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On the hydrodynamics characterization of the straight Maxblend® impeller with Newtonian fluids
chemical engineering research and design 9 0 ( 2 0 1 2 ) 1117–1128
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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
On the hydrodynamics characterization of the straight Maxblend® impeller with Newtonian fluids A. Hidalgo-Millán a , R. Zenit b , C. Palacios b , R. Yatomi c , H. Horiguchi c , P.A. Tanguy d , G. Ascanio a,∗ a
CCADET, Universidad Nacional Autonoma de Mexico, Circuito Exterior, Ciudad Universitaria, 04510 DF, Mexico, Mexico IIM, Universidad Nacional Autonoma de Mexico, Circuito Exterior, Ciudad Universitaria, 04510 DF, Mexico, Mexico c Sumitomo Heavy Industries Process Equipment, Inc., Ehime, Japan d URPEI, Department of Chemical Engineering, Ecole Polytechnique, P.O. Box 6079, Station CV, Montreal, QC, Canada H3C 3A7 b
a b s t r a c t The hydrodynamics generated by the straight version of the Maxblend® impeller with Newtonian fluids in a baffled stirred vessel under the transitional and turbulent regime has been experimentally characterized by means of the particle image velocimetry technique. The flow fields obtained with the Maxblend were compared with those obtained with a double stage classical pitched blade turbine (PBT) and a double Ekato Intermig® impellers under the same specific power draw. It is shown that these open impellers induce complex local flows in the radial and axial direction, with an intensity decreasing away from the blades. By contrast, the Maxblend impeller generates a more regular circulation pattern, with efficient top-to-bottom pumping. © 2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Maxblend® ; Flow patterns; Flow visualization; Particle image velocimetry
1.
Introduction
The importance of mixing as a key unit operation in many industrial processes has long been recognized. A wide variety of impellers are available for accomplishing mixing operations. Open impellers with pumping or radial discharge are commonly used for low to moderate viscosity. On the other hand, close clearance impellers are preferred for high viscosity applications or processes involving time-dependent rheology or non-Newtonian fluids. Indeed, under these conditions, open impellers tend to generate flow segregations and cavern effects leading to poor reaction selectivity and low mixing efficiency. The design of an impeller that can operate efficiently under the complete flow regimes, i.e. turbulent to laminar, is still an open challenge. One possibility is the use of wide impellers, such as the Maxblend. This impeller is extensively used in Japan and South East Asia due to its hydrodynamic characteristics such as lower power consumption and dispersion in a wide range of Reynolds numbers.
∗
The Maxblend impeller is an attractive alternative to more conventional impellers for crystallization and polymerization processes. However, only little information on the hydrodynamic performance of such an impeller has been reported in the literature. Yao et al. (2001) compared the performance of straight shape Maxblend impeller with a double helical ribbon. They found that the Maxblend is capable of producing stronger elongational flow when operating at moderate Reynolds number. Similar results were found by Devals et al. (2008), who carried out a numerical study by analyzing the factors affecting the fluid flow performance of the Maxblend impeller operating from the laminar to the transitional regimes. They found that the impeller better performs when operating at Reynolds numbers higher than 10 with both Newtonian and non-Newtonian fluids. Fradette et al. (2007) performed an experimental study with a wedge shape Maxblend impeller. They found that mixing time decreases with the reciprocal of the Reynolds number with Newtonian and non-Newtonian fluids in the laminar regime, in particular between the end of the laminar regime and the early transition regime. These
Corresponding author. E-mail address: [email protected] (G. Ascanio). Received 8 September 2010; Received in revised form 2 December 2011; Accepted 13 January 2012 0263-8762/$ – see front matter © 2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.cherd.2012.01.006
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2.
Methodology
Nomenclature D H Mw Nq n P PBT PIV Po Qv r R R* Re T TI V Vr Vtip Vturb Vz Vz∗ z z*
impeller diameter, mm liquid height, mm molecular weight, g/mol pumping number impeller speed, rpm power consumption, W pitched blade turbine particle image velocimetry Power number (dimensionless) vertical flow rate, m3 /s radial impeller diameter, mm dimensionless radial position Reynolds number (dimensionless) tank diameter, mm turbulence intensity volume, m3 radial velocity, m/s impeller tip velocity, m/s mean fluctuating velocity, m/s vertical velocity, m/s vertical velocity (mean absolute value), m/s vertical dimensionless vertical position
Greek letters dynamic viscosity, Pa s liquid density, kg/m3 ω vorticity, 1/s
results were confirmed by Iranshahi et al. (2007) based on physical and numerical experiments. Large-scale and close-clearance impellers have been successfully used for solid suspensions and viscous fluids, respectively. Dohi et al. (2004) carried out an experimental study by comparing the hydrodynamic performance of the straight Maxblend with a Fullzone impeller and a triple impeller array under the turbulent regime. It was found that lower power is drawn by the Maxblend in comparison with the Fullzone impeller at a given rotational speed creating a more uniform solid suspension. The triple impeller array showed to be the most effective under aerated conditions. Several studies involving multiple coaxial impellers are reported in the literature investigated the use of a multiple Ekato Intermig impeller configuration by means computational fluid dynamics study (Mishra and Joshi, 1994; Armenante et al., 1999; Aubin and Xuereb, 2006). They found that the flow produced by the Intermig impellers was highly complex and three-dimensional confirming the results reported by Szalai et al. (2004). Foucault et al. (2005) reported the use of coaxial mixer consisting of a wall-scraping anchor and dispersion impellers. They found that the anchor draws more power when dispersion impellers counter-rotate and less energy is required in co-rotating mode. The objective of this paper is to experimentally characterize the hydrodynamics generated by the straight version of the Maxblend impeller with Newtonian fluids in a baffled vessel and compare with that of coaxial impellers mounted with pitched blade turbines and Intermig impellers. Both flow fields and power consumption will be considered.
Fig. 1 shows the experimental mixing system used in this work. It consists of a polycarbonate transparent vessel of diameter T of 165 mm and a liquid height H of 198 mm. The straight Maxblend has a diameter of 88 mm and a height 162.7 mm. Arrays consisting of two coaxial Ekato Intermig® impeller and pitched blade turbines (PBT) having both a diameter of 82.5 mm were also used for comparison purposes (see Fig. 1). The impellers were driven by a DC motor of 248 W (1/3 hp), which speed was set from a DC controller in an openloop mode. Both the agitation shaft and the impellers were painted black for avoiding light reflection. The vessel was a cylinder with semi-spherical bottom and 4 baffles having a width of 13.2 mm. In order to minimize significant changes of the refraction index and optical distortion, the vessel was surrounded by a square jacket containing the same fluid under study. This also allowed maintaining a stable temperature during the experiments. The power drawn by the impeller(s) was determined by measuring the torque using a Lorenz Messtechnik torquemeter placed between the motor and the agitation shaft. Pure water and an aqueous solution of polyethylene glycol at 25 wt% (Mw = 20,000 mol/g, Clariant, Inc.) having a dynamic viscosity of 0.2 Pa s and density of 1100 kg/m3 were used as working fluids. Table 1 summarizes the experimental conditions used for the present study. Series 1 experiments corresponded to the transitional regime while series 2 were for the turbulent regime. A particle image velocimetry (PIV) equipment from Dantec Dynamics was used for visualizing the flow patterns in the stirred vessel. It consisted of a pulsed laser with a wavelength of 532 nm, frequency of 15 Hz and energy of 120 mJ, an optical array for creating a light sheet with a width of the order of 1 mm and a CCD camera placed perpendicularly with respect to the light sheet and synchronized with the laser. Silver coated hollow spheres of 10 m diameter were used as particle tracers. In PIV, the velocity vectors are obtained from sub-sections of the region under investigation seeded with particle tracers by measuring the movement of such particles between two light pulses. The camera is synchronized with light pulse source in separate image frames, which are divided into small interrogations areas. These interrogation areas are cross-correlated with each other, pixel by pixel, which produce a signal peak, identifying the particle displacement. Knowing the displacement and the time between two consecutive two image frames, the velocity is obtained with sub-pixel interpolation (Dantec Dynamics, 2011). Fig. 2 shows the experimental setup for the flow patterns visualization. A series of measurements in the azimuthal direction were performed. For each plane, the camera was positioned in such a way that it captured the motion in the desired plane. In order to obtain statistically robust results 300 individual images with the phase/locking technique was used. An electronic shutter was placed in the agitation shaft and connected to the visualization system in such a way that the position of the impeller with respect to the camera and the baffles was always the same. Table 1 shows the general experimental conditions used for this work. The Power number and the Reynolds number are, respectively, defined as follows Re =
ND2
(1)
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Fig. 1 – Mixing system: (a) General array; (b) Impellers (dimensions in mm).
Table 1 – Experimental conditions. Parameter
Maxblend
3
Specific power, P/V (kW/m ) Torque (N m) Dynamic viscosity, (mPa s) Rotational speed, n (rpm) Reynolds number, Re Power number, Po
2 PBT
2 Intermig
Series 1
Series 2
Series 1
Series 2
Series 1
Series 2
0.652 0.101 200 260 168 6.42
0.1 0.028 1 144 18,000 5.79
0.652 0.0732 200 360 204 2.42
0.1 0.0209 1 193 21,893 2.40
0.652 0.0617 200 427 266 1.45
0.1 0.01205 1 335 38,001 0.46
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Fig. 2 – Experimental setup and azimuthal scanning array. Po =
P N3 D5
(2)
where and are the fluid density in kg/m3 and the fluid dynamic viscosity in Pa s, respectively, N is the impeller speed in rps, D is the impeller diameter in m and P is the power draw by the impeller in W. Although the flow field inside the mixing tank is tridimensional, only the velocity fields in the r–z direction are measured and discussed. In fact, the main flow occurs in the azimuthal direction because the main thrust of the impeller induces motion in this direction. However, as shown below, an enhanced mixing capacity results from impellers that are capable of inducing radial or axial (vertical) flow velocities. Therefore, our analysis is aimed to understand how these r–z currents are modified for different impeller designs.
3.
Results
Fig. 3 shows a typical flow field obtained in the r–z plane for the Maxblend impeller for a Reynolds number of 18,000. As described above, measurements were obtained for several angular positions; the figure shows the velocity field obtained at an angle of 45◦ . The recirculating nature of the field induced by the impeller is noteworthy: near the top and bottom of the impeller, two large vortices are observed, which induced large vertical currents. An important downward flow is observed near the center of the tank. By analyzing and comparing velocity fields like these, produced with different impellers, the effectiveness of the flow patterns to induce good pumping characteristics will be assessed. In Fig. 4, other flow measurements obtained with the PIV system are shown. All quantities are shown in dimensionless form considering Vtip , 2Vtip /T and Vtip (respectively, for the velocity magnitude, the vorticity and the turbulent intensity). From the vector field, the magnitude of the velocity in the (r, z) plane can be calculated as: V=
Vr 2 + Vz 2
(3)
Fig. 4(a) shows the map of velocity magnitude for the flow field shown in Fig. 3.
Fig. 3 – Typical velocity field for a r–z plane at 45◦ for the Maxblend impeller.
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Fig. 4 – Flow fields of the Maxblend impeller: (a) velocity magnitude; (b) vorticity; (c) turbulence intensity. The azimuthal component of the vorticity field, ω , can be obtained calculating the curl of the r–z vector field: ω =
∂Vr ∂Vz − ∂z ∂r
(4)
The vorticity indicates the rate of fluid rotation and large vortices show the regions in which vortexing is important. The vorticity field is shown in Fig. 4(b). Two large vortical structures can be readily identified, near the top and bottom of the impeller, which indicates that the fluid is changing direction from downwards (near the center of the tank) to upwards (in the region between the end of the impeller and the tank wall). Another important quantity that can be inferred from our experimental measurements is the magnitude of velocity fluctuations. As our system is angle-resolved (phase locking technique), measurements of the velocity field can be obtained once every cycle of rotation of the impeller, always in the same angular position. In this manner, a statistically converged measurement can be obtained by averaging many measurements (in our case, up to 500 measurements). In addition to the average velocities, the variance of velocity of the data set can be calculated, which provides a measure of the turbulence intensity through
TI =
Vr 2 + Vz 2 Vtip
(5)
where Vr 2 and Vz 2 are the fluid velocity variance in the horizontal and vertical directions at each (r, z) position, respectively, and Vtip is the impeller tip velocity. In Fig. 4(c) the turbulence intensity field is shown. The largest velocity fluctuations are observed to occur near the bottom of the tank, were the largest solid surface of the impeller is placed. Throughout the tank, significant values of turbulence intensity are observed.
3.1. Angular distribution of the velocity field for the Maxblend impeller The measurements obtained for the Maxblend impeller at different angular positions are shown in Fig. 5. This case corresponds to the Maxblend impeller at Re = 18,000. The shape of the impeller is represented with dashed lines. The horizontal and vertical dimensions (r and z, respectively) are normalized using the radius of the tank (T/2). The color scale shows the velocity magnitude normalized by Vtip . The velocity field clearly changes with the angular distance from the impeller. The largest values of the velocity appear immediately after the passage of the impeller (angle = 0◦ ), which are close to 0.8 that of Vtip . At 90◦ , when the measuring plane is perpendicular to the impeller, the velocity is the smallest in the tank. For larger angles, the velocity increases again, as the fluid is now being pushed by the impeller. At all angles, large recirculations and vertical currents are observed. The case shown in the figure corresponds to the large value of the Reynolds number investigated; for the experiments conducted at a smaller Reynolds number (Re = 168), the velocity field does not change significantly with angle from the impeller. Based on this observation, from now we will consider in the forthcoming only one angle (45◦ ) to conduct comparisons of the nature of the flow induced using different impellers.
3.2.
Comparison of the flow induced by three impellers
A direct comparison of the flow induced in the tank using the three impellers investigated is now shown. The comparison is also made in terms of the power drawn by the impellers for the two values of Reynolds number. Fig. 6 shows velocity magnitude fields for the three impellers in the turbulent and transitional regimes. In such a figure it should be noted the shape of the impeller is shown with dashed lines, the horizontal and vertical dimensions
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Fig. 5 – Velocity magnitude fields of the Maxblend impeller for r–z plane for several angles. (r and z, respectively) are normalized using the radius of the tank (T/2) and the color scale shows the velocity magnitude normalized by Vtip . The velocity induced in the fluid phase is larger for the case of the Maxblend impeller for both levels of the Reynolds number. A large recirculation loop is observed, with an important downward flow near the center of the tank. For the Intermig and tandem PBT impellers, significant velocity is observed in both cases in the regions near the impeller. Vortical structures and recirculation regions appear but they do not extend further away from the impeller. For the three impellers, the normalized liquid velocities (|V|/Vtip ) are larger for the low Reynolds number tests. One characteristic of the flow field that indicates that a good mixing rate will be achieved is the vertical velocities induced in the tank. These currents will transport fluid from the bottom to the top of the tank and vice versa. In Fig. 7, maps of vertical velocity are shown for the three impellers in the turbulent and transitional regimes. In Fig. 7 the shape of the impeller is shown with dashed lines, the horizontal and vertical dimensions (r and z, respectively) are normalized using the radius of the tank (T/2) and the color scale shows the velocity magnitude normalized by Vtip . In general, the Maxblend
impeller induces larger vertical currents than the other two impellers. These currents are both larger in magnitude and in extent. Both the Intermig and PBT impellers induce vertical currents but these have a significant magnitude only near the impeller. The Maxblend induces a very significant downward motion near the center of the tank. To further analyze this behavior, curves of the vertical velocity profile as a function of the radial distance are presented in Fig. 8. Several vertical positions were selected which correspond to the location where the impellers have an immediate interaction with the surrounding fluid. Once again, it is very clear that the vertical currents induced by the Maxblend impeller are much larger than those produced especially by the tandem PBT. Also, the vertical currents are significant for different vertical positions in the tank. On the other hand, for the other two impellers, the vertical currents are nearly absent in regions not close to the position where the impeller passes. In the next section, we will show an averaged spatial measure of these currents. Finally, the other relevant desirable characteristic of the flow induced by a particular impeller design is the capacity to induce velocity fluctuations. It is well known that
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Fig. 6 – Velocity magnitude fields for r–z plane: (a) Maxblend in turbulent regime; (b) 2 Intermig in turbulent regime; (c) 2 PBT in turbulent regime; (d) Maxblend in transitional regime; (e) 2 Intermig in transitional regime; (f) 2 PBT in transitional regime. fluctuations promote mixing (Ottino, 1989). For large Reynolds number flows these fluctuations arise naturally from the turbulent nature of the flow. For small to moderate Reynolds number, however, fluid fluctuations must be induced by using baffles. These “obstructions” cause azimuthal variations in the flow streamlines, which in turn, induce velocity fluctuations. Fig. 9 shows the fields of turbulent intensity (as defined above) for the three impellers in the flow regimes investigated. In such a figure, the shape of the impeller is shown
with dashed lines and the horizontal and vertical dimensions (r and z, respectively) are normalized using the radius of the tank (T/2). The color scale shows the normalized turbulent intensity. Note that each image has its own scale. The Maxblend produces larger velocity fluctuations for both moderate and large Reynolds number flows. The Intermig impeller does not produce significant values of turbulent intensity. Moderate values of fluid fluctuation are observed for the PBT impeller.
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Fig. 7 – Vertical velocity fields for r–z plane: (a) Maxblend in turbulent regime; (b) 2 Intermig in turbulent regime; (c) 2 PBT in turbulent regime; (d) Maxblend in transitional regime; (e) 2 Intermig in transitional regime; (f) 2 PBT in transitional regime.
In summary, the Maxblend has been shown to exhibit a better flow distribution, being this effect more evident for a specific power consumption of 0.652 kW/m3 : it induces larger vertical currents and it generates much larger values of fluid fluctuation especially for moderate Reynolds number flows.
3.3.
Analysis of results
In order to obtain a quantitative assessment of the performance of the different mixing devices, the following quantities are defined. As observed previously, since an enhanced mixing is a result of the vertical currents induced by
the impeller it is proposed to measure an average value of the absolute value of the vertical velocity component in the tank. The mean absolute value of the vertical velocity is defined as
Vz∗
1 = RH
R
H
|Vz |dzdr 0
(6)
0
where R and H are the radius and height of the tank, respectively, and |Vz | is the absolute value of the vertical fluid velocity at each point of the measuring plane (r, z). This quantity measures the fluid vertical motion, either upwards or downwards, in each plane; it is a single value that quantifies how much vertical motion is induced by a particular
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Fig. 8 – Vertical velocity profiles for different values of the vertical coordinate, 2z/Dc: (a) Maxblend in turbulent regime; (b) 2 Intermig in turbulent regime; (c) 2 PBT in turbulent regime; (d) Maxblend in transitional regime; (e) 2 Intermig in transitional regime; (f) 2 PBT in transitional regime. impeller design. Furthermore, the measurements obtained in each plane can be averaged to obtain a bulk measure of Vz∗ . In Table 2, the value of Vz∗ is shown for each of the three impellers tested in this study and for the two power consumption values (corresponding to large and moderate Re numbers). The results are normalized by the impeller tip speed in each case. The vertical motion induced by the Maxblend impeller is significantly stronger than the PBT and the
Intermig mixers. By presenting the results in a dimensionless manner, the comparison is fair based on the concepts of modeling theory (Barenblatt, 2003). If the comparison is conducted in dimensional terms, one must do so keeping the Power number equal in both cases. In our investigation this parameter was indeed keep constant; the axial velocities, in dimensional terms, are higher for the case of the Maxblend impeller.
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Fig. 9 – Turbulent intensity fields for r–z plane: (a) Maxblend in turbulent regime; (b) 2 Intermig in turbulent regime; (c) 2 PBT in turbulent regime; (d) Maxblend in transitional regime; (e) 2 Intermig in transitional regime; (f) 2 PBT in transitional regime.
Table 2 – Results. Vz∗ /Vtip
∗ /V Vturb tip
Nq
144 260
0.123 0.273
0.107 0.192
1.59 1.67
0.1 0.652
193 360
0.039 0.030
0.039 0.011
0.65 0.77
0.1 0.652
335 427
0.013 0.017
0.015 0.004
0.13 0.38
Impeller
P/V (kW/m3 )
Maxblend
0.1 0.652
PBT
Intermig
Re
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Another important factor to ensure rapid and efficient mixing rates is the level of velocity fluctuations induced in the tank. At large Reynolds numbers, these fluctuations are readily related with the turbulent nature of the flow; at low Reynolds, on the other hand, fluctuations are induced by the tortuous path of the fluid particles imposed by the baffles and the impeller geometry. In either case, large fluctuations are preferred as they contribute to the mixing process. Hence, from the PIV measurements reported above, a bulk measure of the fluid fluctuations in the tank is proposed. The mean fluctuating velocity is defined as
1 RH
∗ = Vturb
R
H
(Vz 2 + Vr 2 )dzdr 0
(7)
0
where Vz 2 and Vr 2 are the fluid velocity variances in the vertical and horizontal directions, respectively. These quantities were calculated by considering a time series of instantaneous fluid measurements in several planes. It is observed that, under the same nominal conditions, the Maxblend impeller also induces larger values of the fluctuating velocity. This indicates that this impeller produces faster mixing rates because of the combined action of the induced vertical velocity and turbulent-like velocity fluctuations. On the other hand, the pumping capacity of the impellers used in the present work was also investigated in terms of the pumping number (Nq), which is defined by Nq =
Qv ND3
(8)
where Qv is the total volumetric flow rate in m3 /s, N is the rotational speed in rps and D the impeller diameter in m. The pumping number is a classical indicator of the pumping capacity. The total volumetric flow rate is defined by the following expression:
Qv =
z++
z−−
D|(v0r )r=r++ |dz +
r++
2r|(v0z )z=z++ |dr 0
z++
+ z−−
2r|(v0z )z=z−− |dr
(9)
Here z++ , z−− and r++ refer all to the virtual boundaries of the control volume surrounding the impeller. The superscript “0” is the fluid flowing out from such a control volume. The reader is referred to Hidalgo-Millán et al. (2011) for a detailed description of the method. For that purpose, the volumetric flow rate leaving the turbine blades is calculated as the average of flow rates at the different azimuthal positions every 20◦ . The reader is referred to Hidalgo-Millán et al. (2011) for detailed description of the method employed to calculate the pumping number. As Table 2 shows the best pumping capacity is obtained with the Maxblend impeller in both flow regimes, while the two Intermig impellers exhibit the lowest pumping capacity. One should recall the experiments were made under a specific power consumption, so the pumping capacity is a good parameter for comparing the hydrodynamic performance of the impeller investigated.
3.4.
Interpretation
As shown above, by the extensive experimental evidence, the overall performance of the Maxblend impeller is much better
Fig. 10 – Schematic representation of flow patterns around the Maxblend.
that the other two impellers considered in this study. Nevertheless, the question remains: why is the Maxblend impeller better? The Maxblend design induces vertical currents, which are mainly responsible from circulating fluid from the top to the bottom of the tank. The physical mechanism that induces these vertical currents is very different from that obtained with more common impellers. Common impellers, like the Intermig and PBT, induce, mainly, radial and axial flows by the moving action of their blades. The outwards fluid motion (the fluid current expelled by the centrifugal acceleration) is then deflected by tank walls and the baffles. The deflection, in turn, produces the fluid motion in the vertical direction. On the other hand, the Maxblend does not produce significant radial or axial fluid motion directly. The pumping effect and centrifugal acceleration imposed to the surrounding fluid in minimal. The physical mechanism that induces the vertical motion is depicted schematically in Fig. 10. The lower part of the impeller is essentially a solid surface. If we suppose that the impeller is rotating in a clockwise direction, as shown in the figure, in the right part of this surface a low pressure region appears. Low pressure regions appear behind objects in uniform flows, resulting from the fluid inertial effects. From moderate to large Reynolds numbers, these low pressure regions are generally associated with large recirculation zones, which is in good agreement with the findings reported by Iranshahi et al. (2007), who observed large vortex generated by the Maxblend having a similar geometry of the one used in the presented work. They reported a good hydrodynamic performance of the Maxblend impeller when operated in a baffled vessel under the transition regime. In the present case the pressure is higher in the left part of the surface and the top of the impeller. Additionally, the fluid is also pushed by the forward motion of the impeller in the left side. The combined action of the pressure gradients and the driving action of the impeller induces that the fluid circulates from top to bottom. This idea is supported by the PIV measurement: the region in which the largest down-ward motion is observed is indeed that in the lower right part of the impeller. Therefore, the vertical motion in the Maxblend is a result of pressure gradients induced by the particular geometry of the impeller; this mechanism is very different from that in ordinary impellers. The disadvantage that this particular design may have is that dragging a solid surface across a flow induces large drag forces which, in turn, would result in large power consumptions. The slotted nature of the upper part of the
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Maxblend impeller reduces the drag and also promotes the formation of pressure gradients.
4.
Conclusions
The straight Maxblend has been hydrodynamically evaluated and compared with a double coaxial impeller array by using the particle image velocimetry. Results of the flow fields showed that the double impeller array with both the PBT and the Intermig impellers induce local radial and axial flows in the vicinity of the each impeller. On the other hand, the straight Maxblend behaves much better in terms of the fluid circulation in the vertical direction as a result of the large pressure gradients and the driving action of the impeller.
Acknowledgements The financial support from DGAPA-UNAM through grant IN117908 is highly appreciated. A. Hidalgo thanks the Program of Master and Doctorate in Engineering, UNAM and CONACyT for the scholarship provided during his PhD studies.
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Dantec Dynamics, 2011. http://www.dantecdynamics.com (visited on April 2011). Devals, C., Heniche, M., Takenaka, K., Tanguy, P.A., 2008. CFD analysis of several design parameter affecting the performance of the Maxblend impeller. Comput. Chem. Eng. 32, 1831–1841. Dohi, N., Takahashi, T., Minekawa, K., Kawase, Y., 2004. Power consumption and solid suspension performance of large-scale impellers in gas-liquid-solid three-phase stirred tank reactors. Chem. Eng. J. 97, 103–114. Foucault, S., Ascanio, G., Tanguy, P.A., 2005. Power characteristics in coaxial mixing: Newtonian and non-Newtonian fluids. Ind. Eng. Chem. Res. 44, 5036–5043. Fradette, L., Thomé, G., Tanguy, P.A., Takenaka, K., 2007. Power and mixing time study involving a Maxblend impeller with viscous Newtonian and non-Newtonian fluids. Chem. Eng. Res. Des. 85 (A11), 1514–1523. Hidalgo-Millán, A., Soto, E., Zenit, R., Ascanio, G., 2011. Effect of eccentricity on the pumping capacity in an unbaffled vessel. Can. J. Chem. Eng. 89, 1051–1058. Iranshahi, A., Devals, C., Heniche, M., Fradette, L., Tanguy, P.A., Takenaka, K., 2007. Hydrodynamics characterization of the Maxblend impeller. Chem. Eng. Sci. 62, 3641–3653. Mishra, V.P., Joshi, J.B., 1994. Flow generated by a disc turbine: Part IV: Multiple impellers. Chem. Eng. Res. Des. 72, 657–668. Ottino, J.M., 1989. The Kinematics of Mixing: Stretching, Chaos and Transport. Cambridge University Press, Cambridge, UK. Szalai, E.S., Arratia, P., Johnson, K., Muzzio, F.J., 2004. Mixing analysis in a tank stirred with Ekato Intermig® impellers. Chem. Eng. Sci. 59, 3793–3805. Yao, W., Mishima, M., Takahashi, K., 2001. Numerical Investigation on dispersive mixing characteristics of MAXBLEND and double helical ribbons. Chem. Eng. J. 84, 565–571.
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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
On the hydrodynamics characterization of the straight Maxblend® impeller with Newtonian fluids A. Hidalgo-Millán a , R. Zenit b , C. Palacios b , R. Yatomi c , H. Horiguchi c , P.A. Tanguy d , G. Ascanio a,∗ a
CCADET, Universidad Nacional Autonoma de Mexico, Circuito Exterior, Ciudad Universitaria, 04510 DF, Mexico, Mexico IIM, Universidad Nacional Autonoma de Mexico, Circuito Exterior, Ciudad Universitaria, 04510 DF, Mexico, Mexico c Sumitomo Heavy Industries Process Equipment, Inc., Ehime, Japan d URPEI, Department of Chemical Engineering, Ecole Polytechnique, P.O. Box 6079, Station CV, Montreal, QC, Canada H3C 3A7 b
a b s t r a c t The hydrodynamics generated by the straight version of the Maxblend® impeller with Newtonian fluids in a baffled stirred vessel under the transitional and turbulent regime has been experimentally characterized by means of the particle image velocimetry technique. The flow fields obtained with the Maxblend were compared with those obtained with a double stage classical pitched blade turbine (PBT) and a double Ekato Intermig® impellers under the same specific power draw. It is shown that these open impellers induce complex local flows in the radial and axial direction, with an intensity decreasing away from the blades. By contrast, the Maxblend impeller generates a more regular circulation pattern, with efficient top-to-bottom pumping. © 2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Maxblend® ; Flow patterns; Flow visualization; Particle image velocimetry
1.
Introduction
The importance of mixing as a key unit operation in many industrial processes has long been recognized. A wide variety of impellers are available for accomplishing mixing operations. Open impellers with pumping or radial discharge are commonly used for low to moderate viscosity. On the other hand, close clearance impellers are preferred for high viscosity applications or processes involving time-dependent rheology or non-Newtonian fluids. Indeed, under these conditions, open impellers tend to generate flow segregations and cavern effects leading to poor reaction selectivity and low mixing efficiency. The design of an impeller that can operate efficiently under the complete flow regimes, i.e. turbulent to laminar, is still an open challenge. One possibility is the use of wide impellers, such as the Maxblend. This impeller is extensively used in Japan and South East Asia due to its hydrodynamic characteristics such as lower power consumption and dispersion in a wide range of Reynolds numbers.
∗
The Maxblend impeller is an attractive alternative to more conventional impellers for crystallization and polymerization processes. However, only little information on the hydrodynamic performance of such an impeller has been reported in the literature. Yao et al. (2001) compared the performance of straight shape Maxblend impeller with a double helical ribbon. They found that the Maxblend is capable of producing stronger elongational flow when operating at moderate Reynolds number. Similar results were found by Devals et al. (2008), who carried out a numerical study by analyzing the factors affecting the fluid flow performance of the Maxblend impeller operating from the laminar to the transitional regimes. They found that the impeller better performs when operating at Reynolds numbers higher than 10 with both Newtonian and non-Newtonian fluids. Fradette et al. (2007) performed an experimental study with a wedge shape Maxblend impeller. They found that mixing time decreases with the reciprocal of the Reynolds number with Newtonian and non-Newtonian fluids in the laminar regime, in particular between the end of the laminar regime and the early transition regime. These
Corresponding author. E-mail address: [email protected] (G. Ascanio). Received 8 September 2010; Received in revised form 2 December 2011; Accepted 13 January 2012 0263-8762/$ – see front matter © 2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.cherd.2012.01.006
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2.
Methodology
Nomenclature D H Mw Nq n P PBT PIV Po Qv r R R* Re T TI V Vr Vtip Vturb Vz Vz∗ z z*
impeller diameter, mm liquid height, mm molecular weight, g/mol pumping number impeller speed, rpm power consumption, W pitched blade turbine particle image velocimetry Power number (dimensionless) vertical flow rate, m3 /s radial impeller diameter, mm dimensionless radial position Reynolds number (dimensionless) tank diameter, mm turbulence intensity volume, m3 radial velocity, m/s impeller tip velocity, m/s mean fluctuating velocity, m/s vertical velocity, m/s vertical velocity (mean absolute value), m/s vertical dimensionless vertical position
Greek letters dynamic viscosity, Pa s liquid density, kg/m3 ω vorticity, 1/s
results were confirmed by Iranshahi et al. (2007) based on physical and numerical experiments. Large-scale and close-clearance impellers have been successfully used for solid suspensions and viscous fluids, respectively. Dohi et al. (2004) carried out an experimental study by comparing the hydrodynamic performance of the straight Maxblend with a Fullzone impeller and a triple impeller array under the turbulent regime. It was found that lower power is drawn by the Maxblend in comparison with the Fullzone impeller at a given rotational speed creating a more uniform solid suspension. The triple impeller array showed to be the most effective under aerated conditions. Several studies involving multiple coaxial impellers are reported in the literature investigated the use of a multiple Ekato Intermig impeller configuration by means computational fluid dynamics study (Mishra and Joshi, 1994; Armenante et al., 1999; Aubin and Xuereb, 2006). They found that the flow produced by the Intermig impellers was highly complex and three-dimensional confirming the results reported by Szalai et al. (2004). Foucault et al. (2005) reported the use of coaxial mixer consisting of a wall-scraping anchor and dispersion impellers. They found that the anchor draws more power when dispersion impellers counter-rotate and less energy is required in co-rotating mode. The objective of this paper is to experimentally characterize the hydrodynamics generated by the straight version of the Maxblend impeller with Newtonian fluids in a baffled vessel and compare with that of coaxial impellers mounted with pitched blade turbines and Intermig impellers. Both flow fields and power consumption will be considered.
Fig. 1 shows the experimental mixing system used in this work. It consists of a polycarbonate transparent vessel of diameter T of 165 mm and a liquid height H of 198 mm. The straight Maxblend has a diameter of 88 mm and a height 162.7 mm. Arrays consisting of two coaxial Ekato Intermig® impeller and pitched blade turbines (PBT) having both a diameter of 82.5 mm were also used for comparison purposes (see Fig. 1). The impellers were driven by a DC motor of 248 W (1/3 hp), which speed was set from a DC controller in an openloop mode. Both the agitation shaft and the impellers were painted black for avoiding light reflection. The vessel was a cylinder with semi-spherical bottom and 4 baffles having a width of 13.2 mm. In order to minimize significant changes of the refraction index and optical distortion, the vessel was surrounded by a square jacket containing the same fluid under study. This also allowed maintaining a stable temperature during the experiments. The power drawn by the impeller(s) was determined by measuring the torque using a Lorenz Messtechnik torquemeter placed between the motor and the agitation shaft. Pure water and an aqueous solution of polyethylene glycol at 25 wt% (Mw = 20,000 mol/g, Clariant, Inc.) having a dynamic viscosity of 0.2 Pa s and density of 1100 kg/m3 were used as working fluids. Table 1 summarizes the experimental conditions used for the present study. Series 1 experiments corresponded to the transitional regime while series 2 were for the turbulent regime. A particle image velocimetry (PIV) equipment from Dantec Dynamics was used for visualizing the flow patterns in the stirred vessel. It consisted of a pulsed laser with a wavelength of 532 nm, frequency of 15 Hz and energy of 120 mJ, an optical array for creating a light sheet with a width of the order of 1 mm and a CCD camera placed perpendicularly with respect to the light sheet and synchronized with the laser. Silver coated hollow spheres of 10 m diameter were used as particle tracers. In PIV, the velocity vectors are obtained from sub-sections of the region under investigation seeded with particle tracers by measuring the movement of such particles between two light pulses. The camera is synchronized with light pulse source in separate image frames, which are divided into small interrogations areas. These interrogation areas are cross-correlated with each other, pixel by pixel, which produce a signal peak, identifying the particle displacement. Knowing the displacement and the time between two consecutive two image frames, the velocity is obtained with sub-pixel interpolation (Dantec Dynamics, 2011). Fig. 2 shows the experimental setup for the flow patterns visualization. A series of measurements in the azimuthal direction were performed. For each plane, the camera was positioned in such a way that it captured the motion in the desired plane. In order to obtain statistically robust results 300 individual images with the phase/locking technique was used. An electronic shutter was placed in the agitation shaft and connected to the visualization system in such a way that the position of the impeller with respect to the camera and the baffles was always the same. Table 1 shows the general experimental conditions used for this work. The Power number and the Reynolds number are, respectively, defined as follows Re =
ND2
(1)
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Fig. 1 – Mixing system: (a) General array; (b) Impellers (dimensions in mm).
Table 1 – Experimental conditions. Parameter
Maxblend
3
Specific power, P/V (kW/m ) Torque (N m) Dynamic viscosity, (mPa s) Rotational speed, n (rpm) Reynolds number, Re Power number, Po
2 PBT
2 Intermig
Series 1
Series 2
Series 1
Series 2
Series 1
Series 2
0.652 0.101 200 260 168 6.42
0.1 0.028 1 144 18,000 5.79
0.652 0.0732 200 360 204 2.42
0.1 0.0209 1 193 21,893 2.40
0.652 0.0617 200 427 266 1.45
0.1 0.01205 1 335 38,001 0.46
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Fig. 2 – Experimental setup and azimuthal scanning array. Po =
P N3 D5
(2)
where and are the fluid density in kg/m3 and the fluid dynamic viscosity in Pa s, respectively, N is the impeller speed in rps, D is the impeller diameter in m and P is the power draw by the impeller in W. Although the flow field inside the mixing tank is tridimensional, only the velocity fields in the r–z direction are measured and discussed. In fact, the main flow occurs in the azimuthal direction because the main thrust of the impeller induces motion in this direction. However, as shown below, an enhanced mixing capacity results from impellers that are capable of inducing radial or axial (vertical) flow velocities. Therefore, our analysis is aimed to understand how these r–z currents are modified for different impeller designs.
3.
Results
Fig. 3 shows a typical flow field obtained in the r–z plane for the Maxblend impeller for a Reynolds number of 18,000. As described above, measurements were obtained for several angular positions; the figure shows the velocity field obtained at an angle of 45◦ . The recirculating nature of the field induced by the impeller is noteworthy: near the top and bottom of the impeller, two large vortices are observed, which induced large vertical currents. An important downward flow is observed near the center of the tank. By analyzing and comparing velocity fields like these, produced with different impellers, the effectiveness of the flow patterns to induce good pumping characteristics will be assessed. In Fig. 4, other flow measurements obtained with the PIV system are shown. All quantities are shown in dimensionless form considering Vtip , 2Vtip /T and Vtip (respectively, for the velocity magnitude, the vorticity and the turbulent intensity). From the vector field, the magnitude of the velocity in the (r, z) plane can be calculated as: V=
Vr 2 + Vz 2
(3)
Fig. 4(a) shows the map of velocity magnitude for the flow field shown in Fig. 3.
Fig. 3 – Typical velocity field for a r–z plane at 45◦ for the Maxblend impeller.
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Fig. 4 – Flow fields of the Maxblend impeller: (a) velocity magnitude; (b) vorticity; (c) turbulence intensity. The azimuthal component of the vorticity field, ω , can be obtained calculating the curl of the r–z vector field: ω =
∂Vr ∂Vz − ∂z ∂r
(4)
The vorticity indicates the rate of fluid rotation and large vortices show the regions in which vortexing is important. The vorticity field is shown in Fig. 4(b). Two large vortical structures can be readily identified, near the top and bottom of the impeller, which indicates that the fluid is changing direction from downwards (near the center of the tank) to upwards (in the region between the end of the impeller and the tank wall). Another important quantity that can be inferred from our experimental measurements is the magnitude of velocity fluctuations. As our system is angle-resolved (phase locking technique), measurements of the velocity field can be obtained once every cycle of rotation of the impeller, always in the same angular position. In this manner, a statistically converged measurement can be obtained by averaging many measurements (in our case, up to 500 measurements). In addition to the average velocities, the variance of velocity of the data set can be calculated, which provides a measure of the turbulence intensity through
TI =
Vr 2 + Vz 2 Vtip
(5)
where Vr 2 and Vz 2 are the fluid velocity variance in the horizontal and vertical directions at each (r, z) position, respectively, and Vtip is the impeller tip velocity. In Fig. 4(c) the turbulence intensity field is shown. The largest velocity fluctuations are observed to occur near the bottom of the tank, were the largest solid surface of the impeller is placed. Throughout the tank, significant values of turbulence intensity are observed.
3.1. Angular distribution of the velocity field for the Maxblend impeller The measurements obtained for the Maxblend impeller at different angular positions are shown in Fig. 5. This case corresponds to the Maxblend impeller at Re = 18,000. The shape of the impeller is represented with dashed lines. The horizontal and vertical dimensions (r and z, respectively) are normalized using the radius of the tank (T/2). The color scale shows the velocity magnitude normalized by Vtip . The velocity field clearly changes with the angular distance from the impeller. The largest values of the velocity appear immediately after the passage of the impeller (angle = 0◦ ), which are close to 0.8 that of Vtip . At 90◦ , when the measuring plane is perpendicular to the impeller, the velocity is the smallest in the tank. For larger angles, the velocity increases again, as the fluid is now being pushed by the impeller. At all angles, large recirculations and vertical currents are observed. The case shown in the figure corresponds to the large value of the Reynolds number investigated; for the experiments conducted at a smaller Reynolds number (Re = 168), the velocity field does not change significantly with angle from the impeller. Based on this observation, from now we will consider in the forthcoming only one angle (45◦ ) to conduct comparisons of the nature of the flow induced using different impellers.
3.2.
Comparison of the flow induced by three impellers
A direct comparison of the flow induced in the tank using the three impellers investigated is now shown. The comparison is also made in terms of the power drawn by the impellers for the two values of Reynolds number. Fig. 6 shows velocity magnitude fields for the three impellers in the turbulent and transitional regimes. In such a figure it should be noted the shape of the impeller is shown with dashed lines, the horizontal and vertical dimensions
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Fig. 5 – Velocity magnitude fields of the Maxblend impeller for r–z plane for several angles. (r and z, respectively) are normalized using the radius of the tank (T/2) and the color scale shows the velocity magnitude normalized by Vtip . The velocity induced in the fluid phase is larger for the case of the Maxblend impeller for both levels of the Reynolds number. A large recirculation loop is observed, with an important downward flow near the center of the tank. For the Intermig and tandem PBT impellers, significant velocity is observed in both cases in the regions near the impeller. Vortical structures and recirculation regions appear but they do not extend further away from the impeller. For the three impellers, the normalized liquid velocities (|V|/Vtip ) are larger for the low Reynolds number tests. One characteristic of the flow field that indicates that a good mixing rate will be achieved is the vertical velocities induced in the tank. These currents will transport fluid from the bottom to the top of the tank and vice versa. In Fig. 7, maps of vertical velocity are shown for the three impellers in the turbulent and transitional regimes. In Fig. 7 the shape of the impeller is shown with dashed lines, the horizontal and vertical dimensions (r and z, respectively) are normalized using the radius of the tank (T/2) and the color scale shows the velocity magnitude normalized by Vtip . In general, the Maxblend
impeller induces larger vertical currents than the other two impellers. These currents are both larger in magnitude and in extent. Both the Intermig and PBT impellers induce vertical currents but these have a significant magnitude only near the impeller. The Maxblend induces a very significant downward motion near the center of the tank. To further analyze this behavior, curves of the vertical velocity profile as a function of the radial distance are presented in Fig. 8. Several vertical positions were selected which correspond to the location where the impellers have an immediate interaction with the surrounding fluid. Once again, it is very clear that the vertical currents induced by the Maxblend impeller are much larger than those produced especially by the tandem PBT. Also, the vertical currents are significant for different vertical positions in the tank. On the other hand, for the other two impellers, the vertical currents are nearly absent in regions not close to the position where the impeller passes. In the next section, we will show an averaged spatial measure of these currents. Finally, the other relevant desirable characteristic of the flow induced by a particular impeller design is the capacity to induce velocity fluctuations. It is well known that
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Fig. 6 – Velocity magnitude fields for r–z plane: (a) Maxblend in turbulent regime; (b) 2 Intermig in turbulent regime; (c) 2 PBT in turbulent regime; (d) Maxblend in transitional regime; (e) 2 Intermig in transitional regime; (f) 2 PBT in transitional regime. fluctuations promote mixing (Ottino, 1989). For large Reynolds number flows these fluctuations arise naturally from the turbulent nature of the flow. For small to moderate Reynolds number, however, fluid fluctuations must be induced by using baffles. These “obstructions” cause azimuthal variations in the flow streamlines, which in turn, induce velocity fluctuations. Fig. 9 shows the fields of turbulent intensity (as defined above) for the three impellers in the flow regimes investigated. In such a figure, the shape of the impeller is shown
with dashed lines and the horizontal and vertical dimensions (r and z, respectively) are normalized using the radius of the tank (T/2). The color scale shows the normalized turbulent intensity. Note that each image has its own scale. The Maxblend produces larger velocity fluctuations for both moderate and large Reynolds number flows. The Intermig impeller does not produce significant values of turbulent intensity. Moderate values of fluid fluctuation are observed for the PBT impeller.
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Fig. 7 – Vertical velocity fields for r–z plane: (a) Maxblend in turbulent regime; (b) 2 Intermig in turbulent regime; (c) 2 PBT in turbulent regime; (d) Maxblend in transitional regime; (e) 2 Intermig in transitional regime; (f) 2 PBT in transitional regime.
In summary, the Maxblend has been shown to exhibit a better flow distribution, being this effect more evident for a specific power consumption of 0.652 kW/m3 : it induces larger vertical currents and it generates much larger values of fluid fluctuation especially for moderate Reynolds number flows.
3.3.
Analysis of results
In order to obtain a quantitative assessment of the performance of the different mixing devices, the following quantities are defined. As observed previously, since an enhanced mixing is a result of the vertical currents induced by
the impeller it is proposed to measure an average value of the absolute value of the vertical velocity component in the tank. The mean absolute value of the vertical velocity is defined as
Vz∗
1 = RH
R
H
|Vz |dzdr 0
(6)
0
where R and H are the radius and height of the tank, respectively, and |Vz | is the absolute value of the vertical fluid velocity at each point of the measuring plane (r, z). This quantity measures the fluid vertical motion, either upwards or downwards, in each plane; it is a single value that quantifies how much vertical motion is induced by a particular
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Fig. 8 – Vertical velocity profiles for different values of the vertical coordinate, 2z/Dc: (a) Maxblend in turbulent regime; (b) 2 Intermig in turbulent regime; (c) 2 PBT in turbulent regime; (d) Maxblend in transitional regime; (e) 2 Intermig in transitional regime; (f) 2 PBT in transitional regime. impeller design. Furthermore, the measurements obtained in each plane can be averaged to obtain a bulk measure of Vz∗ . In Table 2, the value of Vz∗ is shown for each of the three impellers tested in this study and for the two power consumption values (corresponding to large and moderate Re numbers). The results are normalized by the impeller tip speed in each case. The vertical motion induced by the Maxblend impeller is significantly stronger than the PBT and the
Intermig mixers. By presenting the results in a dimensionless manner, the comparison is fair based on the concepts of modeling theory (Barenblatt, 2003). If the comparison is conducted in dimensional terms, one must do so keeping the Power number equal in both cases. In our investigation this parameter was indeed keep constant; the axial velocities, in dimensional terms, are higher for the case of the Maxblend impeller.
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Fig. 9 – Turbulent intensity fields for r–z plane: (a) Maxblend in turbulent regime; (b) 2 Intermig in turbulent regime; (c) 2 PBT in turbulent regime; (d) Maxblend in transitional regime; (e) 2 Intermig in transitional regime; (f) 2 PBT in transitional regime.
Table 2 – Results. Vz∗ /Vtip
∗ /V Vturb tip
Nq
144 260
0.123 0.273
0.107 0.192
1.59 1.67
0.1 0.652
193 360
0.039 0.030
0.039 0.011
0.65 0.77
0.1 0.652
335 427
0.013 0.017
0.015 0.004
0.13 0.38
Impeller
P/V (kW/m3 )
Maxblend
0.1 0.652
PBT
Intermig
Re
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Another important factor to ensure rapid and efficient mixing rates is the level of velocity fluctuations induced in the tank. At large Reynolds numbers, these fluctuations are readily related with the turbulent nature of the flow; at low Reynolds, on the other hand, fluctuations are induced by the tortuous path of the fluid particles imposed by the baffles and the impeller geometry. In either case, large fluctuations are preferred as they contribute to the mixing process. Hence, from the PIV measurements reported above, a bulk measure of the fluid fluctuations in the tank is proposed. The mean fluctuating velocity is defined as
1 RH
∗ = Vturb
R
H
(Vz 2 + Vr 2 )dzdr 0
(7)
0
where Vz 2 and Vr 2 are the fluid velocity variances in the vertical and horizontal directions, respectively. These quantities were calculated by considering a time series of instantaneous fluid measurements in several planes. It is observed that, under the same nominal conditions, the Maxblend impeller also induces larger values of the fluctuating velocity. This indicates that this impeller produces faster mixing rates because of the combined action of the induced vertical velocity and turbulent-like velocity fluctuations. On the other hand, the pumping capacity of the impellers used in the present work was also investigated in terms of the pumping number (Nq), which is defined by Nq =
Qv ND3
(8)
where Qv is the total volumetric flow rate in m3 /s, N is the rotational speed in rps and D the impeller diameter in m. The pumping number is a classical indicator of the pumping capacity. The total volumetric flow rate is defined by the following expression:
Qv =
z++
z−−
D|(v0r )r=r++ |dz +
r++
2r|(v0z )z=z++ |dr 0
z++
+ z−−
2r|(v0z )z=z−− |dr
(9)
Here z++ , z−− and r++ refer all to the virtual boundaries of the control volume surrounding the impeller. The superscript “0” is the fluid flowing out from such a control volume. The reader is referred to Hidalgo-Millán et al. (2011) for a detailed description of the method. For that purpose, the volumetric flow rate leaving the turbine blades is calculated as the average of flow rates at the different azimuthal positions every 20◦ . The reader is referred to Hidalgo-Millán et al. (2011) for detailed description of the method employed to calculate the pumping number. As Table 2 shows the best pumping capacity is obtained with the Maxblend impeller in both flow regimes, while the two Intermig impellers exhibit the lowest pumping capacity. One should recall the experiments were made under a specific power consumption, so the pumping capacity is a good parameter for comparing the hydrodynamic performance of the impeller investigated.
3.4.
Interpretation
As shown above, by the extensive experimental evidence, the overall performance of the Maxblend impeller is much better
Fig. 10 – Schematic representation of flow patterns around the Maxblend.
that the other two impellers considered in this study. Nevertheless, the question remains: why is the Maxblend impeller better? The Maxblend design induces vertical currents, which are mainly responsible from circulating fluid from the top to the bottom of the tank. The physical mechanism that induces these vertical currents is very different from that obtained with more common impellers. Common impellers, like the Intermig and PBT, induce, mainly, radial and axial flows by the moving action of their blades. The outwards fluid motion (the fluid current expelled by the centrifugal acceleration) is then deflected by tank walls and the baffles. The deflection, in turn, produces the fluid motion in the vertical direction. On the other hand, the Maxblend does not produce significant radial or axial fluid motion directly. The pumping effect and centrifugal acceleration imposed to the surrounding fluid in minimal. The physical mechanism that induces the vertical motion is depicted schematically in Fig. 10. The lower part of the impeller is essentially a solid surface. If we suppose that the impeller is rotating in a clockwise direction, as shown in the figure, in the right part of this surface a low pressure region appears. Low pressure regions appear behind objects in uniform flows, resulting from the fluid inertial effects. From moderate to large Reynolds numbers, these low pressure regions are generally associated with large recirculation zones, which is in good agreement with the findings reported by Iranshahi et al. (2007), who observed large vortex generated by the Maxblend having a similar geometry of the one used in the presented work. They reported a good hydrodynamic performance of the Maxblend impeller when operated in a baffled vessel under the transition regime. In the present case the pressure is higher in the left part of the surface and the top of the impeller. Additionally, the fluid is also pushed by the forward motion of the impeller in the left side. The combined action of the pressure gradients and the driving action of the impeller induces that the fluid circulates from top to bottom. This idea is supported by the PIV measurement: the region in which the largest down-ward motion is observed is indeed that in the lower right part of the impeller. Therefore, the vertical motion in the Maxblend is a result of pressure gradients induced by the particular geometry of the impeller; this mechanism is very different from that in ordinary impellers. The disadvantage that this particular design may have is that dragging a solid surface across a flow induces large drag forces which, in turn, would result in large power consumptions. The slotted nature of the upper part of the
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Maxblend impeller reduces the drag and also promotes the formation of pressure gradients.
4.
Conclusions
The straight Maxblend has been hydrodynamically evaluated and compared with a double coaxial impeller array by using the particle image velocimetry. Results of the flow fields showed that the double impeller array with both the PBT and the Intermig impellers induce local radial and axial flows in the vicinity of the each impeller. On the other hand, the straight Maxblend behaves much better in terms of the fluid circulation in the vertical direction as a result of the large pressure gradients and the driving action of the impeller.
Acknowledgements The financial support from DGAPA-UNAM through grant IN117908 is highly appreciated. A. Hidalgo thanks the Program of Master and Doctorate in Engineering, UNAM and CONACyT for the scholarship provided during his PhD studies.
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