Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 7.6.1 - Effect of Liquid Velocity on the Hydrodynamics and Heat Transfer of Downward Liquid Flow with Stationary Taylor Bubble
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00190
 Material Information
Title: 7.6.1 - Effect of Liquid Velocity on the Hydrodynamics and Heat Transfer of Downward Liquid Flow with Stationary Taylor Bubble Multiphase Flows with Heat and Mass Transfer
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Kashinsky, O.N.
Kurdyumov, A.S.
Lobanov, P.D.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: Taylor bubble
slug flow
wall shear stress
heat transfer
 Notes
Abstract: The study of time-averaged and fluctuational wall shear stress in downward liquid film over a stationary gas bubble is performed. The superficial liquid velocity was varied from U0 to 2U0 where U0 is the Taylor bubble rise velocity in stagnant liquid. It was shown that in the initial part of the bubble the wall shear stress depends on the distance from the bubble nose and is independent of the bubble length and superficial liquid and gas velocity. Measured heat transfer coefficients show the similar trend. A stabilization of the flow of laminar liquid film takes place at some distance from the bubble nose. A growth of liquid film fluctuations resulting in a change of flow pattern occurs with further increase of the distance from the bubble nose. The highest values of relative wall shear stress fluctuations and heat transfer coefficient in the unit cell studied were detected in the zone of annular vortex behind the bubble bottom.
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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Bibliographic ID: UF00102023
Volume ID: VID00190
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: 761-Kashinsky-ICMF2010.pdf

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


Effect of Liquid Velocity on the Hydrodynamics and Heat Transfer of Downward Liquid
Flow with Stationary Taylor Bubble

Oleg Kashinsky, Alexander Kurdyumov and Pavel Lobanov

Lab. of Physical and Chemical Hydrodynamics, Kutateladze Institute of Thermophysics, Siberian Branch of Russian
Academy of Sciences, Novosibirsk, 630090, Ac. Lavrentyev Ave. 1, Russia
lobanov@itp.nsc.ru


Keywords: Taylor bubble, slug flow, wall shear stress, heat transfer




Abstract

The study of time-averaged and fluctuational wall shear stress in downward liquid film over a stationary gas bubble is
performed. The superficial liquid velocity was varied from Uo to 2Uo where Uo is the Taylor bubble rise velocity in stagnant
liquid. It was shown that in the initial part of the bubble the wall shear stress depends on the distance from the bubble nose and
is independent of the bubble length and superficial liquid and gas velocity. Measured heat transfer coefficients show the similar
trend. A stabilization of the flow of laminar liquid film takes place at some distance from the bubble nose. A growth of liquid
film fluctuations resulting in a change of flow pattern occurs with further increase of the distance from the bubble nose. The
highest values of relative wall shear stress fluctuations and heat transfer coefficient in the unit cell studied were detected in the
zone of annular vortex behind the bubble bottom.


Introduction

Slug flow is one of the most common and complex flow
patterns in two-phase flow. These flows are widely
encountered in technological processes such as oil and gas
wells, gas-liquid pipeline reactors, chemical engineering and
pharmaceutical industry.
The slug flow exists in a wide range of flow parameters. A
specific feature of this flow is the existence of large gas
bubbles occupying almost all cross section of the pipe.
These bubbles are called usually Taylor bubbles. The length
of these objects is usually up to several pipe diameters. In a
slug flow the gas bubbles are alternated by liquid plugs in
which small gas bubbles are suspended. A part of the flow
containing one gas bubble and following liquid slug is called
in the literature as a single unit of the slug flow.
Several theoretical models were suggested to describe the
slug flow (Fernandes et al. 1983, Funada et al. 2005, Zheng
et al. 2007) but a satisfactory model does not exist yet due to
a complicated structure and instability of such flows.
Experimental investigations of slug flows are of great
importance at present.
Previous studies were devoted mainly to the study of gas
phase characteristics (bubble length and frequency,
propagation velocity). An interaction between consecutive
bubbles was investigated in (Aladjem Talvy et. al. 2000).
The experimental technique used allowed to determine
instantaneous shape, position and velocity of bubbles. A
significant deformation and oscillation of the nose of a
bubble in the wake of a preceding bubble was observed. It
was shown that these oscillations were connected with the
oscillations of the bottom of the leading bubble. The effect
of the wake of the leading bubble on the trailing one was


observed at the distance of 50D. An empirical correlation
was suggested for the trailing bubble velocity vs. the length
of the preceding liquid slug.
Statistical parameters of upward slug flow were investigated
in (Van Hout et. al. 2001, Shemer 2003). Measurements of
length of moving bubbles, its nose and tail velocities were
performed at five axial positions along the tube using optical
sensors. It was shown that the increase of the distance from
the pipe inlet resulted in increasing the length of both gas
bubbles and liquid slugs. The study of the dependence of the
bubble velocity on the length of the preceding liquid slug
showed that the highest accelerations are for the bubbles
whose preceding slug is less than 3D.
Liquid phase characteristics are of significant interest. Their
studies become possible with the development of modern
experimental techniques. Instantaneous liquid velocity
profiles in a slug flow were obtained by flow visualization
(Shemer & Barea 1987). Close to the bubble bottom the
velocity profiles are significantly deformed, they recover at
the distance of 12D from the bubble bottom. The flow field
near a single bubble was studied in (Nogweira et. al. 2003)
by PIV and pulsed shadow technique. The slug flow studies
were performed in (Nakoryakov et. al. 1989) using
electrodiffusional technique. Liquid velocity profiles in
liquid slugs were obtained along with wall shear stress
distribution. A significant increase of the flow turbulence
was detected close to the bubble bottom.
The hydraulic characteristics of fully developed gas-liquid
upward slug flow using electrochemical method,
conductivity probes and digital high-speed system were
investigated in (Zheng & Che 2006). The Taylor bubble
shape, the falling film characteristics, the void fraction
distribution in the liquid slug were measured.





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


Local characteristics of the slug flow such as averaged and
fluctuational wall shear stress, liquid velocity profiles, etc.,
can be obtained in the slug flow only statistically by
ensemble averaging technique. Unfortunately, this approach
allows to obtain only averaged characteristics and does not
allow to obtain the dependency of fluctuational
characteristics on the distance from the bubble nose for an
arbitrary bubble. Also some important flow characteristics
can be hardly obtained during the bubble motion.
For this reason, experimental models of the slug flow were
studied in which the downward liquid flow over the stagnant
bubble or its solid model was realized.
The drag force of the solid model of the gas bubble in
downward liquid flow was performed in (Tudose & Kawaji
1999) to obtain the mechanisms of acceleration of the
travelling bubble moving in the wake of the leading one. A
one dimensional model of the flow was developed. It was
shown that the bubble acceleration was caused by the bubble
nose deformation and its radial shift relative to the pipe axis.
The gas entrainment from a stagnant gas bubble in
downward liquid flow was studied in (Delfos et. al. 2001).
Local void fraction and its radial distribution behind the
bubble were measured for different bubble length and liquid
velocities.
Gas entrainment by liquid film from a stationary gas bubble
was studied in (Kockx et. al. 2005) in a pipe 100 mm
diameter. Using the LIF technique the thickness of the film
around the bubble, wave height were measured for the
bubbles of 100 to 1500 mm long. A model was proposed
according to which the gas entrainment is directly
proportional to the film waveness and inverse proportional
to the film thickness.
The present paper presents the results of investigation of
averaged and fluctuational wall shear stress around a
stationary gas bubble and in the region of liquid flow behind
the bubble bottom.

Nomenclature

D inner diameter of pipe (m)
g gravitational constant (ms 2)
L bubble length (m)
Uo Taylor bubble rising velocity in a stagnant water
(ms-1)
VL liquid velocity flow rate (ms-1)
X distance from the bubble nose (m)

Greek letters
a heat transfer coefficient (W m2K 1)
F flow rate density (m2s-1)
S r.m.s. wall shear stress fluctuations (-)
v Kinematic viscosity of liquid (m2s-')
C Liquid film thickness (m)
z, Wall shear stress (Pa)

Experimental Facility

The experimental setup was a flow loop closed for liquid and
open for gas. Liquid from a storage tank was supplied to the
test section by a centrifugal pump. The liquid flow rate was
controlled by valves and measured by a system of rotameters.
The liquid from the rotameters was supplied to the inlet
section, after that it passed through a contractor into the test


liquid


Figure 1: Scheme of bubble injection: 1 -
3 small tube; 4 pipe; 5 spacing unit.


bubble; 2 nozzle


pipe 20 mm inner diameter. The top section of the test pipe
made of stainless steel was connected to a visualization unit
made of polished Plexiglas. The length of this unit was 550
mm. Downstream a measuring unit was placed. It was a
Plexiglas body of rectangular cross section 125 mm long. An
orifice 20 mm diameter was drilled along its axis. The outer
surfaces of the unit were polished to make it optically
transparent. The gas bubble was clearly seen through the
transparent surfaces of visualization and measuring units.
The arrangement for producing stationary gas bubble is
shown in Fig. 1. A thin tube 2 mm outer diameter was placed
in the test section. A Teflon nozzle was at the downward end
of the tube. The tube was fixed on the axis of the test tube by
the spacing unit. A uniform gas flow was supplied to the tube
from the gas flow controller Bronkhorst.
Hydrodynamic characteristics of the flow were measured by
electrodiffusional technique (Nakoryakov et. al. 1989). Two
electrochemical wall shear stress probes were inserted into
the measuring unit. The probes were polished flush with the
wall. The probes were connected to a 2-channel DC
amplifier. Amplified probe signals were supplied to a A-D
transformer of the instrumental board E-440 and after
digitizing they were recorded in the computer memory. The
probe calibration was performed in a single-phase pipe flow.
The calibration coefficients obtained were used to process
the signals in the two-phase flow.
The measurement uncertainty was 3, 7 and 15% for the
bubble length, averaged wall shear stress and wall shear
stress fluctuations, respectively.
The heat transfer measuring unit was a thin wall stainless
steel pipe 20 mm i.d. and 580 mm long. Electric current
from the high current system heated the pipe. The RTD
sensors were utilized to measure the temperature of liquid in
the test pipe entrance, measuring unit and the test pipe exit.
The knowledge of these temperatures allows us to determine






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


S





0
o


0


0 0

00 0


q~- g
0


Figure 2: Photographs of gas bubbles in the flow at VL=0.15 m/s.


the heat transfer coefficients of the flow.
To perform measurements around the bubble 12 temperature
probes were used spaced 10 mm apart. The first one was
placed 225 mm downstream the beginning of the heated
section. The initial liquid temperature was measured
immediately after the rotameters, the final liquid temperature
was measured in the outlet section of the pipe.
Preliminary calibration of the test section was performed in a
single-phase flow. The measurements were made in a range
of liquid velocities of 0.145 to 0.3 m/s (Re = 3000 + 6000). A
comparison with a well known formula:

Nu = 0.021RePr 43, (1)


6





4


0 1
O 1
e 0 2
2 1- l 3
& A 4

S>D 5

0 J ,K>\ I I I
-40 0 40 80 120
X [mm]
Figure 3: Wall shear stress distribution around the gas bubble
VL=0.15 m/s: 1 L=10 mm;1 L=30 mm; 1 L=60 mm; 1 -L=I
mm; 1 L= 140 mm.


Figure 4: Photographs of gas bubbles in the flow at different
liquid velocities: 1-VL=0.15 m/s; 2-VL=0.2 m/s;. 3-VL=0.26 m/s;
4-VL=0.3 m/s.

were Nu is the Nusselt number, Re is the Reynolds number,
Pr is the Prandtl number, was made.
At low liquid Reynolds numbers a deviation of experimental
data from the from the formula of about 5 % was detected.
With increasing the Reynolds number the difference of
experimental and calculated data in a single phase flow
decreases and becomes about 1 % for Re=6000. The
estimated error of measurements by the heat loss was about
one percent.
The resistance of the heated pipe was 0.0272 ohm. The
electric current through the pipe was 112.5 A. Therefore, the
power emitted at the heating section was 345 W.

Results and Discussion

In order to simulate the real slug flow the mean liquid
velocity of downward flow VL should be equal to the rise
velocity of Taylor bubble in stagnant liquid Uo which is
proportional to the square of pipe diameter. For the tube with
inner diameter of 20 mm this velocity is equal approximately
to 0.15 m/s.
The photos of bubbles obtained at this liquid velocity are
shown in Fig. 2. The shape of the bubble nose does not
depend of the bubble length. The thickness of liquid film
around the bubble depends only on the distance from the
bubble nose and not affected by L.
The gas bubble resident in the liquid can be separated in three
regions depending on the shape of its surface. Correlations
are suggested in the literature to calculate the liquid film
thickness around the bubble:
D1
a= X(3D-4X) (2),
2 2
for the bubble nose;

S= 1 (3),
2 2g
for the initial section of the liquid film flow;

( 1 = / (4),

for the region of stabilized liquid film
The studies show that the distributions of wall shear stress
around the bubble also depend on X and are independent of
the bubble length (Fig. 3). The average liquid velocity was
0.15 m/s, the bubble length was varied during the


i'


M_ IPM
ar, M















1 + 0.15
SJ : 0 0.16
SA AA 0.18
A A A 0.20
9 0.22
A 0.26
A 0.30
0.1 I
-40 -20 0 20 40
X [mm]
Figure 5: Wall shear stress distribution upstream the bubble
nose.

experiments from 10 to 140 mm. A sharp increase of wall
shear stress takes place in the region of the bubble nose. The
bubble blocks part of the pipe cross section and the cross
section occupied by liquid significantly decreases which
results in the liquid acceleration. This results in a sharp
increase of zT with increasing X in this region.
A gradual decrease of liquid film thickness resulting in a
gradual increase of wall shear stress t, takes place with
further increase of the distance from the bubble nose. This
region is an initial section of the liquid film flow. A
significant decrease of liquid turbulent fluctuations occurs in
this region so the flow laminarization takes place. The effect
of liquid turbulence reduction is known in the literature. An
assumption concerning the liquid film laminarization in the
initial part of the bubble due to liquid acceleration is made in
(Kockx et. al. 2005). As a result a laminar boundary layer is
formed.
In order to obtain more detailed information on the film flow
between the bubble surface and the pipe wall the mean liquid
velocity was varied in the range 0.15 to 0.3 m/s (Uo+2Uo).
During the experiments a uniform gas flow rate was supplied
to the flow which allowed to obtain the gas bubble whose

8



6 $ ? t

6 4 VL [m/s]
+ 0.15
4:4
0 0.16
0.18
O 0.2
2 9 0.22
A 0.26
A 0.3

0 100 200 300 400 500
X [mm]
Figure 6:. Wall shear stress in downward liwuid film around the
gas bubble.


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

8





7- 0




6

1
-- 2


0.15 0.18 0.21 0.24 0.27 0.3
VL [m/s]
Figure 7: Comparison of measured wall shear stress values in
the region of stabilized film with calculations by formula (4): 1
-experimental data; 2 calculation.
length was more than 500 mm. Wall shear stress
measurements were performed for 0 Visual observations of the bubble demonstrated the change
of the bubble shape with increasing liquid velocity (Fig. 4).
The bubble nose becomes more sharpened at higher liquid
velocities. The film thickness around the bubble increases
with increasing liquid flow rate. This is caused by the
increase of liquid flow rate in the film.
Let us consider the change of the flow structure with the
addition of the gas bubble. Fig. 5 shows wall shear stress
values upstream of the bubble nose. z, values corresponding
to a single phase pipe flow were detected at the distances of
about one pipe diameter from the bubble nose. The decrease
of the distance from the nose results in the increase of wall
shear stress. It is caused by the rearrangement of the liquid
streamlines dye to the presence of the gas bubble. Similar
results can be obtained in the studies of real slug flow
presented in the literature. This effect is more pronounced for
lower liquid velocities. In the initial point of the bubble the
wall shear stress is approximately the same for all VL studied.
The dependency of wall shear stress on the distance from the
bubble nose is shown in Fig. 6 for the bubble which length

0.16
VL [m/s]
+ 0.15
0.12 0 0.16
0.18
0 0.2
0.08 0.22
0.08
A 0.26
A A 0.3
AA
0.04 AA

0 AAA


0 100 200 300 400 500
X [mm]
Figure 8: Relative wall shear stress fluctuations in the liquid
film.





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


- X =500mm
X = 750 mm


0 4


8 12 16


T [Pa]
Figure 9: Probability distribution of wall shear stress.
was 500 mm or 25D. At the bubble nose and intermediate
region of the bubble the wall shear stress values depend only
on the distance from the bubble nose and do not depend on
VL andL.
The limiting thickness of the liquid film depends on the mass
flow rate and increases with the increase of the liquid
velocity. Due to this the establishment of the regime of
limiting film thickness for different VL takes place at
different X values. At VL=0.155 m/s this regime starts at X=
240 mm. At VL=0.3 m/s the regime of limiting film thickness
starts at the distance of more than 500 mm from the bubble
nose.
Local heat transfer from the wall to the liquid film was
studied. Experiments were performed for the values of liquid
velocity 0.15 and 0.3 m/s for the distance of 200 mm from the
bubble nose. The gas flow rate in the experiments varied
from 100 to 1000 ml/min. It was shown that heat transfer
coefficients obtained do not depend on liquid and gas
velocities which corresponds to the wall shear stress values
observed.
A comparison of measured wall shear stress values in the
region of stabilized liquid film with the calculation according
to (4) was performed. The results obtained are shown in Fig.


0 50 100 150 200
X [mm]
Figure 11: Mean and fluctuational wall shear stress.
7. One should note that the data obtained are described with
high accuracy by a known Nusselt formula for a laminar
liquid film. For the highest liquid velocity studied the
establishment of stabilized film flow was not detected at X
less than 500 mm.
The distribution of relative wall shear stress fluctuations
around the bubble vs the distance from its nose are shown in
Fig. 8. In regions 1 and 2 a gradual decrease of relative
fluctuations takes place with increasing distance from the
bubble nose.
A decrease of wall shear stress from single-phase values for
the same liquid velocity VL up to close to zero values was
observed in these regions. The X value at which the highest
decrease of relative liquid fluctuations was observed
correspond to the establishment of stabilized liquid film. An
increase of fluctuational characteristics of the flow with
increasing the distance from the bubble nose was detected in
the region of stabilized film flow. This results from the
generation of waves on the liquid film surface.
Fig. 9 shows the probability density distribution of wall shear
stress for VL=0.15 m/s and different X after the establishment
of stationary liquid film. For X=500 mm the distribution
typical for laminar flow is observed. The deviations from the


A
A 00 CD

O 0
S 0 Qg [ml/min]
0 400


-A 0CD


o I ,


* 700
A 1000
, I I


300 400 500 600 700 800 900 1000
X [mm]
Figure 10: Relative wall shear stress fluctuations in the liquid
film around the bubble.


A
AA


4000


3000



S2000

a


1000


0 50 100
X [mm]
Figure 12: Local heat transfer coefficient.


1.2

1

0.8

0.6

0.4

0.2


A A
A A

A
A
A

A A
A A A


iAMLAA.fA A t @11


0.4



0.3



S0.2



0.1


0
00
0

O
0 0

_000000 00(
00
)


150 200









mean values are small. At X=750 mm a significant increase
of film turbulent fluctuations occurs. The shape of curve
obtained corresponds to the wavy liquid film. Therefore a
flow regime transition happens with increasing the distance
from the gas injection point.
The dependency of turbulent wall shear stress fluctuations on
the distance from the bubble nose is shown in Fig 10.
Experiments were performed at the same liquid velocity
VL=0.15 m/s but different gas flow rates Qg. A decrease of
turbulent fluctuations of the single-phase flow takes place in
the initial part of the bubble. With further increasing X the
laminar film flow is observed. After that the turbulent
fluctuations increase and the film flow regime transition is
observed. The transitional value of X depends on the gas flow
rate and becomes smaller at higher gas flow rates.
Mean and fluctuational wall shear stress were studied in the
zone of annular vortex behind the bubble 60 mm long (Fig.
11). A sharp decrease of mean wall shear stress with
increasing distance from the bubble bottom was obtained. It
was connected with the expansion of the pipe section for the
liquid flow.
A significant increase of turbulent liquid fluctuations was
detected in the zone of annular vortex. This is caused a
complicated vortex flow in the liquid behind the bubble. The
fluctuations in this region are significantly higher than
single-phase values. The wall shear stress probe signal in this
region has a complicated nature with an alternation of regions
with high mean and fluctuational wall shear stress values and
regions with low values of these quantities.
Fig. 12 shows the dependence of heat transfer coefficient on
the distance from the bubble nose for the bubble length of 60
mm. The character of heat transfer distribution around the
bubble is similar to that for wall shear stress. A sharp increase
of a in the initial part of the bubble where the bubble shape is
close to spherical. A further gradual increase of heat transfer
coefficient with increasing X was detected up to the bubble
bottom. A significant increase of a in the region of annular
vortex behind the bubble was shown. The highest values of
a was observed at the distance of 2D from the bubble bottom.
This corresponds to the position of highest wall shear stress
fluctuations.

Conclusions

The study of the flow hydrodynamics for the stationary gas
Taylor bubble in downward liquid flow was performed.
Experimental data on the fluctuation flow structure around
the bubble were obtained. The flow perturbation by the
bubble was shown to start 20 mm upstream of the bubble
nose. The values of wall shear stress around the bubble
increase while the relative fluctuations decrease. In the
region of film flow around the bubble the wall shear stress
increases several times the single-phase value, the flow
laminarization occurs due to the liquid acceleration. It was
shown that the wall shear stress around the bubble depends
on the distance from the bubble nose and is independent on
the bubble length and liquid velocity. Measured heat transfer
coefficients at X=200 mm confirmed this observation. It was
shown that the establishment of stabilized film flow takes
place at different distances for different VL The highest
values of heat transfer coefficient in the unit cell of the slug
flow were observed in the zone of annular vortex behind the
bubble. The position of heat transfer maximum corresponds


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

to the maximum of wall shear stress fluctuations in the vortex
region downstream the bubble bottom.

Acknowledgements

This work was partially supported by the grant of Russian
Foundation of Basic Research Xo08-08-00543.

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

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