Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 7.1.3 - Time resolved PTV measurements in Sub-Milli scale bubbles laden Turbulent Pipe Flows
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00173
 Material Information
Title: 7.1.3 - Time resolved PTV measurements in Sub-Milli scale bubbles laden Turbulent Pipe Flows Bubbly Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Takagi, H.
Lelouvetel, J.
Sato, Y.
Hishida, K.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: sub-milli bubble
turbulence
time resolved PTV
vertical pipe
 Notes
Abstract: The paper describes studies of the turbulence studies in the sub-milli scale bubbly flow. Time resolved Particle Tracking Velocimetry (PTV) with Shape Projection Image (SPI) technique has applied for measurement of the turbulence modifications by sub-milli bubbles in upward and downward flows. Void fractions up to 1.5% were tested at Reynolds number of 15000. In upward flow, bubbles are gathered close to the wall, while in downward bubbles have tendency to locate at the center of pipe. We analyze the mean velocity characteristics, the turbulent kinetic energy (TKE) budget, and the power spectrum of velocity fluctuation. Energy production is decreased although TKE dissipation is increased. The modifications are greater in downward than in upward flows. The initial 5/3 power law of the power spectrums of the velocity fluctuation at center of the pipe, stays at -5/3. In upward flow, length scale do not changed but in downward flow, length scale is modified as enhancement of void fraction.
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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Volume ID: VID00173
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Holding Location: University of Florida
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Resource Identifier: 713-Takagi-ICMF2010.pdf

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Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Time Resolved PTV Measurements in Sub-milli Scale Bubbles Laden Turbulent Pipe Flow


Hiroyuki TAKAGI*, Julie LELOUVETEL*, Yohei SATO*, and Koichi HISHIDA*

Department of System Design Engineering, Keio University
3-14-1 Hiyoshi Kohoku-ku, Yokohana-shi, 223-8522, Japan
takagi(_,tfe.sd.keio.ac.jp, lelouvetel(dtfe.sd.keio.ac.jp, voheik@sd.keio.ac.jp and hishidaA@isd.keio.ac.jp


Keywords: sub-milli bubble, turbulence, time resolved PTV, vertical pipe


Abstract
The paper describes studies of the turbulence studies in the sub-milli scale bubbly flow. Time resolved Particle Tracking
Velocimetry (PTV) with Shape Projection Image (SPI) technique has applied for measurement of the turbulence modifications
by sub-milli bubbles in upward and downward flows. Void fractions up to 1.5% were tested at Reynolds number of 15000. In
upward flow, bubbles are gathered close to the wall, while in downward bubbles have tendency to locate at the center of pipe.
We analyze the mean velocity characteristics, the turbulent kinetic energy (TKE) budget, and the power spectrum of velocity
fluctuation. Energy production is decreased although TKE dissipation is increased. The modifications are greater in downward
than in upward flows. The initial -5/3 power law of the power spectrums of the velocity fluctuation at center of the pipe, stays
at -5/3. In upward flow, length scale do not changed but in downward flow, length scale is modified as enhancement of void
fraction.


1. Introduction
Gas-liquid flows including turbulence appear in a variety of
industrial applications for example, power plants and
chemical processing facilities. Understanding of the
turbulence structure is necessary to develop safe and high
efficiency industrial instruments. However, there are only a
few detail mechanisms of turbulence structure in bubbly
flow because of complicated bubbles and liquids
behaviours.

In vertical pipe turbulent bubbly flow, bubble diameter, Deq,
Reynolds number, Re, void fraction, a, and flow direction
are elements effecting turbulence structure, as reported by
Wang et al. 1987, Kashinsky et al. 1999, Wang et al 1987)
observed that in upward flow, i.e. when the flow direction
and gravity are the opposite, local void fraction distributions
are wall-peaked. In contrast, in downward flow, i.e. when
the flow direction and the gravity are similar, maximum
value of local void fraction takes at center of pipe.
Mechanisms of bubble concentration were also examined by
numerical simulation in microbubble turbulence (Keys, WN
et al. 1993). These previous studies suggest that the
mechanisms of the turbulence modifications are related to
the lift force.

Effects of bubbles to the mean flow characteristics
(Serizawa et al. 1975, Wang et al. 1987), the energy
spectrum (Lance and Bataille, 1991, Shawkat et al. 2008)
and the production and turbulence kinetic energy (TKE)
dissipation rate have been investigated experimentally
(Lelouvetel et al. 2009, Nakagawa et al. 2008, Fujiwara et
al. 2004 )

Up to resent turbulent studies, there are a lot of studies
investigating the importance of bubble diameter (Fujiwara
et al. 2004). However major part of them used milli-order


bubbles, i.e. bubble diameter from 1 to 4mm, (Fujiwara et al.
2004) and only a few reports exist about effect of bubble
diameter in sub-milli scale (Gutierrez et al, 2008), i.e. close
to Kolmogorov length scale, q.

Therefore, in the present study, the main objective is to
investigate the effect of sub-milli bubbles (406utm) on
turbulence structure in upward and downward flow. To
understand the turbulence structure, experiments were
performed using two experimental techniques: time resolved
particle tracking velocimetry (PTV) and shape projection
imaging (SPI). The analyses consist on the study of the
mean flow statistics, the TKE budget, and power spectrums
of the velocity fluctuation.


2. Nomenclature
<> An ensemble-averaged quantity
E, Energy spectrum in z direction
r Distance from the centerline
R Pipe radius
Re Reynolds number
u Fluctuating velocity
U Time averaged velocity
Uc Centerline velocity
P Energy production
a1 Local void fraction
a Mean void fraction
S Dissipation rate
r7 Kolmogorov length scale
:K Wave number
v Kinetic viscosity






Paper No


3. Experimental Facilities
3.1 Experimental Setup
The experimental setup is a vertical pipe, in which
experiment was performed in upward and downward flow,
respectively. The vertical pipe diameter is 2R = 44 mm, and
flow rate is set to 27.30 x 10-3 m3/s. The corresponding
Reynolds number is Re = 2R/v = 15000 and the
Kolmogorov length scale, r = 260 grm.

To eliminate optical distortion due to refraction from the
pipe, the test section is made of fluorinated ethylene
propylene (FEP) that has the same refraction index with
water (Fujiwara et al. 2004). The test section is located at
1.5 m downstream from sub-milli bubble generator. The
total pipe height is 2.2 m. Therefore we assumed that the
flow was fully developed in the test section. The center axis
of the pipe was defined as the origin. Flow direction and
radial direction were taken to be the z-axis and r-axis
respectively.

Sub-milli bubbles were generated by sphere shaped fine
porous illustrated in figure l(a). Bubble generator consisted
of air cave size of 150-200gtm. We injected surfactant
3-Pentanol (400 ppm) in order to avoid bubble cluster. Mean
sub-milli bubble diameter, Deq, is 406 urm +142 Lnm,
corresponding to 1.56 q. The probability density functions
(PDFs) of bubble diameters is illustrated in Figure l(b).
Finally, the mean void fraction, a, is set to be 0.5%, 1.0%
and 1.5% in upward and 0.5%, 0.75% and 1.0% in down
ward. The air pressure and the flow rate were controlled by
pressure gauge and a flow meter, respectively (Fujiwara et
al. 2004).

In downward flow, to avoid rising bubbles due to buoyancy
force we designed the upper tank as shown in Figure 2. The
outlet cross section was designed by B = R because we
already knew that bubbles would go down from the previous
experiment (Nakagawa et al. 2008). At the same time, the
channel has the same cross-section area at entire upper tank,
particularly around the bubble generator (B = 2A), so that
liquid-velocity are the same.


3.2 Measurement System
A time-resolved PTV system and a SPI system, as shown in
Figure 3, were synchronized using a pulse generator to
measure both liquid and bubble motions at the same time.
Two CMOS cameras, for PTV and SPI, were set facing each
other and were focused on the same vertical plane (900 X
600 pixels2 corresponding to 25.7 X 17.1 mm2). So that one
can record the motion of bubbles illuminated by blue LEDs
and the other can record motion of seeding particles
illuminated by a laser sheet. In Figure 4(a) and (b), example
images of PTV and SPI images in a = 0.5% are shown.
Acquisition rate of camera for PTV was set to be 500 Hz.
The camera for SPI was set to be 1 kHz to avoid extension
of bubble images. Indeed, bubbles are faster than liquid
phase and appear as streaks if the exposure time is too long.
Fluorescent particles, which have diameter of 5 tm and
fluorescence wavelength of 600 nm, were used. Coordinate
axes in upward and downward are shown in table 1.


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

To determine the liquid velocity fields from seeding particle
images, time-resolved Particle Tracking Velocimetry (PTV)
was applied. The algorithm consists of applying a Particle
Image Velocimetry and then a PTV algorithm.


0.00 a I'II
0 200 400 600 800 1000 1200 1400 1600
D [Mm]
50mm
Fig. 1 (a)Bubble generator, (b)Bubble diameter
distribution.


pump
Fig.2 Schematic of the upper tank for downward flow.


CCD Camera for PTV
900 x 600[pixels]
Frame rate: 500[Hz]


t= 2ms]



t=41msl


CCD Camera for SPI
900 x 600[pixels]
Frame rate: 1[KHz]



=ot[ms:
n m





Pulse Generator t= 2[ms]



t = 4[ms)


Fig.3 Schematic of the experimental facility.

Tab. Coordinates of upward and downward flows.
Upward Downward











< Uc = 397 [mm/s] < Uc = 324 [mm/s]
< Uc > : Centerline Velocity


a= 0.5%






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


0.2 0.4 0.6 0.8 1.0
r/R


0.0
(b)


0.2 0.4 0.6 0.8 1.0


0.2 0.4 0.6 0.8


1.0 0.0


0.2 0.4 0.6 0.8 1.0


Fig. 4 Example of PTV and SPI images in (a) upward and (b) downward flow.


35

30

25

g 20

8 15
10

> 5


0.0 0.2 0.4 0.6 0.8 1.0


0.0 0.2 0.4 0.6 0.8 1.0


(b)
Fig. 5 Local void fraction in (a) upward and (b) downward flow.


The PTV vectors are then used to reconstruct grid velocity
maps. The grid size is 200utm. This spatial resolution
provides accurate estimation of the TKE dissipation rate.
For SPI images information for bubbles is calculated by
subtracting back noise image first. Then dynamic
binarization was applied to calculate the size and the
position of the bubbles. For the dynamic binarization,
thresholds value on the grey level and gradient are estimated
using the procedure proposed by Tachibana et al. (2005).


4. Results and Discussion
4.1 Local Void Fraction
Figures 5(a) and (b) show the local void fraction profiles in
upward and downward flows, respectively. The horizontal
axis r is normalized by the pipe radius R. The local void
fraction was calculated by equation (1). S(r) is the area of
the SPI image in region r and Sb(r) is the area that are
occupied by bubbles in the same region of the SPI image.
The brackets < > indicate the time and spatial average.


Paper No


0.0

(a)


35

30

S25

20

15

* 10


a(-0%
Sa-0.5% o
o -1.5% o
A A
0
A

O0
0 0
m "
0 n .


* A
A A .

A A A.0
*** A
.* E a
"...



0-0.5% 0
a-0.75%
A o-1.0% *






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


* a--o- *0
=0%
* -=0.5%
Sa1.0%
o a=1.5%


0.2 0.4 0.6 0.8 1.0


1 a
S a-0%
a-0.5%
0.75%
a a01.0%

0.0 0.2 0.4 0.6 0.8 1.0


Fig. 6 Liquid-phase mean velocity in (a) upward and (b) downward flows.


o
1. 00

0.8 U * U

0.6

0.4
4 a=0.5%
a a=1.0%
0.2 o a-1.5%


0.0
0.0


0 0
U c
U
U


0.2 0.4 0.6 0.8 1.0


)







a=0.5%
a-0.75%
2 a- 1.0%


0.0 0.2 0.4 0.6 0.8 1.0


r/R (b) r/R
Fig. 7 Gas-phase (Bubble) mean velocity in (a) upward and (b) downward flows.


a(r)=< ., i ,r)> (1)
Local void fractions reach the max value at 0 < r/R < 0.3 in
Figure 5(a) and at 0.8< r/R < 1.0 in Figure 5(b). This
denotes the sub-milli bubbles tend to gather at the wall
region in upward flow as observed in previous studies
(Wang et al. 1987, Fujiwara et al. 2004). On the other hand,
in downward flow, the sub-milli bubbles are preferentially
distributed in the center region of the pipe (Kashinsky et al.
2006, Lu and Tryggvason 20006, Sun et al. 2004). These
phenomena could be caused by the differences of lift force
directions.

At the same time, the values of local void fractions are
higher in downward than upward. This could be attributed
to flow directions and buoyancy directions. In upward, the
buoyancy direction is the same with flow direction, while in
downward they are in opposite directions. Thus, in
downward flow, bubble velocities are slower, and bubbles
tend to stay at test section, which causes higher void
fraction in downward.


4.2 Mean Velocity Profiles
The liquid-phase stream wise mean velocity in upward
and downward directions are plotted in Figure 6(a), (b). In
both figures, vertical axes are normalized by mean velocity
at the center of pipe, shown in Tab. 1.


In both directions, mean velocity profiles are reduced and
flatten at 0 < r/R < 0.9. They are increased in the wall region.
As void fraction increased mean velocity is modified
strongly. Mean velocities were more modified in downward
flow than upward.

In upward flow, bubbles are gathering at vicinity of the wall
(Figure 5(a)) and accelerate the flow, due to the similar
directions of the buoyancy force and the flow. This
acceleration of the flow close to the wall induces a
deceleration of the flow in the central region. In downward
flow, bubbles, which are gathering at center of the pipe
(Figure 5(b)), decelerate the flow since buoyancy force
direction and flow directions are opposite. This deceleration
induces a deviation of the liquid towards the wall and
causes an increase of the mean velocity close to the wall.

Therefore the existence of bubbles change the mean velocity
profiles clearly, that will also cause modifications for
turbulence intensity profiles.

Figure 7 (a) and (b) show the bubble mean velocity. The
bubble velocity was estimated by applying a PTV algorithm
on the diarized image. In both directions, bubbles mean
velocity profiles seem to have close values at any void
fraction.


Paper No


0.8

0.6

0.4


0.0 -
0.0






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


a-00%
0.2 0 a-0.5%
a- =1.0%
o a-1.5% oa


0.1




0.0
0.0 0.2 0.4 0.6 0.8 1.0


0.002









0.000


0.2
A



0.1


0.0

0.0


a-1.0%








0.0 0.2 0.4 0.6 0.8 1.0


r/R tu; r/R
Fig. 8 Liquid-phase turbulence intensity in (a) upward and (b) downward flows.

0.002

% E a-0.5%o
1.0 .99* w- O.50%
o ..*." a-0.75% 0
S .... 0.001 .*

U... ,..


v 0.000


0.0 0.2 0.4 0.6 0.8 1.0


0.0 0.2 0.4 0.6 0.8 1.0
(b) r/R


Fig. 9 Liquid-phase Reynolds stress profile in (a) upward and (b) downward flows.


In upward flow, the shapes of bubble mean velocity profiles
and value of bubble mean velocity are close to liquid-phase
mean velocity (Figure 6), at 0 < r/R < 0.9. In region 0.9<
r/R < 1.0, bubble mean velocities have higher values.

In downward flow, bubble velocity profiles have lower
value in 0 < r/R < 0.9 and higher in 0.9< r/R < 1.0 compare
to liquid-phase mean velocity. As void fraction increase,
liquid-phase mean velocity get closer to bubble mean
velocity. We observed that bubbles tend to follow the
liquid-phase flow in upward and bubbles modify the flow
stronger in downward.


4.3 Turbulence Intensity Profiles
Figure 8(a) and (b) present the profiles of the turbulence
intensity (< u2, >)1/2 in the both directions. In upward,
turbulence intensities are increased and the shape of profiles
are more flatten as the amount of air increase in pipe center
pipe (0 < r/R < 0.8). At vicinity of the wall (0.8 < r/R < 1.0),
turbulence intensities are increased. In downward, at center
of pipe (0 < r/R < 0.9), we also observed increments of
turbulence intensities as amount of air increased. Moreover,
the turbulence intensity profiles are more flatten compare to
upward. At vicinity of the wall region (0.9 < r/R < 1.0),
there are no big difference with single phase flow.


This observation indicates that the wake of the bubbles
increases the turbulence intensities whatever the distance
from the wall. Moreover, in upward flow, vicinity of the
wall (0.8 < r/R < 1.0) is the region has more bubbles Fig.
5(a). This induces a great enhancement of the turbulence
intensities. However, in downward flow, there are no
differences at vicinity of the wall because there are only few
bubbles in this region.

4.4 Liquid-Phase Reynolds Stress Characteristics
Figure 9(a) and 6(b) portray Reynolds stress profiles in
upward and down, respectively.
In both flow directions, we observed that Reynolds stresses
in every condition take maximum values at vicinity of the
wall (r/R > 0.9). In the center pipe (0 < r/R < 0.9), Reynolds
stress profiles are reduced. We also confirmed that as
amount of air enhanced, Reynolds stresses are more
flattened and reduced. This could be due to the dependence
of the shear stress on the gradient of mean velocity. However
at vicinity of the wall, shear stress is maximized due to high
gradient value of mean velocity.

The lucid difference between upward and downward
profiles is magnitude of reduction. At 0 < r/R < 0.9, every
Reynolds stress profiles of downward flow are close to 0
and take peak at r/R =0.9.


Paper No






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


40000
at0%
30000 a0.5%
a- 1.0%
So a=1.5%
S20000 a o%
S* a-0.5%
10000 a A 1.0%
K e a-1.5%


0 -.m.a

-10000
0.0
(a)




0.7

0.6

0.5

0.4

0.3

0.2

0.1


40000
a=00)%
30000 a5
a 0.75%
a 1.5%


SProduction


SDissip


mmmmmnamu1mmwnn W


)ation .
soA-


LUUl

100(




-100(


0.2 0.4 0.6 0.8 1.0


SProduction


0U a=c%
S=04).5%
0 a).759% Dissipation
a 01.0% J
0
0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0


r/R (b)
Fig. 10 TKE budget profiles in (a) upward and (b) downward flows.


0.5

" 0.4

0.3

0.2

0.1


0.5
(a) r/R


Fig. 11 Instantaneous TKE dissipation in case of a = 1.0% in (a) upward and (b) downward flows.


4.5 Turbulence Kinetic Energy Profiles
In this section, the effect of bubbles on the TKE budget is
discussed. The transport equation for TKE in bubbly flow
can be written in following equation.
Dk dT
Dk + T P, F (2)
Dt O8x k

Pk represents the production, e is the TKE dissipation rate,
and FB is the energy transfer due to bubbles. In the present
study, we used the following equations for production and
dissipation rate.


k(UZ)
Or

)v< 2 2 2" )2 + j2 + )2
or ) 0z ) orz ) 9r )


+2 u
or 0z


PIV measurement noise provides an over estimation of the
TKE dissipation rate (Dejong et al. 2008, Saarerinne and
Piirto 2000). Thus in present study, we apply the correction
technique proposed by Tanaka and Eaton (2007) to compute
the dissipation rate.

S= (5)
3
6l2A is the measured TKE dissipation rate estimated with


double grid spacing, 2Ax. The PTV resolution provides the
calculation of e with an underestimation of 30% (Tanaka and
Eaton 2007).

The production and TKE dissipation rate profiles are plotted
in Figure 10 (a) and 10(b). The first remark is the reduction
of the production in upward and downward. In the center
region (0 < r/R < 0.3), production values are closer to zero as
getting far from the wall. This reduction of production is
more significant for upward and high void fraction. This
decrease could be caused by the reduction of the shear stress
(Fig. 9) and by the flattened mean velocity profiles (Fig.6).

TKE dissipation is increased as mean void fractions is
increased. In upward, at 0 < r/R < 0.3 and 0.9 < r/R < 1.0,
TKE dissipation rate is amplified. In downward, on the other
hand, at 0 < r/R < 0.9, TKE dissipation rate is increased
remarkably, especially in higher void fraction. The
increments of dissipation rate are in broad range. In both up
and downward flows, the region where TKE dissipation rate
is increased corresponds to the region with higher local void
fraction (Fig. 5). TKE dissipation rate in bubbly flow
strongly rely on the existence of bubbles.

We confirmed previous results (Fujiwara et al. 2004)
showing that production and TKE dissipation rate do not
balance. Bubbles reduce energy production and increase
TKE dissipation rate. Even though the tendencies of


Paper No


e [mm2/s3]
20
m soo
a 000
13000


0.5 1.0
r/R
























(a) 01 1


Paper No




10 1


0001

00001


01 1


Fig. 12 Energy spectrum at the pipe center line in (a) upward and (b) downward flows.


production profiles are similar between up and downward,
while the differences of up and downward for TKE
dissipation rates are clear. Thus we can suppose that in
downward flow, turbulence structure modification is more
occurred than in upward flow and that the energy transfer
due to bubbles, FB in eq. (3) could be greater.

In Figure 11, instantaneous TKE dissipation maps are plotted
for a= 1.0%. In both up and downward flow, dissipations are
higher when void fraction is increased.
In upward flow for a =1.0%, instantaneous TKE dissipation
is increased at the vicinity of the wall 0.9 < r/R < 1.0, where
bubbles tend to gather (Fig. 5).

In downward flow for a =1.0%, instantaneous TKE
dissipation is enhanced at almost all the region 0 < r/R < 0.9.
These maps confirm the tendencies the mean TKE
dissipation (Fig. 10). TKE dissipation increases at the region
where bubbles exist and effect of bubble as dissipation is
stronger in downward flow.


4.6 Turbulent Energy Spectrum Profiles
There are a lot of scales of eddies, including smallest scale
such as Kolmogorov length scale to largest scale known as
integral scale. First, main stream provide turbulence energy
to largest scale eddies, this range of eddies corresponds to
the containing range. Then, in the inertial range, the large
scales eddies transfer the energy to the small ones. Finally,
smallest scale eddies dissipate turbulence energy by viscous
effects; this corresponds to the dissipation range. Therefore
to understand the structure of turbulence, we have to
investigate the modifications of turbulence structure in each
scale.

In this paper, we applied the equation (6) proposed by
Foucaut et al. 2004 to our PTV-measured spectrum to
eliminate the measurement error especially at dissipation
range (Foucaut et al. 2004, Westerweel et al. 1996).
E
E since2 (X /2) X (6)
sin(k)
sinc(k) = (7)
k


dB= (8)
3X
In these equations, Xis the interrogation window size, and
the spectral noise density coefficient. C is estimated as the
value of the spectrum measured by PIV, E=pv, at the cut-off
frequency of sine function.(KX = 2.8)

Figures 12 (a) and (b) illustrate energy spectrum at center of
pipe in up and downward flows, respectively. These energy
spectrums are calculated close to the centerline. Vertical
axis, E is normalized by fluid kinetic viscosity, v, and
ensemble-averaged TKE dissipation rate. Horizontal axis is
normalized by Kolmogorov length scale, q.

In both directions, energy spectrum can be divided into
three regions: (1) for Kr < 0.1, energy spectrum is almost
constant, this corresponds to the containing range, (2) for
0.1< Kr <0.6-0.7, energy spectrum follows a -5/3 power law
as usually observed in the inertial range, and (3)
0.6-0.7< Ky7 where energy spectrum corresponds to the
dissipation range of small eddies in single phase flow.

In upward bubbly flow, energy spectrum almost fit the
single phase flow. The classical -5/3 power law stays the
same. However in downward flow, energy spectrum are
increased at 0.2< Ky7. Moreover, in downward flow, the
containing range is creased from K7 < 0.2 to K7 < 0.5. The
inertial range shifts from 0.2 < Ky < 0.8 to 0.5< Ky <1.

Thus, in upward flow, energy spectrum did not change
dramatically because a few bubbles exist at center of pipe.
In contrast, in downward flow, since bubbles are at center of
pipe, energy spectrums are modified. Due to modification of
inertial range, two things could be explained. First, the
energy transfer is less and the energy is transferred by
smaller eddies. Increment of containing range and
decrement of inertial range can explain the higher
dissipation as enhancement of void fraction.

The increment of small eddies' energy spectrum seems the
biggest difference between sub-milli and milli order bubbles
(Nakagawa et al. 2008). In milli order bubbles, power
spectrums of both smaller and larger length scale are
increased. However in sub-milli bubbles, power spectrum of
only smaller length scale is increased. These observations


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indicate that the presence of sub-milli bubbles modifies the
length scales of the energy transfer in the flow.

5 Concluding remarks
The present study consists on an experimental investigation
for up and down flow by using time-resolved PTV and SPI
systems, which allow us to investigate the modifications of
turbulence structures in sub-milli bubbly flow.
In upward flow, bubbles attend to rise at the vicinity of the
wall and in downward bubbles tend to gather at the center of
the pipe. The presence of sub-milli bubbles induces a
reduction of the mean velocity profiles and an increase of
the turbulence intensities

We analyzed the TKE budget by studying the energy
production and the TKE dissipation rate. In upward,
production is reduced and dissipation rate did not change
dramatically. In down ward, a reduction of the production
and an enhancement of the TKE dissipation rate were
observed. This indicates that bubbles modify the energy
transfer.

The analysis of energy spectrum at the center pipe shows no
modifications of the energy spectrum in upward flow
because there are a few bubbles in this region of the flow. In
downward flow, we observe an increment in energy
spectrum and a modification of the length scales governing
the energy transfer from large to small eddies.

6 Acknowledgements
The author would like to thank Mr. M. Nakagawa for
helping the experiments. The second author would like to
acknowledge the financial support provided by the Japanese
Society for Promotion for Science (No. 20:08810).

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