Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 12.6.1 - Dynamical Vortex-shedding from a Zigzagging Rising Bubble
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00310
 Material Information
Title: 12.6.1 - Dynamical Vortex-shedding from a Zigzagging Rising Bubble Fluid Structure Interactions
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Tachibana, R.
Saito, T.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: LIF
mass transfer
vortex-shedding
surrounding liquid motion
bubble surface oscillation
stereo PIV
 Notes
Abstract: The growth process of dynamical vortexes (hairpin-like vortexes) from a CO2 Bubble (zigzagging motion) was investigated by simultaneously using LIF/HPTS (8-hydroxypyrene-1, 3, 6-trisulfonic acid) and Stereo PIV measurements. First, we discuss a relationship between the position of the point of the hairpin-like vortex leg (PPHVL) on the bubble rear surface and the bubble motion (esp. interface motion) from the LIF results. Second, we discuss a relationship between PPHVL and the surrounding liquid motion based on the Stereo PIV measurements. The fluctuation characteristics of PPHVL correspond with the bubble interface motion. Before an inversion point of the zigzagging motion, PPHVL gradually shifted its moving direction on the bubble rear surface. Near the inversion point, the bubble interface motion and PPHVL show distinctive behavior; i.e. PPHVL changed its direction of motion to one side to the other side rapidly, and the line symmetry of the bubble shape collapsed rapidly (i.e. rapid changes of the right-and-left curvature radii). It clearly shows that there is a deep correlation between the bubblesurface oscillations and fluctuations and/or movement of PPHVL. We discuss the surround liquid motion around the bubble and near the bubble wake. These results suggest the specific liquid motion which corresponds with the shift of the wake position. Considering all results, we discuss the deep relationship between the bubble motion, PPHVL and the surrounding liquid motion.
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
 Record Information
Bibliographic ID: UF00102023
Volume ID: VID00310
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: 1261-Tachibana-ICMF2010.pdf

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



Dynamical Vortex-shedding from a Zigzagging Rising Bubble


Rintarou Tachibana1 and Takayuki Saito2

1 Department of Mechanical Engineering, Shizuoka University, Hamamatsu, Japan, f0610086@ipc.shizuoka.ac.jp
2 Graduate School of Science and Engineering, Shizuoka University, Hamamatsu, Japan, ttsaito@ipc.shizuoka.ac.jp



Keywords: LIF, mass transfer, vortex-shedding, surrounding liquid motion, bubble surface oscillation, stereo PIV





Abstract

The growth process of dynamical vortexes (hairpin-like vortexes) from a C02 Bubble (zigzagging motion) was
investigated by simultaneously using LIF/HPTS (8-hydroxypyrene-1, 3, 6-trisulfonic acid) and Stereo PIV
measurements. First, we discuss a relationship between the position of the point of the hairpin-like vortex leg
(PPHVL) on the bubble rear surface and the bubble motion (esp. interface motion) from the LIF results. Second, we
discuss a relationship between PPHVL and the surrounding liquid motion based on the Stereo PIV measurements.
The fluctuation characteristics of PPHVL correspond with the bubble interface motion. Before an inversion point of
the zigzagging motion, PPHVL gradually shifted its moving direction on the bubble rear surface. Near the inversion
point, the bubble interface motion and PPHVL show distinctive behavior; i.e. PPHVL changed its direction of
motion to one side to the other side rapidly, and the line symmetry of the bubble shape collapsed rapidly (i.e. rapid
changes of the right-and-left curvature radii). It clearly shows that there is a deep correlation between the bubble-
surface oscillations and fluctuations and/or movement of PPHVL. We discuss the surround liquid motion around the
bubble and near the bubble wake. These results suggest the specific liquid motion which corresponds with the shift
of the wake position. Considering all results, we discuss the deep relationship between the bubble motion, PPHVL
and the surrounding liquid motion.


1. Introduction
Deep understanding of a relationship between the mass
transfer from a bubble to its surrounding liquid and the flow
structure is essential for the efficient and safe operation of
chemical reactors, bio reactors, and heat exchangers and so on.
Herlina investigated the mass transfer from gas-phase to
liquid-phase across the gas-liquid interface experimentally.
He discussed how the turbulence behaved for the gas transfer.
He concluded that interaction between small-scale flow
structure and large one played an important role in mass
transfer process. Tsuchiya investigated the dissolution process
of a C02 bubble into water using LIF, and also he suggested
the mass transfer is closely related to the flow structure. It is
known that the zigzagging bubbles shed a characteristic
vortex. For instance, Sanada visualized the bubble wake by
using photo chromic dye. Brticker reported periodical vortex
shedding from Zigzagging bubble based on PIV results.


However, these researches are insufficient to discuss the
relationship among the bubble dynamics (surface oscillation,
surface deformation), interaction between the bubble and its
surrounding liquid motion and the dynamical mass transfer
and so on.
In this study, we examine a zigzagging rising single C02
bubble (2.9 mm in equivalent diameter, 850 in Reynolds
number and 3.4 in Weber number). We discuss the
relationship between the wake motion, the bubble interface
motion and its surrounding liquid motion simultaneously by
using LIF/HPTS (LIF with 8-hydroxypyrene-1, 3, 6-
trisulfonic acid) and PIV (Particle Image Velocimetry). These
methods are quite useful for quantitatively visualizing the
dynamical structure of the bubble wake and buoyancy driven
flow. PIV is efficient compared with actual PTV
measurement when researcher visualizes high space
resolution area (i.e. extremely zooming up certain area).







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


Based on these results, we discuss the relationship between
PPHVL and the bubble motion (interface motion), and a
relationship between PPHVL and its surrounding liquid
motion based on the results obtained by the PIV measurement.


2. Nomenclature
Deq equivalent bubble diameter [mm]
C the concentration of the fluorescence material
[mol/m3]
I emission intensity of fluorescence [W/m2]
Io incident light flux [W/m2]
KL left curvature [-]
KR right curvature [-]
PPHVL position of the wake-leg point
Sc Schmidt number [-]
Sh Sherwood number [-]
T temperature [K]
t time [sec]
VP x-direction velocity component of PWLP
[mm/s]
Vpy y-direction velocity component of PWLP
[mm/s]
Vx x-direction velocity component of water
[mm/s]
Vy y-direction velocity component of water
[mm/s]
WL left side hairpin-like vortex
WR right side hairpin-like vortex
x coordinates [mm]
y coordinates [mm]
z coordinates [mm]
a angle of major axis [deg]
0 angle between minor axis and line connecting
centroid with PPHVL [deg]
e quantum efficiency [-]
K curvature radius [1/mm]
0 molar absorbance coefficient [m2/mol]


3. Experimental setup
3.1 Experimental setup and principle of LIF/HPTS
Figure 1 shows schematic diagram of an experimental setup
used in the LIF/HPTS experiments. An acrylic water vessel
(d) (100 x 100 x 300 mm3) was filled with ion-exchanged and
degassed water, and a very small amount of HPTS (8-
hydroxypyrene-1, 3, 6-trisulfonic acid) was dissolved into the
water. An argon ion laser system (a) was used to excite the
HPTS. The laser beam was split by a half mirror (b), and
subsequently each beam was sheeted by a rod lens (c) and
illuminated the interrogation area from both side of the bubble.
A special-made bubble-launch device (g) composed of a
hypodermic needle (f) (inner diameter: 0.44 mm), an acrylic
chamber, an audio speaker and two precise pressure


controllers was employed. By employing this device,
extremely high reproducibility of the size, zigzag trajectory,
shape, position, orientation and surface oscillations of the
bubbles was completely achieved (Saito et al., 2008). As a
result, all the bubbles from the device rise zigzagging
invariably within the same vertical plane; i.e. the zigzagging
bubbles pass through the laser sheet at the same position. A
high-speed video camera (j) (Phantom V9) was mounted on
multi axes precise optical stages. This camera was equipped
with a zoom lens and bellows to obtain high spatial resolution
(27um/pixel for LIF/HPTS, 13um/pixel for PIV). A sharp-cut
filter inserted between the lens and the vessel cuts scattering
light from the bubble surface. The bubble launch-device and
the high-speed video camera were synchronized through a
function generator (h). The single bubbles were filmed at any
given location and at any given timing. Therefore, we were
able to combine the LIF/HPTS results with the Stereo-PIV
results directly. In order to obtain clear images of the bubble
shape, a red LED light (i) (wave length: 630 nm) was used.
Hence, the simultaneous measurements of both bubble
shapes and LIF images were performed.
In this research, HPTS (8-hydroxypyrene-1, 3, 6-trisulfonic
acid) was used as a fluorescent substance to visualize
dynamical mass transfer process from the CO2 bubble to the
surrounding liquid. The Schmidt number (Sc = L/DGL =
529.2, T = 302 K) and the Sherwood number (Sh = kLDeq,
DG-L = 687.5, T = 302 K) were calculated, here DG-L
represents the diffusion factor, VL the kinetic viscosity, kL the
mass-transfer coefficient, and Deq the equivalent diameter.
Hence, the thickness of the concentration boundary layer
around the examined bubble was considered to be much
smaller than that of the velocity boundary layer. This method
easily visualized the dynamical process in which the thin
concentration layer was included in the bubble wake.
Simultaneously, a part of the wake was also visualized. The
CO2 gas (CO2: 99.9%, N2: 0.9ppm, O2:0.9ppm) is supplied
from a gas cylinder through the bubble-launch device. The
properties of the examined bubbles are listed in Table 1.

Table 1: Properties of the examined bubbles.

D,, ReB We Mo
2.9 mm 849 [-] 3.4 [-] 2.6 X 10-11 [-]

HPTS changes its emission intensity, depending on pH of
the solvent and its temperature (Coppeta and Rogers, 1998).
However, the temperature dependency is negligible in the
present experimental conditions. On the other hand, pH
dependency is very large; i.e. HPTS distinguishably changes
its emission intensity at a pH range of 6 9. The emission
intensity I of fluorescence can be expressed by


I = IJCs ,







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


where, Io is the incident light flux, C is the concentration of
the fluorescence material, is the quantum efficiency, and c
is the molar absorbance coefficient. During the ascent of the
CO2 bubble in HPTS solution, the emission intensity
decreases in the regions in which the CO2 included in the
bubble is dissolved. The C02-rich regions are easily
distinguished from the other regions of no dissolution of CO2
due to the brightness differences. Thus, the LIF using HPTS
(LIF/HPTS) provides the visualization of the CO2
transportation (i.e. dynamical process of the mass transfer)
from the bubble surface to the surrounding liquid.
In this research, pH of the bulk solution was controlled in
8.2 by a small addition of NaOH. In advance, it was
confirmed that the solubility of CO2 was not changed by the
addition.


(a) Ar+ion laser, (b) Half mirror, (c) Rod lens, (d) Water
Vessel, (e) Water & HPTS, (f) Hypodermic needle, (g)
Bubble-launch device, (h) Function generator, (i) LED,
(j) Hi-speed video Camera, (k) Sharp-cut filter
Fig. 1: Schematic of the experimental setup used in LIF
measurement.

3.2 Experimental setup for Stereo PIV measurement
Figure 2 shows a schematic diagram of an experimental
setup for the Stereo-PIV measurement. It mainly consists of
an acrylic octagonal water vessel (d), a bubble launch device,
a high-power ND: YAG laser system (a).
The water vessel was filled with ion-exchanged and degassed
water. An appropriate amount of PIV particles (fluorescence
reagent: diameter of 8pm, maximum excitation wavelength of
542 nm and maximum emission wavelength of 612 nm) were
seeded in the water. The laser beams (wavelength of 532 nm)
were sheeted by rod lenses (c) and illuminated the
interrogation area from both side of the bubble. Three high-
speed video cameras (j), (k) and (1) were used in the
experiment. The camera (k) positioned in the center filmed
the gravity-center motion and orientation of the bubble.


(a) ND: YAG Laser, (b) Half Mirror, (c) Rod lens, (d)
Water Vessel, (e) Water & PIV particle, (f) Needle, (g)
Bubble launch device, (h) Function generator, (i) LED, (j)
(k) (1) Hi-speed video Cameras, (m) Sharp-cut filter
Fig. 2: Schematic of the experimental setup of Stereo-PIV.


The other two cameras (j) and (1) positioned on either side
filmed PIV particles. The strong scattering noises from the
bubble surface were removed through a sharp-cut filter (m).
An angle between the optical axes of camera (j or 1) and
camera (k) was 45 degrees. The lenses mounted on the
camera (j) and (1) were set in scheimpflug arrangement. For
the more precise focus on target object, this arrangement
made a modification of a differentia angle between the lens
axis and the camera axis. By employing this arrangement,
film-phase, lens-phase and measurement target-phase crossed
one point; therefore, each camera was able to adjust the focus
on the whole measurement area. By using a calibration plate
in advance, we obtained a matrix to relate the image-plane to
the physical-plane. As a result, we obtained 2-dimensinal-3-
Conponent velocity fields.
The bubble and PIV-particle images in each frame were
separated by image processing. The velocity field of the
surrounding liquid of the bubble was computed by PIV
analysis of the FFT-based recursive cross-correlation
algorithm was adopted (e.g. Saito, et al., 2008, Yassin A.
Hassan, et al., 2004). In addition, vorticity field was
calculated from the velocity field based on Stokes's theorem.

4. Results and discussions
4.1 Bubble motion
A bubble with Weber number ranging from 2 to 3 oscillates
in its own surface at mode 2,0 or mode 2,2 (Lunde and
Perkins, 1997, 1998; Pozrikidis, 2004). We calculated the
coordinates of bubble contours from the bubble images
processed by a Sobel filter, and also the coordinates of the







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


bubble gravity centers were obtained. Furthermore, the
coordinates of each bubble contour were transformed to polar-
coordinate system (r, 0) with its origin at the gravity center
(Fig. 3). The bubble contours were expressed as follows
(Duineveld, 1995);
N
r(O) = Ao + (A, cosnO + B, sinnO), (1)
n=l
where A, and B, were calculated by FFT with mode order N of
8. A major diameter D1 of the bubble image was calculated as
the maximum value (i.e. D1 19 a minor diameter D2 was
calculated as r(01 + z/2) + r(01 + 3 r/2). The aspect ratio was
calculated by D1/D2. The ratio has been used in many former
researchers (e.g. Ellingsen & Risso, 2001); however it is
insufficient for the purpose of discussing shape asymmetry of
a bubble, therefore we introduce right and left edge curvatures,

KR (01 =- at the right edge and KL (01o=e +, at the left edge
in order to quantitatively discuss the time-series shape
asymmetry (Saito, et al., 2008; Miyamoto & Saito, 2005).
They are calculated by

K r2 +2(dr/dO) -r(d2r/d02)
= = (2)
[r2 +(dr / dO)2]2/3

here, = 01 for KC, 0 = 01 + T for KL.
In addition, we defined dimensionless curvatures (KR and KL)
at the right and left edges as follows;


KR = KR (O)Deq,

KL =L (0 +)Deq,


here, Deg represents an equivalent diameter of the bubble. By
calculating curvature of the bubble contour, we can discuss
the time-series magnitude of the shape oscillations of the
bubble, quantitatively.
Figures 4 show the bubble zigzag trajectory, the edge
dimensionless curvatures, respectively. The dominant
frequency, the wavelength and the amplitude of the zigzag
motion were 7 Hz, 39.6 mm and 3.0 mm, respectively. The
dominant frequencies of the edge dimensionless curvatures
were 69.9 Hz for KR and 70.3 Hz for KL, respectively. When
bubble shifted its motion from liner to zigzag motion near the
first inversion point, the shape oscillation of the left edge is
larger than that of the right edge as observed in Figs. 4. After
the first inversion point, the shape oscillation of the left edge
increased, while that of the right edge decreased. At the
second inversion point, KL reaches the maximum value. After
the second inversion point, the shape oscillation of the right
edge increased, while the shape oscillation of the left edge
decreased. This asymmetrical oscillation of the bubble edge
characterizes the zigzag motion. The zigzag motion is closely


Bubble


Minor axis


Major axis


k i I A-


Fig. 3: Evaluation of axes and curvature


15

10

% 5

0
6


0 0.1 0.2 0.3 0.4
Elapsed time [s]
Fig. 4: Trajectory and curvature

related to the bubble surface motion.

4.2 Visualization of a bubble wake
Figure 5 shows a typical visualization result of the bubble
wake (hairpin-like vortexes) near the first inversion point
obtained via the LIF/HPTS method. As marked by red
broken-line rectangular in the figure, C02-rich regions (i.e.
low brightness region) are distinctively observed. These
regions are parts of the bubble wake. Although researchers
succeeded in visualizing the bubble wake structure (e.g.
Sanada et al., 2007; Brticker, 1998), our visualization results
include both the dynamical wake structure and the direct mass
transfer from the bubble surface to the surrounding liquid.







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


4.3 Hairpin-like vortex

Elaps
H


v x


Needle
Needle


Fig. 5: Typical hairpin-like vortexes developing from
the rear of the bubble.

4.3.1 Time series visualized hairpin-like vortex near
the first inversion point
Figures 6 show time-series growth of vortex between the
bubble launch and the first inversion point. A standing vortex
developed from the center of the bubble rear is observed in
Fig. 6 (a), and during this section the bubble rose vertically.
Furthermore, the bubble shape is axisymmetric and the major
axis of the bubble is horizontal. The symmetric property is
gradually collapsing with the bubble ascent and the major axis
is gradually leaning to the left. Just before the first inversion
point, the hairpin-like vortex is shed. The bubble changes its
orientation and the direction of the motion. After this, the
vortex is periodically shed from the bubble rear, and each
time the bubble changes its direction of the motion. After
three times vortex shedding, the bubble moves linearly and
also recovers the axisymmetric property.
The time-series results of the bubble gravity-center motion
and surface motion are plotted in Figs. 7; (A) shows the
trajectory of the gravity center during all measurement period;
(B) the enlarged one during 0.04 0.14 sec; (C) the
dimensionless curvature radius (denotation from (a) to (f)
corresponds with that in Fig. 6). From Figs. 7 (A) and (B),
the bubble changes its direction of the motion gradually. The
dimensionless curvature radius in the right gradually increases
with periodical fluctuation. From a careful observation of Fig.
7 (C) and Figs. 6, when the curvature radius takes a peak, the
vortex is considered to be shed.
As marked by a red broken-line circle in Figs. 6, a position
of the point of the hairpin-like vortex leg (PPHVL) fluctuates


at the rear of the bubble. Before the first inversion point, Fig.
6 (a), PPHVL was positioned just at the minor axis of the
bubble. At this time, the fluctuations of curvature radiuses
were gentle. However, when the curvature radiuses changed
its balance (i.e. curvature radius of right edge increased),
PPHVL are shifted toward the right edge. Associated with the
growth of the fluctuation of curvature radius, the bubble
periodically shed the characteristic vortex (hairpin-like
vortex). When the bubble changes its direction of the zigzag
motion, the oscillation of the curvature radius at the outer
edge is dominant (Miyamoto and Saito, 2006).

4.3.2 Time-series visualized hairpin-like vortex near
the second inversion point
Figures 8 (a) (f) show time-series hairpin-like vortex
before the second inversion point. Figures 9 (A) (C) show
the gravity-center motion surface motion of the bubble. In (a)
- (c), it is observed that a standing-like vortex grows from the
slightly-right side of the bubble rear surface. In (d), a new
vortex begins to grow at the left side of the bubble rear
surface. The new vortex continues to grow. In parallel, the
former vortex sifts from right to left, and decays with the
growth of the later vortex ((e) (f)). The trajectory during this
period forms a sequel to that near the first inversion point;
however the oscillation of the right-side dimensionless
curvature radius is very different from that at the first
inversion point. The periodicity of the oscillation is not clear
compared with that at the first inversion point; in addition the
right-side dimensionless curvature radius reduces with the
oscillation. On the other hand, the left-side dimensionless
curvature radius more periodically oscillates in a half period
of the right-side curvature radius near the first inversion point.
Figures 10 (a) (f) show time-series hairpin-like vortexes just
after the second inversion point. Figures 11 (A) (C) show
the gravity-center motion and surface motion of the bubble.
At the second inversion point (Figs. 10 (a) and (b)), the later
vortex grows. On the other hand, the former vortex is
absorbed by the second one. The vortex draws an arc ((c) -
(d)). The head of the vortex swirls ((e) (f)). These behaviors
are different from those observed at the first inversion point.
The right-side dimensionless curvature radius begins again to
periodically oscillate in a period three times longer than that
at the first inversion point. The left-side one also oscillates in
the same period.

4.3.3 Position of the point of the hairpin-like vortex
leg (PPHVL)
As marked by a red broken-line circle in Figs. 6, a position of
the point of the hairpin-like vortex leg (PPHVL) fluctuates
at the rear of the bubble. Before the second inversion point,
as shown in Figs. 8 (a) (f), PPHVL dances on the bubble
rear. At the second inversion point, as shown in Figs. 10 (a) -
(f), PPHVL shifts from right to left rapidly.







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


(a) t= 54[ms]


(d) t4= t+ 30 [ms]


(b) t2 tl+ 10 [ms]




















(e) t= tl+ 40 [ms]


(c) t3= t+ 20 [ms]


(f) t6= t+ 50 [ms]


Fig. 6: Hairpin-like vortex observed just after launch of the bubble.


15 -
10 -
5
0
0 0.1 0.2 0.3 0.4 0.5
Elapsed time [s]
(A) Trajectory (overall)





0
I I I I I

0.06 0.08 0.1 0.12 0.14
Elapsed time [s]
(B) Trajectory (enlarged)


0.5 Il l


0.4-
0.6 I I I I I
I I I I I


0.5-

0.4-
0.4 I I I I I I




I I h I I I I I I


0.06 0.08 0.1
Elapsed time [s]


Fig. 7: Gravity-center motion and surface motion of the bubble near the first inversion point.


0.12 0.14


(C) Dimensionless curvature radius (right and left)







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


(a) t =132[ms]


(b) t2=t+ 5 [ms]


(c) t3=ti+ 10 [ms]


(d) t4= t+ 15 [ms] (e) t= tl+ 20 [ms] (f) t6= t+ 25 [ms]
Fig. 8: Vortexes observed just before the second inversion point.


10 -
1i -

0 I: i I I I I
0 0.1 0.2 0.3 0.4 0.5
Elapsed time [s]
(A) Trajectory (overall)


12
11 -
Il-
10.-
9 -
S8 -
7 -
0.12


7 0.4

. 0.3


0.4

0.3
0.2


(a) (b) (c) (d) (e) (f)
I I I I I I
I I I I I I

I I I I I

I I I I I
I I I I I
Sj , I I I I I I


1 1 l1i I11111
I I I I I I
- I I I I I I I I I
I I I I I I



I I I. I . I


0.13 0.14 0.15 0.16 0.12 0.13 0.14 0.15 0.16
Elapsed time [s] Elapsed time [s]

(B) Trajectory (enlarged) (C) Dimensionless curvature radius (right and left)
Fig. 9: Gravity-center motion and surface motion of the bubble just before the second inversion point.


3mm


I I I I







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ICMF 2010, Tampa, FL, May 30 -June 4, 2010


(a):ti=164[ms] (b):t2=tl+ 5 [ms]


(c):t3=tl+ 10 [ms]


(d):t4=tl+ 15 [ms] (e):t5=tl+ 20 [ms] (f):t6=tl+ 25 [ms]
Fig. 10: Vortexes observed just after the second inversion point.


) 0.1 0.2 0.3 0.4 0.5
Elapsed time [s]
(A) Trajectory (overall)



r I


0.1


0.4

0.3-

0.2 I
0.4-
0.3 I I I I
0.3 I I. I
I I I I
c I, II I, II I, II


6 0.17 0.18 0.19 0.17 0.18 0.
Elapsed time [s] Elapsed time [s]
(B) Trajectory (enlarged) (C) Dimensionless curvature radius (right and left)

Fig. 11: Gravity-center motion and surface motion of the bubble just after the second inversion point.


19


#;i


12

I
8 10







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ICMF 2010, Tampa, FL, May 30 -June 4, 2010


When the bubble changes its direction of the zigzag motion,
the oscillation of the curvature radius at the outer edge is
dominant (Miyamoto and Saito, 2006). At the second
inversion point in the present study, when PPHVL is
fluctuating in the right side of the bubble rear, the oscillation
of the right edge of the bubble is dominant. After the second
inversion point, PPHVL is fluctuating in the left side of the
bubble rear and the left side oscillation is dominant
conversely. Considering these results, it is obviously that
there is close relationship between the hairpin-like vortex and
the bubble surface oscillation (e.g. Lunde and Perkins, 1990;
Gaudlitzs at el., 2009).

4.3.4 Definition of PPHVL
We defined PPHVL, inclined angles of the major and
minor axes as shown in Fig. 12. As described in chapter 3, we
obtained the centroid of the bubble, the major and minor axes,
and calculated the angles a and 0. The time series a is plotted
in Fig. 13. a linearly decreases from 40 to I 30 degrees in
this period.
The angle 0 between the minor axis and the line connecting
the centroid with PPHVL is defined as shown in Fig. 12. The
vortex positioned in the right side of the minor axis is labeled
as WR and the one in the left side as WL.

4.3.5 Relationship between surface oscillation and
PPHVL
Figures 13 show the trajectory of the gravity-center of the
bubble, time-series dimensionless curvature radii and time-
series 0. At the inversion point (t z 0.16 [s]), the line
symmetry of the bubble shape collapsed rapidly. In other
words, magnitude of the curvature fluctuation at the outside of
the trajectories reached the maximum when the bubble
changed its direction at the second inversion point. PPHVL
shifted its motion direction from the right side to the left side
of the bubble rear very rapidly. The angle 0 of WR fluctuated
on the right side of the bubble rear, and as approaching to the
second inversion point, it gradually decreased. At the same
time, the angle 0 of WL increased. On the other hand, near the
second inversion point, the curvature radius of the right edge
gradually decreased. At the same time, the curvature radius of
the left edge gradually increased. From these results, the shift
of PPHVL closely related to the bubble surface motion.

4.3.6 Velocity of the shift of PPHVL
To compare the fluctuation of PPHVL with the surrounding
liquid motion, the PPHVL expressed in polar coordinate was
recalculated in Cartesian coordinate as illustrated in Fig. 15.
The velocity components of PPHVL were calculated from
displacements of x and y.
Figure 16 (a) shows the fluctuation velocities Ux and U, of
PPHVL before the second inversion point. U fluctuated with
almost constant amplitude. On the other hand, the fluctuation
of Uy was attenuated before the second inversion point, and


gradually approached to 0. This leads to the rapid shift of
PPHVL at the inversion point.
Figure 16 (b) shows the fluctuation velocities of PPHVL
after the second inversion point. As well as those before the
second inversion point, U, fluctuated with almost constant
amplitude. On the other hand, Uy fluctuated with small
amplitude in the beginning; however, the amplitude of Uy
grew.

4.3.7 Frequency Analysis
To clarify the dominant frequencies of curvature radii and
PPHVL, we conducted FFT analysis. Figures 17 (a) and (b)
show the results of FFT analysis. As marked by a red broken
line, each result had a dominant frequency at 60-90[Hz].
Quantification of the fluctuations of curvature was studied by
Miyamoto and Saito (211 14). They also reported the dominant
frequency of curvature is of 80-90 [Hz]. The dominant
frequency (60-90 [Hz]) of PPHVL well agreed with their
results. The fluctuations of PPHVL closely related to that of
curvature radius. Figure 17 (c) shows the FFT results of
PPHVL velocity. As marked by a red broken line. The
velocity had a dominant frequency at 60-90[Hz] as well as
those in Figs. 18 (a) and (b).

4.4 Relationship between PPHVL and the
surrounding liquid motion

Fig. 19 shows the results of two dimensional surrounding
liquid motions around a bubble obtained by PIV measurement
at the second inversion point. This clearly shows the
surrounding liquid motion around the bubble induced by
buoyancy driven flow. Our purpose is to clarify a relationship
between PPHVL and the surrounding liquid motion; therefore,
the specific area was extracted as shown in Fig. 20. This


Minor axis


Major axis


Fig.12: Definition of PPHVL and angles of a and 0.







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


40 -
a 20
-0
1 -20


0.12


0.14 0.16
Elapsed time [s]
Fig. 13: Time-series a.


0.18


The second inversion point


15 -

5
0 I i l
0 0.1 !0.2 0.3 0.4 0.5
Elapsed time [s]
(a) Trajectory (overall).

The second inversion point
12


9
8



I 0.2 I

0.4
0.3


0.12 0.14 0.16 0.18
Elapsed time [s]
(b) Trajectory (enlarged) and dimensionless curvature radius.

The second inversion point
40-
30
WR
20



50 WL
45
0.12 0.14 0.16 0.18
Elapsed time [s]
(c) Time evolution of 0.
Fig. 14: Relationship between the bubble motion and 0.


Fig. 15: Definition of coordinates x and y.


100

1 0
-100


100

0 o

-100


2 0

-100


100


-100


2 0.13 0.14 0.15 0.16
Elapsed time [s]
(a): Before the second inversion point.







- I I I I




- -I I I


Elapsed time [s]
(b): After the second inversion point.
Fig. 16: Velocity of PPHVL.







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


0 1000 2000
Frequency [Hz]
(a) Right-side dimensionless curvature radius.


1000
Frequency [Hz]
(b) 0 before the second inversion point.


1500

1000

500

0

1000


2000


'... 111f
. . .










Fig. 19: Surrounding liquid motion at the second inversion
point (PIV result).


126 areas



Bubble


L


20 areas










b) Extracted area


a) Overall area


Fig. 20: Extracted Velocity Field


2000


-60 L
0.14


1000
Frequency [Hz]
(c) Velocity of PPHVL.
Fig. 18: Results of FFT.


extracted area was just below the right-bottom of the bubble
[20 x 20 area (2mm X 2mm)].We calculated the average of all
velocity included in this area.
Figure 21 shows time-series fluctuation of the average
velocity in the extracted area. The bubble approached to the
second inversion point, the absolute value of the negative
velocity increased. When the bubble was positioned just at


0.15 0 16


0 17


Elapsed time [s]
Fig. 21: Time series fluctuation of velocity

the second inversion point, the value took the maximum.
After this, the absolute value of the negative velocity
decreased. This phenomenon of the surrounding liquid flow
corresponds with the rapid shift of PPHVL at the second
inversion point.







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


5. Conclusions
The dynamical growth process of the vortexes from a
zigzagging CO2 bubble was investigated in terms of a bubble
motion (gravity-center motion of the bubble and its surface
oscillation), the position of the point of the hairpin-like vortex
leg on the bubble rear surface (PPHVL) and the surrounding
liquid motion near the wake.
At first a relationship between the bubble motion and the
PPHVL was discussed based on the LIF/HPTS results. Near
an inversion point, the PPHVL and the bubble surface
oscillation showed distinctive behavior. They were very
similar not only qualitatively but also quantitatively. It has
been found out that there is a deep correlation between the
bubble surface oscillation and the motion of PPHVL.
At second a relationship between the motion of PPHVL
and the surrounding liquid velocity field was discussed based
on the PIV results. As well as the characteristic behavior of
PPHVL at the inversion point, the surrounding liquid around
the wake showed distinctive behavior.
These result obtained by LIF/HPTS and PIV suggest us a
close correlation between the bubble surface motion (surface
oscillation), the motion of PPHVL and the surrounding liquid
motion.

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