Particle Suspension in Vortexing Unbaffled Stirred Tanks - Industrial

Article pubs.acs.org/IECR

Particle Suspension in Vortexing Unbaffled Stirred Tanks Alessandro Tamburini,* Andrea Cipollina, Giorgio Micale, Francesca Scargiali, and Alberto Brucato Dipartimento di Ingegneria Chimica, Gestionale, Informatica, Meccanica, Università di Palermo, Viale delle Scienze Edificio 6, 90128 Palermo, Italy ABSTRACT: Three-phase processes in which particle suspension has to be achieved in conjunction with gas dispersion are traditionally carried out in sparged, baffled stirred tanks. The operation of such tanks can suffer, however, from particles tending to block the sparger holes. A viable alternative might be provided by uncovered unbaffled stirred tanks (UUSTs), where gas self-injection can occur when the free-surface vortex reaches the impeller blades and gas bubbles begin to be ingested by the liquid. In this work, the particle suspension and liquid aeration performances in three-phase UUSTs were experimentally investigated and compared with relevant literature correlations concerning baffled systems. The results show that, at least at the investigated scale, UUSTs are more efficient for suspending particles than relevant baffled systems. Impeller clearance scarcely affects power requirements. Finally, a down-pumping PBT with D/T = 1/3 was found to be the best choice for attaining complete suspension under self-aeration conditions. mammalian cells growth.15,16 At higher rotational speeds, the free-surface vortex reaches the impeller plane, and gas bubbles begin to be ingested inside the reactor (critical rotational speed, Ncr). At N > Ncr (supercritical conditions), significant gas dispersion, and hence bubble bursting, occurs. Under these conditions, shear-sensitive cells might well be damaged. However, in the case of relatively robust cells, a much larger oxygen intake, and hence larger viable cell concentrations, can be guaranteed without the need for installing any (possibly troublesome) air sparger. On the other hand, unbaffled systems are characterized by mixing times significantly larger than those pertaining to baffled systems.17,18 This difference suggests the use of baffled tanks for all processes where mixing time is the controlling factor. However, a number of processes (e.g., soil bioremediation) have kinetics that are so slow that the longer mixing times exhibited by unbaffled vessels are not bound to significantly affect process performance. Moreover, Busciglio and coworkers recently found19 that, in uncovered unbaffled systems operating near critical conditions (free-surface vortex bottom approached the impeller), the mixing efficiencies become practically identical to those of baffled tanks. Notwithstanding all of this well-known evidence, the suspension of solid particles in liquids within free-surface unbaffled tanks has not been sufficiently investigated yet.

1. INTRODUCTION Agitated gas−solid−liquid (three-phase) systems are industrially important for many processes, such as catalytic reactions involving a gas reagent, bioleaching of gold ore, ex situ slurry bioremediation, and many other biological applications. Mixing of solid, liquid, and gas is traditionally carried out in tanks provided with baffles and air spargers. Spargers can be troublesome for such applications, however, as particles tend to block sparger holes.1,2 This is the case for bioslurry reactors for bioremediation, for instance, where insufflation devices require frequent maintenance because of the wear and/or obstruction of pores as a result of the high solid−liquid ratios typically employed. For such processes, free-surface unbaffled stirred tanks might represent a valuable alternative.3 In some cases, the presence of baffles can also cause incrustation issues4 or undesired precipitations.5 Also, in the case of fermentations, mechanical agitation under typical culture conditions does not damage freely suspended cells in the absence of sparging,6−8 whereas shear-sensitive cells, such as mammalian cells, can be damaged by bursting bubbles at the air−liquid interface.9,10 In fact, as pointed out in many studies (e.g., refs 11−13), the shear stress caused by a bubble burst is much higher than that induced by fluid turbulence even near the impeller. This might well make unbaffled vortexing vessels particularly suitable for such applications.14 In fact, they are characterized by the presence of a central free-surface vortex that, at relatively low rotational speeds, does not reach the impeller so that oxygen mass transfer occurs only through the vortexing free-surface interface (subcritica conditions, N < Ncr). The corresponding volumetric mass-transfer coefficient kLa was found to be more than sufficient for several processes including © 2016 American Chemical Society

Received: Revised: Accepted: Published: 7535

February 29, 2016 May 18, 2016 June 15, 2016 June 15, 2016 DOI: 10.1021/acs.iecr.6b00824 Ind. Eng. Chem. Res. 2016, 55, 7535−7547

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7536

formulated only for the specific particle concentration of 105 kg/m3; K is a parameter linked to system geometrical characteristics (shape of vessel bottom, number of impeller blades, pitched-blade angle, etc.); the last term on the right-hand side is related to packing features of the particles employed uncovered unbaffled tanks

suspension of sand and iron ore in various liquids at different solids concentrations in an unbaffled vessel stirred by a marine propeller

⎛ ρ − ρ ⎞−2/3⎛ μ ⎞−1/9⎛ Vp′ ⎞ l ⎜⎜ ⎟⎟ ⎟⎟ ⎜⎜ l ⎟⎟ Njs = KT −2/3d p1/3⎜⎜ s ⎝ ρl ⎠ ⎝ ρl ⎠ ⎝ Vp ⎠ Nagata41

0.7

top-covered unbaffled tanks

uncovered unbaffled tanks

μ0.2 ρl 0.6 D2.5

g 0.6ρs 0.8 d p0.4T1.9

Njs = 0.679B d p

Njs = 0.105

(B)

Pavlushenko et al.40

⎡ g (ρ − ρ ) ⎤0.5⎛ D ⎞−1.4 ⎛ C ⎞0.4 l ⎢ s ⎥ ⎜ ⎟ ⎜ ⎟ D−0.7 ⎢⎣ ⎥⎦ ⎝ T ⎠ ⎝ T ⎠ ρl 0.2 0.1

⎛ ρ − ρ ⎞0.309 l ⎟⎟ Njs = S′d p0.033⎜⎜g s B0.115ν−0.143 ρl ⎠ ⎝ Tamburini et al.43

forward/reverse motion inhibits the central free-surface vortex formation unsteadily stirred unbaffled tanks: (A) 1/10 < C/T < 1/6, (B) 1/6 < C/T < 1/3 Yoshida et al.42

⎡ g (ρ − ρ ) ⎤ ⎛ D ⎞−1.4 ⎛ C ⎞0.7 l ⎥ ⎜ ⎟ ⎜ ⎟ D−0.7 Njs = 1.20B0.1d p0.2⎢ s ⎢⎣ ⎥⎦ ⎝ T ⎠ ⎝ T ⎠ ρl (A)

system 0.5

correlation author(s)

Table 1. List of Correlations for Njs in Unbaffled Stirred Tanks Reported in the Literature

additional details

All stirred tanks where solid−liquid mass-transfer phenomena occur are traditionally operated at the minimum impeller speed for complete suspension. Although a few works have investigated the amount of solid particles suspended at various agitation speeds,20,21 most experimental works so far have been aimed at assessing the minimum agitation speed Njs at which all particles present in the tank are suspended. In fact, Njs represents a viable compromise between the need to (i) guarantee that the entire particle surface is available for mass transfer and (ii) keep the power requirements at reasonable levels. Different methods have been proposed in the past few decades to assess the value of Njs. These can be classified as direct, indirect, and theoretical methods24 according to their fundamentals. The direct methods evaluate Njs by measuring [or predicting by computational fluid dynamics (CFD)] variables that are directly linked to the suspension characteristics such as the amount of the solids resting motionless on the vessel bottom.22−29 Indirect methods focus on the assessment of Njs through the estimation of variables that are only indirectly related to particle suspension, such as “cloud” height and power number graphs.30−35 Some effort has also been directed toward estimating the value of Njs through theoretical models;36−39 however, all of these models are far from having a universal validity. Most direct methods are based on a criterion to distinguish unsuspended and suspended particles and, thus, to identify the achievement of complete suspension conditions. The most accepted criterion is the visual one by Zwietering:22 Particles are judged to be suspended if they do not stay motionless on the vessel bottom for more than 1 s. According to this criterion, Njs is commonly defined as the minimum impeller speed at which all particles are suspended. Zwietering carried out several experiments in a baffled tank and proposed a well-known correlation.22 In contrast, only a few works have proposed a correlation for Njs in unbaffled vessels.40−43 For the sake of clarity, all of these correlations are reported in Table 1, along with additional details. Apart from Njs, the minimum power requirement for particle suspension (Pjs) is another parameter regarding solid−liquid suspensions within stirred tanks, that is possibly more important than Njs.44 In fact, the minimum power drawn to attain complete suspension conditions is more directly linked to operating costs. Few studies have dealt with power consumption for solid− liquid suspension in unbaffled tanks. Most of them concern the case of unbaffled tanks where vortex formation is avoided by some devices: an unsteadily rotating impeller in the cases of Tezura et al.45 and Yoshida et al.,42 an angle-mounted turbine in the study of Myers et al.,46 and a top cover in our previous works.43,47 Very little attention has been paid so far to the investigation of solid−liquid suspensions in vortexing unbaffled tanks and liquid aeration in the presence of particle suspensions. To the authors’ knowledge, only Wang and coworkers27,28 have studied vortexing unbaffled vessels for the case of very high solid loadings and found that the removal of baffles resulted in a strong reduction of Pjs of up to 80%.28 The aim of the present work was to investigate solid−liquid suspension with simultaneous aeration in vortexing unbaffled stirred vessels, in view of critically comparing their performance with that of baffled and top-covered unbaffled vessels. The main outcome of this work is the information gathered on these

the top cover along with a completely filled tank inhibits the formation of a central free-surface vortex

Industrial & Engineering Chemistry Research

DOI: 10.1021/acs.iecr.6b00824 Ind. Eng. Chem. Res. 2016, 55, 7535−7547

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Figure 1. (a) Sketch of the systems studied: top-covered unbaffled (a1), vortexing unbaffled (a2), baffled tank (a3). (b) Turbine types tested: (b1) Rushton impeller (RT), (b2) pitched-blade turbine (PBT), (b3) Lightnin turbine A310.

Table 2. Summary of the Experimental Campaign and Correlations Used for Baffled Systems turbine type RT

turbine diameter D T/3 T/2

PBT

T/3 T/2

A310

T/3 0.45T

turbine clearance C T/3 T/10 T/3 T/10 T/3 T/10 T/3 T/10 T/3 T/10 T/3 T/10

vortexing unbaffled vessel B (%) 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

2.5, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5,

5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,

10, 10, 10 10 10, 10, 10, 10, 10, 10, 10, 10,

20 20

top-covered unbaffled vessel B (%) 0, 0, 0, 0, 0, 0, 0, 0, − − − −

20 20 20 20 20 20 20 20

2.5, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5, 2.5,

5, 5, 5, 5, 5, 5, 5, 5,

10, 10, 10 10 10, 10, 10, 10,

20 20

20 20 20 20

baffled vessel: Njs correlation from the literature Nienow57 Armenante et al.23 Nienow57 Armenante et al.23 Wong et al.55 extrap from Wong et al.55 − − Wong et al.55 extrap from Wong et al.55 Ibrahim and Nienow56 extrap from Ibrahim and Nienow56

The investigated system was a transparent Perspex unbaffled tank with a diameter of T = 0.19 m (Figure 1a). To evaluate the influence of the impeller geometry, three different turbine types were tested: a standard six-bladed Rushton turbine (RT), a downward-pumping four-bladed (45°) pitched-blade turbine (PBT), and an A310 Lightnin turbine with dimensions similar to those typically employed in the literature.48−50 In Figure 1b, a picture of the three impeller geometries investigated is reported for clarity reasons. For the RT and PBT, the turbine diameters D were equal to T/2 and T/3, respectively, and the blade width w was equal to D/5. For the A310 case, D was 0.45T and T/3. Two different impeller clearances, namely, C = T/3 and T/10, were also investigated in all cases. Low clearance impellers were tested in unbaffled tanks as, in baffled tanks, they are known to provide Njs and power numbers lower than high-clearance ones. Notably, radial impellers, which are commonly considered to be less efficient than axial turbines,

three-phase systems, as well as indications of the most efficient system configurations for addressing specific needs.

2. EXPERIMENTAL SECTION The three geometrical configurations studied in this work [unbaffled top-covered, unbaffled uncovered (vortexing), and baffled] are depicted in Figure 1. Here, the minimum impeller speed for complete particle suspension (Njs) and the relevant power consumption (Pjs) were experimentally assessed for the two unbaffled vessels, whereas the same parameters were estimated for the baffled tank on the basis of literature correlations. In addition, in the case of the uncovered unbaffled vessel, the critical impeller speed at which the free-surface vortex reaches the impeller and gas bubbles begin to be ingested inside the reactor (Ncr) and the relevant power consumption (Pcr) were also experimentally assessed. 7537


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various agitation speeds for each liquid viscosity investigated. Details of this inexpensive yet precise apparatus can be found in Brucato et al.47 2.1.4. Pjs Assessment in Baffled Systems. In baffled tanks, Njs values were inferred from correlations available in the literature as reported in Table 2. For Pjs, the literature information indicates that the power drawn under fully suspended conditions can be inferred from particle free power numbers Np (constant under turbulent conditions) by simply using an average pseudofluid density, namely, Pjs = Np(ρsuspNjs3D5). Np was calculated from the power consumption measurements under turbulent conditions in each single-phase system configuration (Table 3). This is only an

have been found to be more effective in three-phase baffled tanks, as well as in solid−liquid top-covered unbaffled vessels,51 and for this reason, they are worthy of investigation. The vessel was filled with weighed quantities (B = 2.5%, 5%, 10%, and 20%, solid-weight/liquid-weight) of silica particles (dp = 250−300 μm, ρs ≈ 2440 kg/m3) and deionized water (ρl ≈ 1000 kg/m3) was added to a height of H = T under noagitation conditions. In contrast to our previous works on solid−liquid suspensions in unbaffled vessels,47,52−54 where a closed vessel (top-covered unbaffled configuration, no free surface present) was studied, in the present work an uncovered unbaffled vessel was mainly employed. In the latter system a more or less pronounced (depending on agitation speed) central free-surface vortex was observed (vortexing unbaffled configuration). For comparison purposes experiments were also carried out in the relevant top-covered unbaffled vessel. Moreover, to include baffled tanks in the comparison, correlations available in the literature22,23,55−57 for Njs assessment were used and relevant power requirements Pjs were properly assessed. A summary of all the cases investigated by experiments or correlations is provided in Table 2. Note that, in the present work, the whole experimental campaign was limited to tanks with a diameter T = 0.19 m, whereas no investigations were performed on a larger scale. Scale-up effects might play a significant role, and their study will be focus of future work. 2.1. Assessments of Njs, Ncr, and Power Requirements. 2.1.1. Njs Assessment: Camera-Assisted Procedure. The minimum turbine speed ensuring the suspension of all particles (Njs) was assessed by the well-known “one-second criterion”.22 According to this criterion, all particles are considered to be suspended when none of them stay still on the vessel bottom for more than 1 s. To confirm this condition, a camera was placed underneath the vessel bottom to collect a number of images (about 20) at each impeller speed. The camera exposure time was set to 1 s in accordance with Zwietering’s criterion, so that motionless particles appeared to be well-defined in the snapshots whereas moving particles were blurred. Njs was chosen as the minimum impeller speed at which no motionless particles could be observed in any of the images. The use of the camera and of the relevant acquired pictures for the Njs assessment largely reduces the subjectivity of Zwietering’s criterion, as already pointed out by Brucato et al.47 Notably, the camera-assisted Zwietering criterion employed in this work is intrinsically based on the definition of on-bottom complete suspension: Particles are considered to be suspended even if they roll on the vessel bottom without any axial velocity.58 2.1.2. Ncr Assessment: Hearing Criterion. When a large number of solid particles are suspended, the three-phase system becomes opaque, and the free-surface shape is no longer visible. Thus, to assess the rotational speed at which the free-surface vortex reaches the impeller plane and gas bubbles begin to be ingested inside the liquid phase, denoted as Ncr,59,60 a simple criterion (called the hearing criterion) was employed. It is based on the distinct noise produced by the rotating turbine when it is ingesting air: The minimum speed at which this noise was heard was identified as Ncr. Visual inspection revealed that it corresponded to the rotational speed at which the turbine started to no longer be fully covered by the liquid phase. 2.1.3. Power Requirement Measurement. A static frictionless turntable and a precision scale were employed for measuring the mechanical power dissipated by the impeller at

Table 3. Np Values Obtained from Power Consumption Measurements at B = 0% and N > 700 rpm for the Case of Baffled Vessels turbine type RT

turbine diameter D T/2 T/3

PBT

T/2 T/3

A310

0.45T T/3

turbine clearance C

power number Np

T/3 T/10 T/3 T/10 T/3 T/10 T/3 T/10 T/3 T/10 T/3 T/10

4.83 3.71 4.88 3.50 1.16 1.43 1.48 1.41 0.33 0.36 0.36 0.35

approximate estimation, but it was considered to be sufficient in view of its use, for comparison purposes only, in this work. Also, this procedure allowed a lower number of power measurements to be carried out (one measurement for one geometry instead of one measurement for each solid loading).

3. RESULTS AND DISCUSSION 3.1. Results Relevant to Each Impeller Geometry. 3.1.1. Rushton Turbine. In Figure 2A1, Njs values measured with the Rushton turbine (D = T/3, offset by one-third from the vessel bottom) are reported both for the case of the vortexing unbaffled system (open triangles) and for the case of the top-covered unbaffled vessel (black triangles). As can be seen, very similar values of Njs were found in the top-covered unbaffled vessel and in the vortexing system, thus suggesting that similar suspension mechanisms occur. Njs increases slightly with increasing average solids concentration, as expected. Moreover, the Njs values in the unbaffled systems are significantly lower than those in the baffled tanks (Zwietering’s correlation along with Nienow’s modification57): An average reduction of about 60% can be inferred from the figure. This is clearly related to the striking difference in the flow fields observed in the two systems. In baffled tanks, the suspension phenomenon is due to a complex combination of turbulence bursts36 and liquid mean velocities actions on the vessel bottom61−63 depending on the type of flow and turbulence generated by a given turbine.61,64 In unbaffled stirred vessels, particles become suspended mainly as a consequence of the liquid mean velocity near the tank bottom.43,47 In Figure 2A1, the measured values of Ncr are also reported as solid diamonds, obviously only for the case of vortexing 7538


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Figure 2. Rushton turbines at C = T/3: (A) D = T/3, (B) D = T/2. (1) Njs or Ncr vs B, (2) Pjs or Pcr vs B.

does not affect the impeller suspension capabilities. This is likely to be related to the different suspension mechanism, which, in the case of unbaffled systems, is related to the highly swirling fluid flow,43,47 and the fact that the mechanism is not significantly affected by gas dispersion. Regarding the data obtained with the smaller Rushton turbine at the lower impeller clearance (C = T/10, Figure 3A1), the gap between the baffled and unbaffled Njs values is greatly reduced: The unbaffled Njs values were found to be only slightly smaller (by about 17%) than those predicted by the Armenante et al.23 correlation (the only work that also included the C = T/10 case). It is worth noting that, for baffled vessels, Njs is much lower at C = T/10 than at C = T/3,23 a feature that is due to the transition from a double-loop to a single-loop flow pattern. In contrast, by comparing Figure 3A1 and Figure 2 A1, it can be seen that, in unbaffled vessels, the Njs values are not significantly affected by impeller clearance. This is in accordance with the previous consideration that particle suspension in this case is mainly related to the average fluid velocity rather than to turbulent fluctuations. In fact, the former can be expected to be only slightly affected by impeller clearance, thus resulting in similar Njs values. Furthermore, also in this case, the top-covered unbaffled configuration was found to provide Njs values coinciding with those observed with the vortexing configuration: Clearly, the presence of a vortex does not appreciably affect the mean velocities near the tank bottom. Figure 3A1 also shows that (i) Ncr > Njs at any solid loading and (ii) the dependence of Ncr on B is lower than that exhibited by Njs. The latter finding suggests that, at higher solid concentrations, particle suspension might become the control-

tanks, as no free surface exists in the case of covered vessels. As can be seen, the Ncr values show a dependence on B similar to that exhibited by Njs, although with somewhat larger absolute values. Experimental observations also indicated that particle suspension is maintained in the supercritical regime (i.e., N > Ncr), despite the presence of the gas phase. Figure 2A2 reports the same cases as Figure 2A1 in terms of power consumption rather than agitation speed, that is, in terms of Pjs (open and black triangles) and Pcr (solid diamonds). Also, in this case, there is no significant difference between the powers needed for just suspension in the vortexing and top-covered unbaffled systems. Conversely, a significant power savings of much more than 1 order of magnitude can be obtained by adopting the unbaffled configurations instead of a corresponding baffled tank. Regarding the Pcr values, the power requirements are larger than those needed for complete suspension (Pcr > Pjs), thus suggesting that air dispersion might be the energetically controlling phenomenon in the case of aerobic bioprocesses. In Figure 2B, results obtained with the D = T/2 Rushton turbine at C = T/3 are reported. In Figure 2B1, it can be seen that the dependence of Njs on B is similar for all systems, although, in this case, the Njs values are no longer smaller than for baffled vessels. However, thanks to the absence of the baffles, which represent a power-dissipative obstacle for tangential flow, a significant Pjs reduction (by about 1 order of magnitude) can be observed in the unbaffled case with the larger RT as well. Also, the Ncr values were found to be not significantly different from the Njs values and, in some cases, to even be slightly lower. This finding can be regarded as further confirmation that, in vortexing unbaffled systems, gas ingestion 7539


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Figure 3. Rushton turbines at C = T/10: (A) D = T/3, (B) D = T/2. (1) Njs or Ncr vs B, (2) Pjs or Pcr vs B.

unbaffled configurations were found to be comparable (Figure 3B2). As already observed for the smaller impeller at this clearance, Ncr shows a dependence on B lower than that of Njs. In contrast to all of the previous cases, here, some differences between the top-covered and vortexing unbaffled configurations can be observed (Figure 3B): In this case, the top-covered configuration appears to be more demanding. 3.1.2. Down-Pumping Pitched-Blade Turbine. Similar results were found for the PBT down-pumping turbine. In Figure 4A1, the Njs values measured with the downpumping PBT turbine (D = T/3, offset by one-third from the vessel bottom) are reported both for the case of the vortexing unbaffled system (open triangles) and for the case of the topcovered unbaffled vessel (black triangles). As can be seen, very similar values of Njs were found in the top-covered unbaffled vessel and in the vortexing system (only a slight lower dependence on B can be observed in the vortexing system), thus suggesting that similar suspension mechanisms occur. Njs increases slightly with increasing average solids concentration, as expected. Moreover, as observed for the Rushton turbine, the Njs values in the unbaffled systems are lower than those in the baffled tanks (Wong et al. correlation55): An average reduction of about 30% can be inferred from the figure. The power requirements for the suspension of all particles in the vortexing unbaffled vessel were found to be almost 1 order of magnitude lower than those in the baffled system (Figure 4A2), whereas very similar performances are exhibited by the vortexing and top-covered unbaffled configurations. For the case of the larger PBT (Figures 4B1, B2), the results obtained in the vortexing unbaffled vessel were found very

ling phenomenon. Notably, by comparing Figure 2A1 and Figure 3A1, it can be observed that a decrease of the impeller clearance leads to an increase in Ncr, as expected given that the vortex depth needed to reach the impeller increases with decreasing impeller clearance. A larger reduction of Pjs, by about 1 order of magnitude, can be observed in Figure 3A2 when comparing the unbaffled and baffled vessel performances. Notably, the reduction in this case is not as large as that observed in Figure 2A2, because of the lower differences in the Njs values between the two tanks. In addition, in this case, the achievement of critical conditions for aeration was not followed by a significant reduction in the mechanical power dissipated, thus resulting in Pcr > Pjs. As already observed for the RT with D = T/3, by comparing Figure 2B1 with Figure 3B1, it can be noted that the collected Njs values appear to be only slightly dependent on the impeller clearance for the RT with D = T/2 as well. Moreover, Figure 3B1 shows that the dependence of Njs on B is similar to that of the baffled system. In contrast to all of the other RT configurations tested, the largest RT at C = T/10 provides Njs values higher than those for the baffled tank: An increase of about 60% can be observed in Figure 3B1. This is due to the fact that this impeller generates significant velocity fluctuations in its proximity, thus leading the turbulence bursts on the vessel bottom to become the controlling mechanism for solid suspension in baffled tanks and, consequently, highly reducing Njs with respect to the values in unbaffled tanks where the mean velocity remains the controlling phenomenon. Because of this difference in Njs, which favors baffled tanks, the power requirements for just-suspension conditions in the baffled and 7540


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Figure 4. PBT at C = T/3: (A) D = T/3, (B) D = T/2. (1) Njs or Ncr vs B, (2) Pjs or Pcr vs B.

Figure 5. PBT at C = T/10: (A) D = T/3, (B) D = T/2. (1) Njs or Ncr vs B, (2) Pjs or Pcr vs B.

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Figure 6. A310 at C = T/3: (A) D = T/3, (B) D = 0.45T. (1) Njs or Ncr vs B, (2) Pjs or Pcr vs B.

data relevant to the baffled vessels were obtained (i) first by fitting the S parameters of Zwietering’s equation provided by Wong et al.,55 one at each impeller clearance, and (ii) then by inferring the S value at the desired clearance (i.e., C = T/10) from the obtained equation. As already seen at the larger clearance, the larger PBT again exhibited a decrease in Njs with the solid loading (Figure 5B1), thus suggesting that this behavior is a peculiarity of this turbine. Evident differences between the two unbaffled configurations can be observed only for the larger turbine (Figure 5B): As can be seen in Figure 5B2, the presence of the vortex appears to favor complete suspension at larger concentrations, whereas the opposite occurs at lower concentrations. As expected, the reduction of the impeller clearance leads the values of Ncr to increase, as the vortex depth is a function of the Froude number. All of the PBT configurations show very little dependence of Ncr on the solid loading. Moreover, Ncr and Pcr were found to be higher than Njs and Pjs, respectively, in all of these cases, thus suggesting that the aeration of the solid−liquid system is more demanding than the complete suspension of the particles. 3.1.3. A310 Impeller. For the case of the smaller A310 impeller, very high and somewhat similar Njs values were found for the baffled (from the literature) and vortexing unbaffled vessels (from experiments) (Figure 6A1). At B ≥ 10%, an impeller speed of 1500 rpm was not sufficient to suspend the particles. Higher impeller speeds were not investigated to avoid the occurrence of any mechanical problems in the motor− pulley−shaft connection. This did not happen when the larger impeller was employed because of its higher suspension capability (Figure 6B1). In particular, the larger impeller is more efficient in suspending solid particles in the vortexing

similar to those obtained in the top-covered unbaffled system, thus confirming that the presence of the free-surface vortex does not modify the vessel fluid dynamics very much. Unfortunately, no available values or correlations relevant to baffled tanks were found in the literature, so no comparison with relevant baffled systems can be made in this case. It is worth noting the “unusual” behavior of the experimental Njs value (and relevant Pjs value) obtained in the vortexing system at the lowest B value. As can be seen in Figure 4B1, an abrupt decrease of Njs with B can be observed at low concentrations. This can be explained because this particular configuration leads part of the sediment to move first on the bottom as a whole before gradually suspending off-bottom and being dispersed. Therefore, this unusual decrease of Njs with B is a consequence of the on-bottom complete suspension criterion chosen for the assessment of Njs: Particle agglomerates rolling on the bottom are blurred in the images and are judged as “suspended”. Comparison of Figures 4 and 5 shows the effects of turbine clearance. For the D = T/3 turbine, the reduction in the clearance leads to an increase in the Njs values in the unbaffled vessel (Figure 5A1 vs Figure 4A1). This might be because, when the turbine is placed just over the vessel bottom, the flow partially discharged downward by the turbine itself is significantly dumped by the close bottom. Conversely, this effect is irrelevant for the case of the larger turbine (Figure 5B1 vs Figure 4B1). Only data relevant to the small turbine were found for the baffled tank, which provides Njs values lower than the unbaffled configurations (Figure 5A1). However, the lower power requirements typical of the unbaffled configurations ensure that similar Pjs values were found in the two different tanks (i.e., baffled and unbaffled) (Figure 5A2). Notably, the 7542


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Figure 7. A310 at C = T/10: (A) D = T/3, (B) D = 0.45T. (1) Njs or Ncr vs B, (2) Pjs or Pcr vs B.

Figure 8. Comparison between top-covered and vortexing unbaffled tanks: (A) Njs, (B) Pjs.

In all cases, the smaller A310 impeller provided very similar Njs and Ncr values (Figure 7 and Figure 6), whereas the larger one guaranteed the achievement of complete suspension conditions at impeller speeds (and relevant power drawn) lower than those necessary for gas dispersion (supercritical regime). Notably, no experiments were carried out in the top-covered configuration for this impeller. 3.2. Comparison between Top-Covered and Uncovered (Vortexing) Unbaffled Tanks. In Figure 8, a comparison between the vortexing and top-covered configurations is presented. As can be seen, both the Njs and Pjs values were quite similar for the two configurations, and no substantial

unbaffled tank (Figure 6A2 vs Figure 6B2). Very similar dependences of Njs on solid concentration were found in this case between the baffled and vortexing unbaffled tanks (Figure 6B1). However, for both of the turbines, the baffled configuration was more power-demanding than the vortexing unbaffled one (Figures 6A2, B2). The reduction of the impeller clearance for the A310 impeller did not provide a large reduction of Njs in the vortexing unbaffled tank, unlike in the baffled configuration, where a significant reduction was observed, especially for the smaller A310 impeller (Figure 7 vs Figure 6). In particular, a lower power dissipation Pjs for the baffled tank was found for the smaller A310 impeller at C = T/10. 7543


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In Figure 9, the power requirements (Pcr) measured at the critical rotational speed (Ncr) are reported as a function of the just-suspension-conditions power requirements (Pjs). The four graphs refer to the four different investigated solid loadings. A suitable criterion is required to judge when a (Pcr, Pjs) pair is better than another. Such a criterion should be defined on the basis of the specific process under consideration, as different criteria could be proposed depending on which phenomenon (either suspension or aeration) is the controlling one. Just as an example, if the cell oxygen demand is low, the oxygen transfer rate through the vortex-free surface might be sufficient, thus making complete suspension the controlling phenomenon and Pjs the parameter on which basis optimal configurations are identified. Conversely, when both complete suspension and aeration are equally important, the “isopower lines” reported in Figure 10 as dotted lines can conveniently be employed for identifying optimal configurations. In fact, a certain configuration 1, characterized by a given point on the graph (Pcr,1, Pjs,1), is equivalent to another configuration 2, (Pcr,2, Pjs,2), as long as max[(Pcr,1, Pjs,1)] = max[(Pcr,2, Pjs,2)], and the pair (Pcr,1, Pjs,1) is better than (Pcr,2, Pjs,2) when max[(Pcr,1, Pjs,1)] < max[(Pcr,2, Pjs,2)]. In other words, the experimental points that are located inside the isopower lines nearer to the origin indicate the configurations with the lowest power consumption to achieve both just-suspension and aeration conditions, whereas data points located on the farther isopower lines indicate the most power-demanding systems. In light of this criterion, considering the results reported in Figure 10, if both particle suspension and gas ingestion are required, then the PBT with D = T/3 and C = T/3 (red squares in the graphs) is the best geometrical configuration for B ≤ 10%, whereas the PBT with D = T/2 and C = T/3 is the most convenient for B = 20%. Interesting results are obtained for the A310 impeller with D = 0.45T and C = T/3 and the RT with D = T/3 and C = T/3, which can be considered as valuable alternatives. If only particle suspension is required, then the A310 impeller with D = 0.45T and C = T/3 is the most efficient configuration at the lower solid loadings (i.e., B < 5%), whereas at higher particle concentrations (i.e., B > 10%), the PBT with D = T/2 and C = T/10 becomes the best. Clearly, other cases are all easily considered using the graphs in Figure 10.

differences can be found. This occurrence suggests that the same suspension mechanism takes place in the two cases, that is, particle suspension is probably driven by the direct action of the relatively large tangential liquid mean velocities near the tank bottom. In fact, these velocities exert a coherent swirling drag action on circumferential particle ensembles that eases their detachment from the fillet. Such velocities on the tank bottom are substantially unaffected by the presence or absence of the cover, which mainly modifies the flow field in the upper portion of the vessel, thus resulting in practically identical values of Njs. 3.3. Comparison between Unbaffled (Vortexing) and Baffled Tank Configurations. In Figure 9, the power

Figure 9. Comparison between Pjs observed in vortexing unbaffled tanks and Pjs estimated in corresponding baffled systems (i.e., same impeller type, size, and clearance; same particle concentration).

requirements Pjs estimated for baffled systems are reported versus the relevant values observed in unbaffled (vortexing) vessels. Each data point represents, in practice, a given geometrical configuration (i.e., same impeller type, size, and clearance) as well as same particle concentration, with the only difference between the two Pjs values being the presence or absence of baffles. As already remarked, vortexing unbaffled configurations exhibit values of Pjs much smaller, even by more than 1 order of magnitude, than those of the corresponding baffled configurations. Only in a very few cases does the baffled configuration appear to require a slightly smaller power consumption. It is worth noting, however, that, for these few cases, the baffled Pjs values are highly uncertain, as these were obtained from literature correlations55,56 by extrapolations outside their range of validity. It can be concluded that, in terms of particle suspension, unbaffled vessels might be a much better choice than the more commonly adopted baffled tanks, as already found in previous works.27,43,45,47 Of course, scaleup effects might play a role and still are to be properly assessed before the present conclusions are applied to the industrial scale, although a very recent confirmation of the advantage of unbaffled vessels for full-scale solids suspensions can be found in ref 65. 3.4. Performance Comparison of Turbine Configurations. All results reported in the previous sections for the various impeller geometries investigated in the uncovered system are now compared to each other to find the most promising configuration for either or both complete particle suspension and system aeration.

4. CONCLUSIONS Free-surface (“vortexing”) and top-covered unbaffled stirred tanks filled with monodisperse particles and water were investigated. The obtained results can be summarized as follows: • The unbaffled systems (either top-covered or vortexing) were found to be more efficient for particle suspension than the corresponding baffled tanks, with Pjs values in baffled tanks up to more than 1 order of magnitude larger than in the corresponding unbaffled system. • The top-covered and vortexing unbaffled configurations provided similar performances in terms of both Njs and Pjs. This means that either of the two unbaffled configurations can be employed depending on the specific process needs. • Regarding the effects of impeller clearance, in contrast to the case for baffled tanks, Njs was found to be scarcely affected by turbine clearance. 7544


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Figure 10. Power consumptions at the critical rotational speed (Pcr) vs power consumption at the just suspension speed (Pjs), for all of the vortexing unbaffled configurations investigated, for solid particle loadings B from 2.5% to 20%.

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• In the vortexing configuration, system aeration through gas ingestion did not affect the particle suspension regime. • Different impeller-to-tank configurations can conveniently be used depending on the aim of the process (particle suspension and/or gas ingestion): • When complete suspension is the main process requirement, the large A310 impeller at C = T/3 is the most efficient (i.e., lowest Pjs) impeller at low solids loadings (B < 5%), whereas the large down-pumping PBT at C = T/10 is the best option for denser suspensions (B > 5%). • When gas ingestion is the main process goal, the small PBT at C = T/3 guarantees the highest efficiency (i.e., lowest Pcr) at almost all solid loadings tested. • When both complete suspension and gas ingestion are sought, the down-pumping PBT with D = T/3 and C = T/3 was found to be the best compromise. Good suspension and aeration capability were also obtained by the large A310 impeller at C = T/3 and the small RT at C = T/3, which should be considered as valuable alternatives.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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It can be concluded that, for the case of particle suspension in aerobic processes, unbaffled vessels might be a much better choice than the more commonly employed baffled tanks. Of course, scaleup effects might play a crucial role and should be properly assessed before the present conclusions are applied at the industrial level. 7545

NOTATION B = particle concentration as solids-weight/liquid-weight (%) C = impeller clearance (m) D = impeller diameter (m) dp = particle diameter (m) g = gravitational constant (m s−2) H = liquid height (m) K = geometrical parameter in Nagata’s correlation41 (1975) N = rotational impeller speed (rpm) Ncr = critical rotational speed (rpm or rps) Njs = just suspension speed (rpm or rps) Np = power number P = power (W) Pcr = power consumption at Ncr (W) Pjs = power consumption at Njs (W) r = steady cone radius, (m) S = geometrical parameter in Zwietering’s correlation22 (1958) S′ = geometrical parameter in Tamburini et al.’s correlation43 (2014) T = tank diameter (m) Vp = solid volume (m3) Vp′ = apparent solid volume (m3) DOI: 10.1021/acs.iecr.6b00824 Ind. Eng. Chem. Res. 2016, 55, 7535−7547

Article


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w = blade width (m) Greek Letters

μ = viscosity (Pa s) ν = kinematic viscosity (m2 s−1) ρ = density (kg m−3) Subscripts

l = liquid phase s = solid phase susp = suspension

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Particle Suspension in Vortexing Unbaffled Stirred Tanks - Industrial

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