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Mechanisms of solids drawdown in stirred tanks.

INTRODUCTION

Particles may float on a liquid surface due to a density difference, due to low wettability combined with a large contact area, or due to low bulk density of the solid powder. When a single particle is placed at the surface of a stationary denser and/or non-wetting liquid, as shown in Figure 1, the particle stays at the surface if the combined buoyancy and surface tension forces are greater than the gravitational force. Once the impeller is turned on and the fluid is in motion, two additional forces emerge in the system: the mean drag force and the dynamic forces due to turbulent velocity fluctuations and coherent meso-scale eddies. These forces and the gravitational force have to overcome the buoyancy and surface tension forces to draw the floating particles down from the surface, allowing them to be distributed throughout the tank. In this paper, the mechanisms for the drawdown of floating solids are explored for a range of stirred tank geometries in order to determine both the dominant mechanism, and the most efficient design strategy.

The underlying design objective associated with the drawdown of floating solids is to maximize contact between the solid and liquid phases for mass transfer and reaction. This problem can be divided into two parts: first finding the best way to drawdown the floating particles from the surface, and second distributing the particles evenly throughout the tank. The first criterion is measured using [N.sub.jd], the just drawn down speed, and the solids distribution is quantified using CD, the cloud depth. While clumping of solids is often observed and can be problematic, it is important for only a subset of particles, and is not addressed in this work.

[FIGURE 1 OMITTED]

The literature for the suspension of negatively buoyant particles from the bottom of a stirred tank is well developed (Zwietering, 1958; Nienow, 1968; Baldi et al., 1978; Rao et al., 1988; Mak, 1992; Choudhury, 1997), and the mechanisms are quitewell understood (Paul et al., 2004). The drawdown of positively buoyant particles yields few references in the literature. It is a more complex problem due to the free liquid surface, which may sustain a large stable surface vortex, and the solids wettability, which can have a significant impact on the results for otherwise similar particles. The few results currently available in the literature are summarized below.

The first paper on solids drawdown is by Joosten et al. (1977) who correlated the minimum drawdown speed by:

[Fr.sub.JS] = 3.6 x [10.sup.-2] x [(D/T).sup.3.65] [([DELTA][rho]/[rho].sub.L]).sup.0.42]

They used a single partial baffle 0.2 T wide, immersed from the top of the liquid to a depth of 0.3 T, an axial impeller of 0.6 T diameter, and the impeller off bottom clearance in the range of (T/9 - 3T/9) as the optimum configuration. In this configuration, an eccentric surface vortex draws the solids down to the impeller.

Later work by Hemrajani et al. (1988) observed a two-step process in unbaffled tanks. In the first step the centrifugal forces resulting from the swirl moved the light particles along the liquid surface into the centre of the vortex. From there the liquid velocities at the surface were high enough to incorporate the particles into the bulk liquid.

Bakker and Frijlink (1989) used three different types of impellers: a six bladed disc turbine and two inclined blade impellers with six blades at angles of either 45[degrees] or 60[degrees] blade angle and six blades. The latter were used in down- and up-pumping modes. All the impellers had a diameter of D = 0.4 T. They found that the 45[degrees] up-pumping impeller is the most energy efficient as a result of the low speed and power number obtained. However, the particles tended to concentrate in the upper half of the vessel and the suspension was not homogeneous in all cases.

Kuzmanic and Ljubicic (2001) reported that in a fully baffled tank, the intensity of turbulence is primarily responsible for the dispersion of floating solids. They also concluded that with an increase in impeller diameter, there is less decay in the turbulence from the impeller to the surface, because the normalized distance is shorter (normalized distance [varies] S/D). Moreover, the liquid velocity increases with an increase in impeller diameter at the same N. These two effects lead to a significant dependence on impeller diameter.

Previous investigations (Joosten et al., 1977; Thring and Edwards, 1990; Takahashi and Sasaki, 1999; Ozcan-Taskin and McGrath, 2001) showed that substantial savings can be achieved by choosing the proper impeller geometry and diameter. All of the investigators concluded that radial flow impellers are not energy efficient for solids drawdown. Mixed flow impellers achieved better results than purely axial flow impellers, although the performance of the mixed flowimpellers is still notwell defined when they are compared based on the pumping mode of the impeller (up- or down-pumping).

In a later study, Ozcan-Taskin and Wei (2003) observed that solids are drawn down in different ways depending on the impeller pumping mode, submergence, and number of baffles. They worked with a pitched blade turbine (PBT) in the upand down-pumping modes and the LE-20 impeller in the uppumping mode. All three impellers were studied for D = T/2 and D = T/3. Four different submergences were used (S = T/3, S = T/2, S = 2T/3 and S = 3T/4). The conclusion of their work is that for most cases, decreasing the impeller submergence increases the speed and power required to draw down the solids. This result seems counter-intuitive. The opposite behaviour was observed when a down-pumping impeller with D = T/3 was used: in this case a larger submergence was less effective.

The literature to date consists of initial investigations into the effect of geometry on solids draw down performance for selected geometries. A number of mechanisms have been identified, primarily as a means to explain experimental results. In this work, measurements of [N.sub.jd] and CD are combined with flow visualization and computational fluid dynamics (CFD) simulations to investigate the interactions between impeller and tank geometry, drawdown and distribution performance, and dominant drawdown mechanism. Three impellers, one axial and two mixed flow were tested over a range of solids concentration (2 - 10% by volume), and impeller submergence (0.05 T - 0.5 T). Three baffle configurations were considered for all three impellers. The solids density and shape were varied over a relatively narrow range, as was the fluid. The results provide a framework for understanding previous work and for selecting geometries which are well suited to the drawdown of various kinds of solids.

EXPERIMENTAL

Experiments were performed in a 0.24 m diameter flat bottom transparent cylindrical tank, shown in Figure 2. The liquid height was maintained constant (H = T = 0.24 m). The distance from the surface of the liquid to the centreline of the impeller (submergence, S) was varied from the impeller blade height to half of the total liquid depth (0.01 m < S < 0.12 m). Three impellers were used, as shown in Table 1: a standard 45[degrees] pitched four-blade turbine (PBT) in both up- and down-pumping modes, and an A340 impeller (provided by Lightnin) which operates only in the uppumping mode. Three baffle configurations were studied: zero, one and four baffles. All of the baffles had the same dimensions: baffle width (W = T/10), baffle height ([B.sub.H] = 1.1 T) and baffle thickness ([B.sub.T] = T/120).

[FIGURE 2 OMITTED]

Four particle species as given in Table 2 were used in the experiments: three different densities of expandable polystyrene beads (EPS), and polyethylene (PE) grids. The EPS beads were used to compare the effect of reducing solids density, and the PE grids were used to test the effect of a large wetted perimeter on [N.sub.jd] for a neutrally buoyant particle. The EPS beads were prepared from unexpanded samples by holding them under hot water (Te [approximately equal to] 70[degrees]C) until no particles remained on the bottom of the beaker. After expansion, the particles were sieved to separate them by size and their density was measured using a pycnometer. Tap water ([[rho].sub.W] = 998 kg/[m.sup.3]) and Bayol ([[rho].sub.B] = 794 kg/[m.sup.3]) were used as the working fluids. All of the particles are partially wetting in water, and fully wetting in Bayol. Only the EPS 3 particles floated in Bayol.

For every series of experiments, the particles were weighed and gently dropped down the side of the tank with the impeller turned off. Next, a small impeller speed was set giving stagnant zones where a number of particles agglomerated at the surface (Figure 3a). Then the speed of the impeller was gradually increased at intervals of 5 rpm until the stagnant zones of solids completely broke up and no solids remained at the liquid surface for more than 1-2 s (Figure 3b). This speed was characterized as [N.sub.jd]. It was difficult to determine [N.sub.jd] exactly because even at higher impeller speeds some solid particles reappeared on the liquid surface. To minimize the error in [N.sub.jd], each value of [N.sub.jd] was obtained from three different runs and averaged. The final results reported here are repeatable to [+ or -] 5 rpm.

The cloud depth (CD), shown in Figure 4, is the perpendicular distance from the lowest point on the free surface of the liquid to the point where the concentration of particles drops dramatically. While [N.sub.jd] gives the point where all of the particles leave the surface, and allows both design and motor sizing, the cloud depth gives an indication of how well the particles are dispersed throughout the tank. The cloud depth reported here is a subjective measure of the drop in concentration. For some configurations, the solids layer is very compressed and the CD measurement is straightforward. For other configurations, the concentration of solids changes in several stages, and the CD reported is the point beyond which very few particles penetrate. No direct measurement of concentration was available for this study. The CD was simply measured using a ruler, and averaged over three runs. The results are accurate to approximately 0.1 T.

CFD PROTOCOL

Many papers have been published on the CFD simulation of flow in stirred tanks, and several conclusions may be drawn about the accuracy of these simulations:

[FIGURE 3 OMITTED]

1. The recirculation flow produces a strong coupling of momentum exchange between the impeller and the tank geometry, so the impeller must be simulated directly (Fokema et al., 1994).

2. Predicted circulation patterns are always qualitatively accurate, and the transitions from one circulation pattern to another, predominantly with changes in off bottom clearance, are also accurately predicted (Fokema et al., 1994; Coy et al., 1996).

[FIGURE 4 OMITTED]

3. Turbulence and flow are typically under-predicted in the bulk of the tank, primarily because the k-[epsilon] model is over diffusive for round jets (Bhattacharya and Kresta, 2002). LES promises more accurate simulation of the turbulence, but simulation times are still very long (1 month for LES/SGS model vs. 1 h for MRF/k-[epsilon]).

4. Small concentrations of a second phase do not significantly affect overall circulation patterns, but the meaning of "small" in this context is not well established (Montante et al., 2001).

Simulations were used in this project to explore large changes and trends in the mean flow and turbulence near the surface of the tank. This allowed us to confirm visual observations from the laboratory and thus provide a better understanding of the dominant mechanisms for various geometries. With these observations in place, a direction for future investigations can be established, and it is our intent that these results serve to guide later researchers in the design of experiments to further explore the detailed fluid mechanics associated with drawdown of floating solids. With this limited objective for the CFD simulations in mind, several gross assumptions were made:

1. Single phase simulations will show the same trends for gross changes in mean flow and turbulence as exist in the flow field with solids present. Experiments were performed to establish the effect of solids concentration on the results, and it will be shown later that the trends observed are independent of solids concentration, which lends support to this difficult assumption.

2. The distortion of the free surface for the fully baffled (four full height baffles) is negligible in terms of its effect on the simulations. Accurate prediction of surface turbulence and the medium scale transient eddies observed for the single baffle case would require a more accurate treatment of the free surface, but for the fully baffled case this approximation is reasonable.

3. The multiple reference frames (MRF) protocol defined by Bhattacharya and Kresta (2002) is suitable for the PBTU as well as the PBTD. The full details of the protocol development are given in Bhattacharya and Kresta (2002), and the conditions used here are summarized in Table 3.

Simulations were carried out using the multiple reference frames (MRF) formulation, where a rotating volume is associated with the impeller and a stationary zone is associated with the baffles and the tank wall. The surface was modelled as a symmetry plane (zero velocity gradients) and no-slip boundary conditions were used for the tank wall, impeller, shaft, and baffles. The submergence was varied for four fully baffled configurations running at [N.sub.jd] with a single impeller diameter. Full details of the four geometries are given in Table 4.

RESULTS

Flow visualization, CFD, and experimental measurements of cloud depth and [N.sub.jd] are combined to gain a better understanding of the dominant drawdown mechanisms for various impeller and tank geometries; and varying solids properties. The results are presented in five parts. First, an overview of the experimental observations and mechanisms is used to set the framework for the discussion. Next, the performance of a large stable surface vortex in an unbaffled tank is presented in terms of cloud depth, and shown to be very poor. The stable vortex, in fact, acts as a centrifuge and separates the light particles from the heavier fluid. Third, the mechanisms for the fully baffled configuration are shown for varying submergences and impeller geometries using experimental observations and confirmatory CFD experiments. Next, the CFD results are used to interpret the [N.sub.jd] results for all configurations. Finally, the solids properties are varied over a moderate range to determine whether the trends observed will hold for conditions slightly outside the envelope of the bulk of the data.

OVERVIEW

Observations of the dispersion from above and through the side of the vessel by flow visualization, samples of which are shown in Table 5, suggest that solids may be drawn down by three different mechanisms:

1. Single vortex formation: this mechanism is characterized by a large stable vortex which forms in the centre of the tank only when no baffles are present. This vortex breaks up the stagnant zones at the surface with [N.sub.jd]'s comparable to those for the baffled configurations, but does not distribute the solids throughout the tank. Instead, the solids are concentrated close to the surface of the vortex by centrifugal forces. A variant on this mechanism is the unstable, off-centre vortex which forms for the single baffle configuration. The distribution of solids is better for this configuration, but there is still a strong tendency for the particles to concentrate around the vortex.

2. Turbulent fluctuations: this mechanism is characterized by a wavy and splashy surface with energetic surface eddies, particularly when small submergences are used. These eddies appear and vanish quickly, pulling solids down from the surface in small packets. Eddies smaller than the particles do not have the energy necessary to draw down the particles, and very large eddies tend to be oriented with the mean circulation loops. Turbulent fluctuations are associated with the meso-scale eddies, roughly 2-4% of the tank diameter in size; or 3-10 times the size of a particle.

3. Mean drag: this mechanism is characterized by large swirls and waves which develop over the entire free liquid surface, breaking up the stagnant zones intermittently and ingesting more solids. Macro-instabilities in the mean flow clearly assist the break-up of solid clumps and the drawdown of particles. Strong mean circulation leads to a better distribution of particles in the tank than a strong central vortex. The axial component of the mean velocity must be larger than the particle slip velocity at some point close to the liquid surface for this mechanism to be effective.

Combinations of these mechanisms can be found in most tank configurations, but one mechanism will generally dominate.

Table 5 provides pictures and sketches of the solids distribution and flow patterns for different baffle configurations. The unbaffled and one-baffle configuration pictures clearly show the single vortex formation mechanism and how poor the distribution of particles is throughout the tank in these cases. Most of the particles for these two configurations accumulate at the surface of the vortex. On the other hand, the picture of the fully baffled configuration shows good solids distribution and the absence of a single stable surface vortex. The solids distribution is similar for both the PBTU and the PBTD, but the flow patterns are quite different. The key differences between the four full baffles and the partially baffled or unbaffled cases are the top to bottom circulation, and the elimination of the surface vortex. The drawdown mechanisms defined before and partially illustrated in Table 5 suggest that the best way to draw down and distribute floating particles is to avoid the formation of a large surface vortex while promoting turbulence and strong mean circulation at the surface.

STABLE CENTRAL VORTEX AND CLOUD DEPTH

As shown in Figure 4, the cloud depth is the perpendicular distance from the surface of the liquid to the point where the concentration of particles drops dramatically, and is an indication of how the particles are distributed throughout the tank. It is analogous to the cloud height for solids suspension, but is slightly complicated by the possibility of large deformations of the free surface. For the unbaffled configuration, the cloud depth was calculated by subtracting the vortex depth from the distance to the bottom of the particle layer when particles are added.

Figure 5 shows the vortex depth at [N.sub.jd] for all the impellers studied at varying impeller submergences. Since the A340 is designed for purely axial flow and is less dependent on the action of baffles, its vortex depth is consistently smaller even at larger values of [N.sub.jd]. Note also that a larger [N.sub.jd] is not the same as a larger power requirement. For all three impellers, [N.sub.jd] and the power requirement increase as the vortex depth and impeller submergence increase.

[FIGURE 5 OMITTED]

Figure 6 shows that the cloud depth for the unbaffled configuration gets smaller as S increases for all three impellers. Recall from Figure 5 that as S increases, [N.sub.jd] increases, and in fully turbulent flow, all of the mean velocities in the tank will scale with [N.sub.jd]. Thus, as S and [N.sub.jd] increase the centrifugal forces on the particles due to mean flow will also increase, giving better particle separation, or more intense segregation of the phases. Clearly, the performance of the unbaffled tank is significantly poorer than the single baffle and the fully baffled cases.

[FIGURE 6 OMITTED]

The results for the single baffle case fall between those for the surface vortex and the fully baffled case, as we might expect, but are much closer to the fully baffled case. With a light solid like the expandable polystyrene beads, the concentration of particles is not uniform in the tank even after large values of cloud depth are obtained. This non-uniformity for the single baffle case is not captured by the cloud depth results, because the surface vortex is unstable and the mean vortex depth could not be measured visually.

For the fully baffled configuration and the single baffle configuration, the cloud depth varies with S/T. Figures 7a and b show that the top to bottom recirculation loop is larger when S/T = 0.5 than when S/T = 0.25 (fully baffled tank, PBTD). This indicates that the particles should be driven deeper in the tank for S/T = 0.5, which agrees with the trends in Figure 6a. This result illustrates the link between top to bottom circulation and solids distribution throughout the tank, a link which is consistently seen for all impellers and tank configurations. Figure 6b shows the effect of submergence on cloud depth for the PBTU. For this impeller, complete dispersion of particles into the liquid phase is easily achieved all the way to the bottom of the tank for both the four baffle and one baffle configurations.

Results for the A340 in Figure 6c show that while the performance of the unbaffled tank is somewhat better than for either the PBTD and the PBTU, the cloud depth is limited in the baffled tanks, even for large values of S and high [N.sub.jd]. Observations of the mean flow for the up-pumping A340 showed fast top to bottom circulation loops which reach all the way to the surface even for large values of S/T. This purely axial discharge flow quickly returns the particles to the surface at all submergences, limiting the cloud depth. For the A340, the one baffle configuration performs better in terms of cloud depth than the fully baffled case for S/T > 0.3, but higher values of [N.sub.jd] are required under these conditions.

[FIGURE 7 OMITTED]

MECHANISMS FOR FULLY BAFFLED TANKS: CFD SIMULATIONS

It is clear from the cloud depth results that use of a stable surface vortex for solids drawdown is a poor choice. To better understand the balance between drag on particles due to mean flow, and engulfment of particles from the surface by turbulent eddies, CFD simulations were performed for four different fully baffled tank configurations: the PBTD and the PBTU at S = T/2 and S = T/4, all at [N.sub.jd]. The resulting circulation patterns are shown in Figure 7. Note the direction and magnitude of the flow and the size of the different recirculation loops present for the four cases. In some configurations, the mean circulation at the surface is strong enough to drag the particles from the surface and distribute them throughout the tank. In other cases, the circulation at the surface is quite weak, and turbulence may be expected to play a more important role.

For the PBTD, the direction and magnitude of the velocity arrows at the surface indicates that the particles are carried from the walls and then immersed around the shaft for both submergences. For this configuration the secondary circulation loop in the bottom of the tank is relatively weak because [N.sub.jd] is less than the speed (N = 400 rpm) used in Figure 7c for the PBTU.

The results for the PBTU shown in Figures 7c and d are quite different from those for the PBTD. The impeller discharge flow reaches the wall before it reaches the surface, splitting into two branches and forming a weak secondary circulation loop at the surface. In the upper circulation loop, the velocity is low and therefore the mixing is expected to be poor at the surface. When the up-pumping impeller is used with a small submergence, the flow at the surface is much stronger and the particles are swept from the surface to the walls, where a zone of rapid downward circulation is found. This downward flow occurs when the primary discharge flow from the up-pumping impeller reaches the surface before it reaches the sidewalls of the vessel. Flow visualization results and measurements of [N.sub.jd] (see Figure 9b) indicate that the transition in the circulation pattern from single circulation loop to double circulation loop occurs at S/T = 0.375 for the D = T/2 PBTU.

Given the circulation patterns in these four tank configurations, the next step is a quantitative analysis of the mean velocity and turbulent kinetic energy (TKE or k) profiles at the surface, as shown in Figure 8. The axial velocity at the surface (Figure 8a) is very large at large submergences, and very small at small submergences for both the PBTU and PBTD. Figure 8b shows that the TKE is small at large submergences, so mean drag dominates at large submergences. At small submergences, when the impeller is close to the surface, k is large and the mean axial velocity is small. The turbulence is observed in the flow visualization experiments as waves, swirls or small vortex formations at the surface. The peaks in k close to the centre of the tank for the PBTD and closer to the walls for the PBTU agree with what one would expect from the impeller suction and discharge flows at small submergences and confirm the presence of strong turbulent fluctuations at the surface. Turbulent engulfment dominates at small submergences. Figure 8c shows the radial velocity for the same four configurations. In this figure only the PBTU at S = T/4 has a positive (outward) radial velocity. Observations during the experiments agree with this behaviour. This is the only one of the four configurations where the solids are transported outward to the walls and then a region of fast down flow close to the wall draws the particles down into the tank. When the PBTU is used, the particles are drawn down in this region. For submergences close to T/2 and for all the submergences using the PBTD the opposite occurs. The particles in these configurations are drawn down close to the centre of the tank.

[FIGURE 8 OMITTED]

From the CFD results, in conjunction with flow visualization, it is concluded that mean drag is the dominant mechanism for the two large submergence cases and turbulent engulfment is the dominant mechanism for the small submergences. The circulation patterns in the tank determine where the particles are drawn down, how far they will penetrate into the tank, and how quickly they will return to the surface. The A340 and the PBTD both form a single circulation loop between the impeller and the surface while the PBTU forms a secondary circulation loop at the surface for S/T > 0.375, mirroring the behaviour of the PBTD which forms a secondary circulation loop in the bottom of the tank once the off bottom clearance (C) exceeds 0.35 T (Kresta and Wood, 1993).

DRAWDOWN PERFORMANCE IN TERMS OF [N.sub.jd]

Figure 9a shows the [N.sub.jd] results for the PBTD for all three baffle configurations. For the PBTD, there is little effect of S/T or baffle configuration on [N.sub.jd], even though there was a dramatic difference in the cloud depth for the three configurations (Figure 6a). As shown from the CFD simulation results, at very small submergences, the drawdown is dominated by turbulent engulfment at the surface and [N.sub.jd] is quite small. As the impeller descends beyond 0.4 T, the dominant mechanism shifts to mean drag and [N.sub.jd] increases rapidly. From 0.25 < S/T < 0.4, both mechanisms appear to be active and [N.sub.jd] is nearly constant. The rapid increase of [N.sub.jd] beyond S/T = 0.4 is due to changes in the intensity of the circulation loops and the turbulence at the surface. Once the distance between the impeller and the liquid surface exceeds S/T = 0.3, the wall jet which drives the up-flow in the recirculation loop disintegrates at z/T = 0.7 (Bhattacharya and Kresta, 2002) so the mean flow and turbulence no longer penetrate to the surface. The just draw down speed increases rapidly as a result.

The [N.sub.jd] results for the PBTU, shown in Figure 9b, show different trends for the different baffle configurations. The trend for the unbaffled configuration is similar to the PBTD unbaffled case, differing only in the maximum [N.sub.jd] required at large submergences (350 rpm vs. 375 rpm). The fully baffled configuration shows dramatically different behaviour. As the submergence increases from 0.32 to 0.42 and the secondary circulation loop forms at the surface (Figures 7c and d), [N.sub.jd] increases dramatically.

The [N.sub.jd] results for the A340, shown in Figure 9c, are most interesting in terms of comparison of the absolute values of [N.sub.jd] and CD. For the unbaffled case, the maximum [N.sub.jd] at large submergences is highest (500 rpm > 375 rpm > 350 rpm) for the A340. Recalling that this impeller has a relatively small power number ([N.sub.p] = 0.64), the calculated difference in power consumption is smaller than the difference in [N.sub.jd] (5.1 W < 7.7 W > 6.7 W), and the cloud depth at high submergences is somewhat better than for the other two impellers (CD = 0.04 m vs. 0.02 m). For the fully baffled case, the A340 will require less power than the PBTD at more typical submergences (for S = 0.25 T, [N.sub.jd] = 300, 225 and 350 rpm for the PBTD, PBTU, and A340, respectively, with P = 4.2, 1.7 and 1.7 W and CD = 0.21, 0.24 and 0.16 m). For more information on power consumption data refer to Khazam (2007).

[FIGURE 9 OMITTED]

The [N.sub.jd] results do not show the same dramatic differences between the baffled and unbaffled cases as the cloud depth results in Figure 6. When the CD results and the [N.sub.jd] results for the single baffle and the fully baffled cases are compared, the single baffle case consistently has a larger [N.sub.jd], and a smaller CD, and the trends in the two variables track each other consistently for all three impellers. Without full data for [N.sub.p], it is not possible to link CD to total power consumption, but a correlation between the two is indicated from the data. The differences observed between the three impellers and the three baffle configurations reinforce the statement that "geometry is everything in stirred tanks". As observed for a number of other process objectives (air entrainment by Bhattacharya et al. (2007); mixing sensitive reactions by Nienow and Bujalski (2004); solids suspension by Zwietering (1958)), interactions between the impeller and the tank geometry can have a dramatic effect on the flow field and the process results. Details of the geometry thus determine the dominant mechanism(s) driving solids drawdown from the surface of the tank.

EFFECT OF SOLIDS PROPERTIES

The last set of experimental results are related to the effect of solid and liquid properties on [N.sub.jd]. The effects of solids concentration and wetting properties, density difference, particle size, and contact area, liquid density and foaming behaviour are explored for four different particles and two different fluids. Due to the nature of the particles and the constraints on fluid properties, it was not possible to change variables independently, so several properties often change at the same time.

Figure 10 shows a linear increase in [N.sub.jd] with increasing solids concentration (volume %) for both partially wetting solids (EPS1 in water, Figure 10a) and fully wetting solids (EPS3 in Bayol, Figure 10b). Thring and Edwards (1990) also evaluated the effect of solids concentration (0.75-3.75% (w/w) for [[rho].sub.S] = 925 kg/[m.sup.3]) and concluded that an increase in concentration has a negligible effect on [N.sub.jd]. We note that the range of concentrations evaluated by Thring and Edwards was very small, and that more generally an effect of concentration on [N.sub.jd] should be expected. For the range of conditions examined here, the relationship between solids concentration and [N.sub.jd] is linear.

It is also apparent from Figure 10 that decreasing the impeller submergence results in a lower speed requirement for drawdown in both down- and up-pumping modes. When pumping up, the impeller discharge flow acts on the liquid surface to draw down solids efficiently because of the turbulence and energy generated by the discharge flow, as described earlier. This is only observed when working at small submergences (S/T < 0.375). At a larger submergences (S/T > 0.375) the performance of the up-pumping impeller decreases drastically in comparison with the down-pumping configuration. The energy that the PBTD uses in the recirculation loop to draw down the solids is stable and strong over the range of submergences tested. The PBTU, on the other hand, depends on the impeller discharge flow for drawdown energy. When the submergence is small, the discharge flow reaches the surface first, but as the submergence is increased to T/2, the discharge flow becomes completely submerged and reaches the wall before reaching the surface. At this point, a lot of the energy and mean flow are dissipated, or redirected downwards into the tank. This dramatically reduces the amount of energy available for solids drawdown. There are significant differences for the two pumping modes, and the PBTU performs much better at smaller submergences for the fully baffled configuration.

[FIGURE 10 OMITTED]

The final set of observations concerns the effect of the density difference on solids drawdown, as shown in Figure 11. The primary effect of density difference on [N.sub.jd] from previous works (Joosten et al., 1977; Takahashi and Sasaki, 1999; Kuzmanic and Ljubicic, 2001) is reflected by the exponent in the correlation by Joosten et al. (1977). In our experiments, the change in [N.sub.jd] is also affected by the difference in density between the two phases, as shown in Figure 11. The explanation for this behaviour is that an increase in [DELTA][rho] means an increase of the buoyancy force, therefore additional mean velocity is needed to increase turbulent and drag forces in the vicinity of the surface to draw down the particles. In the specific case when Bayol was used as the working fluid, the formation of a layer of foam retains the particles at the surface. This layer of foam is the reason why the values of [N.sub.jd] obtained for the EPS beads 3/Bayol system are significantly bigger even though the density difference is barely larger than with the EPS beads 2/Water system.

[FIGURE 11 OMITTED]

CONCLUSIONS

The main objective of this paper was to understand the connections between tank and impeller configuration, and the dominant mechanism for solids drawdown. From this knowledge, tanks can be designed or reconfigured to address the key mixing objectives for a given application.

The first important result of the work is the realization that a stable central vortex is a poor way to draw down and to distribute solids in a stirred tank. The vortex acts as a centrifuge, concentrating a layer of solids close to the surface of the liquid. As the impeller submergence increases and [N.sub.jd] increases, the centrifugal effect gets stronger and the solids layer is further compressed. When comparing the three impellers in terms of the surface vortex, the A340 surface vortex is smaller in diameter and depth than the ones created by the PBTD and PBTU for both the unbaffled and the one baffle configurations.

Based on the experimental observations and CFD simulations, two mechanisms for solids drawdown are active in fully baffled tanks: mean drag and turbulent fluctuations. Using baffles to suppress surface vortex formation and increase mean velocity and turbulence at the surface is the best way to draw down floating solids. Turbulence is the main mechanism at small submergences for both the PBTD and PBTU. The turbulent kinetic energy profiles from CFD simulations confirm this conclusion. For large submergences for both the down- and up-pumping impellers, profiles of axial velocity at the surface show that mean drag is the main mechanism of solids drawdown. Visual observations of the surface also support this conclusion.

Drawdown performance is sensitive to submergence for both PBT impellers, but much more so for the PBTU. This is due to the formation of a secondary circulation loop at the top of the tank. Visual observations suggest that the transition occurs close to S/T = 0.375. CFD simulations with a PBTU confirm this circulation pattern for the fully baffled configuration at S/T = 0.5. Experimental observations and the values of radial velocity at the surface show that the particles are draw down in the vicinity of the shaft for three of the four configurations simulated. The opposite occurs for smaller submergences (S/T < 0.375) with a PBTU impeller where the particles are drawn down close to the walls. Four full baffles and a PBTD is the mixing geometry recommended for large submergences, while for smaller submergences the results suggest that the up-pumping PBT will be much more efficient.

Solids properties also affect [N.sub.jd], particularly the density and concentration. The relationship between solids concentration and [N.sub.jd] is linear. Finally, as the difference in density between the phases increases the velocity needed to pull the particles down ([N.sub.jd]) increases.

These results provide a basis for further studies on solids drawdown, including the effect of baffles which cover only a portion of the liquid depth. The combination of cloud depth, [N.sub.jd], and CFD with flow visualization has allowed a better understanding of the drawdown mechanisms and the effect of geometry. Power consumption for different impellers is a necessary complement to further analysis in terms of effective design.
NOMENCLATURE

[B.sub.H] baffle height (m)
[B.sub.T] baffle thickness (m)
C clearance, distance from the bottom of the tank to the
 centre of the impeller (m)
CD cloud depth (m)
CFD computational fluid dynamics
[d.sub.p] particle size (mm)
[d.sub.T] impeller blade thickness (m)
D impeller diameter (m)
EPS expandable polystyrene beads
[F.sub.b] buoyancy force (N)
[F.sub.g] gravitational force (N)
[F.sub.surf] surface tension force (N)
[Fr.sub.JS] Froud number at [N.sub.js]
H liquid height in tank (m)
k turbulent kinetic energy (TKE) per unit mass
 ([m.sup.2]/[s.sup.2])
MRF multiple reference frames
N impeller speed (rps or rpm)
[N.sub.jd] just draw down impeller speed (rps or rpm)
[N.sub.P] power number of impeller
P impeller power consumption (W)
PBTD down-pumping pitched blade turbine
PBTU up-pumping pitched blade turbine
PE polyethylene grids
[Re.sub.I] impeller Reynolds number
S submergence, distance from the surface to the
 centreline of the impeller (m)
SG specific gravity
T tank diameter (m)
Te temperature ([degrees]C)
[V.sub.r] radial velocity (m/s)
v/v volume of particles/total volume
W baffle width (m)
w impeller blade width (m)
z vertical distance from the tank bottom (m)

Greek Symbols

[epsilon] local rate of dissipation of turbulent kinetic energy
 per unit mass at any location ([m.sup.2]/[s.sup.3])
[[rho].sub.B] Bayol density (kg/[m.sup.3])
[[rho].sub.L] liquid density (kg/[m.sup.3])
[[rho].sub.S] solid density (kg/[m.sup.3])
[[rho].sub.W] tap water density (kg/[m.sup.3])
[DELTA][rho] density difference, [[rho].sub.L] -[[rho].sub.S]
 (kg/[m.sup.3])
v kinematic viscosity ([m.sup.2]/s)


Manuscript received July 28, 2007; revised manuscript received December 7, 2007; accepted for publication December 30, 2007.

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Oscar Khazam and Suzanne M. Kresta * Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada T6G 2G6

* Author to whom correspondence may be addressed. E-mail address: suzanne.kresta@ualberta.ca
Table 1. Impeller specifications

Impeller PBT A340

Diameter D = T/2 and T/3 D = 4T/9
Pumping mode Down and up Up
Blade width, w D/5 4D/9
Blade thickness, [d.sub.T] D/60 D/60

Table 2. Particle specifications for expanded polystyrene spheres and
polyethylene grids

Particle Specific gravity (SG) Particle size ([d.sub.p])

EPS 1 0.9 1 mm
EPS 2 0.4 1.5 mm
EPS 3 0.3 2 mm
PE grids 1 8 mm x 8 mm x 1 mm

Table 3. CFD simulation protocol

Commercial code Fluent 4.2.16

Flow equations Navier-Stokes equations

Turbulence model k-[epsilon] model with standard
 constants

Other model equations None

Impeller model MRF with full impeller geometry;
 boundary placed at 2/3 of the
 tank radius

Grid generator MixSim 1.7; hexahedral mesh

Grid resolution 1 million cells total 60 cells
 across the tank diameter

Numerical scheme Second order discretization by the
 Segregated Solution Method

Convergence criterion All normalized residuals
 <2 x [10.sup.-5]

Boundary conditions See text

Working fluid Water, v = 1 x [10.sup.-6]
 [m.sup.2]/s; = 1 000 kg/[m.sup.3]

Table 4. Four fully baffled geometries simulated using CFD

Configuration 1 2 3 4

Impeller PBTD PBTD PBTU PBTU
Diameter (D) T/2 T/2 T/2 T/2
Submergence (S) T/2 T/4 T/2 T/4
[N.sub.jd] (rpm) 350 280 400 230
[Re.sub.l] 84 000 67 200 96 000 55 200
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Author:Khazam, Oscar; Kresta, Suzanne M.
Publication:Canadian Journal of Chemical Engineering
Date:Aug 1, 2008
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