Investigation of Flow Patterns in Continuous-flow
Stirred Vessels by Laser Doppler Velocimetry
Paul Mavros1*, Catherine Xuereb2, Ivan Fořt3 and Joël Bertrand2
1
2
3
Department of Chemistry, Aristotle University, Thessaloniki, Greece
Laboratoire de Génie Chimique, ENSIACET, Toulouse, France
Department of Chemical and Food Process Equipment & Design, Czech Technical University, Prague, Czech Republic
T
he design and geometrical configuration of a stirred vessel is
usually geared to some specific process. For example, batch stirred
tanks usually have their outlet located at the bottom of the vessel,
to facilitate emptying and cleaning. In continuous-flow stirred vessels, on
the other hand, the outlet is located often at mid-height, or the liquid
exits by overflowing, as is the case with flotation cells.
Ideally, one should be able to use an optimally-designed stirred vessel
for a specific task. However, in real life, it is often necessary to make use
of a given stirred tank for a variety of recipes, and its configuration may
lead to flow pathologies and sub-optimal process performance. For
example, the inlet tube is often positioned close to the turbine, so that
the entering liquid is fed straight into the liquid being drawn in the
agitator-swept region. In a bottom-outlet vessel, one would expect, even
intuitively, that this might lead to short-circuiting.
One way to investigate the appropriateness of a particular design is by
determining its effect on the flow patterns in the stirred vessel. However,
most of the work published so far is related to batch cases — see Mavros
and Bertrand (2002) and Mezaki et al. (2000), among others. On the
other hand, although continuous-flow stirred cells have been used for an
extremely long time – a plate in Agricola’s De Re Metallica (1556) depicts
a set of stirred tanks connected on series – there is relatively little work
published on the flow patterns in continuous-flow stirred vessels.
Recently, flow patterns have been determined by laser Doppler
velocimetry in continuous-flow stirred tanks for a radial-flow turbine
(Alliet et al., 2001) and for an axial-flow impeller (Mavros et al., 1997, 2000,
2002; the latter also contains a review of the recent relevant literature).
In this work, the effects of the position of the inlet and of mean
residence time of the flow-through liquid on the flow pattern are studied
by laser Doppler velocimetry (LDV) for a standard-configuration agitated
vessel equipped with a Rushton turbine, in order to determine possible
flow problems and the limits of vessel operability.
Experimental Apparatus and Procedure
The LDV measurements were taken in a fully-baffled (b = T/10) cylindrical
vessel (T = 0.19 m), with a dished bottom (with a curvature radius R = 0.19 m).
The height of the liquid (tap-water) in the vessel (H) was kept constant
at 0.19 m, resulting in a liquid volume (VL) of 5.15 ¥ 10–3 m3. The vessel
was located inside a square transparent box, with a high-quality optical
The flow structure of a continuous-flow reactor
stirred by a Rushton turbine was investigated by laser
Doppler velocimetry for two different mean residence
time-mixing time ratios. Velocity measurements were
obtained for two inlet locations, corresponding to the
incoming liquid stream being fed co-currently or
counter-currently to the flow discharged by the
turbine. In all investigated configurations and for all
operating conditions, it was found that the flow
disruption caused by the incoming liquid stream was
observable mainly in the first vessel quarter, which
followed the feed-tube plane. From comparison of the
velocities encountered in the various planes in the
continuous-flow reactor to the velocities of the batch
reactor, it was also concluded that it may be possible
to intensify the usage of the turbine-stirred vessel by
decreasing the characteristic times ratio, without
considerable flow by-pass and/or short-circuiting
problems.
Les écoulements dans une cuve agitée par une
turbine de Rushton opérant en mode continu ont été
étudiés par vélocimétrie à rayons laser à effet Doppler,
pour le cas de deux taux de temps de résidence /
temps de mélange. Les champs de vitesses ont été
obtenus pour deux points d’alimentation, l’un
introduisant le liquide dans le courrant d’aspiration de
la turbine, et l’autre à contre-courrant du jet sortant
du coté des pales de la turbine. Pour toutes les
configurations étudiées et tous les modes opératoires,
l’effet de la présence du jet d’alimentation du liquide
ont été observé surtout dans le quart de la cuve en
aval du plan du tube d’alimentation. La comparaison
entre les vitesses dans le cas de l’opération de la cuve
en mode « batch » et en mode continu avec la turbine
de Rushton a démontré qu’il serait possible d’intensifier
l’utilisation de la cuve agitée, en augmentant le débit
d’alimentation sans causer des problèmes aux
écoulements par court-circuit ou par déviations.
Keywords: mixing, agitation, continuous, stirred tank,
laser Doppler velocimetry, Rushton turbine, Mixel.
*Author to whom correspondence may be addressed. E-mail address: pmavros@
eng.auth.gr
The Canadian Journal of Chemical Engineering, Volume 80, August 2002
591
Figure 1. (a) Location of the inlet tubes and of the vessel outlet. (b-f)
Planes of LDV measurements (plan view); the small circle indicates the
position of the liquid feed tube. The inlet tubes are located at the mid-plane
between two adjacent baffles.
loop. In the second set of LDV measurements, the tube was
positioned so as to face the side of the Rushton turbine blades;
this is termed the ‘counter-current’ configuration, since the
liquid fed into the vessel opposes the liquid being ejected
sideways by the rotating turbine. In both cases, the liquid outlet
was located at the center of the dished bottom of the vessel.
The LDV apparatus (Dantec) had two laser beams, allowing
the simultaneous determination of two of the three velocity
components. From 35 to 89 points were measured in each of
the three planes: the feed plane, the one 90° in front, and the
one 180° in front of the feed plane (Figures 1b to 1f). At least
two thousand points were validated at each LDV measurement.
The flow was seeded periodically with small seed particles
[Iriodin 111 Rutile Fine Satin (Merck), dp = 15 mm].
The data yielded by the Flow Velocity Analyser were collected
and stored in a PC. The Floware software (v. 3.2) calculated
dynamically the mean velocity (Ui ) from the instantaneous fluid
velocity (ui ):
n
Ui = Â tkuik
glass (altuglass) window, which allowed the laser beams to
focus inside the stirred liquid with minimal distortion; the box
was also filled with tap-water.
The impeller used was a standard Rushton turbine (D = T/2),
located at a clearance of C = T/2 from the vessel bottom. The
shaft used for these measurements had an o.d. (dS) equal to
0.008 m, and extended to the bottom of the vessel. The agitator
rotation speed was held constant at N = 3 rps (= 180 rpm).
Liquid was fed into the vessel via a tube, with an i.d. of 10 mm
and an o.d. of 12 mm, positioned in the q = 45º plane (between
two adjacent baffles). In the first set of LDV measurements, the tube
was located above the impeller, with its tip 48 mm from the
liquid free surface and 11 mm from the agitator shaft (Figure 1a);
this is termed the co-current configuration, since the entering
liquid joins the liquid flowing in the upper primary circulation
k =1
n
 tk , i = r , z ,t
k =1
(1)
where r, z, and t refer to the radial, axial and tangential velocity
component, respectively. In this equation, the bias of the fast-moving
seed particles is accounted for by taking into consideration the
time (tk) spent by the particle inside the measuring volume.
It should be noted also that the calculated velocities include the
variations due to turbulence and to the periodic blade passage.
In continuous-flow processes, one major variable is the time
spent by the through-flowing liquid in the vessel; a typical
measure of this is the mean residence time (t). Usually, this is
chosen in relation to the mixing time, i.e., the time necessary
for the homogenization of the vessel contents. The latter has
been related to the vessel and agitator dimensions and the
power number (Po) (Ruszkowski, 1994; Nienow, 1997):
Figure 2. 2-D flow maps for the co-current liquid inlet (t/tM = 9.6) and comparison with the batch-case flow map (data taken from Mavros et al., 1996).
592
The Canadian Journal of Chemical Engineering, Volume 80, August 2002
Figure 3. Spatial distribution of 2-D composite velocity ratios (U *r z,cont / U *rz,batch) for the lower liquid feed flow rate in the co-current mode (t/tM = 9.6).
Figure 4. Spatial distribution of tangential velocity ratios (U *t,cont / U *t,batch) for the lower liquid feed flow rate in the co-current mode (t/tM = 9.6).
2
NtM = 5.3 Po -1/3 (T D )
(2)
although an even simpler empirical correlation holds for the
most common impellers (Roustan and Pharamond, 1988;
Tatterson, 1991):
2
NtM = 4 (T D )
(3)
Customarily, the two times have been chosen so as to obtain
a ratio of t/tM ≈ 10, which is considered to correspond to a
CSTR. However, one possible question is whether it would be
possible to force the stirred vessel by increasing the through-flow
rate, which corresponds to lower values of the mean residence
The Canadian Journal of Chemical Engineering, Volume 80, August 2002
time and the t/tM ratio. In order to investigate the limits of
vessel operability, two different volumetric flow-through rates
were also chosen, to simulate a normal and an intensified vessel
utilization: FL = 6.1 L min–1 (corresponding to a near-normal
vessel utilization: t/tM = 9.6), and FL= 12.1 L min–1 (corresponding
to an enhanced utilization: t/tM = 4.8). In calculating characteristic
times ratio, the simpler Equation (3) was used.
Results & Discussion
Co-Current Liquid Feed
Figure 2 presents the 2D flow patterns in three planes — the
feed tube plane and the 90° and 180° downstream planes —
and compares them to the batch-case flow pattern. As
expected, below the tip of the tube a high velocity region may
be observed, with the incoming jet joining the circulating liquid
and flowing towards the upper side of the turbine disk. It is
593
interesting to note that, at this lower flow rate, the typical two
primary-loops flow pattern induced by the Rushton turbine is
observed, with only slightly higher velocities found below the
turbine disk. The two downstream-plane (90° and 180°) flow
maps look similar to the batch-case one, indicating that the
effect of the incoming liquid is restricted to the immediate
vicinity of the feed tube plane.
A better way of utilizing the LDV data to visualize the changes
induced by the incoming liquid jet is by plotting the 2D-composite
dimensionless velocity (U *rz) ratio, i.e., the ratio U *rz,cont /U *rz,batch.
The composite velocity is obtained from Equation (4):
(
*
Urz
= Ur*2 + Uz*2
1/ 2
)
(4)
where U *r and U *z are the dimensionless mean radial and axial
velocities, respectively, obtained by dividing the mean velocities
by the agitator tip speed:
Ui* = Ui Utip , i = r , z ,t
(5)
Figure 3 presents the spatial distributions of this ratio for the
three planes studied in this work; the batch-case flow pattern is
also provided for comparison (Figure 3a). For the low flow rate,
corresponding to the high characteristic times ratio, the feedtube plane (Figure 3b) shows a difference in velocity
magnitudes close to the feed tube tip, with velocities in that
region about nine times higher than the spatially-corresponding
batch-mode velocities. All over the other regions of this plane,
the differences seem quite small, and U *rz,cont are found to be of
the same order of magnitude as U *rz,batch. Moving downstream,
at the 90° plane (Figure 3c), a region of high velocities in
comparison with the batch case, is seen in the upper circulation
loop, close to the vessel walls. However, the maximum velocity
ratio is lower (@6), indicating that the effect of the incoming
liquid stream is gradually attenuated. Again, in the other parts of
Figure 5. 2-D flow patterns for the increased liquid flow rate (t/tM = 4.8) and the co-current mode of operation.
Figure 6. Spatial distribution of 2-D composite velocity ratios (U*r z,cont / U*r z,batch) for the higher liquid feed flow rate in the co-current mode (t/tM = 4.8).
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The Canadian Journal of Chemical Engineering, Volume 80, August 2002
the vessel, the 2D-flow pattern seems to remain similar to the
batch case. Further downstream (180° plane, Figure 3d), a region
of higher U *rz velocities is identified, in the same place as previously
but with velocity magnitude differences practically halved.
The 2-D velocity vectors plotted in these figures miss the
important third dimension of the flow in the stirred vessel,
especially in the neighborhood of the turbine. Hence, plots of
dimensionless tangential velocity ratios are also necessary to
obtain a fuller and more meaningful view of the flow structure
in the stirred tank and the effect of the flow-through liquid
stream. Figure 4a presents the spatial distribution of tangential
velocities in the batch case. As expected, the highest velocities are
found close to the agitator blade tips. In the case of continuous-flow
operation, measurements were obtained only in the two
downstream planes and the ratio U *t,cont / U *t,batch distributions
are plotted in Figures 4b and 4c. It is interesting to note that in
these two downstream planes, for the lower liquid flow rate, the
changes brought to the tangential velocities are located almost
Figure 7. Spatial distribution of tangential velocity ratios (U *t / U *tip ) for the higher liquid feed flow rate in the co-current mode (t/tM = 4.8).
Figure 8. 2-D flow patterns for the lower liquid feed flow rate (t/tM = 9.6) and the counter-current mode of operation.
The Canadian Journal of Chemical Engineering, Volume 80, August 2002
595
at the bottom of the vessel, as if the incoming stream has been
diverted sideways and downwards in a spiral-like deviation. A
more important feature is the region of liquid circulating
counter-clockwise in the upper part of the vessel, seen from the
large negative U *t ratios. This pattern may be indicative of a suction
effect caused by the incoming jet, which becomes apparent in the
vessel quarter downstream from the feed tube plane.
From these figures, it may be deduced that at lower volumetric flow rate, the effect of the co-currently fed stream is
restricted to the upper part of the vessel, where it joins the
recirculating liquid, and that this effect is observable mainly in
the region of the feeding tube. As one moves downstream,
following the agitator rotation, the effect of the flow-through
liquid is gradually lost.
When the flow rate of the co-current feed is increased, the
high-velocity jet is deflected radially and at the same time
upwards by the rotating disk, and this is observed clearly at the
90°-downstream plane (Figures 5c, 6c). The typical two-loop
flow structure appears again to be recovered at the 180°downstream plane (Figures 5d, 6d). The tangential velocity
ratio distributions (Figure 7) show the effect of the incoming
liquid stream more clearly: this time, the changes appear close
to the rotating impeller, with velocities considerably higher
than in the batch case (Figure 7b). Further downstream, in the
180° plane (Figure 7c), the region with velocity differences is
diminished, but retains similar top velocity differences.
From these flow maps it may be deduced that in the case of
the Rushton turbine, the introduction of the liquid stream in the
upper part of the vessel and co-current with the liquid being
drawn in by the impeller rotation, only partially affects the flow
structure. This region seems to be limited to the vessel quarter
between the feeding-tube plane and the one 90° downstream.
Figure 9. Spatial distribution of 2-D composite velocity ratios (U *r z,cont / U *r z,batch) for the lower liquid feed flow rate in the counter-current mode
(t/tM = 9.6).
Figure 10. Spatial distribution of tangential velocity ratios (U *t,cont / U *t,batch) for the lower liquid feed flow rate in the counter-current mode (t/tM = 9.6).
596
The Canadian Journal of Chemical Engineering, Volume 80, August 2002
Figure 11. 2-D flow patterns for the higher liquid flow rate (t/tM = 4.8) and the counter-current mode of operation.
Figure 12. Spatial distribution of 2-D composite velocity ratios (U *r z,cont / U *r z,batch) for the higher liquid feed flow rate in the counter-current mode
(t/tM = 4.8).
Figure 13. Spatial distribution of tangential velocity ratios (U *t,cont / U *t,batch) for the higher liquid feed flow rate in the counter-current mode (t/tM = 4.8).
The Canadian Journal of Chemical Engineering, Volume 80, August 2002
597
It should be noted that this discussion is limited to the
present geometrical configuration; it is obvious that a different
tube outlet, e.g., a wider tube, or a diffuser-type outlet, would
result in different local incoming jet velocities, and perhaps
would affect the overall flow patterns in a different way.
Counter-current Liquid Feed
The second set of LDV measurements was made with the tip of
the feeding tube positioned at the side of the Rushton turbine
blades, with the tube set against the vessel walls, equidistant
from two neighboring baffles (Figure 1). Thus, the liquid exiting
from the feeding tube faced the stream of liquid being ejected
radially outwards and towards the vessel walls by the rotating
turbine — the counter-current feed mode, since the incoming
stream flows against the pumped-out stream. This creates a
region of intense turbulence and mixing in the space between
such regions are usually created in practice by two opposing jets,
in order to achieve appropriate conditions for the crystallization
process (Stavek et al., 1990; Benet et al., 1999; Mumtaz et al., 2000;
among others).
Figure 8 illustrates the 2-D flow patterns for the three planes
(feed-tube, 90° and 180° downstream) and compares them to
Figure 14. Comparison of 2-D flow maps (U *r z / U *tip) generated by the Rushton turbine to the flow maps generated by an axial-flow (Mixel TT)
impeller (Mavros et al., 2002) in continuous-mode operation: effects of volumetric flow rate and feed position (co-current, counter-current).
All maps represent the flow structure in the feed-tube plane.
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The Canadian Journal of Chemical Engineering, Volume 80, August 2002
the batch-case flow map for the lower flow rate (t/tM = 9.6). As
in the case of the co-current feed, the flow map disruption is
observed mainly in the feed-tube plane. In the two downstream
planes, the double-loop structure is recovered.
The spatial distribution of the relative composite velocities
(U *r z,cont / U *r z,batch ; Figure 9) shows in a more quantitative way
the evolution and change of the regions where the changes
induced by the incoming feed are found. In the feed-tube plane
(Figure 9b), the major velocity change is found, as expected,
close to the blade edge. In the 90°-downstream plane (Figure 9c),
a slight increase in velocities is observed above the turbine disk,
indicating that the incoming liquid stream is slightly misaligned
with respect to the horizontal line and the turbine disk plane.
However, as one moves further downstream (180°-pane, Figure 9d),
the region where changes are observed is found in the upper
circulation loop and close to the vessel walls, indicating the
complex 3-dimensional movement of the incoming liquid
stream. If the maps of tangential velocity ratios are also taken
into account (Figure 10), then it is possible to hypothesize that,
at the lower flow rate and given the slight misalignment, the
incoming liquid stream is entrained by the strong rotary
movement of the turbine into the upper circulation loop.
However, even when the flow rate of the incoming liquid
stream is increased, the changes in flow pattern in the stirred
tank are not extreme (Figure 11). Obviously, the flow patterns in
the feed-tube and the 90°-downstream planes are changed by
high velocity incoming streams, but as the 180°-downstream
plane is reached, the typical double-loop structure is found
again. The spatial distributions of relative 2-D composite velocities
(Figure 12) indicate that, indeed, the regions of major
magnitude change are to be found close to the impeller edge
(feed-tube plane) and the upper side of the turbine disk (90°-plane).
Interestingly, in the 180°-downstream plane, two regions are
observed with relatively important composite velocity change.
The tangential velocity ratio distributions (Figure 13) show a
similar pattern of changes, with most of the flow map differences
observed in the 90°-downstream plane.
These figures indicate, on the one hand, that at the higher
volumetric flow rate, the change in flow structure affects a
larger part of the entire vessel, while on the other hand, the
typical double-loop flow structure induced by the Rushton
turbine is only partially disrupted by the incoming liquid
stream. Thus, it may be concluded that, for the given vessel
configuration, with the outlet located at the bottom, and
especially with the simple dip pipe used for introducing the
liquid stream into the vessel, it is possible to position the inlet
for the incoming liquid either co- or counter-currently to the
primary circulation loop without major flow pattern disruptions.
Comparison with an Axial-Flow Impeller
Since quite a few stirred vessels use axial-flow impellers, an
investigation of the continuous-mode operation by LDV
measurement was also carried out (Mavros et al., 2002) with a
Mixel TT. This three-blade impeller has a relatively low solidity
ratio of @ 0.40 (Mavros and Bertrand, 2002), which produces a
composite axial-radial discharge (Mavros et al., 1996). Figure 14
compares the feed-plane flow maps for both impellers.
(Although the power requirements of the two impellers are
completely different — the Mixel TT has a power number about
seven times smaller than the Rushton turbine (Aubin et al.,
2001) — their comparison remains possible, because all results
are scaled according to the same Utip ).
The Canadian Journal of Chemical Engineering, Volume 80, August 2002
As observed above, in the co-current feed mode there seems
to be no particular problem with the turbine flow maps (Figures
14a, b). However, in the case of the Mixel TT, the incoming
liquid stream is added to the recirculating liquid from the
primary circulation loop and the two streams emerge combined
from the lower side of the TT (Figure 14e). At the lower flow
rate, the radial character of the TT discharge remains strong and
prevailing, and the primary circulation loop is maintained. But,
when the characteristic times ratio is lowered, the high-velocity
incoming jet seems to prevail, and the emerging jet from
the bottom of the TT is directed, most pointedly towards the
bottom of the vessel (Figure 14f). And since the vessel outlet is
located at the bottom of the vessel, this combination of
inlet-outlet position and operating conditions seems to lead to
problems with short-circuiting.
When the liquid is fed counter-currently, the resulting flow
structure again depends upon the ratio of characteristic times.
At the high t/tM condition, the circulation induced by the
rotating TT prevails and the incoming stream combine with
the liquid ejected by the impeller. Obviously, a considerable
portion of the incoming liquid will be diverted tangentially but
this is missed in the 2-D flow maps. When the t/tM ratio is
lowered, corresponding to an intensification in vessel usage, the
flow structure appears to be disrupted and a secondary loop is
established in the upper part of the vessel, where liquid
circulates in the opposite direction to the one usually found in
axial agitators. In fact, even simple visual observation showed
that under these conditions, the incoming stream periodically
reached the free surface of the liquid in the vessel.
Both the flow patterns and visual observations lead to the
conclusion that, while it is possible to operate the radial
agitator at high or low t/tM values, in the case of the axial
agitator, the location of the vessel outlet directly below the
impeller discharge may lead to liquid short-circuiting and vessel
dysfunction.
Conclusions
The flow structure of a continuous-stirred tank reactor was
investigated by laser Doppler velocimetry for two mean residence
times: mixing time ratios and two different inlet locations,
corresponding to co-current or counter-current liquid feed with
respect to the liquid stream discharged by the rotating impeller. The
agitator used for these measurements was a standard Rushton
turbine, and the vessel outlet was located at the bottom of the vessel.
In all the investigated configurations and for all operating
conditions, it was found that the flow disruption caused by the
incoming liquid stream was observable only in the first vessel
quarter, which followed the plane where the feeding-tube was
located. The typical double-loop circulation generated by the
Rushton turbine was usually recovered, as illustrated by the flow
patterns observed in the 180°-downstream plane.
From comparison of the velocities encountered in the various
planes in the continuous-flow reactor with those in the batch reactor,
it may be concluded that for either given vessel configuration, it is
possible to intensify the usage of the stirred vessel to some
extent by decreasing the characteristic times ratio, which is
equivalent to increasing liquid flow-through or volumetric flow
rate, without apparent flow pattern problems. Residence time
distribution measurements could reveal whether these flow rate
increases and vessel configurations also lead to flow pathologies in
terms of short-circuiting or the by-passing of some vessel regions.
599
Acknowledgements
Thanks are due to the European Union (contract BRITE-EURAM BRRT
CT97 5035, thematic network "MIXNET") for the partial financial
support of this work. One of the authors, Prof. Ivan Fořt, also acknowledges the financial support of this work by the Czech Republic Ministry
of Education (Research Project J04/98:212200008).
Part of this work, with only inlet-outlet configuration, was presented
at the 4th Int. Symp. on Mixing in Industrial Processes (ISMIP4,
Toulouse, France, May 14-16, 2001).
Nomenclature
b
D
dp
dS
H
k
N
Po
R
tk
tM
T
u
U
U*
Utip
VL
baffle width (m)
agitator diameter (m)
seed particle diameter (m)
agitator shaft diameter (m)
liquid height in vessel (m)
turbulent kinetic energy (m2·s–2)
agitator rotation speed (rps)
power number
vessel bottom curvature radius (m)
time spent by the seeding particle inside the LDV-measuring
volume (s)
mixing time (s)
vessel diameter (m)
instantaneous velocity (m·s–1)
mean velocity (m·s–1)
dimensionless velocity (= U / Utip )
agitator tip velocity (m·s–1)
liquid volume (m3)
Greek Symbol
t
mean residence time, (s)
Subscripts
cont
r
t
z
continuous-mode
radial
tangential
axial
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Manuscript received August 9, 2001; revised manuscript received
April 11, 2002; accepted for publication May 9, 2002.
The Canadian Journal of Chemical Engineering, Volume 80, August 2002