the trend appeared to be less well de® ned as compared with that for the free baf¯ e area ratios. Nevertheless, a baf¯ e spacing of 2D gave overall the lowest mixing time for both locationsand is recommendedas the optimalbaf¯ e spacingfor an OBC with an oscillating-baf¯ e mechanism. This baf¯ e spacing was found to be comparable but rather higher than that identi® ed for OBCs with a pulsing ¯ uid mechanism (1.8 D)32 . It should be noted that the oscillation amplitudes for OBCs with the oscillating-baf¯ e mechanism are generally much greater than those with the pulsing ¯ uid mechanism, and that this could be related to the impact of momentum for the two types. It is envisaged that pulsing ¯ uid in OBCs exerts a larger initial momentum than oscillating baf¯ es, and the increase in the oscillation amplitude for the latter mechanism is to compensate the difference in the initial momentum. Once this has been achieved in OBCs, the effect in mixingseems to be more or less the same for the two mechanisms.
The generation of vortices by each baf¯ e of an OBC is similar to that of vortices shed by ¯ uid ¯ owing around an object. Each eddy needs a certain edge to cling on for an optimal time prior to the process of shedding. Would there be an optimal baf¯ e thickness? In this study six baf¯ e thickness were investigated including 1, 3, 6, 12, 24 and 48 mm. As the baf¯ es got thicker, it was dif® cult to use two conductivity probes since the position of baf¯ es will interfere with the probe locations. For the baf¯ e thickness of 12, 24 and 48 mm in particular, only the lower probe could be employed and for this reason instead of two injection ports, only the top one was used. Consequently, all the data for this type of experiments shown in Figures 12 and 13 were from the lower probe and for the top injection. It can be seen that a similar trend in mixing time to that described earlier was found here, the mixing time decreased with the increase of oscillation frequency/amplitude. Overall, the results suggest that the thinner baf¯ es favoured the generation of vortices, and it seems that if the time needed for vortices to cling on a baf¯ e edge is too long prior to shedding, their shape could have been distorted somewhat, and this subsequently affected the mixing time. The baf¯ e thickness of 2 to 3 mm is identi® ed as the optimal value for good mixing. Although the effect of the baf¯ e thickness on mixing in OBC has not previously been investigated, the intuitive value of 3 to 4 mm in baf¯ e thickness was chosen, which has been used throughout the oscillatory baf¯ ed ¯ ow
Figure 9. Mixing time vs. baf¯ e spacing. Oscillation amplitude = 20 mm, Injection location = top.
Figure 11. Mixing time vs. baf¯ e spacing. Oscillation frequency = 20 mm, Injection location = bottom.
The Effects of Baf¯ e Thickness
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Table 2. Optimal parameters identi® ed. OBCs Parameters Ratio of free baf¯ e area Baf¯ e spacing Baf¯ e thickness
Figure 12. Mixing time vs. baf¯ e thickness. Oscillation amplitude = 20 mm, Injection location = top.
Greek a r v
Oscillating baf¯ es
Pulsing ¯ uid
20±22% 2D 2±3 mm
20±22% 1.8 D26 2±3 mm
symbols free baf¯ e area density of ¯ uid, kg m2 3 angular oscillation frequency, rad s2
1
REFERENCES related research. From this study, it con® rms that the choice is very close to the best. CONCLUSIONS A systematic experimental investigation on the effect of the free baf¯ e area, baf¯ e spacing and baf¯ e thickness on mixing time has been reported in batch OBCs with two types of oscillation mechanism. The optimal parameters for better mixing in OBCs have been identi® ed and summarized in Table 2. Based on a previous study in scale up correlation26 , it is envisaged that both the optimal free baf¯ e area ratio and baf¯ e spacing identi® ed above could be used for any scale-up reactors without modi® cation. The baf¯ e thickness would be increased at a rate of 2 mm per tube diameter for the durability reasons. NOMENCLATURE C CD D Do E N P/V t U V xo Z
concentration of species, mg l2 1 ori® ce discharge coef® cient tube diameter, m ori® ce diameter, m axial dispersion coef® cient, m2 s2 1 number of baf¯ es per unit length, m power density de® ned in equation (4) time variable, s mean axial velocity of ¯ ow, m s2 1 volume of species, m3 oscillation amplitude, m direction of ¯ ow caused by either pressure or concentration gradient
Figure 13. Mixing time vs. baf¯ e thickness. Oscillation frequency = 3 Hz, Injection location = top.
Trans IChemE, Vol 76, Part A, July 1998
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22. 23. 24. 25. 26. 27. 28. 29.
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Enhancement of gas-liquid mass transfer using oscillatory ¯ ow in a baf¯ ed tube, Chem Eng Sci, 48: 799±809. Ni, X., Gao, S., Cumming, R. H. and Pritchard, D. W., 1995, A comparative study of mass transfer in yeast for a batch pulsed baf¯ ed bioreactor and a stirred tank fermenter, Chem Eng Sci, 50: 2127±2136. Ni, X., Gao, S. and Pritchard, D. W., 1995, A study of mass transfer in yeast in a pulsed baf¯ ed bioreactor, Biotechnol/Bioeng, 45: 165±175. Mackley, M. R., Smith, K. B. and Wise, N. P., 1993, The mixing and separation of particle suspensions using oscillatory ¯ ow in baf¯ ed tubes, Trans IChemE, 71(A): 649±656. Ni, X. and Mackley, M. R., 1993, Chemical reaction in batch pulsatile ¯ ow and stirred tank reactors, The Chem Eng J, 52: 107±114. Ni, X. and Gao, S., 1996, Scale up correlation for mass transfer coef® cients in pulsed baf¯ ed reactors, The Chem Eng J, 63: 157±166. Harnby, N., Edwards, M. F. and Nienow, A. W., 1992, Mixing in the Process Industries, 2nd Ed, (Butterworth-Heinemann Ltd). Cussler, E. L., 1984, Diffusion, Mass Transfer in Fluid Systems, (Cambridge University Press, Cambridge). Emin Erdogan, M. and Chatwin, P. C., 1967, The effects of curvature
and buoyancy on the laminar dispersion of solute in a horizontal tube, J Fluid Mech, 29: 465±484. 30. Holmes, T. L., Kar, A. E. and Baird, M. H. I., 1991, Effect of unfavorable continuous phase density gradient on axial mixing, AIChE J, 37: 360±366. 31. Aravamudan, K. and Baird, M. H. I., 1996, Effect of unstable density gradients on back-mixing in a reciprocating plate column, AIChE J, 42: 2128±2140. 32. Ni, X. and Gao, S., 1996, Mass transfer characteristics of a pilot pulsed baf¯ ed reactor, J Chem Tech Biotechnol, 65: 65±71.
ADDRESS Correspondence concerning this paper should be addressed to Dr X. Ni, Department of Mechanical and Chemical Engineering, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK. The manuscript was received 6 August 1997 and accepted for publication after revision 12 January 1998.
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A SYSTEMATIC STUDY OF THE EFFECT OF GEOMETRICAL PARAMETERS ON MIXING TIME IN OSCILLATORY BAFFLED COLUMNS X. NI (MEMBER), G. BROGAN*, A. STRUTHERS*, D. C. BENNETT* and S. F. WILSON* Department of Mechanical and Chemical Engineering, Heriot-Watt University, Edinburgh, UK *Department of Chemical and Process Engineering, University of Strathclyde, Glasgow, UK
T
he systematic experimental investigation on the effect of baf¯ e free area, baf¯ e spacing and baf¯ e thickness on mixing time in batch oscillatory baf¯ ed columns is reported where the form of oscillation can be achieved by either pulsing the ¯ uid from the base of the column or oscillating the baf¯ es at the top. Local concentration pro® les are measured using conductivity probes at two locations along each column. The mixing time was determined based on the equilibrium concentration format. The experimental results have identi® ed the optimal geometrical parameters for obtaining the lowest mixing times in such columns. Keywords: mixing time; oscillatory baf¯ ed column; free baf¯ e area; baf¯ e spacing; baf¯ e thickness
INTRODUCTION
baf¯ ed reactor, and a single parameter, namely the axial dispersion coef® cient, was evaluated from the RTD curves and used to quantify characteristics of mixing in the system. For batch processes, however, the characteristics of mixing in oscillatory baf¯ ed columns (OBCs) are less well studied with no previous reports on mixing time in particular, although the batch OBCs have been used extensively for mass transfer212 23 , particle mixing and separation24 , reaction25 and scale-up studies26 . In this paper, the research efforts are concentrated on a systematic investigation of geometrical parameters on mixing time in batch OBCs where the form of oscillation can be achieved by either pulsing the ¯ uid from the base of the column or oscillating the baf¯ es at the top. The mixing times evaluated are based on the equilibrium concentration method27 , i.e. when the concentration differences measured by probes are brought into closer physical proximity with the equilibrium concentration. The aim of this paper is to examine the effect of baf¯ e free area, baf¯ e spacing and baf¯ e thickness on mixing time in OBCs with a view to identifying optimal parameters systematically which could be used for scale up purposes.
Oscillatory ¯ ow has been around for a long time, applications in pulsed packed columns and reciprocating plate solvent extraction are the earliest examples12 9 . In packed columns10 the mixing energy is transmitted hydraulically to ® xed plates or packings. Their principal advantage is that no mechanical moving parts come in contact with the process ¯ uid11 . In reciprocating plate columns, oscillatory ¯ ow is produced by the displacement of liquid through the plate perforations while oscillation is not present in regions of the ¯ uid remote from the plates. The resulting enhancement in mixing is due to the superimposition of an unsteady oscillatory ¯ ow component to the system12 11 . Further developments have been reported in the biomedical ® eld where oscillatory ¯ ow in furrowed channels has been the subject of interest for both ¯ ow visualization12 and numerical studies13 . More recently, the studies on oscillatory ¯ ow in an ori® ce baf¯ ed tube, or oscillatory baf¯ ed ¯ ow, have extended the previous investigations and shown that the vortex mixing mechanism is the key factor responsible for the signi® cant enhancement of mixing achieved in the systems142 18 . The mixing mechanism in question breaks down into two halves of a cycle, i.e. the formation of vortices behind baf¯ es, drawing ¯ uid and substance from the walls, and their subsequent ejection at ¯ ow reversal, moving ¯ uid and substance from walls to the centre. In this way, radial mixing is signi® cantly increased in the cells. This mechanism has also been reported to be present in wavy-walled19 and baf¯ e channels20 . The characteristics of mixing in oscillatory baf¯ ed ¯ ow have been studied previously152 18 from the residence time distribution (RTD) perspective, i.e. the changes of concentration are measured as a function of time as the mixing takes place, in a continuous oscillatory
EXPERIMENTAL FACILITIES AND PROCEDURE Three oscillatory baf¯ ed columns were used in this work; two of the three employed a mechanism of oscillatingbaf¯ es as the means of achieving oscillation while one pulsed the ¯ uid. A schematic diagram of the experimental apparatus and facilities is given in Figure 1. The OBCs are made of Perspex columns of two diameters and their dimensions are listed in Table 1. A number of sets of ori® ce baf¯ es, made of polyethylene plates, were used in the experiments, with baf¯ e free areas ranging from 11 to 51%, baf¯ e spacing from 1 to 2.5 times 635
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Figure 1. Schematic diagram of the oscillatory baf¯ ed columns. (a) Pulsing ¯ uid mechanism. (b) Oscillating baf¯ e mechanism.
the tube diameter used, and baf¯ e thickness from 1 to 48 mm. For the OBC (1) where oscillation was located at the base of the column, a 50 mm diameter stainless steel bellows was used to achieve the pulsation, and for the OBC (2&3) where oscillation was initiated at the top of the columns, the motion of baf¯ es was powered by a motor with a linking cam. Oscillation frequencies from 1 to 10 Hz and oscillation amplitudes from 1 to 20 mm centre-to-peak can be obtained in the OBCs. Two Vernier conductivity probes were used to monitor the changes of concentration of NaCl against time along the height of each column. The probes are automatically temperature compensated between temperatures of 5 and 35°C. Prior to the start of the experiments, the conductivity probes were calibrated using the standard two-point method at 0 mg l2 1 (using deionized water) and 500 mg l2 1 concentration of NaCl. The probes, of 10 mm in diameter and 100 mm in length, were placed so that the tips of the probes are located in the centre of the column at a 45 degree angle. The sensors were connected to a Multi Purpose Lab Interface (MPLI) and the signals are shown in real-time graphic mode as well as in a tabulated form.
The rate of data gathering was set at 3 readings per second for both sensors simultaneously for a typical period of 3 minutes. The upper probe was labelled A and the lower probe B. The experiments started by applying oscillation to the columns ® lled with water at pre-set oscillation amplitude and frequency, and then initiating the MPLI program. After a known delay, say 10 seconds, the NaCl tracer was injected via either the top or bottom port, and the data recording in this way contains both the pre and in situ events of concentration vs. time in the columns. For the top injection port, 4 ml of 40 g l2 1 NaCl tracer was used, while for the bottom part, 6 ml was added due to the construction of the port channel where an estimated 2 ml of tracer was contained by the channel itself. The MPLI program stops automatically when the duration of the pre-set experimental time is reached. The columns were then drained and washed with water before a new experiment was initiated. A large number, 351 in total, of experiments were carried out, covering all the pre-described parameters and conditions. In addition, approximately ® ve percent of the experiments were repeated for consistency.
Table 1. Detail speci® cation of OBCs. OBC (1) Oscillating mechanism Parameter investigated Tube diameter (D) Overall height (H ) Operational height Location of top injection port Location of bottom injection port No. of conductivity probes used Location of probe A (HA ) Location of probe A (HB ) No. of baf¯ es
pulsing ¯ uid from the base baf¯ e free area (11, 20, 28, 35, 40, 45, 51%) 50 mm 950 mm 865 mm 900 mm 50 mm Two 530 mm 240 mm 9
OBC (2) oscillating baf¯ es at the top baf¯ e thickness (1, 3, 6, 12, 24, 48 mm) 50 mm 990 mm 750 mm 850 mm 50 mm One/Two 570 mm 200 mm 9 to 5 depending on thickness
OBC (3) oscillating baf¯ es at the top baf¯ e spacing (1, 1.25, 1.5, 1.75, 2, 2.5 D) 90 mm 730 mm 500 mm 700 mm 25 mm Two 410 mm 125 mm 9 to 6 depending on spacing
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CHARACTERIZATION OF MIXING Axial Dispersion Coef® cient In a manner analogous to Fick’ s law of molecular diffusion28 , the contributions due to eddy mixing in oscillatory baf¯ ed ¯ ow can be described by a quantitative parameter, E, the axial dispersion coef® cient. The governing equation for a continuous mode is 2 ¶C ¶ C ¶C = E U (1) 2 2 ¶t ¶Z ¶Z where U is the mean axial velocity of the ¯ ow (m s2 1 ). For a batch operation it becomes
¶C ¶ C = E (2) 2 t ¶ ¶Z where Z is the axial direction of ¯ ow (m). An exact analytical solution of the partial differential equations is dif® cult to obtain, however, approximate mathematical solutions or numerical results are widely used. The numerical solutions usually require a minimization procedure, i.e. E is estimated (and U for the open one) and C calculated, then the values of E (and U ) are adjusted in such a way that the sum of the squared difference between the measured concentrations and the calculated ones is a minimum. The degree of the minimization gives the con® dence level, which in turn measures the error in the evaluation of E. For the case of a net ¯ ow in a baf¯ ed tube superimposed by an oscillatory motion, the residence time distributions (RTDs) have displayed a nearly perfect form of a Gaussian curve172 18 . In those circumstances, the minimization process was quick and the E values obtained are of very high levels of con® dence, from 95% to 100%. However, when the RTDs are not in the form of the Gaussian distribution, such as the RTDs obtained in a smooth tube in a laminar ¯ ow with or without oscillation where the concentration pro® les have a long tail after a sharp break through, the E values can only be obtained at much reduced con® dence levels, e.g. less than 60% depending on operational conditions172 18 . For a batch OBC, a known volume of NaCl tracer, of a similar viscosity to the bulk liquid, is added to the column containing water and by means of two conductivity probes located along each OBC, as shown in Figure 1, the tracer concentrations are measured as a function of time. The typical pro® les are illustrated in Figures 2 and 3. It can be 2
Figure 3. Concentration vs. time. Oscillation frequency = 1.7 Hz, Oscillation amplitude = 20 mm, Baf¯ e spacing = 1 D, Injection location = bottom. Oscillation mechanism = Oscillating baf¯ es, Rig used = OBC (3).
seen that the change of concentrations is instantly detected by the top probe for the top injection (Figure 2). The change registered by the bottom probe was smaller and slightly later than that by the top probe. Both concentration curves quickly converged to an equilibrium concentration. For the bottom injection (Figure 3), a similar pro® le but with the reverse probe order can clearly be noticed as compared to that shown in Figure 2. In this case, it was the bottom probe that responded ® rst for the bottom injection, and the top probe that followed. The responses from the upper probe for the top injection (or the lower probe for the bottom injection) can be approximated to a Gaussian form, although the ® nal concentration is higher than the initial one, but the pro® les from the lower probe (or the upper probe for the bottom injection) are not at all in the form of a Gaussian distribution. For those cases, the errors in evaluating E are as high as 70%. It was considered that one error code could not be applied to all the E evaluated from the experimental data. As a consequence of this, the axial dispersion coef® cient was not applied in this paper. Mixing Time `Mixing time’ should be the time measured from the instant of tracer addition until the column contents have reached a speci® ed degree of uniformity 27 . As the volume of the tracer added is known in these experiments, the equilibrium concentration, C¥ , can be calculated via Vinitial Cinitial 1
Figure 2. Concentration vs. time. Oscillation frequency = 1.7 Hz, Oscillation amplitude = 20 mm, Baf¯ e spacing = 1 D, Injection location = top. Oscillation mechanism = Oscillating baf¯ es, Rig used = OBC (3).
Trans IChemE, Vol 76, Part A, July 1998
Vinjection Cinjection = Vfinal C¥
(3)
where V and C stand for volume (m 3 ) and concentration (g l2 1 ) respectively. The mixing time can now be de® ned as the time required from the instant of NaCl addition for the concentrations at the two locations of A and B to reach the equilibrium value, C¥ 27 . Taking the pro® les shown in Figure 2 for example, the mixing time equals (t2 2 t1 ), where t1 and t2 are the times denoting the instant of tracer injection and when it reaches the equilibrium value. For the majority of the experiments carried out, the concentration-time data obtained have displayed a similar format to those shown in Figures 2 and 3, i.e. the degree of convergence of the two curves to the equilibrium value is very high, consequently the determination of the mixing
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time is a straightforward process and independent of the injection locations. For the extreme geometrical parameters investigated in this study, such as the largest free baf¯ e area and the thickest baf¯ es at the lowest oscillation intensity, however, the concentrations measured at two locations approached C¥ in an asymptotic manner and it was dif® cult to detect the end point of the experiment with precision. In those circumstances, either the experiment has to be prolonged or the percentage of deviation from the ® nal equilibrium value has to be reduced. By trial and error, a 6 5% of deviation from C¥ can be regarded as the end point for 98% of the experiments carried out, irrespective of injecting locations and experimental durations, and was subsequently used in all the following presentations. By doing this, it was considered that the results are consistent and the presentation uni® ed. In order to ensure that the starting point at which the tracer was added is the same for each type of experiment, a row number in the tabulated form of the MPLI program was identi® ed as the precise time that the tracer was injected, usually about 10 seconds after the MPLI program had been initiated. The determination of the mixing time also depends on the way in which the tracer is added. For all the parameters investigated in this study, 20 ml syringes were used for the purpose of tracer injection, and the tracer was added in a one shot manner. The time of the injection was kept as constant as possible, generally within 1 second. For the top injection, 4 ml of 40 g l2 1 NaCl tracer was added to the surface of the liquid, while for the bottom injection, the tracer was added through a channel perpendicularly situated at a short distance above the base (Table 1). The opening/closing of the port was controlled by a one-way valve, which was connected to the syringe. This design also allows a one shot injection, similar to the top port. An extra 2 ml of tracer was used for the bottom injection since about 2 ml tracer was contained by the channel itself. In this way, the total volume of tracer injection at the bottom is the same as that at the top. In summary, the application of a mixing time to the characterization of mixing in the batch OBCs gave more consistent results with higher levels of con® dence than when using the axial dispersion coef® cient; mixing time has therefore been used throughout this work. RESULTS AND DISCUSSIONS The Effect of Tracer Concentration The effect of the tracer concentration on dispersion in continuous oscillatory baf¯ ed reactors was investigated172 18 . The results showed that when there were neither baf¯ es nor ¯ uid oscillation present in the ¯ ow, such an effect is signi® cant. The velocity pro® les skewed to the bottom for the horizontal tubes and ¯ atted for the vertical tubes. In some experiments, sugar was used to neutralize such an effect in order to obtain the appropriate pro® les. However, when both baf¯ es and oscillation were applied to the system, the effect in question was found to be insigni® cant172 18 . For batch operations, however, there is no net ¯ ow and a density gradient between the tracer and the bulk ¯ uid could have a signi® cant effect on mixing and dispersion, specially in vertical columns. Taking the pro® les shown in Figures 2 and 3 for example, the difference in
mixing time between the top and bottom injections is clearly noticeable. As a result of the concentration gradient of the denser tracer, the mixing time evaluated from Figure 2 for the top injection was 34% shorter than that derived from Figure 3 for the bottom injection. All the differences in mixing time between the two injection modes were calculated for all the experiments carried out, and the results show that the enhancements due to the sinking of the denser tracer decreased with the increase in oscillation intensity in terms of oscillation frequency, amplitude and baf¯ e geometrical design. Such enhancements ranged from 74% for the lowest level of oscillation used combined with the extreme baf¯ e geometrical parameters, e.g. the largest free area with the largest baf¯ e thickness and baf¯ e spacing, to merely 0.7% for the strongest oscillation intensity and the optimal baf¯ e geometry. The average enhancement in mixing time was around 32%. Although there are few data on mixing time reported in relation to oscillatory baf¯ ed ¯ ow, these results have found a common ground with many of the previous studies on the effect of the concentration gradient on dispersion, e.g. Emin Erdogan and Chatwin29 in 1967 investigated and modelled the effect of buoyancy on the laminar dispersion of solute in a horizontal tube and reported that buoyancy should have a noticeable effect on dispersion only when the effects of gravity and lateral mixing are not in balance. Holmes, Kar and Baird 30 found that axial dispersion coef® cients were 10 to 20 times higher than the values in reciprocating plate liquid±liquid extraction systems with uniform densities. More recently, Aravamudan and Baird 31 have reported that even under well-agitated conditions, the dispersion can be increased by as much as 25% in the presence of an unstable density gradient. Although no direct comparison could be made here, the similar effect on mixing time was indeed observed. It should be noted that since the bottom-injection results are not affected by the density gradient, they should be taken as more reliable than the top-injection results which are also presented in this paper. The Effect of Free Baf¯ e Area The ratio of the free baf¯ e area, a, is de® ned as the ratio of the free baf¯ e area to the tube area, i.e. pD 2o /4/pD 2 /4 = (Do /D)2 , where Do and D are the diameter of the hole of ori® ce plates (m), and the diameter of the tube (m) respectively. The free baf¯ e area controls the width of vortices within each baf¯ ed cell in an OBC. The larger the free baf¯ e area, the shallower the width of the eddies, consequently the poorer the mixing within the OBC. An alternative term of baf¯ e restriction ratio is de® ned as (1 2 a). A restriction ratio of 66%, a = 34%, was evaluated in ¯ ow visualization studies15 as the optimal value for effective mixing and has since been used in the oscillatory baf¯ ed ¯ ow research. In this study, seven ratios of the free baf¯ e area ranging from 11% to 51% were examined with a view to assessing the effect of such ratios on mixing time in OBC and verifying the optimal value. Figures 4 to 7 show the mixing time as a function of a with both top and bottom injections. It can be seen that the mixing time decreased as the oscillation frequency or amplitude increased. This is expected; as the intensity of mixing, in terms of the product of the oscillation frequency and amplitude, increases, it Trans IChemE, Vol 76, Part A, July 1998
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Figure 4. Mixing time vs. free baf¯ e area. Oscillation amplitude = 5 mm, Injection location = top.
Figure 6. Mixing time vs. free baf¯ e area. Oscillation amplitude = 5 mm, Injection location = bottom.
leads to better mixing and consequently shorter mixing time. However, the degree of the decrease in mixing time was found to be less for higher products of oscillation frequency and amplitude than for the lower ones. This could suggest that a threshold in the uniformity of mixing in OBC exists, once the column has reached such a uniformity; further increase in either oscillation frequency or amplitude would lead to a much smaller improvement in mixing time. In addition, it can also be noted that the degree of the decrease in mixing time was generally small for the free baf¯ e ratios from 11% to about 35% and increased for the larger ratios. To explain this, the following equation is introduced evaluating the power density for OBCs23 as
of oscillatory frequency and amplitude. As for the optimal ratios of the free baf¯ e area, 20 to 22% is recommended, at which the shortest mixing times were obtained irrespective of injection locations. In addition, the difference in mixing time between the top and bottom injections at 20% free baf¯ e area was found to be small, ranging from 1% to 14%. Although a free baf¯ e area of 34% has widely been used in the past, it should be pointed out that it is not the optimal one. It is also envisaged that such optimal ratios could be used for the scale up of OBCs using either oscillation mechanism without any modi® cations.
P 2 rN 1 2 a 2 3 3 = x ov V 3pC 2D a 2
(W/m3 )
(4)
where N is the number of baf¯ es per unit length (m2 1 ), r the density of ¯ uid (kg m2 3 ), xo the oscillation amplitude (m), v the angular oscillation frequency (rad s2 1 ) and CD the ori® ce discharge coef® cient (usually 0.7). It can be seen that the smaller a, the larger the term of (1 2 a 2 )/a 2 in equation (4), suggesting that the large is the mixing intensity and the shorter the mixing time. This again re¯ ects the suggestion of the existence of a threshold in the uniformity of mixing in OBCs. The decrease in the free baf¯ e area ratio would have a similar effect on mixing time as the increase of the product
Figure 5. Mixing time vs. free baf¯ e area. Oscillation frequency = 3 Hz, Injection location = top.
Trans IChemE, Vol 76, Part A, July 1998
The Effect of Baf¯ e Spacing Baf¯ e spacing is a key design parameter in OBC since it in¯ uences the shape/length of the eddies within each baf¯ e cavity for a given oscillation amplitude. The optimal baf¯ e spacing in any OBC should ensure a full expansion of eddies generated behind baf¯ es so that the vortices will spread effectively throughout the entire interbaf¯ e region. In the previous studies, 1.5 times the tube diameter was reported as the optimal baf¯ e spacing by Brunold et al.15 from ¯ ow visualization studies, and 1.8 times the tube diameter was suggested by Ni and Gao32 in their mass transfer studies. It should be noted, however, that all the previous investigations on baf¯ e spacing were based on the mechanism of pulsing ¯ uid at the base of OBCs. In this work, the systematic examination of the effect of baf¯ e spacing on mixing time was carried out in an OBC employing
Figure 7. Mixing time vs. free baf¯ e area. Oscillation frequency = 3 Hz, Injection location = bottom.
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Figure 8. Mixing time vs. baf¯ e spacing. Oscillation frequency = 2.8 Hz, Injection location = top.
Figure 10. Mixing time vs baf¯ e spacing. Oscillation frequency = 2.8 Hz, Injection location = bottom.
the mechanism of oscillating baf¯ es, and the results can serve as a comparison with those from the pulsing ¯ uid OBCs. Figures 8±11 show the pro® les of mixing time vs. the ratio of the baf¯ e spacing to the column diameter for both top and bottom injections and for a range of oscillation frequencies and amplitudes tested. The general conclusions made from all the graphs shown here are similar to those described earlier, i.e. the increase in oscillation frequency/ amplitude led to the decrease in mixing time, and the degree of the decrease in mixingtime was much less for high products ofoscillationfrequencyandamplitudethanfor lowones. As to the identi® cation of the optimal baf¯ e spacing, the trend appeared to be less well de® ned as compared with that for the free baf¯ e area ratios. Nevertheless, a baf¯ e spacing of 2D gave overall the lowest mixing time for both locationsand is recommendedas the optimalbaf¯ e spacingfor an OBC with an oscillating-baf¯ e mechanism. This baf¯ e spacing was found to be comparable but rather higher than that identi® ed for OBCs with a pulsing ¯ uid mechanism (1.8 D)32 . It should be noted that the oscillation amplitudes for OBCs with the oscillating-baf¯ e mechanism are generally much greater than those with the pulsing ¯ uid mechanism, and that this could be related to the impact of momentum for the two types. It is envisaged that pulsing ¯ uid in OBCs exerts a larger initial momentum than oscillating baf¯ es, and the increase in the oscillation amplitude for the latter mechanism is to compensate the difference in the initial momentum. Once this has been achieved in OBCs, the effect in mixingseems to be more or less the same for the two mechanisms.
The generation of vortices by each baf¯ e of an OBC is similar to that of vortices shed by ¯ uid ¯ owing around an object. Each eddy needs a certain edge to cling on for an optimal time prior to the process of shedding. Would there be an optimal baf¯ e thickness? In this study six baf¯ e thickness were investigated including 1, 3, 6, 12, 24 and 48 mm. As the baf¯ es got thicker, it was dif® cult to use two conductivity probes since the position of baf¯ es will interfere with the probe locations. For the baf¯ e thickness of 12, 24 and 48 mm in particular, only the lower probe could be employed and for this reason instead of two injection ports, only the top one was used. Consequently, all the data for this type of experiments shown in Figures 12 and 13 were from the lower probe and for the top injection. It can be seen that a similar trend in mixing time to that described earlier was found here, the mixing time decreased with the increase of oscillation frequency/amplitude. Overall, the results suggest that the thinner baf¯ es favoured the generation of vortices, and it seems that if the time needed for vortices to cling on a baf¯ e edge is too long prior to shedding, their shape could have been distorted somewhat, and this subsequently affected the mixing time. The baf¯ e thickness of 2 to 3 mm is identi® ed as the optimal value for good mixing. Although the effect of the baf¯ e thickness on mixing in OBC has not previously been investigated, the intuitive value of 3 to 4 mm in baf¯ e thickness was chosen, which has been used throughout the oscillatory baf¯ ed ¯ ow
Figure 9. Mixing time vs. baf¯ e spacing. Oscillation amplitude = 20 mm, Injection location = top.
Figure 11. Mixing time vs. baf¯ e spacing. Oscillation frequency = 20 mm, Injection location = bottom.
The Effects of Baf¯ e Thickness
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Table 2. Optimal parameters identi® ed. OBCs Parameters Ratio of free baf¯ e area Baf¯ e spacing Baf¯ e thickness
Figure 12. Mixing time vs. baf¯ e thickness. Oscillation amplitude = 20 mm, Injection location = top.
Greek a r v
Oscillating baf¯ es
Pulsing ¯ uid
20±22% 2D 2±3 mm
20±22% 1.8 D26 2±3 mm
symbols free baf¯ e area density of ¯ uid, kg m2 3 angular oscillation frequency, rad s2
1
REFERENCES related research. From this study, it con® rms that the choice is very close to the best. CONCLUSIONS A systematic experimental investigation on the effect of the free baf¯ e area, baf¯ e spacing and baf¯ e thickness on mixing time has been reported in batch OBCs with two types of oscillation mechanism. The optimal parameters for better mixing in OBCs have been identi® ed and summarized in Table 2. Based on a previous study in scale up correlation26 , it is envisaged that both the optimal free baf¯ e area ratio and baf¯ e spacing identi® ed above could be used for any scale-up reactors without modi® cation. The baf¯ e thickness would be increased at a rate of 2 mm per tube diameter for the durability reasons. NOMENCLATURE C CD D Do E N P/V t U V xo Z
concentration of species, mg l2 1 ori® ce discharge coef® cient tube diameter, m ori® ce diameter, m axial dispersion coef® cient, m2 s2 1 number of baf¯ es per unit length, m power density de® ned in equation (4) time variable, s mean axial velocity of ¯ ow, m s2 1 volume of species, m3 oscillation amplitude, m direction of ¯ ow caused by either pressure or concentration gradient
Figure 13. Mixing time vs. baf¯ e thickness. Oscillation frequency = 3 Hz, Injection location = top.
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ADDRESS Correspondence concerning this paper should be addressed to Dr X. Ni, Department of Mechanical and Chemical Engineering, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, UK. The manuscript was received 6 August 1997 and accepted for publication after revision 12 January 1998.
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