Experiments in Fluids [Suppl.] S194±S201 Ó Springer-Verlag 2000
Velocity measurements of liquid and gaseous phase for a system
of bubbles rising in water
R. Lindken, W. Merzkirch
S194
Abstract An experimental procedure for performing simultaneous, phase-separated measurements in a bubbly,
two-phase ¯ow is described and demonstrated with the
application to a system of bubbles rising in water. PIV
measurements using a vertical laser light sheet are combined with the simultaneous recording of the bubbles'
motion by means of a digital high-speed camera viewing
the bubbles from above. This experimental approach is
aimed at providing a means for characterizing the ``pseudo-turbulence'' induced by the bubbles in the liquid phase.
1
Introduction
Bubble column reactors are designed to allow an intensive
mass transfer between a gas and a liquid in which the gas
rises in the form of swarms of bubbles. For the modeling
and scaling of such an apparatus, detailed knowledge of
the ¯uid mechanical processes in the vicinity of the contact surfaces of the two phases is needed. Of particular
interest is the turbulence ®eld induced by the bubbles
rising in the liquid phase. In earlier attempts to model
bubble column reactors, this turbulence was assumed to be
isotropic, but since the results obtained when using this
assumption were not satisfactory, it is evident that the
turbulence characteristics are more complex.
It must be expected that the ¯ow ®eld considered includes turbulent processes of two different length scales.
Small-scaled turbulence (small in comparison with a
bubble diameter) governs the direct mass transfer between
the two phases at the interfaces. Large-scale turbulence
(the scale being comparable with a bubble diameter) is
produced by the motion of the bubbles in the liquid, and it
can in¯uence the motion of (other) bubbles; it is sometimes called ``pseudo-turbulence'' (Lance and Bataille
1991). As a consequence of the existence of pseudoturbulence in the liquid phase, the bubbles in a swarm rise
at a speed different from that of a single bubble rising in
stagnant water (for a review see, e.g., SchluÈter and RaÈbiger
1998). This phenomenon is attributed to the fact that a
R. Lindken (&), W. Merzkirch
Lehrstuhl fuÈr StroÈmungslehre, UniversitaÈt Essen, 45117 Essen
Germany
This research was supported by a grant from Deutsche
Forschungsgemeinschaft (DFG Az. Me 484/32). The authors are
also grateful for the technical support by LaVision GmbH,
GoÈttingen, Germany.
bubble in a swarm can move in the wake of a preceding
bubble, as demonstrated quantitatively for a single line of
successively rising bubbles both theoretically (Harper
1997) and experimentally (Tassin and Nikitopoulos 1995).
The situation in a swarm is more complex than for a single
line of bubbles: bubbles can be sucked into the wake of
preceding bubbles. This may cause a horizontal velocity
component of the bubble which can follow a helical path
(Tsuchiya et al. 1989).
The velocity and turbulence ®elds in this two-phase
¯ow can be surveyed using particle image velocimetry
(PIV). In such studies, it is necessary to separate the
information on the velocity of the two phases, gas and
liquid, and to account for three-dimensional effects,
particularly in view of the desired information on the
pseudo-turbulence. Hassan et al. (1998) and Ortiz-Villafuerte et al. (1998) performed PIV measurements in
combination with a forward-projection shadow method
for determining 3D velocity values and the size of
bubbles rising in water inside a vertical pipe. They also
showed that, with this experimental arrangement, it is
possible to determine Reynolds stresses which may serve
for modeling the pseudo-turbulence of the liquid phase
(Ortiz-Villafuerte et al. 1999; Tokuhiro et al. 1997, 1998).
BruÈcker (1998) investigated the 3D velocity ®eld around
a system of rising bubbles by means of a PIV scanning
technique.
Lindken et al. (1999) have shown that the application of
a digital mask technique for separating the PIV signals
originating from the two phases (Gui and Merzkirch
1996a) allows for a high spatial resolution of the velocity
measurements in water close to the interfaces, i.e., the
bubble contours. These experiments did not provide information on the instantaneous 3D position of the bubbles, i.e., illumination in the form of a laser light sheet
provided images of both the bubbles and the tracer particles with which the water was seeded. But if the aim is to
analyze the pseudo-turbulence, it is desirable to know the
exact position of a bubble, whose diameter is several times
the thickness of the light sheet, relative (normal) to the
plane of the sheet. In this paper, we describe and demonstrate an experimental set-up for performing both PIV
measurements in the two phases and high-speed visualizations of the bubbles. Information on the instantaneous
3D coordinates of the rising bubbles, their 3D velocity, and
the 2D velocity distribution in the liquid phase is thus
provided. The results which can be obtained with the
system described can be used for characterizing the turbulent ¯ow in the liquid phase. This will be demonstrated
with the visualization and measurement of turbulent vortical structures which can also be predicted using direct
numerical simulation (DNS) of this type of ¯ow (Esmaeeli
and Tryggvason 1999).
2
Experiment
2.1
Test rig
The experiments are performed in a transparent cylindrical tank of 200 mm i.d. ®lled with deionized water. In
order to minimize distortions in the optical measurements, the test tank is placed inside a water-®lled rectangular tank with transparent plane walls. A bubble
generator at the bottom of the tank allows the production
of systems of bubbles with a high reproducibility regarding number and volume of the bubbles.
Systems of multiples of seven gas bubbles (``swarms'')
are produced with an apparatus consisting of seven individual bubble generators. The principle of the apparatus
and the design of a single generator are shown in Fig. 1.
The generators release de®ned portions of pressurized air
by means of two magnetic valves. The two valves are arranged in series and at a short distance apart, so that a
reproducible volume of air for generating a single bubble
is available. A rough variation in the bubble size is
achieved by changing the control of the valves up to an
overlap of the opening times, and the ®ne control of the
bubble size is accomplished by varying the upstream air
pressure. To ensure a constant pressure during the experiments, the compressed air is stored in a 60 liter
pressurized tank at an overpressure of 0.12±0.26 bar. The
Fig. 1. Bubble swarm generator
separation of the air bubbles from the generators without
collapsing is realized by ejecting the air through a nozzle
with very small opening and high pressure drop into a
capillary of larger diameter. The indicated variation in the
air pressure allows bubbles to be produced with diameters
in the range of 4.0±7.0 mm, and with a very small variation
in size at a given pressure. The seven bubbles forming a
swarm or system are nearly monodisperse and do not
show satellite bubbles. Such a system of bubbles can be
produced at any desired instant of time.
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2.2
PIV measurements
PIV measurements serve to investigate the ¯ow induced in
the water (continuous phase) by the rising bubbles
(dispersed phase). For this purpose, the water is seeded
with tracer particles 12 lm in size (``Vestosint 1018'' of
HuÈls AG) that are neutrally buoyant in water. Although the
particle concentration with a nominal volume fraction of
10)5 is very low, the presence of the tracer particles may
affect the properties of the air/water interfaces, as discussed in the literature (Clift et al. 1978; Ortiz-Villafuerte
et al. 1999). Possible effects of this ``contamination'' of the
water by the tracer material are: (a) hydrophobility of the
tracers resulting in a tracer motion away from the bubble
surface; (b) settling of the tracers on the bubble surface,
thus making the bubble surface more rigid; (c) change of
the bubbles' rise velocity in the contaminated water. We
have investigated the in¯uence of this contamination on
our measurement results, and in visualization studies we
could not detect particles moving away from the bubbles,
nor particles settling on the bubbles' surfaces.
Systematic measurements of single bubbles' size and
rise velocity for the two systems deionized water/clean air
and deionized water seeded with tracer particles/clean air
at 296 K were performed for bubble sizes in the range
from 4.0 to 6.5 mm. The bubble rise velocities and the
bubble sizes were obtained by means of multiple shadowgraphy measurements. The resulting distribution of the
bubble rise velocities against the equivalent bubble
diameter (Fig. 2) shows no dependency on whether the
water was seeded or not. The rise velocities with and
without added tracer material differ by no more than 1%,
which is in the range of the reproducibility of the measurement. The measured rise velocities are up to 3% below
the value for pure water as given by Clift et al. (1978), thus
indicating that the contamination effect can be neglected
for the range of bubble sizes and the tracer material used
in our experiments.
The light source in the PIV system (Fig. 3) is a doublepulsed frequency-doubled Nd:YAG laser emitting at
532 nm. The particle image patterns are recorded with a
CCD camera, either ``Flowmaster 2'' of LaVision
(1000 ´ 1000 pixels at 30 Hz) or ``Flowmaster 3''
(1300 ´ 1000 pixels at 8 Hz), with both cameras in the
double shutter mode. The cameras are equipped with a
532 nm optical ®lter with a band width of 3 nm in order to
eliminate light from the light source used for the 3D
scanning of the bubbles (see below). The viewing direction
of the camera is normal to the plane of the light sheet. PIV
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recordings of the two-phase ¯ow are taken with an interval
of 1.5 ms between the two exposures.
Depending on the instantaneous position and shape of a
bubble, it is possible that the light sheet intersects with a
bubble such that a considerable amount of laser light is
directly re¯ected from the bubble surface towards the
camera. Then, a large portion of the ®eld of view can be
affected by the strong laser radiation so that an evaluation
of the PIV recording might become impossible. Situations
where the signal quality is too low for quantitative evaluation due to unwanted laser light re¯ection occur approximately every 20th or 30th recording of a PIV time
series. Moderate disturbances due to light re¯ection from
the bubbles can be removed with the mask techniques
described in Sect. 2.3.
Fig. 2. Comparison between measured and theoretical bubble
rise velocity
The 3D position of the bubbles cannot be derived from
the PIV measurements. In order to have this information
additionally available, a second, independent illuminationand-recording system is used simultaneously. It consists of
a 2.5-W cw Ar+ laser providing a light sheet orthogonal to
the PIV (Nd:YAG laser) light sheet, and a digital highspeed camera (Phantom V3.0 from Vision Research with
512 ´ 512 pixels at 576 Hz) positioned above the tank.
This way, a series of images of the bubbles when penetrating the Ar+ laser light sheet is captured. The recordings
of the two cameras are synchronized by means of the light
signal originating from the pulsed Nd:YAG laser. Both
cameras are equipped with objectives providing a small
depth of focus so that gas bubbles outside the ®eld of
interest and illuminated by scattered light appear as
blurred images.
2.3
PIV evaluation
The digital PIV recordings are evaluated using the minimum quadratic difference (MQD) method (Gui and Merzkirch 1996b; Gui et al. 1998). Since the two phases, gas
bubbles and water, move at different speeds, it is necessary
to separate the signals from the two phases in the PIV
recordings. The signi®cant difference in size of the gas
bubbles and the tracer particles with which the water is
seeded allows a digital mask technique to be applied (Gui
and Merzkirch 1996a). The patterns of tracer particles and
bubbles are recognized by image processing, and the ¯ow
velocity of the water and the rise velocity of the bubbles
are determined separately and simultaneously. For
distinguishing between the signals resulting from the
different phases in a pair of PIV recordings, a digital mask
D(i, j) is generated such that
Fig. 3. Experimental set-up for simultaneous PIV measurements (Nd:YAG laser with vertical light sheet and PIV-CCD camera) and
3D bubble visualization (argon ion laser with horizontal light sheet and digital high-speed camera)
D(i, j) ˆ 0 if pixel (i, j) belongs to phase A
D(i, j) ˆ 1 if pixel (i, j) belongs to phase B.
The de®nition of whether a pixel belongs to phase A or B is
based on the size of the particle image, including the respective pixel. A size threshold is set separating A and B.
The mask is combined with the MQD algorithm for determining the velocities of the two phases separately in two
steps, with the step for the liquid phase requiring more
intensive computation, but with the result that the water
velocity can be measured accurately also in close proximity to the interfaces separating the two phases. This is in
contrast to the use of ¯uorescing tracer particles and is an
alternative for separating the signals from the two phases
(Gui et al. 1997).
2.4
Reconstruction of the 3D bubble positions
As mentioned in Sect. 2.2, the vertical movement of the
bubbles through the horizontal Ar+ laser light sheet is
observed and continuously recorded with a digital highspeed camera. In this projection, the bubbles are only
visible when they are illuminated by this light sheet. This is
illustrated in Fig. 4, which shows four frames selected
from a time series recorded at a rate of 576 frames per
second. In Fig. 4a, one bubble is just passing the horizontal light sheet, while in Fig. 4b a second bubble has
entered the sheet. At the instant of time at which Fig. 4c
was recorded, the vertical light sheet produced by the
Nd:YAG laser was initiated for taking a PIV recording. The
trace of this PIV light sheet is visible in Fig. 4c, and this
allows the positions of the bubbles relative to the PIV light
sheet to be accurately determined. The ®rst bubble has left
the light sheet in Fig. 4d. One should note that the PIV
single exposures are separated by a time interval
Dt ˆ 1.5 ms; it is thus ensured that a high-speed frame
showing the trace of the PIV light sheet, such as that in
Fig. 4c, is always available.
The images of the recorded bubbles taken with the highspeed camera are processed and binarized. From a time
series of these recordings (Fig. 5) and the rise velocities as
determined in the PIV measurements, a 3D picture of the
system of bubbles, including an estimate of the bubbles'
size and shape, can be reconstructed. The result is information on the instantaneous 3D bubble positions, threecomponent (3C) bubble motion, and the 2C velocity ®eld
of the water ¯ow, as presented in the following section.
The experimental conditions in are summarized in
Table 1.
3
Results and discussion
A speci®c, instantaneous ¯ow situation is depicted in
Fig. 6. The distribution of the water velocity is presented
in the form of vectors in the vertical measurement plane,
the PIV light sheet. In agreement with number values reported for comparable PIV measurements and systems,
the inaccuracy of the 2D PIV velocities is estimated to be
between 1 and 2%. The 3D positions of the ®ve bubbles in
the measurement area are indicated by their projections
onto the horizontal ground plane. These positions result
from the bubble images visible in the PIV recording, as
well as from the recordings taken with the high-speed
camera in a downward (negative y) direction. Two bubbles
intersect with the vertical PIV light sheet. The viewing
direction of the PIV camera was in the z-direction.
Therefore, the two bubbles in front of the PIV light sheet
are blocking off the sight and cause the existence of the
two white areas in the center of the measurement plane
without information on the water velocity. Also, the bubble on the left-hand side, which intersects with the light
sheet close to its edge, causes a smaller area without
velocity signals. The instantaneous position, the volume
and the approximate shape of the bubbles are derived both
from the PIV images and from the high-speed recordings
Fig. 5. The space/time series of the bubble motion shown in
Fig. 4. Each horizontal plane corresponds to a different instant of
Fig. 4. Four selected frames from a time series recorded with the time of the series recorded with a frequency of 576 frames per
digital high-speed camera after binarization of the bubble images. second. The y-scale indicates the respective separation in space.
Illumination by horizontal light sheet. At the instant of Fig. 4c the The bubble contours are reconstructed from the 2D projections of
this time series and the PIV data
vertical PIV light sheet is initiated
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Table 1. Experimental parameters
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General properties
System
Temperature
Tank diameter
Liquid height
Liquid height of measurement
position
Average bubble diameter
Distance between bubbles
Local gas hold
Reynolds number
Weber number
EoÈtvos number
Deionized water/clean air
298 K
200 [mm]
750 [mm]
350 [mm]
5.5 [mm]
1±1.8 [diameters]
2.5 [%]
1,400
5.5
4.0
Seeding
Product
Mean diameter
Volume fraction
Vestosint 1018 (®ltered)
12 [lm]
10)4±10)5
PIV image recording
Image size
Object ®eld
Time interval between pulses
Optical ®lter
1008 ´ 984 [pixels]
30.9 ´ 30.2 [mm]
1.5 [ms]
532 ‹ 1.5 [nm]
Nd:YAG PIV laser
Wavelength
Power
Pulse length
Light sheet thickness
532 [nm]
<50 [mJ]
8 [ns]
1 [mm]
High-speed camera
Image size
Object ®eld
Frame rate
512 ´ 512 [pixels]
63 ´ 63 [mm]
576 [Hz]
Ar+ Visualization laser
Wavelength
Power
Light sheet thickness
514.5 [nm]
2.5 [W]
0.3 [mm]
PIV Interrogation
Algorithm
Phase separation
Interrogation resolution (window)
Interrogation increment
Equivalent probe volume
Minimum quadratic
difference
Digital phase mask
29 ´ 29 [pixels2]
16 ´ 16 [pixels2]
0.9 ´ 0.9 ´ 1.0 [mm3]
taken during the time when a bubble moves through the
horizontal light sheet in an upward direction. A bubble
changes its shape during its motion due to the interaction
with the pseudo-turbulent liquid phase in which it moves,
and the instantaneous shape has an effect on the production of the (pseudo-)turbulence. From the two projections in horizontal and vertical directions, the volume
of a bubble is determined with an accuracy of not better
than 10%, because the image of the bubble contour is
blurred to some extent. A value of the bubble volume is
needed for calculating a Reynolds number that includes
the bubble's ``eqivalent'' diameter as the characteristic
length. The position of the center of gravity of a bubble
can be measured at a precision better than 5% in terms of
the relative error. The availability of a multiple of successive images taken with the digital high-speed camera is
helpful and serves to identify the individual bubbles of the
swarm visible in a PIV recording. The observable bubble
Fig. 6. Vector diagram of the 2D velocity distribution of the
¯ow in the liquid phase as induced by the system of ®ve bubbles
rising in water. The 3D velocity of the bubbles is indicated by an
arrow in the interior of each bubble, while the 3D position of
the bubbles is given by the respective projections onto the
ground plate
shapes were never strictly ellipsoidal or spherical as often
assumed in the analysis of bubble motion.
The 3D velocity of the bubbles, as indicated by an arrow
at the center of each bubble, results from the PIV measurement and from the measurement made with the highspeed camera. The velocity component in the x-direction
is available from both measurements, and a comparison of
these two measurement results can serve as a check for the
accuracy of this experimental result, which is estimated to
be accurate to within 8%. The indicated velocity includes
contributions from the bubble motion in the liquid phase
and from surface deformations due to the change in
bubble form.
The vector plot for the water velocity clearly shows a
wake produced by the bubble in the middle of the light
sheet plane. This oblique wake structure and the measured
bubble velocity suggest that the bubble is not rising vertically but follows a helical path. This supports the earlier
observations that bubbles in a swarm can be entrained into
the wakes of other bubbles, but it may be anticipated also
that different wakes interact with each other like multiple
parallel jets do. Finally, it is interesting to note that three
bubbles rise at a velocity of approximately 20 cm/s,
whereas the lower bubble in front of the light sheet has a
rise velocity of 31 cm/s. This must be explained by this
bubble moving in the wake of the bubble seen above it and
slightly displaced to the right.
It can be seen in Fig. 6 that several vortices separate
from the wake. In order to quantify this process of vortex
formation, we have determined the distributions of the
swirling strength as de®ned by Adrian et al. (2000) and
vorticity. The areas covered in these ®gures comprise only
the wake ¯ow visible in Fig. 6; see also the x and y coordinate values that correspond to those given in Fig. 6.
While the vorticitiy contours (Fig. 7) indicate not only
vortices but also regimes with high shear, the information
obtained from the swirling strength (Fig. 8) is restricted to
the appearance of vortices with closed streamlines. In
Fig. 8, it is evident that such vortices, marked here as I to
III, separate from the wake and then move as free vortices
in the liquid phase. In addition, spots showing high values
of the swirling strength appear, in Fig. 8 designated as IV
Fig. 7. Vorticity and velocity distribution in the wake region
shown in Fig. 6
Fig. 8. Square of the swirling strength and velocity distribution
in the wake region shown in Fig. 6
to VI, without a visible vortex-like pattern of the velocity
vectors. It is known (Adrian et al. 2000) that these
``hidden'' vortices become apparent by applying a Galilei
transformation to the vector ®eld with the negative value
of the velocity measured in the center of the spots of high
swirling strength, i.e., by setting the velocity of this center
to zero.
The result of this Galilei transformation when applied to
the six areas of high swirling strength, designated as I to
VI, is shown in Fig. 9. In contrast to Fig. 8, the vortical
structure of the areas IV to VI is now evident. Also given
in Fig. 9 are the components of the convection velocities
Ucon, Vcon, with which the (centers of the ) structures move
in the frame of Fig. 8. A signi®cant difference in the
V-components of the structures I to III and IV to VI is
apparent. Two pairs of counterrotating vortices, I and IV,
II and V, can be identi®ed, with the two vortices forming a
pair laying on different sides of the ``axis'' of the wake. It
might be possible that these pairs are the cross-sectional
cuts of vortex rings surrounding the wake, but for a better
estimate it would be necessary to have a 3D picture. It is
not likely that the structures III and VI form such a pair;
III appears to be separated from the wake, and it could
also be the residual of a preceding wake phenomenon.
4
Summary and conclusion
We have described an experimental set-up for the quantitative analysis of a bubbly two-phase ¯ow. The three
components of the 3D velocity ®eld of air bubbles can be
measured simultaneously with the 2D±2C velocity distribution of the liquid phase. The two velocity components in
water are measured in the plane of a light sheet. The
performance of the experimental set-up is demonstrated
with the reported investigation of a system of bubbles
rising in water.
The aim of future measurements is to characterize the
turbulent ¯ow induced by the bubbles in the liquid phase,
i.e., the ``pseudo-turbulence'' which is governed by length
scales comparable to the bubble diameters and visible in
form of the free vortices in Fig. 8. This approach needs, in
principle, 3D information that is not available with our
present system, which could be supplemented, however,
by a stereo PIV set-up. It is intended that the experimental
turbulence characteristics can be employed as input data
for numerical analysis of the ¯ow in bubble column reactors. For this purpose, two ways of using the experimental data are possible, depending on the kind of
numerical approach: for developing an algebraic turbulence model statistical quantities, e.g., Reynolds stresses,
are required. This will make it necessary to perform series
of experiments like those for which results are shown in
Fig. 6; experiments with the light sheet at various positions
and also normal to the present sheet should then be performed. If the numerical approach is a direct numerical
simulation, as described by Esmaeeli and Tryggvason
(1999), a direct comparison of the computed and measured results, including vortical structures, would be
desirable for checking the quality of the computation. The
reported DNS results apply, at this time, only to moderate
Reynolds numbers, which are still more than an order of
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Fig. 9. Galilei transformation applied to the areas of high
swirling strength designated as I to VI in Fig. 8
magnitude below the values applying to the ¯ow in a
bubble reactor, and used in the present experiments.
References
Adrian RJ; Christensen KT; Liu Z-C (2000) Analysis and interpretation of instantaneous turbulent velocity ®elds. Exp Fluids
(in print)
BruÈcker C (1998) 3D measurements of wake interaction in a
bubbly two-phase ¯ow using scanning PIV (SPIV) and stereoimaging. 9th Int Symp on Applications of Laser Techniques to
Fluid Mechanics, Instituto Superior TeÂcnico, Lisbon, Portugal,
pp 27.4.1±27.4.10
Clift R; Grace JR; Weber ME (1978) Bubbles, drops, and particles.
Academic Press, New York
Esmaeeli A; Tryggvason G (1999) Direct numerical simulations of
bubbly ¯ows Part 2. Moderate Reynolds number arrays. J Fluid
Mech 385: 325±358
Gui L; Lindken R; Merzkirch W (1997) Phase-separated PIV
measurements of the ¯ow around systems of bubbles rising in
water. ASME-FEDSM97-3103. American Society of Mechanical
Engineers Fluids Engineering Division
Gui L; Merzkirch W (1996a) Phase-separated PIV measurements
in two phase ¯ow by applying a digital mask technique. ERCOFTAC Bulletin 30: 45±48
Gui L; Merzkirch W (1996b) A method of tracking ensembles of
particles. Exp Fluids 21: 465±468
Gui L; Merzkirch W; Lindken R (1998) An advanced MQD
tracking algorithm for DPIV. 9th Int Symp on Applications of
Laser Techniques to Fluid Mechanics, Instituto Superior TeÂcnico, Lisbon, Portugal, pp 10.5.1±10.5.6
Harper JF (1997) Bubbles rising in line: why is the ®rst approximation so bad? J Fluid Mech 351: 289±300
Hassan YA; Schmidt WD; Ortiz-Villafuerte J (1998) Investigation
of three-dimensional two-phase ¯ow structure in a bubbly pipe
¯ow. Meas Sci Technol 9: 309±326
Lance M; Bataille J (1991) Turbulence in the liquid phase of a
uniform bubbly air-water ¯ow. J. Fluid Mech 222: 95±118
Lindken R; Merzkirch W (1999) Phase separated PIV and shadow-image measurements in bubbly two-phase ¯ow. Proc 8th
Int Conf on Laser Anemometry ± Advances and Applications.
``La Sapienza'', University of Rome, pp 165±171
Lindken R; Gui L; Merzkirch W (1999) Velocity measurements in
multiphase ¯ow by means of particle image velocimetry. Chem
Eng Technol 22: 202± 206
Ortiz-Villafuerte J; Hassan YA; Schmidl WD (1998) Investigation
of three-dimensional bubbly ¯ow measurement using displacement particle image velocimetry technique. 9th Int Symp on
Applications of Laser Techniques to Fluid Mechanics, Instituto
Superior TeÂcnico, Lisbon, Portugal pp 27.5.1±27.5.9
Ortiz-Villafuerte J; Schmidl WD; Hassan YA (1999) Three-dimensional PIV experimental study of the wake of a bubble
rising in a liquid. In: Adrian RJ; et al (eds) Proc Third Int
Workshop on PIV'99 ± Santa Barbara, University of California,
Santa Barbara, CA, pp 119±138
SchluÈter M; RaÈbiger N (1998) Bubble swarm velocity in two phase
¯ows. HTD-Vol. 361-5, Proc ASME Heat Transfer Division 5:
275±280
Tassin AL; Nikitopoulos DE (1995) Non-intrusive measurements
of bubble size and velocity. Exp Fluids 19: 121±132
Tokuhiro A; Maekawa M; Fujiwara A; Hishida K; Maeda M
(1997) Measurements in the wake of two bubbles in close
proximity by combined shadow-image and PIV technique.
ASME-FEDSM97-3067. American Society of Mechanical
Engineers Fluids Engineering Division
Tokuhiro A; Maekawa M; Iizuka K; Hishida K; Maeda M (1998)
Turbulent ¯ow past a bubble and an ellipsoid using shadowimage and PIV techniques. Int J Multiphase Flow 24: 1383±1406
Tsuchiya K; Miyahara T; Fan L-S (1989) Visualization of
bubble±wake interactions for a stream of bubbles in a twodimensional liquid±solid ¯uidized bed. Int J Multiphase Flow
15: 35±49
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