Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 10.1.1 - Velocity field measurements around a Taylor bubble rising in stagnant and flowing water
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 Material Information
Title: 10.1.1 - Velocity field measurements around a Taylor bubble rising in stagnant and flowing water Bubbly Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Saad, G.A.
Bugg, J.D.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: particle image velocimetry
two-phase flow
Taylor bubbles
wakes
slug flow
 Notes
Abstract: In this work, the experimental facility was designed to provide instantaneous 2-D velocity field measurements using particle image velocimetry (PIV) around Taylor bubbles rising in a vertical tube containing a stagnant or upward moving liquid. The working fluids were filtered tap water and air. Three liquid flow rates were investigated which yielded Reynolds numbers of 9200, 13600, and 17800. Mean axial velocity profiles, axial turbulence intensity profiles, and streamlines are presented for ensembles of at least 200 bubbles. Verification of measurements was done by a mass balance around the nose. In stagnant liquid, the size of the primary recirculation zone in the near wake of the Taylor bubble was smaller (1.3D) than in the upward flowing liquid. In the flowing liquid, the recirculation zone was 1.7D for all three Reynolds number tested. The axial velocities in the near-wake region become smaller relative the corresponding bubble rise velocity as the Reynolds number of the flowing liquid increases. Based on the velocity measurements, the minimum stable liquid slug length (the minimum distance needed to have no interaction between two consecutive Taylor bubbles) was found to be in the range of 8~12D.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Velocity Field Measurements around a Taylor Bubble
Rising In Stagnant and Flowing Water

G. A. Saad and J. D. Bugg


Department of Mechanical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, SK, Canada
gas637@mail.usask.ca and jim.bugg@usask.ca
Keywords: Particle image velocimetry, two-phase flow, Taylor bubbles, wakes, slug flow





Abstract

In this work, the experimental facility was designed to provide instantaneous 2-D velocity field measurements using particle
image velocimetry (PIV) around Taylor bubbles rising in a vertical tube containing a stagnant or upward moving liquid. The
working fluids were filtered tap water and air. Three liquid flow rates were investigated which yielded Reynolds numbers of
9200, 13600, and 17800. Mean axial velocity profiles, axial turbulence intensity profiles, and streamlines are presented for
ensembles of at least 200 bubbles. Verification of measurements was done by a mass balance around the nose. In stagnant
liquid, the size of the primary recirculation zone in the near wake of the Taylor bubble was smaller (1.3D) than in the upward
flowing liquid. In the flowing liquid, the recirculation zone was 1.7D for all three Reynolds number tested. The axial velocities
in the near-wake region become smaller relative the corresponding bubble rise velocity as the Reynolds number of the flowing
liquid increases. Based on the velocity measurements, the minimum stable liquid slug length (the minimum distance needed to
have no interaction between two consecutive Taylor bubbles) was found to be in the range of 8-12D.


Introduction

Slug flow is one of the most common and complex flow
patterns in two-phase, gas-liquid flow. Slug flow exists over
a broad range of gas and liquid flow rates. In vertical tubes,
most of the gas is located in large bullet-shaped bubbles
which occupy most of the pipe cross section and move with
a relatively constant velocity. These bubbles are called
Taylor bubbles. The liquid between the Taylor bubbles and
the pipe walls flows as a thin film. When the liquid film
penetrates into the liquid slug behind the bubble, it creates
vortices and intense mixing. The liquid slug may or may not
contain a dispersion of small gas bubbles. The size and
structure of the wake behind a Taylor bubble depends on the
liquid properties and the tube diameter as well as the
relative motion between the bubble and the liquid. The
development of slug flow along a pipe is governed by the
interaction between consecutive Taylor bubbles. In general,
it is assumed that the trailing bubble nose is affected by the
velocity field in the liquid ahead of it (Moissis & Griffith,
1962). The wake of the leading bubble strongly affects the
shape and the translation velocity of the trailing bubble.
Therefore, a detailed understanding of the hydrodynamics of
Taylor bubble wakes is very important.

Campos & Guedes DeCarvalho (1988) photographically
studied the wake region behind Taylor bubbles rising in
stagnant liquid in tubes of 19-25 mm diameter. They pointed
out that the flow pattern in the wake of a gas bubble rising
in a vertical tube depends on the dimensional group N, often

called the inverse viscosity N= p(Dg) .

They classified the flow in the wake into three different flow


patterns. Type I closed axisymmetric wake: N<500,Type II
closed unaxisymetric wake: 500 wake with recirculating flow: N>1500

Pinto et al. (1998) extended Campos & Guedes DeCarvalho
(1988) and conducted an experimental investigation of the
influence of the liquid flow on the coalescence of two
Taylor bubbles rising in co-current flow for different tube
sizes. The wake flow pattern in these investigations was
turbulent and the liquid flow regimes were laminar and
turbulent. They used differential pressure transducers to
measure the velocity and minimum spacing between two
bubbles (the minimum spacing is the distance for which
there is no interaction between the two bubbles). They
defined three different flow patterns in the wake based on
the Reynolds number of the liquid relative to the bubble

ReR =PD(UTB -UL )
where D is the tube diameter, t is the liquid viscosity, p is
liquid density, UL is mean superficial liquid velocity and
UTB Taylor bubble terminal velocity.

These wake pattern are Type I laminar wake : ReR <175,
type II transition wake: 175 turbulent wake: ReR >525.

Several workers have used PIV to make velocity
measurements around Taylor bubbles rising through a
stagnant liquid. Examples are Van Hout et al. (2002), Bugg
& Saad (2002), Nogueira et al. (2003), and Sousa et al.
(2005).

Shemer et al. (2005) studied the wake of Taylor bubbles









rising in upward moving liquid in a 0.026 m diameter tube
using PIV They investigated the mean and instantaneous
measured velocity field for two liquid flow rates
corresponding to laminar i./, =.I"n and turbulent
(ReL=7500) flow. The vortex rings behind the bubble existed
for both flow rates. This similarity was due to the fact that
the wake was turbulent regardless of the moving liquid flow
regime. These toriodal vortex rings were not found in the
instantaneous velocity field. In both cases the velocity
profile remains undeveloped even at a very large distance
behind the bubbles. The velocity profile approaches the
fully developed shape in the turbulent case much faster than
in the laminar case. This work was extended by Shemer et al.
(2007) to include three different tube sizes at different flow
rates. Their findings were consistent with their previous
work. The near wake behind the bubbles (up to distance of
Z/D= 4) was similar for all cases regardless of the
background flow regime. For the laminar background flow,
the fully-developed flow velocity profile was not achieved
even at Z/D>70 and for the turbulent flow was achieved at
around Z/D= 25.

Several researchers have studied this flow by placing a solid
object in the shape of a Taylor bubble inside a tube.
Tudose & Kawaji (1999) found that this did not have a
major effect on the structure of wake. There are some
reports in the literature of velocity measurements in the
wake of confined axisymmetric bluff bodies in pipes. Taylor
& Whitelaw (1984) studied the effects of the blockage ratio
of the bluff body on the structure of the wake using LDV
They found that the near wake length and the maximum
centreline velocity increases with increasing blockage ratio.
Sotiriadis & Thorpe (2005) investigated the wake of both
a cylindrical bluff body and a ventilated cavity attached to a
central sparger in turbulent flow using LDV They suggest
that the bluff body provides a convenient experimental
substitute for the study of the flow past a ventilated cavity.
Also, they confirmed that the size of vortex in the near wake
does not change with increasing liquid flow rate.

This study concentrates on a simplified form of the slug
flow regime for vertical flow. It will consider the case of a
single Taylor bubble rising in a stagnant and an upward
flowing liquid in a vertical tube The significance of this
work is to increase our understanding of slug flow in
vertical tubes and to provide reliable data for validation of
numerical models developed to predict the behaviour of
slug flow.


Nomenclature


tube diameter (m)
acceleration due to gravity (m s-2)
inverse viscosity number
distance from the tube centre (m)
Reynolds number
velocity (m s 1)
velocity (m s 1)
distance from the bubble bottom (m)
distance from the bubble nose (m)


Greek letters


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

L dynamic viscosity (kg m-1 s-1)
P liquid density (kg m-3)
Subsripts
L liquid
R relative to the bubble velocity
r radial component
rms turbulence fluctuations
TB Taylor bubble
Z axial component



Experimental Facility

The experiment described in this section was designed to
provide instantaneous 2-D velocity field measurements
around Taylor bubbles rising in a vertical tube containing a
stagnant or moving liquid. A schematic diagram of the
apparatus is shown in figure 1. The working fluids were
filtered tap water and air. The water flows in a closed loop
driven by a multistage centrifugal pump controlled by a
Toshiba H3 variable speed drive. The Taylor bubbles were
produced in the lower part of a vertical tube 25 mm in
diameter. The air was injected manually after its volume
was measured carefully. The bypass section was essential to
produce Taylor bubbles with wakes that were free of small
bubbles especially for the flowing liquid cases. It consists
of an injection valve, a drainage valve, a bubble release
valve, and a bypass valve.

The vertical tube was equipped with two phase-transition
detectors. The phase-transition detectors were designed to
detect the presence of Taylor bubbles in the liquid. Each
consists of an infrared diode and detector. The infrared
diode produces a continuous signal to the detector. The
single is interrupted when a bubble passes between the
diode and the detector. The diode and the detector are
perpendicular to the wall of the tubes. A plastic base was
used to hold the detector and the diode properly aligned.
The signal from one of the phase detectors is used to trigger
the PIV measurements. Two such phase detectors were used
to measure the rise velocity of the Taylor bubbles by putting
them at a know distance apart and measuring the time for
the bubble to travel between them. To minimize the optical
distortion induced by the curvature of the tube wall, a
rectangular box filled with liquid was attached to the tube at
the PIV measurement location.

The PIV system consisted of dual Nd:YAG lasers each with
a nominal pulse energy of 50 mJ. To generate the light sheet,
the laser beam passes through a spherical and a cylindrical
lens. The illuminated plane was recorded using a Redlake
MegaPlus ES4020 camera with 2048x2048 active pixels.
The camera was fitted with an AF Micro-Nikkor 60 mm
lens. The laser pulse separation was controlled by a
Berkeley Nucleonics 505 digital pulse/delay generator. The
fluorescent particles used to seed the flow were PMMA
Rhodamine B-Particles. These particles emit light a 584 nm
and have a density of 1.51 gm/cm3. A filter was placed on
the camera lens to block reflected laser light from the
bubble interface and the tube walls and allow only the
particles images to be recorded on the camera's CCD.






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Pump & speed controller


1.2

1

0.8

N0.6

20.4

0.2

0

-0.2


zID =0.004


* zD =0.5
-0-- -.- 0- -










-0.4 -0.2 0 0.2 0.4


Figure 2: Radial profiles of axial velocity at various
positions above the nose of a Taylor bubble rising in
stagnant water.


Liquid drain


Figure 1: Schematic diagram of the apparatus.


To obtain a field of view at the desired position relative to
the bubble (nose, wake), the signal from the lower phase
detector (when the nose of the bubble triggered it) was used
to trigger a Berkeley Nucleonics 500B digital pulse/delay
generator. This pulse generator waits for a programmed
delay period before it sends a trigger signal to the pulse
generator which synchronises the camera and the laser. This
delay time is a function of the Taylor bubble velocity and
the desired measurement location relative the bubble. The
measurement location was 4.5 m from the bubble release
valve.


Results and Discussion

A representative example of the velocity near the nose of a
Taylor bubble rising in a stagnant liquid is given in figure 2
and 3. Figure 2 shows axial velocity profiles at different
axial locations above the nose. It is clear that the velocity
profiles exhibit axial symmetry. Figure 3 shows the radial
velocity profile at several axial locations above the nose. In
the nose region, the velocity field shows the characteristics
expected. The fluid close to the wall moves downward
while the fluid at the centre of the tube moves upward. The
fluid midway between the tube wall and the tube centre has
a strong radial velocity toward the tube wall as the fluid
moves away from the rising bubble. Near the nose of the
bubble, the axial velocity of the fluid is approximately
equal to the terminal velocity of the bubble but drops quite
rapidly ahead of the bubble. The maximum radial velocity
is located between 0.1

0.2

0

-0.2

-0.4


-0.6


Figure 3: Radial profiles of radial velocity at various
positions above the nose of a Taylor bubble rising in
stagnant water.

In contrast to the nose, the tails of Taylor bubbles are
unstable under these conditions. Therefore, the shape of the
bubble bottom is different from image to image. Also the
location of the tail was different from image to image. To
overcome this problem, the location of the interface was
determined using Matrox Inspector@ image processing
software. After the PIV image analysis and the post
processing calculations were performed, the velocity field
data were shifted axially based on the tail location for each
bubble. Then, an ensemble average of the shifted data was
calculated. The velocity at the tail for the shifted image was
very close to the bubble rise velocity. Figure 4 shows the
velocity vectors and the streamlines in a frame of reference
moving at the bubble velocity in the near wake of the
bubble for the four flow conditions presented in table 1. At
the tail, the falling annular film penetrates into the liquid
below the bubble driving a toroidal recirculation zone just
behind the bubble. These wakes were classified as Type
III as defined by Compaos & Geudes de Carvalho (1988)


-0.4 -0.2 0 02 0.4









and Pinto et al. (1998). In all case given in table 1, the cores
of the vortices are located at -0.50D from the bubble bottom
and about 0.28D from the tube centerline. These parameter
are within the range given by Shemer et al. (2007). A
stagnation point is clearly located at -1.3D behind the
bubble bottom for Taylor bubble rising in stagnant liquid
which agrees well with Sotiriadis & Thorpe (2005) for a
bluff body and a ventilated cavity in a vertical tube of
0.105m diameter. However, for all three cases of bubbles
rising in flowing liquid, the size of the near wake increases
and the stagnation point is located at -1.7D This agrees
with the finding of Sotiriadis and Thorpe (2005) that the size
of the near wake does not depend on the volumetric flow
rate of the liquid.

Figure 5 illustrates the axial velocity on the tube centreline
as a function of the distance from bubble tail for the four
cases. The axial velocity at the tube axis initially increases
from a value close to the Taylor bubble rise velocity to reach
a maximum value at a distance of around Z=0.6D. In the
stagnant case the maximum upward velocity is more than
three times the Taylor bubble rise velocity. It then decreases
rapidly and becomes zero around Z=-1.3D. Then it becomes
negative and eventually return to zero at around Z=-5D (not
shown in the figure). This change in the velocity sign is
strong evidence of the existence of a sequence of vortices
with opposite senses of rotation. This observation was also
reported by Van Hout et al. (2002) and Dejesus et al. (1995).

In the flowing liquid, the magnitude of maximum upward
velocity is between 1.6-1.8 of the value of the
corresponding bubble rise velocity. Although it seems like a
very slight change at this investigated Reynolds number,
this change may due to the fact that the velocity of the
falling film of Taylor decreases with increasing liquid flow
rates as reported by Shemer et al. (2007).

Since the mean flow is axisymmetric around the tube
centerline, the results presented in all figures were obtained
from averaging of the left and the right halves of the
velocity fields. This doubles the ensemble size which ranged
from 400 to 1000.

Radial profiles of the axial velocity at various axial
locations in the near wake of the bubble are presented in
figure 6 for all cases in table 1. In figure 6, for the stagnant
liquid, immediately behind the bubble (Z= -0.1D) the axial
velocity profile in the central region is approximately flat
and the value of the velocity is close to the terminal velocity
of the bubble. However, for the moving liquid case, at Z=
-0.1D the velocity of the liquid is a little higher than the
terminal velocity of the bubble and the velocity profile in
the core of upward flowing liquid is not flat as in the
stagnant case. The centre of the tube the liquid core moves
upward with a velocity larger than the terminal velocity of
the bubble. This core extends from the tail to around 1.2D
below the bubble tail.


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

The velocity profiles start to collapse to the superficial
liquid velocity profile at around Z=-8D and fully collapse at
-12D for the three cases of flowing water. The falling
liquid film entering the wake can be considered as an
axisymmetric wall jet impinging on the stagnant liquid
below the bubble. The falling liquid film reduces in
velocity and spreads in the liquid behind the bubble. The
maximum downward velocity decreases with increasing
flow rate.

Table 1: Flow parameters for rising Taylor bubbles in
vertical tubes.

ReL UTB (m/s) ReR UL (m/s)

0 0.173 4380 0
9200 0.61 6254 0.363
13600 0.819 7134 0.537
17800 1.018 7974 0.703



Axial velocity fluctuations are illustrated in figure 7. In
the radial profile, the maximum value of the fluctuation is
attained in the region where the annular jet enters the wake.
The peak of the fluctuation close to wall tends to flatten as
the distance increases from the bubble bottom. This is due
to spreading of the annular jet. The high fluctuations
immediately behind the bubble may be due to the oscillation
of the bubble bottom. The fluctuations decrease with
distance away from the bubble bottom and become very
small around Z/D= -12. It is interesting to notice that the
radial profiles of the fluctuation close to bottom have two
maximum peaks and two minimum peaks. The first
maximum is close to the wall and the value decreases
strongly to hit the first minimum value. It increases again
but not as high as the first maximum then decreases slightly
to the second minimum at the tube centre. This minimum
is not as low as the first one. This double-peak observation
is not seen in case number four. The values of the
fluctuations relative to the Taylor bubble rise velocity
decreases with increasing liquid flow rate.

For the flowing liquid case the radial profiles collapse with
the superficial ones between 8-12D behind the bubble tail.
The wake region of Taylor bubbles is crucial in determining
the characteristics of fully-developed slug flow. The
minimum stable liquid slug length is defined as the
minimum distance needed to reestablish the fully-developed
velocity distribution in the liquid in front of the trailing
Taylor bubble (Mossis & Griffith, 1962). They also stated
that the trailing Taylor bubble is influenced by the flow
velocity distribution ahead of it. They were also the first to
note (using a camera moving with the leading bubble) that
the nose of the trailing bubble distorts, and becomes
alternatively eccentric in the tube cross section. This has
since been viewed by many investigators. They obtained a





7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


UTB=0.173 m/s













"" llllll\\\\\\\.- L|''/ tttl





|"""I llltlllllllllllB llilllll


-0.4 -0.2 0 0.2
r/D


0.4
a


UTB=0.82 m/s

-0 iv.4....2. 0.11T
,- ,, Ittvn, t

_ IL I,,-,ttttttttlI{I









- i i- t0''','-. 4






-0.4 -0.2 0.0 0.2 0.4
/7r~ o


r/D b


IUTB=1.02 m/s


-0.4 -0.2 0.0
/7~\


0.2 0.4


r/u r/u d
Figure 4: Streamlines and velocity vectors in a moving frame of reference in the near wake of Taylor bubbles:
a: stagnant water, b: flowing water (Re=9200), c: flowing water (Re=13600), flowing water (Re=17800).


_1






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


minimum stable length of 12-16D. Since that, the process
of slug development and the prediction of minimum stable
liquid slug length have been investigated by several
researchers (Pinto and Campos (1996), Van Hout et
al.(2002), Zheng & Che (2006), and Mayor et al.(2008)).

Now, based on the PIV measurements of the velocity
profiles in the wake of a single Taylor bubble, an attempt to
explain the coalescence mechanism of the trailing bubble
with the leading can be made. First, the trailing bubble
accelerates following the maximum velocity ahead of it.
Then, it enters the second region where the maximum
upward velocity is located close to the walls. In this region,
it becomes eccentric and distorts towards one side of the
tube wall. When the bubble enters the near wake region, it
distorts due to the high turbulence intensity and eventually
merges with the leading one. According to the PIV
measurements, the minimum stable liquid slug was found to
be 8-12D.


0.20 r0.30
0r/D


0.40 0.50


3.5

3.0

2.5

2.0

1.5

1 o.


-0.5
-2


.0


-1.5 -1.0
Z/D


-0.5 0.0


Figure 5: Comparison of the axial velocity at the
centreline of the tube in the near wake of Taylor bubbles
rising in stagnant liquid and at different liquid flow rates.


0.1 0.2 0.3
r/D


0.4 0.:

b


-.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5
r/D r/D
d

Figure 6: Radial profiles of the axial velocity in the wake of Taylor bubble rising in: stagnant water, b: flowing water
(Re=9200), c: flowing water (Re=13600), flowing water (Re=17800).


x ,tg
-0 Re=9200
A Re=13600 x

x x
x x
S X^
X X


x X
X


1 O---- ----







A Z/D=-0.1
-1 0 Z/D=-0.5
-2Z/D-_I M A
-2 Z/ =-2 a
-3 Z/D=-4 -0
x Z/ )=-8 E A
0 z/>D=-12
-4


[0 Z/D=-0.4
0 ---- -- D- L- --1--
0 Z/D=-2 1
Z/D =-4
5 -7/n- Q
>0 Z/D=-12
flo ing liquid only


1.0


I






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


A Z/L -0.1
0 0 Z/E --0.5
0 Z/L 1--21
S Z/L -2 A
S Z/L -4
5 X- Z4- -8-8 --
0 Z/L -12 a
A c

.. .. A Ai



MEEENEEEMM- ...EE.. MuEfE..

0.10 0.20 0.30 0.40 0.'
r/D


r/L


flying liqu d only
8 -A- Z/-0.1
S Z/L =-0.4
Z/L =-1
*- Z/L -2
6 Z/= -4
S Z/ =-8 A


0 0.2 0. .4



, . ; . . *. .

0.1 0.2 0.3 0.4 0.


b


Figure 7: Radial profiles of axial turbulence intensity in the wake of Taylor bubble rising in: stagnant water, b: flowing
water (Re=9200), c: flowing water (Re=13600), flowing water (Re=17800).


Acknowledgements


PIV velocity field measurements around a Taylor bubble
rising in a vertical tube containing stagnant or upward
moving liquid were successfully made. In the stagnant
liquid, the primary recirculation zone in the near wake was
1.3D. It was 1.7D for all three flow rates of upward
flowing liquid. The maximum axial velocity in the near
wake becomes smaller relative to the rising bubble velocity
in the upward flowing liquid compared to the stagnant case.
Based on the PIV velocity measurements for the four cases
tested in this study, the minimum stable length was
determined to be between 8-12D behind the bubble.


The support of the Natural Sciences and Engineering
Research Council of Canada is gratefully acknowledged.
GS would like to thank the Libyan Ministry of Education
and the University of Saskatchewan for their financial
support.

References


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bubble rising in a stagnant viscous fluid: numerical and
experimental results. Int. J. Multiphase Flow, Vol. 28,
791-803 (2002).


2.


1.

1.


5


Conclusions









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experimental study of the wake of gas slugs rising in
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(2003).
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Pinto, A. M. F. R., Coelho Pinheiro, M. N., Campos, J. B. L.
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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Shemer, L., Gulitski, A. and Bamea, D, Experiments on the
turbulent structure and void fraction distribution in the
Taylor bubble wake. Multiphase Sci. Technol. 16.1,
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