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Effect of the geometry on the performance of the MaxblendЩ impeller with viscous Newtonian fluids.

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ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING
Asia-Pac. J. Chem. Eng. 2009; 4: 528–536
Published online 14 May 2009 in Wiley InterScience
(www.interscience.wiley.com) DOI:10.1002/apj.275
Special Theme Research Article
Effect of the geometry on the performance of the
Maxblend impeller with viscous Newtonian fluids
Yoann Guntzburger,1 Louis Fradette,1 * Maya Farhat,1 Mourad Héniche,1 Philippe A. Tanguy,1 and
Katsuhide Takenaka2
1
2
URPEI, Department of Chemical Engineering, Ecole Polytechnique, P.O. Box 6079, Station CV, Montréal, Canada H3C 3A7
SHI Mechanical & Equipment Inc., Ehime, Japan
Received 26 September 2008; Revised 10 January 2009; Accepted 11 January 2009
ABSTRACT: Experimental and numerical investigations have been carried out to assess the effect of the vessel
geometry (number of baffles) and the shape of the Maxblend impeller (configuration of the bottom paddle and angle of
the upper grid) with viscous Newtonian fluids in the laminar and lower turbulent mixing regimes. Two parameters have
been explored namely the power consumption of the impeller and the mixing time. Videos of the discoloration process
have also been taken to get access to the mixing patterns. A nominal 50-l vessel has been used in the experiments. The
number of baffles has been varied from 1 to 4, and the bottom paddle has been modified by making openings to allow
flow passage. Finally, the effect of using a straight grid in the upper part of the Maxblend has been studied under the
same conditions. It is shown that the number of baffles does not have a significant effect on the power consumption,
the mixing evolution, and the mixing time regardless of the flow regime. Making openings in the bottom paddle allows
for the destruction of the segregated zones at the bottom of the tank at the expense of a very slight increase in power
consumption and mixing time. Finally, the power and mixing time are both increased with a straight grid Maxblend.
 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
KEYWORDS: mixing time; power consumption; modified Maxblend ; Newtonian; viscous fluid
INTRODUCTION
Mixing in vessels is a very common operation in
industrial processes. It consists of homogenizing a
medium by the mechanical action provided by one
(or more) rotating impeller. In recent years, several
new impellers have been proposed to handle widely
varying viscosity situations characterized by a change
of mixing flow regime (usually from turbulent to
laminar) over the course of the process.[1] To address
such a requirement, the Maxblend impeller (Sumitomo
Mechanical Equipment, Ehime, Japan), presented in
Fig. 1, seems to be one of the most efficient impeller
of the new generation. It is composed of a large
bottom paddle, which acts as a pump, and an upper
grid providing a capacity of dispersion as well as a
top-to-bottom guiding mechanism. The impeller bottom
clearance is critical for the flow circulation.
Several numerical and experimental investigations on
the performance of the Maxblend impeller have lately
appeared in the literature,[2,3] which have shed some
*Correspondence to: Louis Fradette, URPEI, Department of Chemical Engineering, Ecole Polytechnique, P.O. Box 6079, Station CV,
Montréal, Canada H3C 3A7. E-mail: louis.fradette@polymtl.ca
 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
light on the parameters that govern mixing efficiency.
In particular, it was found by Iranshahi et al .[4] that two
recirculation zones formed behind the bottom paddle in
the laminar regime (Fig. 2). It is important to eliminate
or at least control this phenomenon that can yield
possible segregations. Other missing information for
design purposes is the “optimal” number of baffles
needed in the vessel. At present, the two options
suggested by the supplier are either 0 (no baffles) or
4 baffles.
The objective of this work is to provide answers to
these two issues. We propose to determine the impact
of the number of baffles and the geometry (straight or
wedge grid, bottom paddle) on the mixing performance
of the Maxblend impeller. By performance, we mean
the power consumption, the mixing time and the flow
pattern in the laminar, transition and low turbulent
regime with single-phase Newtonian fluids.
MATERIALS AND METHODS
The original Maxblend design (Fig. 1) was not designed
to work in the deep laminar regime. This was the
motivation to investigate the possibility to improve its
Asia-Pacific Journal of Chemical Engineering
EFFECT OF THE GEOMETRY ON THE PERFORMANCE OF THE MAXBLEND
Figure 1. Wedge Maxblend impeller.
behavior at low Re by slight geometrical modifications
and in the mean time to maintain its very good performance at higher Re. Prior to experimental investigations, computational fluid dynamics (CFD) analysis
has been conducted to rapidly assess the blending efficiency in deep laminar regime of several Maxblend
prototypes using computer-aided-design and trial-error
runs. To speed-up the calculations only the unbaffled
configuration was considered in the calculations since
it enables to perform steady-state simulations using the
classical Lagrangian frame of reference technique. The
numerical investigations were carried out for a Re value
(a)
ranging from 20 to 70 using the finite element software Poly3D (Rheosoft Inc). The details of the CFD
methodology are discussed in Iranshahi et al .[4] Using
the computed velocity field at Re = 40, the potential of
dispersion of each design was evaluated using a cluster
of 5000 tracers that was injected in the unmixed lower
region (Fig. 2). The two designs retained in this work
(see Fig. 3(a)-(b)) were found the most efficient.
The first geometry shown on Fig. 3 is called
Maxblend modified N◦ 1 and presents small apertures
accounting for 1/3 of the paddle surface. The second one
is called Maxblend modified N◦ 2 and presents larger
openings, about 2/3 of the bottom paddle surface. The
size of the holes is limited by the connection points that
link the impeller to the shaft and also by the mechanical integrity of the Maxblend structure which has to be
maintained during the mixing of highly viscous fluids.
The shape of the Maxblend is known to influence
the overall pumping capability. The wedge shape is
reserved for viscous applications while the straight
shape is used in the turbulent regime. The study of a
straight Maxblend as illustrated in Fig. 4 will also be
presented in this article.
The experimental setup used in our experimental
work has already been described in Fradette et al .[3] .
The geometrical details of the four types of Maxblend,
i.e. the wedge Maxblend, the Maxblend modified N◦ 1,
the Maxblend modified N◦ 2 and the straight Maxblend
are given in Table 1.
The different impellers are actuated by a variable
speed motor (3.7 kW) allowing the rotational speed to
be varied between 0 and 120 rpm. The power consumption is derived from torque (Ono Sokki SS-201 and
SS-200, noncontact torque detector, 1% FS) and rotational speed measurements. The bottom clearance has
been set at 5 mm, the mixer design recommended value.
Considering the range of rotational speed and the
impeller dimensions, several Newtonian fluids were prepared in order to cover the laminar, transition and
(b)
Illustration of the recirculation zones: (a) experiments and
(b) numerical simulation. This figure is available in colour online at
www.apjChemEng.com.
Figure 2.
 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
Asia-Pac. J. Chem. Eng. 2009; 4: 528–536
DOI: 10.1002/apj
529
530
Y. GUNTZBURGER ET AL.
Asia-Pacific Journal of Chemical Engineering
(a)
(b)
Figure 3. Maxblend modified (a) N◦ 1 and (b) N◦ 2.
Table 1. Geometrical details of the different types of
Maxblend used.
Mixing
System
Wedge
Maxblend
Maxblend
modified
N◦ 1
Maxblend
modified
N◦ 2
Straight
Maxblend
Tank
Dimension
Impeller
T = 0.354 m D = 0.255 m C = 5.0 mm
H = 0.409 m
w = 0.026 m
V = 35.4 l
T = 0.354 m D = 0.185 m C = 5.0 mm
H = 0.409 m
w = 0.026 m
V = 35.4 l
Re =
ρND 2
µ
(2)
In the laminar regime, the Np – Re log–log plot
shows a straight line of slope −1, expressed as
Figure 4. Straight Maxblend.
low turbulent regimes. The fluids were based on an
aqueous glucose solution (Glucose Enzone 62DE, Univar). A viscometer (Bohlin Visco88 and TA-Instruments
AR2000) was used to determine the rheological properties of the Newtonian fluids. The density was measured
by precisely weighing (APX 402 scale, Denver Instrument) 10 ml of the aqueous solution.
In mixing, the power consumption of the agitator
is expressed as an Np – Re plot where Np and Re
are respectively the power and the Reynolds number,
defined as
Np =
Bottom
Clearance
p
ρN 3 D 5
(1)
 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
Np =
Kp
Re
(3)
The constant Kp , is used to scale the power consumption of an impeller. A slightly different equation can
also be used where a wider range of Re can be fitted:
Np =
KpT
+ NpT
Re
(4)
where NpT is the value taken by Np when Re → ∞. The
numerical values of KpT and NpT have been obtained
by a weighted least square regression. Each data point
was weighted according to the error on the torque
Asia-Pac. J. Chem. Eng. 2009; 4: 528–536
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
EFFECT OF THE GEOMETRY ON THE PERFORMANCE OF THE MAXBLEND
measurement. As a general rule, the measurements
made at low speed are all less accurate than the ones at
higher revolution speeds because low torque values are
more prone to uncertainty.
In cases where the weighted regression is made on
the laminar regime data only, NpT value is forced to 0
and so KpT = Kp .
It is essential to calibrate the torquemeter accurately
to obtain reliable measurements. This was carried out
by applying known torques to the impeller shaft. The
residual torque from the two bearings guiding the shaft
was systematically removed from the measured torque
value.
(5)
Mc = Mm − Mr
where Mc is the corrected value, Mm , the measured
value and Mr , the residual value. The corrected torque
value was used to calculate the power dissipated by the
agitator using:
(6)
P = 2 π NMc
The method developed by Cabaret et al .[5] based on
advanced image analysis has been selected to characterize the mixing time. To this end, the cylindrical mixing
tank was inserted in a rectangular water-filled chamber in order to minimize the optical distortions due
to the curvature of the tank. A digital video camera
linked to a computer was used to record the mixing process evolution (Digital Handycam DCR-PC101, Sony).
The indicator used was purple bromocresol (0.08% w/w
aqueous solution). With this indicator, the color of a
basic solution is purple, and it turns to yellow when the
pH becomes acidic. The color evolution from purple to
yellow was chosen because it is far easier and more reliable to detect purple unmixed areas in a yellow medium
that the opposite. The basic glucose aqueous solution
was obtained by adding a NaOH solution (10 mol/l)
drop by drop until the characteristic purple color was
reached. Then, concentrated chloride acid (10 mol/l)
was mixed with a tank sample of the glucose solution
at the ratio of 1 ml of acid for 10 l of stirred solution.
The acidic mixture of glucose solution was then poured
in the tank during the video recording. The temperature
in the vessel had to be checked regularly. In fact, the
shearing as well as the successive acid-base reaction
may increase the temperature which has a direct effect
on the viscosity of the solution.
The video was sampled frame by frame and analyzed
using in-house image analysis software coded in java.
The software analyzes each pixel of the frame and
determines the intensity of the green color of the RedGreen-Blue model. This intensity is then compared to
the threshold value for discoloration, which is defined
as half the sum of the green intensity of pixel ij in the
first frame and pixel ij in the last frame (1 < i < 512,
1 < j < 256). The mixing evolution curve reports in
percentage the proportion of discolored pixels as a
 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
function of time. The mixing time is defined as the
time necessary to reach a discoloration rate above a
chosen percentage. In our experiments reported here,
this threshold was set at 99% discoloration. An example
of typical mixing evolution curve is presented in Fig. 5
along with the determination of the mixing time at 99%
discoloration.
Cabaret et al .[5] demonstrated that this method is
robust to uneven illumination and operators errors, has
a high degree of reliability and repeatability, and the
possible consideration of unmixed zones can yield an
accurate mixing time.
The plot of the mixing energy vs. the Reynolds
mixing time is an additional measure suggested for
the comparison of impellers. ReMT and dimensionless
mixing energy EM are defined respectively as:
ReMT =
EM =
ρT 2
µtm
Ptm2
µT 3
RESULTS AND DISCUSSION
Impact of the number of baffles
Figure 6 shows the Newtonian power curve for the 1, 2
and 4 baffled Maxblend standard wedge impeller. The
power number (Np ) is defined following Eqn 1 and the
Reynolds number (Re), with Eqn 2. The Kp value was
found to be very similar for the three baffled systems.
This result was expected, the velocity field being little
affected by the baffles presence in the laminar regime.
While not shown here, error bars for some points could
reach up to 100% of the Np value. This is explained
by the fact that the torque measured at low speed with
Typical mixing evolution curve. This figure is
available in colour online at www.apjChemEng.com.
Figure 5.
Asia-Pac. J. Chem. Eng. 2009; 4: 528–536
DOI: 10.1002/apj
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532
Y. GUNTZBURGER ET AL.
Asia-Pacific Journal of Chemical Engineering
Figure 6. Power curves for Newtonian fluids with 1, 2 and
4 baffles in the laminar regime.
Figure 8. Analysis window (
) for image processing
excluding recirculation areas ( . . . . . ). This figure is available
in colour online at www.apjChemEng.com.
Figure 7. Complete power curves for Newtonian fluids with
2 and 4 baffles.
lower viscosity fluids did not allow for a reliable torque
value to be measured. Consequently, the Kp values
obtained for the three configurations can be considered
as one single value.
Figure 7 illustrates the power draw for the 2 and 4baffled systems in the laminar and low turbulent regime.
Not surprisingly, the power draw appears less important
with the 2-baffled system once the transient regime is
reached.
The mixing times were obtained by the method
developed by Cabaret et al .[5] This method requires the
analysis of an area of the vessel as illustrated in Fig. 8.
This area excludes the bottom of the vessel. Thus, the
mixing time presented here scales the time required to
obtain a complete discoloration of the analysis window.
Figure 9 shows the mixing time curves for the 2 and 4baffled systems. The resolution of the method and the
resulting mixing times spread does not allow for a clear
or marked difference in performance between the two
configurations to be noticed.
 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
Figure 9. Comparative mixing time curves for Newtonian
fluids in 35.4 l with 2 and 4 baffles, laminar, transient and
turbulent regime.
Modified bottom paddle effect
We have already shown in Fig. 3 the two different
models of modified Maxblend. The dimension of the
holes as well as their best positioning was determined
by numerical simulations. Post-processing of the flow
fields allowed for the inspection for dead- or unmixed
zones by means of tracers in order to further validate
the flow field. The tracer numerical experiment with
the two new configurations and the standard geometry
is presented on Fig. 10.
From the numerical mixing experiments, both new
configurations appear to mix adequately and provide
better mixing than the standard wedge geometry. Following these results, experiments on the modified
Maxblend impellers have been done with a 2-baffled
vessel only. The power consumption and mixing time
Asia-Pac. J. Chem. Eng. 2009; 4: 528–536
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
(a)
(b)
EFFECT OF THE GEOMETRY ON THE PERFORMANCE OF THE MAXBLEND
(c)
t = 0s
Figure 11. Power curves for the wedge Maxblend, the
Maxblend modified N◦ 1 and 2 for Newtonian fluids with
2 baffles.
(b)
(a)
(c)
t = 5s
Table 2. Kp values obtained with the wedge Maxblend,
the Maxblend modified N◦ 1 and the Maxblend
modified N◦ 2 with 2 baffles.
Type of Maxblend
(b)
(a)
(c)
Wedge
Modified N◦ 1
Modified N◦ 2
Straight
Kp value
166
172
172
214
t = 20s
(a)
(b)
(c)
t = 35s
Simulation of the mixing evolution for the
modified Maxblend (a) N◦ 1, (b) N◦ 2 and (c) the wedge
Maxblend with an injection point in the dead zones
at Re = 40. This figure is available in colour online at
www.apjChemEng.com.
Figure 10.
curves associated to those impellers are shown in the
following figures.
As shown on Fig. 11, Kp values for each of impeller
tested are very similar. The numerical values are given
in Table 2. The NpT value is slightly less important for
the Maxblend modified N◦ 2 than for the N◦ 1. This
could be explained by the larger hole size with the N◦ 2
impeller. Trend lines equations are Np = 154.3 Re −1 +
1.64 and Np = 154.0 Re −1 + 1.47 respectively for the
Maxblend modified N◦ 1 and N◦ 2. Thus, the physical
modification made on the bottom paddle does not have
a significant effect on the power draw of the mixer.
The slight difference observed in the laminar regime
shows that the modified Maxblend impellers bring
 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
Figure 12. Mixing time curves for the wedge Maxblend,
the Maxblend modified N◦ 1 and 2 for Newtonian fluids
with 2 baffles.
a potential mixing energy that is beneficial for the
medium homogenization at low Reynolds. The same
conclusion on the mixing time can be made from
Fig. 12 as the three different mixers provide about the
same mixing efficiency. Therefore, as illustrated by
the comparison of pictures of Fig. 13, the recirculation
zones in the bottom paddle region are not longer present
with the modified designs. This result confirms the
numerical prediction of Iranshahi et al .[4]
Asia-Pac. J. Chem. Eng. 2009; 4: 528–536
DOI: 10.1002/apj
533
534
Y. GUNTZBURGER ET AL.
(a)
Asia-Pacific Journal of Chemical Engineering
(b)
(c)
Figure 13. Comparison of homogeneity at Re = 12 for the (a) wedge Maxblend, (b) the
Maxblend modified N◦ 1 and (c) N◦ 2 with 2 baffles after 3 min of mixing. This figure is available
in colour online at www.apjChemEng.com.
Figure 14. Power consumption curve for the wedge and
the straight Maxblend.
Figure 15. Mixing times curves for the wedge and the
straight Maxblend.
Effect of the upper grid geometry
The Kp value of the straight grid Maxblend is presented in Table 2, whereas Figs. 14 and 15 compare
respectively the power draw and the mixing times.
The Kp value measured experimentally for the straight
grid impeller was roughly 25% higher than the wedge
design. This difference originates from the smaller
diameter of the straight compared to the slant grid. The
results shown here also demonstrate the efficiency of the
larger impeller at putting the fluid in motion effectively
without using more energy than smaller impellers.
Figure 15 shows that the straight Maxblend yields
longer mixing times than the wedge design. This phenomenon could be explained as follows: the discoloration method used here is based on a window from
which the bottom part of the vessel is excluded, as illustrated on Fig. 8. Under laminar flow regime conditions,
the straight Maxblend generates segregated areas at the
top, at the bottom of the impeller and along the shaft, as
illustrated in Fig. 16(a). The lower recirculation zones
move upward in the tank and appear at mid-height of
the mixer when the Re is closer to the laminar-transition
 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
regime [Fig. 16(b)]. The zones completely disappear if
agitation is maintained long enough or when the flow
regime is brought in the transitional regime [Fig. 16(c)].
Contrary to the wedge case, these recirculation areas
appear in the window analyzed during image analysis
and hence result in longer discoloration times for the
straight geometry. For Re = 14, as shown on Fig. 17,
90% of the discoloration is reached after 53 s for the
straight Maxblend and 43 s for the wedge one. On the
same curve, a threshold of 99% is reached after 67 s for
the straight Maxblend and 48 s for the wedge one, i.e.
two times the difference seen at 90% discoloration. That
means that the parameters set to determine the mixing
time has a direct influence on the efficiency found for an
impeller. If the straight Maxblend is still less efficient
if the mixing time is set after 90% of discoloration, its
efficiency is more comparable to the wedge one.
Figure 18 presents the mixing energy as a function of
the ReMT , allowing for the combined analysis of power
and mixing time. It shows that the three experimental
designs of the Maxblend impeller used here consume
Asia-Pac. J. Chem. Eng. 2009; 4: 528–536
DOI: 10.1002/apj
Asia-Pacific Journal of Chemical Engineering
(a)
EFFECT OF THE GEOMETRY ON THE PERFORMANCE OF THE MAXBLEND
(b)
(c)
Figure 16. Illustration of the segregated zones obtained with the straight Maxblend at three
different Re: (a) Re = 14, (b) Re = 45 and (c) Re = 60. This figure is available in colour online
at www.apjChemEng.com.
Figure 17. Mixing evolution curves for the straight Maxblend and the wedge
Maxblend.
CONCLUSION
Figure 18. Mixing energy for the wedge Maxblend, the
Maxblend modified N◦ 1, the Maxblend modified N◦ 2 and
the straight Maxblend.
very similar amount of energy yielding overall similar mixing performances. However, both the modified
designs avoid the generation of the bottom recirculation
zones as observed with the original wedge design.
 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
The effect of the geometry on the performance of
the Maxblend impeller was investigated experimentally
with Newtonian fluids. The number of baffles in the
vessel was not found to have an impact, neither on
the power consumption nor on the mixing time in the
laminar regime. The power draw in the transient and
turbulent regime seems to be less important with 2
baffles but yields the same mixing time than with 4
baffles. The use of only 2 baffles for the industrial
application should be recommended. The recirculation
areas observed under certain conditions of viscosity
with the wedge Maxblend can be removed by making
openings in the bottom paddle. While a slightly higher
torque is observed with this modified paddle, these
alterations do not have a significant impact on the
mixing energy. The size and location of the holes was
determined by numerical simulations and were limited
in size in order to maintain the physical integrity of
the impeller. Grid shape has a direct impact on the
power consumption. The straight grid used generated
peripheral dead zones at specific flow regimes and
Asia-Pac. J. Chem. Eng. 2009; 4: 528–536
DOI: 10.1002/apj
535
536
Y. GUNTZBURGER ET AL.
Asia-Pacific Journal of Chemical Engineering
thus adversely affected the mixing times. Finally, the
modified geometries proposed here utilize the same
mixing energy than the standard wedge Maxblend while
avoiding the creation of unmixed volumes.
NOMENCLATURE
Symbol
D
T
N
P
tm
V
µ
P
Kp
Np
Re
ReMT
EM
Description
Units
Impeller diameter (Fig. 2)
Tank Diameter (Fig. 2)
Rotational speed
Power
Mixing time
Volume
Newtonian viscosity
Density
Impeller power constant
Power number
Reynolds number
Reynolds mixing time
Dimensionless mixing energy
(m)
(m)
(rps)
(W )
(s)
(m 3 )
(Pa.s)
(kg/m 3 )
(−)
(−)
(−)
(−)
(−)
 2009 Curtin University of Technology and John Wiley & Sons, Ltd.
REFERENCES
[1] K. Yamamoto, K. Abe, A. Tarumoto, K. Nishi, M. Kaminoyama,
M. Kamiwano. Journal of Chemical Engineering of Japan,
1998; 31(3), 355–365.
[2] C. Devals, M. Heniche, K. Takenaka, P.A. Tanguy. Computers
and Chemical Engineering, 2008; 32(8), 1831–1841.
[3] L. Fradette, G. Thome, P.A. Tanguy, K. Takenaka. Chemical
engineering research and design, 2007; 85, 1514–1523.
[4] A. Iranshahi, C. Devals, M. Heniche, L. Fradette, P.A. Tanguy,
K. Takenaka. Chemical Engineering Science, 2007; 62,
3641–3653.
[5] F. Cabaret, S. Bonnot, L. Fradette, P.A. Tanguy. Ind Eng Chem
Res, 2007; 46(14), 5032–5042.
Asia-Pac. J. Chem. Eng. 2009; 4: 528–536
DOI: 10.1002/apj
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