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Reduced IMRs in a mixing tank via agitation improvement
chemical engineering research and design 9 1 ( 2 0 1 3 ) 1009–1017
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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Reduced IMRs in a mixing tank via agitation improvement Steven Wang a,b,∗ , Jie Wu c , EngYing Bong c a b c
Department of Chemical Engineering, Monash University, Clayton, Victoria 3800, Australia CSIRO Earth Science and Resource Engineering, Clayton, Victoria 3168, Australia CSIRO Process Science and Engineering, Highett, Victoria 3190, Australia
a b s t r a c t Mixing of Newtonian fluids in a stirred tank at low Reynolds numbers was investigated experimentally by means of a visual decolourization technique and shaft power measurements. The research was focused on the Isolated Mixing Regions (IMRs), which are “doughnut-shaped” structures in a stirred tank exhibiting little mixing with bulk of the fluids. The effect of Reynolds number on the IMRs was determined. The critical Reynolds numbers beyond which IMRs are destroyed were presented. The study was focused on agitation design which consumes less power input to destroy the IMRs. A pitch-bladed impeller with an alternating pitch was found more energy efficient than other test impellers in eliminating IMRs in both baffled and unbaffled configurations. It was also found that dramatic reduction in the power consumption could be achieved with installation of baffles to eliminate IMRs at typically low Reynolds numbers. The improved energy efficiency was thought related to generation of more chaotic mixing from the disturbance generated by the baffles, or impeller blade asymmetry such as alternating pitch. An energy parameter was introduced to account for the mixing time scale and the power required in regimes above the critical Reynolds number, in order to evaluate the energy efficiency when IMRs are non-existent. © 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: IMRs; Isolated mixing regions; Laminar mixing; Newtonian fluids; Stirred tank; Agitator
1.
Introduction
Mechanically agitated vessels are widely used unit operations in the modern processing industry. Mixing vessels are critical for bulk materials chemical slurry processing such as leaching, digestion, crystallization, adsorption, ion-exchange and polymerization (Nienow, 1994; Wu et al., 2011). Homogeneous mixing is vital for product blending consistency and purity of the reaction products. Inconsistent solute distribution and non-homogeneous blending due to poor mixing can lead to undesirable by-product which is often unacceptable in terms of product quality. One distinctive phenomenon related to poor mixing in a stirred vessel is the formation of isolated mixing regions. Isolated mixing regions or IMRs refer to regions of confined mixed zone, segregated by well-defined boundary layer, as described by Lamberto et al. (1996). Isolated mixing regions (IMRs) in a stirred vessel are commonly found in laminar flows at low
Reynolds numbers. The structure of IMRs was first discovered by Norwood and Metzner (1960). At low Reynolds numbers, these regions are present in the form of toroidal vortices above and below the impellers (Bresler et al., 1997; Makino et al., 2001). The structural property of IMRs in the stirred vessel has been experimentally studied by Makino et al. (2000, 2001) and Hashimoto et al. (2009). They revealed that IMRs consist of several filaments and core torus. Hashimoto et al. (2009) recently suggested that the filaments only exist in the range: 20 < Re < 94, with Re defined as Reynolds number based on the tip velocity, impeller diameter, based on tests using a two-bladed paddle impeller. Makino et al. (2001) concluded that the structure of IMRs is highly complex, consisting of various Kolmogorov–Arnold–Moser (KAM tori). Makino et al. (2000) also showed that the geometric structure of IMRs could be controlled by varying the number of blades and the rotational speed of impeller. They showed that the velocity fluctuations of fluid flow created by the impeller blades caused periodical perturbations, affecting the structure of IMRs.
∗ Corresponding author at: Department of Chemical Engineering, Monash University, Clayton, Victoria 3800, Australia. Tel.: +61 3 9545 8380. E-mail address: [email protected] (S. Wang). Received 1 August 2012; Received in revised form 11 January 2013; Accepted 14 January 2013 0263-8762/$ – see front matter © 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cherd.2013.01.009
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Nomenclature D e c H N Ntm P R r T tm V
impeller diameter (m) shaft essceenity (m) impeller off-bottom clearance (m) liquid level (m) impeller speed (rev/s, rpm) dimensionless mixing time power (w) tank radius (m) the distance between the shaft and vertical centre line of the tank revolution complete decolourization time (min) tank volume (m3 )
The formation of such structures in a mixing vessel could be problematic for purpose of mixing homogeneity since there is little material exchange between isolated mixing regions (IMRs) and active mixing regions (AMRs). It could be suggested that the IMRs structures could lead to poor processing performance, e.g. incomplete extraction in leach processing or production of by-products due to incorrect level of chemical concentrations within the structures. Takahashi and Motoda (2009) also pointed out that very long mixing times and high-energy inputs are required to achieve a complete liquid homogenization with presence of IMRs. As will be discussed later in this paper, the long time scale required to homogenize the fluids with the presence of IMRs can be considered as practically “infinite” when compared with the mixing time scale without IMRs. This “infinite” mixing time scale is clearly unacceptable for many mixing applications, and therefore the IMR structures should be removed. Extensive efforts have been devoted to eliminate IMRs completely in agitated vessels. Increasing the agitator speed to operate at sufficiently high Reynolds number has been
found effective to destroy IMRs in the literature. This approach is however not always practical due to its potential consequences including increased power, erosion damage on impellers or damage to the shear-sensitive materials essential in the biological processes. Another approach was to use unsteady rotation speed (Lamberto et al., 1996) to destroy IMRs, which can be effective due to the impact of chaotic mixing produced in perturbation. Yao et al. (1998) also introduced a similar method using unsteady RPM as an effective method in destroying the IMRs in low Reynolds numbers. Other methods associated with the elimination of IMRs include large object insertion (Takahashi and Motoda, 2009), novel perturbation waveforms (Yek et al., 2009) and installation of eccentricstirred impellers (Cabaret et al., 2008; Takahashi et al., 2012). The present work is driven by a need to eliminate IMRs at high viscosities with practical engineering designs. This is related to the background of processing of viscous slurry materials at larger industrial mixing tanks, such as those used in the minerals hydrometallurgical operations. Due to large equipment dimensions and motor power used in such operations, it is impractical to employ methods such as oscillating speeds or higher Reynolds numbers, i.e. increased speed at significantly higher power input. It is desirable to explore simple tank geometrical changes practical for industrial applications at low Reynolds numbers, at less power input. It is ideal that IMRs are eliminated without major equipment upgrade or motor power increase. To this aim, the current paper aims to explore simple geometrical change on IMRs under laminar flow conditions. Particular attention will be paid on the effect of the impeller design, impeller location and baffle installation on the mixing performance.
2.
Experimental
2.1.
Test rig
Flow visualization experiments were carried out in a mixing research rig (Fig. 1) consisting of a 190 mm diameter
Fig. 1 – Schematic illustration of experimental apparatus.
chemical engineering research and design 9 1 ( 2 0 1 3 ) 1009–1017
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Fig. 2 – Photographs of impellers used in this study. (a) PR30, (b) A-45PBT6, (c) DT6, and (d) DI.
cylindrical tank with a flat bottom placed inside a rectangular outer acrylic tank. The outer tank was filled with tap water to minimize the optical distortion. Sequential digital images were taken with a digital video camera, in order to reveal IMR structures and the flow pattern during the experiments. In order to capture the cross-sectional areas of the IMRs, a plane sheet of light passing through the 5-mm slits at the centre of the cardboards located on both sides of the tank illuminated the IMRs, as shown in Fig. 1. The light sources used were two 1000 W Arri IP23 lamps.
2.2.
Impellers
Four impellers, including a 3-blade propeller (PR30, supplier: Heidolph), a 6-alternating pitched (45◦ ) blade turbine (A45PBT6), a 6-blade disc turbine (DT6) and a disc impeller (DI), were chosen in the experiments. The blades of A-45PBT6 arranged in such a way that they alternatively pump upward and downward, potentially introduce more chaotic flow and eventually minimize the IMRs. Photographs of the impellers used in this study are shown in Fig. 2. All impellers have identical diameter of 70 mm (i.e. diameter to tank ratio of 0.36), except that DI (without the blades) has diameter of 50 mm (D/T = 0.26). The detailed specifications of all impellers are shown in Table 1. It should be pointed out that the diameter of DI is smaller than the other impellers, but it is still reasonably hypothesized that even if the diameter of the DI is equivalent to the other impellers, the bladeless geometry will probably still be the least efficient of the four impellers.
Table 1 – Specifications of the impellers used in this study (length unit: mm).
Blade height Impeller diameter No. of blades Angle of blades D/T
PR30
A-45PBT6
DT6
DI
10 70 3 – 0.36
10 70 6 ±45◦ 0.36
10 70 6 90◦ 0.36
10 50 – – 0.26
2.3.
Test fluids and experimental methodology
Glycerin (>99.7%, w/w) was used as the working fluids and the viscosities of glycerine were found to be in the range of 0.75–0.85 Pa s, at the room temperature 20–22 ◦ C. A well-known decolourization technique (refer to Takahashi and Motoda, 2009), involving the neutralization reaction of NaOH and HCL was used to visualize the IMRs. A passive tracer fluorescent dye, as a pH indicator, was injected and homogenized in the working fluid. In order to remove all the air bubbles, the working fluid mixed with fluorescent dye was allowed to be settled for about 12 h before conducting the experiments. Refer to Fig. 3a, the working fluid mixed with fluorescent dye was made basic by blending it with a basic solution consisting of 10 ml of 2 M NaOH. The working fluid was then stirred at 500 rpm for ∼2 h in order to fully disperse the base solution throughout the tank, leading to a uniform colour distribution (refer to Fig. 3a). After the agitator reached the test speed, a small amount of acidic solution (HCl: 10 ml 2 M) was injected at the blade tip and consequently the decolourization took place due to neutralization reaction in the active mixing regions (i.e. transparent area), as shown in Fig. 3c–f. The formation of isolated mixing regions, IMRs, corresponding to the green areas shown in Fig. 3f, is a consequence of a lack of mixing with the acidic fluids in the AMRs, causing the pH to remain basic and fluorescent dye green in the IMRs. The colour of AMRs, on the other hand, changed significantly due to substantial change in pH as a result of the neutralization reaction by mixing with acid fluid injected at the blade tip, located in the AMRs. The “doughnut-shaped” IMR structure was found to be unchanged in size for a few hours (∼3 h) in our experiments, implying that materials exchange between AMRs and IMRs is extremely poor. In this study, the dimensionless mixing time (Ntm ) was used to evaluate the overall mixing efficiency for different configurations. Note that N is the impeller speed and tm is the decolourization time in the system. Ntm on the other hand also indicates the number of agitator rotations required to eliminate the IMRs in the laminar systems.
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Fig. 3 – Decolourization demonstration based on acid–base reaction. (a) t = −5 s, pre-injection, acidic solution; (b) t = 0, injection of base; (c) t = 2 s; (d) t = 10 s; (e) t = 120 s; (f) t = 1600 s (highlighted green areas: isolated mixing regions [IMRs]; transparent area: active mixing regions [AMRs]). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
3.
Results
3.1.
Effect of Reynolds number
systems since they require a higher power input to for purpose of minimization of IMRs.
3.3. Fig. 4a shows the flow visualization results of four impellers; it can be commented that the IMRs are clearly different in terms of shape, size and location, depending on the impeller type and Reynolds number. In the case of axial-flow propeller PR30, the IMR above the impeller is smaller than that located below the impeller, most likely owing to its downwards-pumping direction, whereas for other impellers, the IMRs are about the same size in all four quadrants. Fig. 4b shows the variation of a/A as a function of Reynolds number for different impellers in the unbaffled condition, where a is the total cross-sectional area of the IMRs and A is the cross-sectional area of the tank. It can be seen from the figures that at a given Reynolds number, the disk impeller produced the largest IMR structures, whereas the Rushton turbine (DT6) had the smallest IMR structures. It must be pointed out that further increase in Reynolds number for PR30 and Disk exceeded the speed limit of the test rig (∼2000 rpm), thus the a/A vs. Re data could only be obtained up to Re ∼ 250 in the current test set-up (Fig. 4b). To understand the effect of Reynolds number on IMRs, the central positions of the IMRs produced by DT6 and PR30 are estimated from the visual images and plotted in Fig. 5. As the Reynolds number increases, the IMR above the impeller move further away from the impeller in the horizontal direction and move closer to horizontal centre line of the impeller in the vertical direction. Similar tendency can be observed for the IMR below the impeller.
3.2.
Power comparison among the impellers
The variation of the area of the IMRs as a function of the power consumption is expressed as a/A vs. (P/V: W/m3 ) for different impellers in Fig. 6. Among the impellers, the modified pitched blade turbine (A-45PBT6) appears to be the most energy efficient in producing smaller IMRs. In contrast, it is less efficient to use PR30 and the disk impeller in the viscous
Effect of impeller clearance
Rushton turbine DT6 was used to study the effect of impeller to tank bottom clearance (c/H) as shown in Fig. 7, where c is the distance to the bottom and H is the liquid height in the tank. The tests were carried out at different Reynolds numbers as shown in Fig. 7. At c/H = 0.5, there are two IMRs, i.e. doughnut-shaped rings, one above and the other below the impeller (Fig. 7a). At c/H = 0.05, only a single doughnut-shaped ring above the impeller was formed, with the impeller close to the tank bottom (Fig. 7b). On the other hand, at c/H = 0.72, the shift in impeller location toward the liquid surface destroyed the ring above the impeller, leading to formation of a single doughnut-shaped IMR below the impeller (Fig. 7c).
3.4.
Effect of baffle installation
The impact of number of baffles on the level of mixing homogeneity in a stirred tank equipped with a Rushton turbine (DT6) is shown in Fig. 8a–c. The tests were conducted at the Reynolds number of 41, which is in the regime close to Re = Rec . Fig. 8d shows the specific power at this critical regime (i.e. beyond which IMRs are eliminated) is insensitive to the number of baffles. It must be noted out that in our tests for all the baffled configurations, further increase in impeller speed led to complete destruction of the IMRs, suggesting that the critical Reynolds number (Rec ) for the DT6 impeller in the baffled tank is approximately equal to 40–50, for baffles of x2 to x4. The effect of baffles on the minimum power required to destroy IMRs are presented in Fig. 9 for three different impellers. Under baffled conditions, at Rec , the power input for all the impellers is approximately equal. Under unbaffled condition, the axial-flow impeller (PR30) is much less efficient than other two impellers. Based on Fig. 9, the power required to accomplish the homogenous condition in the baffled tank is approximately 5 times higher than that for the unbaffled tank
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Fig. 4 – IMRs size vs. Reynolds number: (a) visualization images; (b) a/A vs. Re plot.
for the DT6 and A-45PBT6. The impact is more substantial for the axial flow impeller: PR30. In the case of PR30, to achieve similar homogeneity, the baffled configuration is much more energy-efficient than unbaffled tank as 25 times power reduction can be achieved by simply installing the baffles. It must be pointed out that the significant power difference is mainly attributed to substantial variation in Rec at the baffled and unbaffled conditions. It is interesting to investigate the critical Reynolds number Rec , at which point the IMRs disappeared owing to the presence of flow perturbations. Nabil Noui-Mehidi et al. (2008) highlighted the mechanism of IMR disappearance using a Rushton turbine and they showed that the disappearance of the IMRs in the system was attributed to two factors: stretching and shrinking in the presence of perturbations. A similar mechanism was observed for the impellers used
in our study and our results show that the critical values of the Reynolds number are highly dependent on impeller type (refer to Table 2). Under unbaffled condition, among the impellers, DT6/A-45PBT4 has the smallest critical Rec and the Table 2 – Estimated critical Reynolds number (Rec ) for different impellers. Impeller
Flow type
DT6 A-45PBT6 PR30 Disk
Radial Mixed Axial –
a
Rec(unbaffled) 136 135 304a 524a
Rec(baffled) 40–50 40–50 40–50 40–50
These values were estimated based on the data trend shown in Fig. 4b. In our experiments, at least 1 h was allowed to determine the Rec for each condition.
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Fig. 5 – Shift of IMR centre with increasing Re. Impellers: DT6 and PR30 (red dots: the centres of the IMRs). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
disk has the largest critical value. In the baffled configuration, it was observed that the isolated mixing regions disappeared at 40–50, for all the impellers tested, as shown in Table 2.
3.5.
Energy efficiency
For mixing in the regime of Re > Rec , IMRs do not exist. The selection of an appropriate impeller under baffled condition should be measured in terms of the mixing time and the energy required. Fig. 10 shows the dimensionless mixing time: Ntm (the product of the dimensional mixing time tm and the speed N) for three test impellers, all under baffled condition (x4 baffles). It can be seen that the modified pitch-bladed impeller (A-45PBT4) requires less mixing time compared to the radialflow Rushton turbine (DT6). On the other hand, the mixing
time data for disk impeller is not included in this figure as complete mixing did not complete in a reasonable duration. Among the three impellers shown in Fig. 10, the PR30 impeller performs relatively less effective considering the longest blend time that it requires. To investigate the impact of impeller type on the energy efficiency in the baffled condition, the specific energy (E: J/m3 ) required to achieve complete mixing is defined as follows: E=
where P/V is the specific power consumption (W/m3 ), and tm is the time (s) required to reach the homogenous condition in the laminar systems. The dependence of specific energy on the impeller type is shown in Fig. 11. It can be seen from the figure that the A-45PBT4 has smallest E value, and the other impellers (axial-flow: PR30 and radial-flow: DT6) have relatively greater E values. This is consistent with the feature of its lower specific power consumption in destroying IMRs for Re < Rec , as presented in Fig. 6, Section 3.2. On the other hand, this implies that the general performance of radial-flow impeller is similar to that of axial-flow impeller in liquid blending, in the baffled configuration.
4.
Fig. 6 – a/A as a function of specific power input (a: total IMR area; A: tank area). 24 < Re < 140, c/H = 0.5, without baffles.
P × tm V
Discussion
The laboratory experience with IMRs was that the viscous systems at Re < Rec could only be homogenized through a slow diffusion process. The required long diffusion time process is practically “infinitive” in the engineering sense, although diffusion does eventually provide “complete” mixing between IMRs and AMRs, and thus destruction of IMRs. This long time scale, e.g. hours or days are often unacceptable when
chemical engineering research and design 9 1 ( 2 0 1 3 ) 1009–1017
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Fig. 7 – Formation of IMR(s) with shaft located in tank centre. (a) c/H = 0.5; (b) c/H = 0.05; (c) c/H = 0.72. Impeller: DT6.
considering against the time scale of importance, e.g. a chemical reaction, which may require a complete mixing in minutes. The improved energy efficiency in destroying IMRs with installation of baffles or using the pitch bladed turbine with alternating pitch as demonstrated in this paper was thought to be related to the fundamental effect of chaotic mixing. Disturbance generated by the asymmetrical perturbation was thought to improve the process of the exponential stretching and folding between fluids materials. This is essential for complete mixing, i.e. mutual contact between all fluid elements in a tank. This effect of “disturbance” is more energy efficient than otherwise operating say with a higher speed. For example, in the case of the Rushton turbine, the baffled system was found to require less power to destroy the IMRs than unbaffled system. This suggests that the disturbance introduced by baffles is effective in improving the energy efficiency, in the context of destroying IMRs. It can also be hypothesized that the disturbance, thought to produce the effect of chaotic mixing, suggests in a fundamental sense that chaotic mixing is more energy efficient, and therefore should be considered for engineering implementation as demonstrated in this paper. It was found that under laminar flow conditions, the A45PBT6 impeller led to formation of smallest IMRs at a given Reynolds number, as evident from a/A vs. specific power data. Alvarez et al. (2002) conducted the experiments based on the time progression of fluorescent dye injection and they demonstrated that the periodic perturbation caused by impeller blades triggers chaos in laminar systems. The perturbation introduced by the blades is thus the main factor causing the reduction in IMR size in our experiments; therefore it is not surprising to note that the impellers with more blades (e.g. DT6 and 45-PBT6 here) have the smallest IMRs, owing to the introduction of the greater perturbation by their blades.
However, it is unsure to us whether installation of more blades in an impeller can actually lead to better mixing quality as it approaches geometry similar to a disc. In addition, it should be noted that the asymmetrical design of our impeller (A-45PBT6) also contribute to the introduction of greater periodic perturbation, and the more effective mixing results make it the first option for liquid blending, regardless of baffled and unbaffled conditions. Hashimoto et al. (2011) suggested that baffles can effectively transform the circumferential flow to vertical and radial flows. Their study, based on the streak flow pattern, showed that in baffled vessels, both the vicinity of the vessel wall and the tip of baffles causes a streak lobe formation and folds of streak in the vertical and circumferential directions can be enhanced with the installation of baffles. As a consequence of this enhancement mechanism, the isolated toroidal mixing regions in a baffle tank became distorted. It is also very interesting to comment that using baffles more than 2 does not improve mixing in the tank. Finally, it is useful to comment that the conclusion that baffles are more energy efficient for mixing is limited to viscous low Reynolds number applications. At high Reynolds numbers, e.g. in slurries such as that made of sand and water, the mixing is not an issue. The mixing time in this regime is so short in comparison with the process time scale that achieving good mixing is not normally an issue (Wu et al., 2011). Other process condition could be more important, e.g. off-bottom solids suspension. It is useful to alert to the readers that removal of baffles is more energy efficient for solids suspension at high Reynolds numbers, contrary to the low Reynolds number situations in this paper. Refer to Wu et al. (2011) and Wang et al. (2012) for more detailed information on this topic.
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Fig. 8 – Impact of number of baffles installed in the tank on IMRs and power at Re ∼ Rec . (a) Two baffles; (b) three baffles; (c) four baffles; (d) power comparison for different configurations. Impeller: DT6. Re = 41 (T: rotations).
Fig. 9 – Estimated minimum specific power (at Re ∼ Rec ) required to achieve homogenous mixing in the tank. Note: The values of Rec at baffled and unbaffled conditions are summaried at Table 2. Four baffles were installed in the baffled systems. (+number times = (power at baffled condition)/(power at unbaffled condition)).
Fig. 10 – Normalized mixing time at Re = 61 (above Rec ): time required for complete mixing in the baffled tank.
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Fig. 11 – Specific energy required to achieve homogenous mixing at Re = 61 (above Rec ) in the baffled tank.
5.
Conclusions
The features of the IMRs formed in the viscous Newtonian systems in a stirred tank have been studied in this paper. The effect of Reynolds number on the IMRs was determined. The critical Reynolds numbers beyond which IMRs are destroyed were presented. A pitch-bladed impeller with an alternating pitch was found more energy efficient than other test impellers in eliminating IMRs in both baffled and unbaffled configurations. It was also found that dramatic reduction in the power consumption could be achieved with installation of baffles to eliminate IMRs at typically low Reynolds numbers. The improved energy efficiency was thought related to generation of more chaotic mixing from the disturbance generated by the baffles, or impeller blade asymmetry such as alternating pitch. An energy parameter was introduced to account for the mixing time scale and the power required in regimes below the critical Reynolds number, in order to evaluate the energy efficiency when IMRs are non-existent.
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Cabaret, C., Fradette, L., Tanguy, P.A., 2008. New turbine impeller for viscous mixing. Chem. Eng. Technol. 31, 1806–1815. Hashimoto, S., Ito, H., Inoue, Y., 2009. Experimental study on geometric structure of isolated mixing region in impeller agitated vessel. Chem. Eng. Sci. 64, 5173–5181. Hashimoto, S., Natami, K., Inoue, Y., 2011. Mechanism of mixing enhancement with baffles in impeller-agitated vessel, part I: a case study based on cross-sections of streak sheet. Chem. Eng. Sci., http://dx.doi.org/10.1016/j.ces.2011.06.032. Lamberto, D.J., Muzzio, F.J., Swanson, P.D., Tonkovich, A.L., 1996. Using time-dependent RPM to enhance mixing in stirred vessels. Chem. Eng. Sci. 51, 733–741. Makino, T., Kaise, T., Ohmura, N., Kataoka, K., 2000. Laser-optical observation of chaotic mixing structure in a stirred vessel. In: Laser Techniques for Fluid Mechanics: Selected Papers from the 10th International Symposium, Lisbon, Portugal, July 10–13. Makino, T., Ohmura, N., Kataoka, K., 2001. Observation of isolated mixing regions in stirred vessel. J. Chem. Eng. Jpn. 34, 574–578. Nienow, A.W., 1994. The suspension of solid particles. In: Mixing in the Process Industries. Butterworths, London, UK, pp. 364–393. Noui-Mehidi, M.N., Ohmura, N., Wu, J., Nguyen, B.V., Nishioka, N., Takigawa, T., 2008. Characterisation of isolated mixing regions in a stirred vessel. Int. J. Chem. React. Eng. 6, 1–10. Takahashi, K., Motoda, M., 2009. Chaotic mixing created by object inserted in a vessel agitated by an impeller. Chem. Eng. Res. Des. 87, 386–390. Takahashi, J., Daisuke, S., Takahata, D., Yasuyuki, T., 2012. Laminar mixing in eccentric stirred tank with different bottom. J. Chem. Eng. Jpn. 44, 931–935. Yao, W.G., Sato, H., Takahashi, K., Koyama, K., 1998. Mixing performance experiments in impeller stirred tanks subjected to unsteady rotational speeds. Chem. Eng. Sci. 53, 3031–3040. Yek, W.M., Noui-Mehidi, M.N., Parthasarathy, R., Bhattacharya, S.N., Wu, J., Ohmura, N., Nishioka, N., 2009. Enhanced mixing of Newtonian fluids in a stirred vessel using impeller speed modulation. Can. J. Chem. Eng. 87, 839–846. Norwood, K.W., Metzner, A.B., 1960. Flow patterns and mixing rates in agitated vessels. AIChE J. 6, 432–437. Wang, S., Wu, J., Boger, D.V., 2012. Energy efficient solids suspension in an agitated vessel-water slurry. Chem. Eng. Sci. 74, 233–243. Wu, J., Wang, S., Graham, L., Parthasarathy, R., Nguyen, B., 2011. High solids concentration agitation for minerals process intensification. AIChE J. 57 (9), 2316–2324.
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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Reduced IMRs in a mixing tank via agitation improvement Steven Wang a,b,∗ , Jie Wu c , EngYing Bong c a b c
Department of Chemical Engineering, Monash University, Clayton, Victoria 3800, Australia CSIRO Earth Science and Resource Engineering, Clayton, Victoria 3168, Australia CSIRO Process Science and Engineering, Highett, Victoria 3190, Australia
a b s t r a c t Mixing of Newtonian fluids in a stirred tank at low Reynolds numbers was investigated experimentally by means of a visual decolourization technique and shaft power measurements. The research was focused on the Isolated Mixing Regions (IMRs), which are “doughnut-shaped” structures in a stirred tank exhibiting little mixing with bulk of the fluids. The effect of Reynolds number on the IMRs was determined. The critical Reynolds numbers beyond which IMRs are destroyed were presented. The study was focused on agitation design which consumes less power input to destroy the IMRs. A pitch-bladed impeller with an alternating pitch was found more energy efficient than other test impellers in eliminating IMRs in both baffled and unbaffled configurations. It was also found that dramatic reduction in the power consumption could be achieved with installation of baffles to eliminate IMRs at typically low Reynolds numbers. The improved energy efficiency was thought related to generation of more chaotic mixing from the disturbance generated by the baffles, or impeller blade asymmetry such as alternating pitch. An energy parameter was introduced to account for the mixing time scale and the power required in regimes above the critical Reynolds number, in order to evaluate the energy efficiency when IMRs are non-existent. © 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: IMRs; Isolated mixing regions; Laminar mixing; Newtonian fluids; Stirred tank; Agitator
1.
Introduction
Mechanically agitated vessels are widely used unit operations in the modern processing industry. Mixing vessels are critical for bulk materials chemical slurry processing such as leaching, digestion, crystallization, adsorption, ion-exchange and polymerization (Nienow, 1994; Wu et al., 2011). Homogeneous mixing is vital for product blending consistency and purity of the reaction products. Inconsistent solute distribution and non-homogeneous blending due to poor mixing can lead to undesirable by-product which is often unacceptable in terms of product quality. One distinctive phenomenon related to poor mixing in a stirred vessel is the formation of isolated mixing regions. Isolated mixing regions or IMRs refer to regions of confined mixed zone, segregated by well-defined boundary layer, as described by Lamberto et al. (1996). Isolated mixing regions (IMRs) in a stirred vessel are commonly found in laminar flows at low
Reynolds numbers. The structure of IMRs was first discovered by Norwood and Metzner (1960). At low Reynolds numbers, these regions are present in the form of toroidal vortices above and below the impellers (Bresler et al., 1997; Makino et al., 2001). The structural property of IMRs in the stirred vessel has been experimentally studied by Makino et al. (2000, 2001) and Hashimoto et al. (2009). They revealed that IMRs consist of several filaments and core torus. Hashimoto et al. (2009) recently suggested that the filaments only exist in the range: 20 < Re < 94, with Re defined as Reynolds number based on the tip velocity, impeller diameter, based on tests using a two-bladed paddle impeller. Makino et al. (2001) concluded that the structure of IMRs is highly complex, consisting of various Kolmogorov–Arnold–Moser (KAM tori). Makino et al. (2000) also showed that the geometric structure of IMRs could be controlled by varying the number of blades and the rotational speed of impeller. They showed that the velocity fluctuations of fluid flow created by the impeller blades caused periodical perturbations, affecting the structure of IMRs.
∗ Corresponding author at: Department of Chemical Engineering, Monash University, Clayton, Victoria 3800, Australia. Tel.: +61 3 9545 8380. E-mail address: [email protected] (S. Wang). Received 1 August 2012; Received in revised form 11 January 2013; Accepted 14 January 2013 0263-8762/$ – see front matter © 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cherd.2013.01.009
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Nomenclature D e c H N Ntm P R r T tm V
impeller diameter (m) shaft essceenity (m) impeller off-bottom clearance (m) liquid level (m) impeller speed (rev/s, rpm) dimensionless mixing time power (w) tank radius (m) the distance between the shaft and vertical centre line of the tank revolution complete decolourization time (min) tank volume (m3 )
The formation of such structures in a mixing vessel could be problematic for purpose of mixing homogeneity since there is little material exchange between isolated mixing regions (IMRs) and active mixing regions (AMRs). It could be suggested that the IMRs structures could lead to poor processing performance, e.g. incomplete extraction in leach processing or production of by-products due to incorrect level of chemical concentrations within the structures. Takahashi and Motoda (2009) also pointed out that very long mixing times and high-energy inputs are required to achieve a complete liquid homogenization with presence of IMRs. As will be discussed later in this paper, the long time scale required to homogenize the fluids with the presence of IMRs can be considered as practically “infinite” when compared with the mixing time scale without IMRs. This “infinite” mixing time scale is clearly unacceptable for many mixing applications, and therefore the IMR structures should be removed. Extensive efforts have been devoted to eliminate IMRs completely in agitated vessels. Increasing the agitator speed to operate at sufficiently high Reynolds number has been
found effective to destroy IMRs in the literature. This approach is however not always practical due to its potential consequences including increased power, erosion damage on impellers or damage to the shear-sensitive materials essential in the biological processes. Another approach was to use unsteady rotation speed (Lamberto et al., 1996) to destroy IMRs, which can be effective due to the impact of chaotic mixing produced in perturbation. Yao et al. (1998) also introduced a similar method using unsteady RPM as an effective method in destroying the IMRs in low Reynolds numbers. Other methods associated with the elimination of IMRs include large object insertion (Takahashi and Motoda, 2009), novel perturbation waveforms (Yek et al., 2009) and installation of eccentricstirred impellers (Cabaret et al., 2008; Takahashi et al., 2012). The present work is driven by a need to eliminate IMRs at high viscosities with practical engineering designs. This is related to the background of processing of viscous slurry materials at larger industrial mixing tanks, such as those used in the minerals hydrometallurgical operations. Due to large equipment dimensions and motor power used in such operations, it is impractical to employ methods such as oscillating speeds or higher Reynolds numbers, i.e. increased speed at significantly higher power input. It is desirable to explore simple tank geometrical changes practical for industrial applications at low Reynolds numbers, at less power input. It is ideal that IMRs are eliminated without major equipment upgrade or motor power increase. To this aim, the current paper aims to explore simple geometrical change on IMRs under laminar flow conditions. Particular attention will be paid on the effect of the impeller design, impeller location and baffle installation on the mixing performance.
2.
Experimental
2.1.
Test rig
Flow visualization experiments were carried out in a mixing research rig (Fig. 1) consisting of a 190 mm diameter
Fig. 1 – Schematic illustration of experimental apparatus.
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Fig. 2 – Photographs of impellers used in this study. (a) PR30, (b) A-45PBT6, (c) DT6, and (d) DI.
cylindrical tank with a flat bottom placed inside a rectangular outer acrylic tank. The outer tank was filled with tap water to minimize the optical distortion. Sequential digital images were taken with a digital video camera, in order to reveal IMR structures and the flow pattern during the experiments. In order to capture the cross-sectional areas of the IMRs, a plane sheet of light passing through the 5-mm slits at the centre of the cardboards located on both sides of the tank illuminated the IMRs, as shown in Fig. 1. The light sources used were two 1000 W Arri IP23 lamps.
2.2.
Impellers
Four impellers, including a 3-blade propeller (PR30, supplier: Heidolph), a 6-alternating pitched (45◦ ) blade turbine (A45PBT6), a 6-blade disc turbine (DT6) and a disc impeller (DI), were chosen in the experiments. The blades of A-45PBT6 arranged in such a way that they alternatively pump upward and downward, potentially introduce more chaotic flow and eventually minimize the IMRs. Photographs of the impellers used in this study are shown in Fig. 2. All impellers have identical diameter of 70 mm (i.e. diameter to tank ratio of 0.36), except that DI (without the blades) has diameter of 50 mm (D/T = 0.26). The detailed specifications of all impellers are shown in Table 1. It should be pointed out that the diameter of DI is smaller than the other impellers, but it is still reasonably hypothesized that even if the diameter of the DI is equivalent to the other impellers, the bladeless geometry will probably still be the least efficient of the four impellers.
Table 1 – Specifications of the impellers used in this study (length unit: mm).
Blade height Impeller diameter No. of blades Angle of blades D/T
PR30
A-45PBT6
DT6
DI
10 70 3 – 0.36
10 70 6 ±45◦ 0.36
10 70 6 90◦ 0.36
10 50 – – 0.26
2.3.
Test fluids and experimental methodology
Glycerin (>99.7%, w/w) was used as the working fluids and the viscosities of glycerine were found to be in the range of 0.75–0.85 Pa s, at the room temperature 20–22 ◦ C. A well-known decolourization technique (refer to Takahashi and Motoda, 2009), involving the neutralization reaction of NaOH and HCL was used to visualize the IMRs. A passive tracer fluorescent dye, as a pH indicator, was injected and homogenized in the working fluid. In order to remove all the air bubbles, the working fluid mixed with fluorescent dye was allowed to be settled for about 12 h before conducting the experiments. Refer to Fig. 3a, the working fluid mixed with fluorescent dye was made basic by blending it with a basic solution consisting of 10 ml of 2 M NaOH. The working fluid was then stirred at 500 rpm for ∼2 h in order to fully disperse the base solution throughout the tank, leading to a uniform colour distribution (refer to Fig. 3a). After the agitator reached the test speed, a small amount of acidic solution (HCl: 10 ml 2 M) was injected at the blade tip and consequently the decolourization took place due to neutralization reaction in the active mixing regions (i.e. transparent area), as shown in Fig. 3c–f. The formation of isolated mixing regions, IMRs, corresponding to the green areas shown in Fig. 3f, is a consequence of a lack of mixing with the acidic fluids in the AMRs, causing the pH to remain basic and fluorescent dye green in the IMRs. The colour of AMRs, on the other hand, changed significantly due to substantial change in pH as a result of the neutralization reaction by mixing with acid fluid injected at the blade tip, located in the AMRs. The “doughnut-shaped” IMR structure was found to be unchanged in size for a few hours (∼3 h) in our experiments, implying that materials exchange between AMRs and IMRs is extremely poor. In this study, the dimensionless mixing time (Ntm ) was used to evaluate the overall mixing efficiency for different configurations. Note that N is the impeller speed and tm is the decolourization time in the system. Ntm on the other hand also indicates the number of agitator rotations required to eliminate the IMRs in the laminar systems.
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Fig. 3 – Decolourization demonstration based on acid–base reaction. (a) t = −5 s, pre-injection, acidic solution; (b) t = 0, injection of base; (c) t = 2 s; (d) t = 10 s; (e) t = 120 s; (f) t = 1600 s (highlighted green areas: isolated mixing regions [IMRs]; transparent area: active mixing regions [AMRs]). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
3.
Results
3.1.
Effect of Reynolds number
systems since they require a higher power input to for purpose of minimization of IMRs.
3.3. Fig. 4a shows the flow visualization results of four impellers; it can be commented that the IMRs are clearly different in terms of shape, size and location, depending on the impeller type and Reynolds number. In the case of axial-flow propeller PR30, the IMR above the impeller is smaller than that located below the impeller, most likely owing to its downwards-pumping direction, whereas for other impellers, the IMRs are about the same size in all four quadrants. Fig. 4b shows the variation of a/A as a function of Reynolds number for different impellers in the unbaffled condition, where a is the total cross-sectional area of the IMRs and A is the cross-sectional area of the tank. It can be seen from the figures that at a given Reynolds number, the disk impeller produced the largest IMR structures, whereas the Rushton turbine (DT6) had the smallest IMR structures. It must be pointed out that further increase in Reynolds number for PR30 and Disk exceeded the speed limit of the test rig (∼2000 rpm), thus the a/A vs. Re data could only be obtained up to Re ∼ 250 in the current test set-up (Fig. 4b). To understand the effect of Reynolds number on IMRs, the central positions of the IMRs produced by DT6 and PR30 are estimated from the visual images and plotted in Fig. 5. As the Reynolds number increases, the IMR above the impeller move further away from the impeller in the horizontal direction and move closer to horizontal centre line of the impeller in the vertical direction. Similar tendency can be observed for the IMR below the impeller.
3.2.
Power comparison among the impellers
The variation of the area of the IMRs as a function of the power consumption is expressed as a/A vs. (P/V: W/m3 ) for different impellers in Fig. 6. Among the impellers, the modified pitched blade turbine (A-45PBT6) appears to be the most energy efficient in producing smaller IMRs. In contrast, it is less efficient to use PR30 and the disk impeller in the viscous
Effect of impeller clearance
Rushton turbine DT6 was used to study the effect of impeller to tank bottom clearance (c/H) as shown in Fig. 7, where c is the distance to the bottom and H is the liquid height in the tank. The tests were carried out at different Reynolds numbers as shown in Fig. 7. At c/H = 0.5, there are two IMRs, i.e. doughnut-shaped rings, one above and the other below the impeller (Fig. 7a). At c/H = 0.05, only a single doughnut-shaped ring above the impeller was formed, with the impeller close to the tank bottom (Fig. 7b). On the other hand, at c/H = 0.72, the shift in impeller location toward the liquid surface destroyed the ring above the impeller, leading to formation of a single doughnut-shaped IMR below the impeller (Fig. 7c).
3.4.
Effect of baffle installation
The impact of number of baffles on the level of mixing homogeneity in a stirred tank equipped with a Rushton turbine (DT6) is shown in Fig. 8a–c. The tests were conducted at the Reynolds number of 41, which is in the regime close to Re = Rec . Fig. 8d shows the specific power at this critical regime (i.e. beyond which IMRs are eliminated) is insensitive to the number of baffles. It must be noted out that in our tests for all the baffled configurations, further increase in impeller speed led to complete destruction of the IMRs, suggesting that the critical Reynolds number (Rec ) for the DT6 impeller in the baffled tank is approximately equal to 40–50, for baffles of x2 to x4. The effect of baffles on the minimum power required to destroy IMRs are presented in Fig. 9 for three different impellers. Under baffled conditions, at Rec , the power input for all the impellers is approximately equal. Under unbaffled condition, the axial-flow impeller (PR30) is much less efficient than other two impellers. Based on Fig. 9, the power required to accomplish the homogenous condition in the baffled tank is approximately 5 times higher than that for the unbaffled tank
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Fig. 4 – IMRs size vs. Reynolds number: (a) visualization images; (b) a/A vs. Re plot.
for the DT6 and A-45PBT6. The impact is more substantial for the axial flow impeller: PR30. In the case of PR30, to achieve similar homogeneity, the baffled configuration is much more energy-efficient than unbaffled tank as 25 times power reduction can be achieved by simply installing the baffles. It must be pointed out that the significant power difference is mainly attributed to substantial variation in Rec at the baffled and unbaffled conditions. It is interesting to investigate the critical Reynolds number Rec , at which point the IMRs disappeared owing to the presence of flow perturbations. Nabil Noui-Mehidi et al. (2008) highlighted the mechanism of IMR disappearance using a Rushton turbine and they showed that the disappearance of the IMRs in the system was attributed to two factors: stretching and shrinking in the presence of perturbations. A similar mechanism was observed for the impellers used
in our study and our results show that the critical values of the Reynolds number are highly dependent on impeller type (refer to Table 2). Under unbaffled condition, among the impellers, DT6/A-45PBT4 has the smallest critical Rec and the Table 2 – Estimated critical Reynolds number (Rec ) for different impellers. Impeller
Flow type
DT6 A-45PBT6 PR30 Disk
Radial Mixed Axial –
a
Rec(unbaffled) 136 135 304a 524a
Rec(baffled) 40–50 40–50 40–50 40–50
These values were estimated based on the data trend shown in Fig. 4b. In our experiments, at least 1 h was allowed to determine the Rec for each condition.
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Fig. 5 – Shift of IMR centre with increasing Re. Impellers: DT6 and PR30 (red dots: the centres of the IMRs). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
disk has the largest critical value. In the baffled configuration, it was observed that the isolated mixing regions disappeared at 40–50, for all the impellers tested, as shown in Table 2.
3.5.
Energy efficiency
For mixing in the regime of Re > Rec , IMRs do not exist. The selection of an appropriate impeller under baffled condition should be measured in terms of the mixing time and the energy required. Fig. 10 shows the dimensionless mixing time: Ntm (the product of the dimensional mixing time tm and the speed N) for three test impellers, all under baffled condition (x4 baffles). It can be seen that the modified pitch-bladed impeller (A-45PBT4) requires less mixing time compared to the radialflow Rushton turbine (DT6). On the other hand, the mixing
time data for disk impeller is not included in this figure as complete mixing did not complete in a reasonable duration. Among the three impellers shown in Fig. 10, the PR30 impeller performs relatively less effective considering the longest blend time that it requires. To investigate the impact of impeller type on the energy efficiency in the baffled condition, the specific energy (E: J/m3 ) required to achieve complete mixing is defined as follows: E=
where P/V is the specific power consumption (W/m3 ), and tm is the time (s) required to reach the homogenous condition in the laminar systems. The dependence of specific energy on the impeller type is shown in Fig. 11. It can be seen from the figure that the A-45PBT4 has smallest E value, and the other impellers (axial-flow: PR30 and radial-flow: DT6) have relatively greater E values. This is consistent with the feature of its lower specific power consumption in destroying IMRs for Re < Rec , as presented in Fig. 6, Section 3.2. On the other hand, this implies that the general performance of radial-flow impeller is similar to that of axial-flow impeller in liquid blending, in the baffled configuration.
4.
Fig. 6 – a/A as a function of specific power input (a: total IMR area; A: tank area). 24 < Re < 140, c/H = 0.5, without baffles.
P × tm V
Discussion
The laboratory experience with IMRs was that the viscous systems at Re < Rec could only be homogenized through a slow diffusion process. The required long diffusion time process is practically “infinitive” in the engineering sense, although diffusion does eventually provide “complete” mixing between IMRs and AMRs, and thus destruction of IMRs. This long time scale, e.g. hours or days are often unacceptable when
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Fig. 7 – Formation of IMR(s) with shaft located in tank centre. (a) c/H = 0.5; (b) c/H = 0.05; (c) c/H = 0.72. Impeller: DT6.
considering against the time scale of importance, e.g. a chemical reaction, which may require a complete mixing in minutes. The improved energy efficiency in destroying IMRs with installation of baffles or using the pitch bladed turbine with alternating pitch as demonstrated in this paper was thought to be related to the fundamental effect of chaotic mixing. Disturbance generated by the asymmetrical perturbation was thought to improve the process of the exponential stretching and folding between fluids materials. This is essential for complete mixing, i.e. mutual contact between all fluid elements in a tank. This effect of “disturbance” is more energy efficient than otherwise operating say with a higher speed. For example, in the case of the Rushton turbine, the baffled system was found to require less power to destroy the IMRs than unbaffled system. This suggests that the disturbance introduced by baffles is effective in improving the energy efficiency, in the context of destroying IMRs. It can also be hypothesized that the disturbance, thought to produce the effect of chaotic mixing, suggests in a fundamental sense that chaotic mixing is more energy efficient, and therefore should be considered for engineering implementation as demonstrated in this paper. It was found that under laminar flow conditions, the A45PBT6 impeller led to formation of smallest IMRs at a given Reynolds number, as evident from a/A vs. specific power data. Alvarez et al. (2002) conducted the experiments based on the time progression of fluorescent dye injection and they demonstrated that the periodic perturbation caused by impeller blades triggers chaos in laminar systems. The perturbation introduced by the blades is thus the main factor causing the reduction in IMR size in our experiments; therefore it is not surprising to note that the impellers with more blades (e.g. DT6 and 45-PBT6 here) have the smallest IMRs, owing to the introduction of the greater perturbation by their blades.
However, it is unsure to us whether installation of more blades in an impeller can actually lead to better mixing quality as it approaches geometry similar to a disc. In addition, it should be noted that the asymmetrical design of our impeller (A-45PBT6) also contribute to the introduction of greater periodic perturbation, and the more effective mixing results make it the first option for liquid blending, regardless of baffled and unbaffled conditions. Hashimoto et al. (2011) suggested that baffles can effectively transform the circumferential flow to vertical and radial flows. Their study, based on the streak flow pattern, showed that in baffled vessels, both the vicinity of the vessel wall and the tip of baffles causes a streak lobe formation and folds of streak in the vertical and circumferential directions can be enhanced with the installation of baffles. As a consequence of this enhancement mechanism, the isolated toroidal mixing regions in a baffle tank became distorted. It is also very interesting to comment that using baffles more than 2 does not improve mixing in the tank. Finally, it is useful to comment that the conclusion that baffles are more energy efficient for mixing is limited to viscous low Reynolds number applications. At high Reynolds numbers, e.g. in slurries such as that made of sand and water, the mixing is not an issue. The mixing time in this regime is so short in comparison with the process time scale that achieving good mixing is not normally an issue (Wu et al., 2011). Other process condition could be more important, e.g. off-bottom solids suspension. It is useful to alert to the readers that removal of baffles is more energy efficient for solids suspension at high Reynolds numbers, contrary to the low Reynolds number situations in this paper. Refer to Wu et al. (2011) and Wang et al. (2012) for more detailed information on this topic.
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Fig. 8 – Impact of number of baffles installed in the tank on IMRs and power at Re ∼ Rec . (a) Two baffles; (b) three baffles; (c) four baffles; (d) power comparison for different configurations. Impeller: DT6. Re = 41 (T: rotations).
Fig. 9 – Estimated minimum specific power (at Re ∼ Rec ) required to achieve homogenous mixing in the tank. Note: The values of Rec at baffled and unbaffled conditions are summaried at Table 2. Four baffles were installed in the baffled systems. (+number times = (power at baffled condition)/(power at unbaffled condition)).
Fig. 10 – Normalized mixing time at Re = 61 (above Rec ): time required for complete mixing in the baffled tank.
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Fig. 11 – Specific energy required to achieve homogenous mixing at Re = 61 (above Rec ) in the baffled tank.
5.
Conclusions
The features of the IMRs formed in the viscous Newtonian systems in a stirred tank have been studied in this paper. The effect of Reynolds number on the IMRs was determined. The critical Reynolds numbers beyond which IMRs are destroyed were presented. A pitch-bladed impeller with an alternating pitch was found more energy efficient than other test impellers in eliminating IMRs in both baffled and unbaffled configurations. It was also found that dramatic reduction in the power consumption could be achieved with installation of baffles to eliminate IMRs at typically low Reynolds numbers. The improved energy efficiency was thought related to generation of more chaotic mixing from the disturbance generated by the baffles, or impeller blade asymmetry such as alternating pitch. An energy parameter was introduced to account for the mixing time scale and the power required in regimes below the critical Reynolds number, in order to evaluate the energy efficiency when IMRs are non-existent.
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