Chinese J. Chem. Eng., 14(5) 618—625 (2006)
Investigation on Eccentric Agitation in the Stirred Vessel Using
3D-Laser Doppler Velocimeter*
WANG Bo(王波)a,b,**, ZHANG Jieyu(张捷宇)c, HE Youduo(贺友多)a and AN Shengli(安胜利)a,b
a
Material and Metallurgical School, Inner Mongolia University of Science & Technology, Baotou 014010, China
School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing
100083, China
c
School of Materials Science and Engineering, Shanghai University, Shanghai 200072, China
b
Abstract The spatial structure of the velocity field in a stirred vessel with water has been measured and analyzed
using the laser Doppler velocimeter technique, with the immersing depth and agitation speed of the impeller remaining approximately constant. The experimental results were provided such as the mean velocity field, fluctuating velocities, turbulent kinetic energy, Reynolds shear stress and time series of the velocity in the stirred tank.
These results probably provided the valuable basis to further optimize and enlarge the stirred tank in the industrial
process.
Keywords stirred vessel, laser Doppler velocimeter, eccentric agitation, mean velocity
1
INTRODUCTION
Stirred vessel reactors are often used in industrial
processes of metallurgy, chemistry, energy source and
environment. Up till recently, empirical correlations
have been used as tools for designs, scale-up and operation of stirred vessels. Due to the absence of
boundary conditions and turbulent models, the simulation results of computational fluid dynamics (CFD)
are apparently inadequate. To fully understand the
process occurring in the mixing vessels, the spatial
structure of the velocity field in the stirred vessel has
been measured using the laser Doppler velocimeter or
particle image velocimeter[1,2].
Stirred vessels are commonly equipped with baffles, which break the primary vortex and improve the
small-scale mixing. However unbaffled vessels are
nevertheless important from both fundamental and an
industrial point of view. The absence of baffles in a
vessel typically results in the generation of a central
vortex and a swirling flow. In the past, attention has
been mainly paid to baffled tanks and only a few
studies were focused on unbaffled vessels [2, 3]. Eccentric agitation in the stirred vessels still lacks study.
Moreover, validation of CFD as a predictive tool
requires comparison of the numerical simulation results with experimental velocity data[4―12]. Most of
the simulations applied to stirred vessels still use the
k-ε turbulence model that is based on the hypothesis of
isotropic turbulence. For baffled vessels, the k-ε model
gives satisfactory prediction of the mean fluid flow,
whereas some deviations between experimental and
predicted data are usually found near the impeller. On
the contrast, the k-ε turbulence model completely fails
when it is applied to unbaffled configurations, even
though the regions considered are far away from the
impeller[13].
In this article we report a direct measurement of
the global velocity field in the stirred vessel using
3D-laser Doppler velocimeter (LDV) technique[14―16].
The main features of LDV are the small measurement
volume, the high temporal resolution and no disturbing flow. Although being a time-consuming technique
for both set-up and data acquisition, LDV is still the
technique of choice for high-accuracy measurements.
In particular, 3D-LDV can synchronously measure
three components of the velocity at a point. The great
advantage of LDV is that turbulence can be measured
at a particular location in the flow field with a very
high accuracy. Our experiment was conducted in the
eccentric agitation in the stirred vessel while the immersing depth and agitation speed of the impeller remained constant. In addition to the mean velocity field,
some statistical quantities, such as the root mean
square (rms), turbulent kinetic energy and Reynolds
shear stress fields were also measured in the whole
stirred vessel. The measurement reveals detailed
structures and properties of the flow field in the stirred
vessel.
2 EXPERIMENTAL
2.1 Apparatus
The choice of the shape of the stirred vessel is
based on the following consideration. For the most
widely used cylindrical shape, the curved sidewall will
introduce refraction effects. As a result, the location of
the measurement volume moves and the amount of
scattered light that can be collected by the receiving
optics assembly is generally reduced. Although these
Received 2005-05-23, accepted 2005-11-28.
* Supported by the Natural Science Foundation of Inner Mongolia (No.200408020715).
** To whom correspondence should be addressed. E-mail: [email protected]
Investigation on Eccentric Agitation in the Stirred Vessel Using 3D-Laser Doppler Velocimeter
Figure 1
Schematic drawing of the stirred vessel and the coordinates of the experiment
effects can be partly corrected by fitting a sealed box
with a flat glass window outside the stirred vessel, the
box filled with working liquid unavoidably limits the
measurement accuracy. With these in mind, a rectangular shape is chosen for the stirred vessel.
The dimension of the stirred vessel is
310mm×150mm×350mm. The sidewall and bottom
of the stirred vessel are made of glass. The stirred
vessel has no lid. To prevent impurity in water from
disturbing the laser scatter effect, distilled water was
selected as working fluid. In the measurement process,
the liquid level remains constant (310mm). The agitation system consists of the general semiellipse impeller and a 0.3kW power motor [Fig.1(c)]. The rotational speed of the impeller remains constant,
－
N=500r·min 1. The Reynold number Re is 2.8×106
2
(Re=ND /ν, D—impeller diameter, m; ν—dynamic
－
viscosity, m2·s 1). The shaft is located in the perpendicular center plane and the distance is 90mm off z
axis. The impeller is mounted 155mm off the vessel
bottom, as measured from the bottom of the impeller.
Fig.1 shows a schematic drawing of the stirred vessel.
2.2
619
The LDV Measurement
LDV is a non-intrusive laser optical technique
with high spatial and temporal resolution that gives
information about flow velocity and turbulence. It is
based on the fact that particle scattered light contains
the Doppler frequency fD, which is proportional to the
velocity component u perpendicular to the bisector of
two laser beams. With the known wavelength λ of the
laser light, the angle β between the beams, and a constant factor between Doppler frequency fD, the velocity u can be calculated as
fDλ
u=
2sin( β 2)
The velocity field is measured with backward
scatter, 3-color, and 5-beam LDV system. The LDV
system consists of a 2W Argon-ion laser operating at
514.5nm (green), 488nm (blue) and 476.5nm (violet),
a fiber light multicolor beam generator for the frequency shifting, a three-channel photo detector module (PDM1000), multibit digital burst correlation
(FSA3500) for data processing, a fiberoptic probe, a
3-axis traverse system and a LDV control and analysis
software (Flowsizer, TSI, Inc.). Fig.2 illustrates the
schematic drawing of 3D-LDV system.
computer and flowsizer
FSA3500
PDM1000
5-beam fiberoptic
probe
laser
Figure 2
laser
fiberlight
fiberlight
Schematic drawing of 3D-LDV system
Distilled water is seeded with hollow glass
spheres (mean diameter of 10—15μm and density of
－
1.05—1.15g·cm 3). The three components of the velocity of a certain given point are obtained by
3D-LDV in the global stirred vessel. Since sampling
rate is very low near sidewall, wall velocity field is
not measured in this experiment. As shown in Fig.1,
the Cartesian coordinate for the experiment is defined,
its x axis points to the right, the z axis points upward,
and the y axis points inward. We chose 24, 10 and 24
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620
points which are measured by 3D-LDV in x, y and z
directions, respectively. The distance between two
adjacent points is 10mm. Through measuring these
points, the whole velocity field and turbulent characteristic are obtained in the stirred vessel.
3 RESULTS AND DISCUSSION
3.1 Time-averaged velocity field
We first look at the gross features of the mean
flow field by examining the 2D vector map. Fig.3
shows the vector maps of the flow field inside the
stirred vessel, at (a) 20mm from the front wall, (b)
40mm from the front wall, (c) 60mm from the front
wall (at this plane which impeller located), and (d)
90mm from the front wall, respectively, which are
obtained by combining U with W. In the Fig.3 the
magnitude of the mean velocity (U2+W2)1/2 is coded
Figure 3
by the length of the arrow, where U and W are the
time-averaged x and z components of the velocity,
respectively. Fig.3 shows clearly that the mean flow is
a big single clockwise rotatory motion and the high
velocity regions are mainly near the impeller. The
center of the circumfluence is near the bottom right of
the impeller. A closer inspection of the figures shows
that there is a smaller velocity field at the top right
corner of the measuring region. For eccentric agitation
in this study, owing to impeller far away from a sidewall, it forms a big vortex and a small velocity field at
the center and top right corner of the measuring region,
respectively. From Fig.3(a), it can be observed that
there is only a big vortex near the front wall. In addition,
it can be found in Fig.3(a)—(d) that the core of the big
vortex is gradually moving from the tip of the impeller
toward the lower-right corner of the measured region.
Vector maps of the mean velocity field with the magnitude
U +W
2
distances from the front wall
October, 2006
2
coded in the size of the arrow for different
Investigation on Eccentric Agitation in the Stirred Vessel Using 3D-Laser Doppler Velocimeter
Distribution of the mean flow kinetic energy at
different distances from the front wall
3.2
z
y
x
200
150
z
Statistical quantities of the velocity field
We now present some statistical quantities for
eccentric agitation in the vessel. Fig.7 shows the distribution of the rms velocity fluctuations color coded
－
in unit of m·s 1. Fig.7(a) and (b) show the horizontal
rms velocity urms, the transverse rms velocity vrms and
the vertical rms velocity wrms at the xz central plane,
respectively; Fig.7(c) and (d) show the horizontal rms
velocity urms, the transverse rms velocity vrms and the
vertical rms velocity wrms at the xy central plane, respectively. If we note the scales of color bars, it is
clear that the magnitude of velocity fluctuation near
the impeller is much higher than that of the one far
away from the impeller. These large fluctuations are
caused by the agitation energy of impeller. We also
note that the magnitude of vrms is much higher than
that of urms and wrms near the impeller. This is because
the impeller used in this experiment generates the better radial agitation effect and the aspect ratio of the
vessel is smaller. The distributions of rms velocity are
Figure 4
100
50
0
0
50
100
x
Figure 5
150
50
200
y
The mean kinetic energy of the flow field is shown
in Fig.4, where the color-coded mean kinetic energy in
－
the xz plane K=(U2+W2)/2, in units of (m·s 1)2, respectively, at (a) 20mm from the front wall, and (b) 60mm
from the front wall. From Fig.4, it can be seen that the
high kinetic energy region are near the impeller. The
pumping capacity of the impeller is mainly dissipated
in these regions. The agitation energy drives the big
rotational bulk flow in the stirred vessel. The distributions of mean kinetic energy are the same as that of
mean velocity.
The vector plot Fig.5 illustrates the flow field inside the stirred vessel as a combination of the
time-averaged x and y components of the velocity at
the different horizontal planes. The figure shows
clearly that the mean flow is a rotation motion and its
direction is the same as the direction of tangential velocity of impeller in the xy plane. The velocities are
higher near the impeller. It appears to us that the good
effects of radial agitation occur in the rectangular
stirred vessel.
By using 3D-LDV, we can measure three components of the velocity at a particular point. To obtain
a more complete picture on the flow field in the stirred
vessel we give the vector plot of the yz plane. Fig.6
shows the time-averaged velocity vector maps in this
plane (at x=40mm, 70mm, 100mm and130mm). For
the eccentric agitation, the mean flow pattern shows
that fluid flows in opposite direction at the top and
bottom of the impeller. From Fig.6, it can be seen that
the direction of the velocity is becoming increasingly
changed at different yz planes. This is because impeller is mounted at the eccentric position and the width
of vessel is narrow. In addition, Fig.6 also shows that
as the fluid hit the sidewalls some will deflect to create the vortices at the corners.
621
Vector maps of the mean velocity field at the
different xy planes
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622
coincident with that of mean flow in the stirred vessel.
To study the dynamics that drives the turbulent
flow in the system, we examine the turbulent energy
and Reynolds shear stress. Fig.8 presents the distributions
of
the
turbulent
kinetic
energy
2
2
k = (urms
+ wrms
) / 2 . Similar to the mean kinetic energy, Fig.8 shows that turbulent energy is mainly concentrated near the impeller (at the left of the middle
part of vessel). Figs.9(a), (b) and (c) illustrate the
distributions of the Reynolds shear stress, u′v′, u′w′
and v′w′, respectively, where u' = u − U , v' = v − V
and w' = w − W are the fluctuating parts of u, v and w.
The Reynolds stress is responsible for the exchange
momentum between turbulence and the mean flow and
its existence requires the correlated fluctuations of u, v
and w. From Fig.9 we see that the regions of large Reynolds stress correspond to where agitation energy is
stronger and the fluctuation velocity is higher. Since
turbulence production is proportional to Reynolds stress,
we see that the turbulent kinetic energy largely comes
from the agitation energy of the impeller.
Figure 7
3.3
Figure 6 Mean velocity vector maps in yz planes at
different distances from the left sidewall
October, 2006
Contours of rms velocity
Instant velocity
Although the sampling rates of our measurement are rather low, LDV still allows us to obtain
some useful information about the instant flow velocity. Fig.10 shows the distributions of the instantaneous
velocity with time varying at five positions in the
vessel, one is close to the top and bottom of the
Investigation on Eccentric Agitation in the Stirred Vessel Using 3D-Laser Doppler Velocimeter
Figure 8
623
Contour map plots of the turbulent kinetic energy at different distances from the front wall
Figure 9 Contour map plots of the Reynolds shear stress at the xz central plane
Chinese J. Ch. E. 14(5) 618 (2006)
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Chinese J. Ch. E. (Vol. 14, No.5)
Figure 10
measuring region and is near the left and right sidewalls, and one is at the measuring region center.
Fig.10(a) shows the horizontal velocity u(t) close to the
top, bottom and the center. Fig.10(b) shows the vertical
velocity w(t) near the sidewalls and at the center. From
Fig.10(b), we see that the flow is upward-going (defined as positive) and downward-going (defined as
negative) near the left-sidewall and right-sidewall, respectively, which is of course consistent with the fact
that the overall flow is clockwise. At the center the velocity fluctuates in both directions with a zero mean.
From Fig.10(a), it can be seen that the value of the u
velocity is negative at the center and the bottom of the
vessel, which is consistent with the fact that a big circumfluence flow is formed at the right of the lower
center of the vessel for eccentric agitation.
October, 2006
Time series
4
SUMMARY AND CONCLUSIONS
The properties of the velocity field in the
eccentric agitation of the stirred vessel were studied
systematically. Time-averaged 3D velocity fields were
measured using the Laser Doppler velocimetry technique. Meanwhile, certain statistical and dynamical
quantities of the velocity field were also obtained. The
measurement provides a direct and clear understanding for the spatial structure of the velocity field in the
stirred vessel. These results may provide the valuable
basis to further optimize and enlarge the stirred tank in
the industrial process.
From the measured 3D velocity field in the
stirred vessel, the prominent features or regions of the
flow field were identified: (1) A strong circumferential
flow beside the impeller in the stirred vessel; (2) A
Investigation on Eccentric Agitation in the Stirred Vessel Using 3D-Laser Doppler Velocimeter
small low-velocity zone at the upper-right corner; (3)
Velocity vector distributions in the yz plane reveal that
the small aspect ratio affect the structure of the fluid
flow; (4) Good effect of radial agitation occur in the
rectangular stirred vessel.
The measurements made for statistic quantities
reveal the following properties: (1) The rms maps of
the velocity field show that the velocity fluctuation
near the impeller is neither homogenous nor isotropic,
these further show that there are large asymmetric
velocity fluctuations even in the bulk regions; (2) The
measured Reynolds shear stress distributions indicate
that a strong circumferential flow is driven by agitation energy.
With LDV measurement of the flow field, we
obtain the very detailed information about the structure of fluid flow in the stirred vessel. These results
will not only provide the valuable basis to further optimize and enlarge the stirred tank in the industrial
process, but also validate the validity of CFD methods
in predicting flow of stirred vessels.
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Chinese J. Ch. E. 14(5) 618 (2006)