7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Analysis on effective factors of bubble plume instability in an aeration tank
B. W. Hu1, W. Cheng1'2, W. J. Cheng1, Yuichi Murai3
1:Key Laboratory of Northwest Water Resources and Environmental Ecology of Education Ministry Xi'an University of
Technology, Xi,an 710048, China, Yuanpei College, ShaoXing University, ShaoXing 312000, China Email: hbw@t
zscas.edu.cn
2: State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiao tong University, Xi'an 710048, China,
wencheng @xaut.edu.cn
3: Division of Energy and Environmental System, Faculty of Engineering, Hokkaido University, Sapporo, Japan
murai@ eng.hokudai.ac.jp
Keywords: Bubble plume, bubble velocity, void fraction, PIV
Abstract
Bubble plume is a complex twophase flow that enables active aeration. In a limited space of aeration the flow pattern of
bubble plume is affected by multiple factors. In this study, after preprocessing is imposed on the visualized images of bubble
plume with image binarzation, the velocity vector field is figured out by PIV as well as the void fraction by image processing.
The bubble plume flow field and the void fraction were analysed to evaluate the instability in the spatiotemporal structure of
bubble plume via frequency spectral analysis of oscillatory bubble plume that occurs at different water depths. Three impact
factors of pressure, void fraction and aspect ratio of the container were assessed to have concluded that aspect ratio was the
one of the main governing factor that sways the dynamic behaviour of bubble plumes.
Introduction
With the development of modern industries, the research of
twophase flow was rapidly developed into an important
branch of discipline. Twophase flow has been widely used
in the industrial sectors, such as energy, power, petroleum,
chemical, refrigeration, metallurgy and other fields, which
includes technical fields, such as nuclear energy, aerospace,
rocket, material, and so on. Twophase flow has great
application into many projects, such as controlling the
stratification structure of reservoirs and lakes to improve
water quality, enhancement of the material mixing, heat
exchange, and chemical reaction process in reactors.
Futhermore, it prevents channel and harbor from being
frozen. Especially in last few years, with the largescale
offshore oil and gas are extracted, the serious pollution
incidents were caused by underwater oil gas explosion.
Understanding the hydrodynamic characteristics of blowout,
and use the "grease trap wall" with surface flow of the
bubble plume, it plays an important role to control the
spread of oil in a lesser extent and reduce pressure on the
environment. Dynamic behaviour of bubble plume has
become an important subject in such a research field..
This study aims at elucidating fundamental structure in
bubble plume via image processing that consists of
obtaining bubble velocity and void fraction distribution in
laboratory experiments. The Recursive Cross Correlation
(RCC) technique has been used to measure the bubble
velocity vector distribution that actively changes in time.
Simultaneously the void fraction distribution has been
obtained with the correlation between the local averaged
image brightness and projection void fraction. These two
processes enable us to grasp the flow field quantitatively.
Meanwhile, frequency spectra of bubble plume oscillation
which depends on the water depth is evaluated so that the
bubble instability in a limited space of container can be
deeper understood. In particular, we focus on space
dependence of the frequency spectrum of bubble velocity
field, which has not been cleared by any researchers to date.
Experimental configuration and conditions
The experimental setup is shown in Fig. 2. A planer bubble
plume is generated in a thin rectangular tank that has 300
mm in width, 800 mm in height and 40 mm in horizontal
depth. Air bubbles are injected into the bottom of the tank
through three rows of capillary tubes, by which bubble size
and the number density can be precisely controlled. In order
to study the instability behaviour of bubble plume, 18 test
cases of experiments have been performed, which consists
of changes in gas flow rate, void fraction, and bubble size. A
CCD camera was used to record the spatiotemporal
structure of the twophase flow.
In this study, tap water is used as liquid phase, which has a
kinematic viscosity of 106 m2/s and a density of 1000 kg/m3,
while the gas phase is laboratory room air with density of
1.28 kg/m3. The experimental temperature is 1315 degree C.
The experimental control parameters that we vary in this
series of experiments are Q; the gas flow rate, H/W; the
aspect ratio of container, and R; the mean bubble radius
realized in the tank. The bubble size is measured by image
processing for separated series of local images. The initial
height of the water surface without bubbles is 0.3 m.
Measurement of void fraction distribution
In this study, the velocity vector field information of bubble
plume was obtained by recursive cross correlation PIV
(Cheng et al, 2005). The RCCPIV measurement algorithm
based on gray level distribution has been employed to
calculate the velocity of the flow field. The cross correlation
coefficient is defined as:
M N
C =l J= l
~Ml N MN
Where f and g are the brightness, the indexes i and j are
digitalized image coordinates, M and N are the size of the
interrogation area. The similarity of two images was
evaluated by use of gray level (brightness) that is subtracted
by the local average gray level of each interrogation window
in the formula. The RCCPIV measurement algorithm can
reduce the computational burden and increase the output
density of spatial data in the final calculation results from
calculation of large query region to small query region.
Using image processing, the relationship between the void
fraction and the distribution of the bubble shadow can be
obtained. It calculates the locally average brightness of non
overlapping probability of the bubbles, and refers to the
projection void fraction obtained separately. Thus, it is
necessary to obtain the void fraction as a function of 2D
coordinates of the image projection void fraction. The
projection void fraction is defined as the ratio of the volume
of the gas phase to the total volume in each volume element
of the grid. In terms of overlapping probability of the
bubbleimages under various conditions, we utilize a
correlation curve between the bubbles' locally averaged
brightness in planer bubble plume and the projection void
fraction as given below.
The projection void fraction can be defined as:
(4 ) R3 N
a(N) =(3) R
AL
There is a single spherical bubble with a radius of R in a
rectangular space whose volume is A, times L, the void
fraction is given by the above equation for N= 1. When there
are N bubbles in the same volume, the shadow void fraction
is estimated as
[N(N L Z i/ (i)]Ab
,8(N) 
A
Where Ab stands for the shadow area of a single bubble in
the projection direction. There is a relationship regarding the
number of bubbles existing in the volume as
B(i,j)= f(i, j)[1 f(N)]
The indexes i and j are digitized image coordinates of
bubble. When N bubbles images are inside a grid space, the
bubble locally averaged brightness in plane bubble plume
can be expressed as:
B(N) = [ B(i, j) / As + B,
Where ni and nj are pixels in the horizontal direction and
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
vertical direction of the area, B is the background
brightness of the original image.
The correlation curve between projection void fraction in
the three different aspect ratios and the bubbles locally
averaged brightness can be obtained by the calculation. The
correlation curve can be seen in Fig. 1.And then the void
fraction can be calculated.
0 0.05 0.1 0.15 0.2
The aspect ratio of 1 5 I The aspect ratio of 2 0 The aspect ratio of 1 0I
I polynomzal 15 Polnomzal 1 0 olynomzal 2 00
Figure 1: The correlation curve between the bubbles locally
averaged brightness and projection void fraction.
17(.)I)fn,
S125(m) A
2lo(mmn)ma
S' 00 200 330 100 21 200 100 200 00
300(mm)
Figure 2: The sketch map of aeration tank crosssection at
different depths and timecontinuous bubble plume images.
In this study, the crosssection of bubble plume was selected
at three different depths, the location of the picture was
intercepted, then timecontinuous bubble plume images
under three aspect ratios was obtained by image mosaic and
the movement patterns and rules of bubble plume was
studied in the 40s.Next, center offset of bubble plume at
three different depths was calculated and used the Fast
Fourier transform to get the frequency spectra of bubble
plume vibration.
Figure 3: The selected location of the bubble fluctuation
spectrum with three different aspect ratios.
The movement patterns were realized by analysis frequency
spectra of bubble fluctuation velocities. The Fig.3 shows the
selection location of velocity. First, calculated the average
velocity ( x ) at selected locations and subtracted with the
instantaneous velocity. At last, frequency spectra of bubble
fluctuation velocities were got by the Fast Fourier
transform.
Results and Discussion
Based on the experimental conditions there are many factors
affecting on the movement of the bubble plume. The
pressure is the important factor to influence the bubble
plume movement. The flow field of bubble plumes and void
fraction in three different aspect ratios with the pressure of
15Kpa has been analyzed in this study.
VI
i .
(a) The averaged brightness, timeserial bubble velocity, total
turbulent intensity, void fraction in the aspect ration of 1.0.
Us
.[P..] too IM ..10u, u s.
(b) The averaged brightness, timeserial bubble velocity, total
turbulent intensity, void fraction in the aspect ration of 1.5.
(c) The averaged brightness, timeserial bubble velocity, total
turbulent intensity, void fraction in the aspect ration of 2.0
Figure 4: Timedependent bubble flow field and void
fraction in 3 different cases with pressure of 15Kpa.
In the pressure of 15Kpa, flow field of bubble plume and
void fraction are different under the different aspect ratio,
which is shown in Fig.2. When in aspect ratio of 1.0, the
timeserial of bubble plume is evenly distributed in both
sides of the bubble plume. The bubble plume rises along
the centerline in the aspect ratio of 1.0 the total turbulent
intensity is shown in the underside, and the maximum
value is 0.134m/s. At this time the void fraction appeared
the phenomenon of alternating in the bottom of the bubble
plume. When in aspect ratio of 1.5, the timeserial of
bubble plume is also evenly distributed; the total turbulent
intensity is shown in the middle, and the maximum value is
0. 7m/s. The maximum value of void fraction can also be
found in the middle. When in aspect ratio of 2.0, the
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
movement of bubble plume is bent and snakelike; the total
turbulent intensity is shown in the upper part, and the
maximum value is 0.145m/s. The void fraction also
appeared the phenomenon of alternating and the maximum
value can be found in the upper part, the top of the bubbles
are easy to overflow the device, which makes an impact on
the motion of bubble plume.
Figure 5: Frequency spectra of bubble plume vibration at
different water depths when pressure of 15Kpa.
' k i ] ii '
Figure 6: Frequency spectra of bubble fluctuation velocities
when pressure of 15Kpa.
In the pressure of 15Kpa, it is found that vibration
frequency and peak of bubble plume are large in the lower.
When in aspect ratio of 1.0, the vibration frequency of the
bubble plume was similar, the frequency spectra of bubble
fluctuation velocities is also not obvious, the bubble plume
structural is stability; When in aspect ratio of 1.5, peak of
the spectrum in the middle part of bubble plume is smaller
than top and the lower water depths, amplitude of swing is
not obvious at the middle part of bubble plume; Peak of
bubble velocity fluctuations have reduced and frequency of
fluctuation is about 0.015Hz, the bubble plume structural at
the middle part is not stability. When in aspect ratio of 2.0,
vibration frequency and peak of bubble plume is small in
the top of bubble plume, but Frequency and peak of bubble
fluctuation velocities are large in the top of bubble plume,
the top of bubble plume structural is not stability
Conclusions
In this study, we have conducted a series of experiments on
bubble plume behaviour that takes place in a pseudo planer
container. Use of recursive cross correlation technique for
PIV and shadowtovoid fraction computation, the dynamic
instability of the bubble plume has been elucidated. In
particular, we focused on space dependency of the
frequency spectrum in bubble velocity field in order to
characterize the turbulent intensity that is created by rising
bubbles. Through the experiments, our conclusions are
obtained as listed below.
(1) The bubble flow morphology can be obtained in a
relatively short time by RCCPIV measurement algorithm.
The method from the local averaged brightness methods and
the real local void fraction is suitable to measure the void
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
fraction of gasliquid twophase flow; it can simply and
directly obtain the void fraction distribution even in high
void fraction.
(2)The aspect ratio is the one of the main factor that
affecting the bubble plumes movement. When in aspect
ratio of 1.0, the timeserial of bubble plume enter into the
both sides of the stability vortex structure and stay longer.
The change of vibration frequency is not very evidence by
comparing with the aspect ratio of 1.5 and 2.0. So the device
was designed the aspect ratio of 1.0 in the same
experimental condition, it will be important to improve the
aerating efficiency.
(3) The whole structure of the bubble plume is stability
when the aspect ratio of 1.0; The pattern and structure of the
middle bubble plume is instability when the aspect ratio of
1.5; The pattern and structure of the top bubble plume is
instability when the aspect ratio of 2.0.
Acknowledgements
This research was supported by the National Natural
Science Foundation of China (Grant No: 50679071).
References
J.Huang, Y.Murai, F.Yamamoto, Quadrant analysis of
bubble induced velocity fluctuation in a transitional
boundary layer, Journal of Hydrodynamics, Elsevier,Vol.21,
No.1, pp.9399
Murray R. Snyder. Analysis of the behavior of bubbles and
droplets in isoteopic turbulence. United States: The Johns
Hopkins University, 2007
Wen Cheng, Yuichi Murai, Fujio Yamamoto. Estimation of
the liquid velocity field in twophase flows using inverse
analysis and particle tracking velocimetry. Flow
Measurement and Instrumentation. 2005, 16: 303308
A.Susset, J.M.Most, D.Honore. A novel architecture for a
superresolution PIV algorithm developed for the
improvement of the resolution of large velocity gradient
measurements. Experiments in Fluids. 2006
W. Cheng, Y. Murai, F Yamamoto. Bubble Velocity
Measurement with recursive cross correlation PIV technique.
Flow Measurement and Instrument, Vol.16 (2005), No.l,
3546
Y.Murai, S.Ohta, A.Shigetomi, Y.Tasaka, Y.Takeda,
Development of ultrasonic void fraction profiler,
Measurement Science and Technology, Vol. 20, (2009)
No.114003.
Cao weili. Theory and Method of Fast Fourier Transform.
Journal of shanghai university of electric power.2006, 6
Yanglijuan, Zhang baihua, Ye xuzheng. Fast Fourier
Transform and the Application. Optoelectronic Engineering,
2004, 12
