Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 14.1.4 - Dynamic Drop Size Measurement in Vertical Annular Two-phase Flow
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 Material Information
Title: 14.1.4 - Dynamic Drop Size Measurement in Vertical Annular Two-phase Flow Droplet Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Alamu, M.B.
Van der Meulen, G.P.
Azzopardi, B.J.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: drop size
entrainment fraction
pressure drop
film thickness
void fraction
time resolved
 Notes
Abstract: The mechanisms of atomization of part of the liquid film to form drops in annular two-phase flow are not entirely understood. It has been observed that drop creation only occurs when there are large disturbance waves present on the film interface. Woodmansee and Hanratty (1969) observed that ripples on these waves were a precursor to drops. Though it has been reported that drops occur in bursts Azzopardi (2006) almost all previous drop size or concentration measurements have been time integrated. Dynamic time averaged drop-size measurements are reported for the first time for annular two-phase flow. It was carried out on a 19 mm internal diameter vertical pipe with air and water as fluids. A laser light scattering technique was employed to obtain the drop size and concentration variations in time. Simultaneously, time-resolved measurements were made of: film thickness using conductance probes employing a pair of flush mounted rings as electrodes and of pressure gradient. The gas superficial velocity was 13-43 m/s at liquid superficial velocities of 0.05 and 0.15 m/s. Additional tests were carried out with the gas velocity at 14 m/s for liquid superficial velocities of 0.03-0.18 m/s. Though structures are not clearly visible in the signals acquired they have been analyzed in amplitude and frequency space to yield Probability Density Function (PDF) and to identify the dominant frequency. Cross-correlation between two film thickness probes provides the wave velocities. Characteristic frequencies for both waves on the film interface and drop concentration have been reported.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Bibliographic ID: UF00102023
Volume ID: VID00341
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: 1414-Alamu-ICMF2010.pdf

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



Dynamic Drop Size Measurement in Vertical Annular Two-phase Flow


Munhir B. Alamu, Gerrit P. Van der Meulen, Barry J. Azzopardi

University of Nottingham, Process and Environmental Engineering Research Division, Faculty of Engineering,
University Park, Nottingham, NG7 2RD, United Kingdom
E-mail: Barry.azzopardiii~nottingham.ac.uk


Keywords: Drop size, entrainment fraction, pressure drop, film thickness, void fraction, time resolved

Abstract

The mechanisms of atomization of part of the liquid film to form drops in annular two -phase flow are not entirely understood.
It has been observed that drop creation only occurs when there are large disturbance waves present on the film interface.
Woodmansee and Hanratty (1969) observed that ripples on these waves were a precursor to drops. Though it has been reported
that drops occur in bursts Azzopardi (2006) almost all previous drop size or concentration measurements have been time
integrated. Dynamic time averaged drop-size measurements are reported for the first time for annular two-phase flow. It was
carried out on a 19 mm internal diameter vertical pipe with air and water as fluids. A laser light scattering technique was
employed to obtain the drop size and concentration variations in time. Simultaneously, time-resolved measurements were
made of: film thickness using conductance probes employing a pair of flush mounted rings as electrodes and of pressure
gradient. The gas superficial velocity was 13-43 m/s at liquid superficial velocities of 0.05 and 0.15 m/s. Additional tests
were carried out with the gas velocity at 14 m/s for liquid superficial velocities of 0.03-0.18 m/s. Though structures are not
clearly visible in the signals acquired they have been analyzed in amplitude and frequency space to yield Probability Density
Function (PDF) and to identify the dominant frequency. Cross-correlation between two film thickness probes provides the wave
velocities. Characteristic frequencies for both waves on the film interface and drop concentration have been reported.


Introduction
Understanding drop size distribution is key in the modeling
of annular flow in applications from nuclear reactors to oil
and gas exploration and production. In annular flow the
liquid flow as film on the pipe wall with a droplet laden
gas stream in the center of pipe. Damage done by erosion
oand/or corrosion depends on drop and velocity of the
drops as noted by Zaidi et al. (1998).
Despite its importance and the attention it has received so
far, there are many prominent, unresolved issues in annular
flow. Part of the problems not yet fully understood are the
mechanisms responsible for exchange of mass and
momentum between the film and the gas core as well as
quantification of disturbances cause by droplets when they
re-deposit on liquid film. This work contributes to the
on-going efforts in flow assurance study of annular
two-phase flow by taking dynamic data of film thickness,
drop size, drop concentration, entrained fraction and
pressure drop in a simultaneous manner.
Drop size data has been measured in vertical annular
two-phase flow using optical techniques. Azzopardi et al.
(1980, 1991) have used the angular scattering of light into
small forward angles. The same approach has been used
by Simmons and Hanratty (2001) and Al-**** and
Hanratty (lrl I) for horizontal annular flow. The
instruments employed used the assumption that the
scattering was dominated by Fraunhofer diffraction and
time averaging was almost inevitably employed to improve
measurement accuracy. The method provides average
values over a finite volume. Drops size distributions are
extracted from the angular variation of scattered light. In
addition, information of the time averaged concentrations
were also determined. The other approach used utilized


Phase Doppler anemometry, Azzopardi and Teixeira (1994),
van't Westende (2007). This provides data at one point in
space. The sampling position has to be traversed about
the pipe cross section to obtain fully representative data.
This approach also provides velocity information about
drop velocity. Azzopardi & Teixeira 1994) have shown
that the drop size distribution from the diffraction and
Phase Doppler anemometry instruments are the same if the
are both converted to the same basis.
The concentrations measured with the laser diffraction
instruments can be converted to entrained fraction by the
formula
E =PIudc (1)
F,

Where tid iS the drop velocity, Pi is the liquid density, c is
the volumetric drop concentration and riz, is the total
liquid mass flux. From the available measurements,
Azzopardi & Teixeira (1994), Fore & Dukler (1995), Zaidi
et al. (1998), van't Westende et al. (2007), it can be seen
that the gas superficial velocity is a good approximation to
the drop velocity at centre-line. The gas superficial
velocity can therefore be used in place of drop velocity in
equation (1).
Woodmansee & Hanratty (1969) showed evidence that the
creation of drops from the film on the channel walls did
not take place from of the film but specifically from
periodic structures, usually called disturbance waves which
travel over the film at velocities of a few metres per second.
Azzopardi (2006) presents more evidence of this.
Therefore, it might be expected that there would be an
interrelationship between the fluctuations of drop
concentration and the frequency of disturbance waves.
Unfortunately, hitherto there has been hardly any work













































40


+0li0015 mon A45 Ere&Dutler
on 016 00 032 an 048 Azzopardi & Terrelra

U 01 0 02 0 04 \an't Westendeet al
-Llquid superficalul elocits(m/s)


l





) 10 20 30
Gas superficial velocity (m/s)


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


Paper No


presenting information about the way in which the drop
concentration varies with time. The most useful study is
that of Azzopardi & Whalley (1980) who used a camera
looking axially up the pipe to record drops passing up the
pipe. To ensure that it was known which waves the drops
came from, a method of injecting artificial waves was
employed. The liquid flow rate was set at the value just
before disturbance waves appeared. A small volume of
liquid was then injected rapidly into the film. This
produced a single wave which travelled up the vertical pipe.
The cine films taken with this technique were analysed
manually. It was found that before liquid injection there
were no drops. Whilst the wave was in the pipe there
were an increasing number of drops as the wave
approached the camera at the end of the pipe. However,
the increase was not monotonic, drops came in bursts or
waves. Once the disturbance wave had exited the pipe no
more drops were seen.


kdz time delay (s)
hi augmented film flow rate (kg s ')
hib base film flow rate (kg s ')
viz mass flux (kg m~s )
R,, Auto covariance function
P,, Power Spectral Density
t Time (s)
T sampling time (s)
itvelocity (m s- )
I' volume (m )
Greek letters
At Injection time (s)
g film thickness (m)
E, void fraction (-)
p density (kg m )
Interrogating time delay (s)
Subsripts
d drop
1 liquid
SwaYO


E
a, 40

a 30


O 20

> 10

0


Experimental arrangements
The experiments were carried out on a vertical 19 mm
diameter 7 m long pipe using air and water as the fluids at
with an operating pressure of 1.5 bar absolute. The flow
facility is shown schematically in Figure 2.Drop size and
drop concentration data (entrained fraction) were taken svith
a light scattering technique using a Malvern Spraytec
instrument. Film thickness was measured using
conductance probe employing a pair of flush mounted rings
as electrodes. Pressure drop across the system was
monitored with a differential pressure cell. The output
from the conductance probes and the differential pressure
cell were fed into a PC via a National Instruments
acquisition card and processed using a LabView
programme.


Figure 1: Dependence of mean drop velocity at centre-line
with gas superficial velocity.

Another pertinent issue is non-existence of time resolved
drop size data before the present study. While time
resolved measurements are common for film thickness and
pressure drop, dynamic, timed averaged drop size and
entrained fraction measurements in annular two-phase flow
are just beginning.
In practice, drop size data are usually time integrated. This
integration over time may compromise the quality of the
data because of the complex mathematics and the
assumptions made in time and space. Hence, analyzing
data this way in amplitude and frequency space with
respect to time to yield Probability Density Functions and
or to identify the dominant structure frequency using
Power Spectrum Density may often give misleading
interpretations.
Therefore, this work contributes experimentally to provide
information on mechanisms responsible for liquid
entrainment in annular two-phase flow by providing new
data taken simultaneously for film thickness (waves), drop
sizes/concentration and pressure drop measurements.
Nomenclature


Figure 2: Schematic flow diagram of the rig used in the
present study

The flow facility, used previously by Kaji [8], has recently
been modified to accommodate a special test section which
includes conductance probes, liquid film extractor and an
improved optical access, Figure 3.


c drop concentration (-)
d pipe diameter (m)
Ef entrained fraction
f frequency






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

energy distribution of refraction through small particles.
The earlier mathematical inversion procedure was based
solely on the Fraunhofer diffraction theory interpreted this
portion of light energy as diffracted light and
overestimated the small particle population.
These features enable the instrument to provide accurate
size distribution information in environments that other
laser-diffraction systems cannot. Corcoran et al. (2000)
reported use of the Lorenz-Mie theory considerably
improves the instrument performances when measuring
very fine sprays. Time resolved drop-size measurement is
possible with the special in-built insitec card. The insitec
card records cycle-to-cycle temporal variations of the
droplet laden gas core as the instrument scans the detector.
The Spraytec includes features designed to enhance the
measurement of short duration events, including Flash
Mode data acquisition software (required to achieve the
full 2.5 kd~z data acquisition rate), and a trigger input
allowing measurement to be triggered by external devices.
The system is able to measure particles ranging from 0.5 to
1000 microns (depending on lens configuration) at
measurement rates of up to 2.5 kd~z. The latest version of
the instrument can handle measurements rate up to 10 kHz
as according to Dumouchel et al. (2009).
Dumouchel et al. (2009) identified beam steering, the
vignetting and the light multiple scattering effects as the
phenomena which can affect the quality of the laser
diffraction data. They recommend a comprehensive
experimental protocol to follow when laser light
diffraction measurements are performed in severe
operating conditions. Although their application was
different to that of the present study the recommendations
were used in this work as a guide to check the quality of
the data.
Beam steering effect is the manifestation of light scattered
because of a refractive index gradient in the gas phase. A
refractive index gradient in the surrounded gas flow can be
caused by temperature gradients or by the presence of
liquid vapor. The mathematical inversion procedure
interprets this supplementary scattered light as being due to
the presence of drops and calculates the drop-size
distribution accordingly. Beam steering deviates light at
small angles and mainly affects the proportion of light
detected by the first inner diodes, i.e., those sensitive to the
big drops. In consequence, the drop-size distribution
overestimates the big drop population and may exhibit a
supplementary peak in this range of droplets. A
characteristic feature of the presence of beam steering is a
peak of light intensity detected by the first diode according
to Dumouchel et al. (2009). Beam steering does not
affect the quality result of the present study.
Vignetting is avoided by setting the separation distance
between the emitter and receiver to 300mm i.e. 1.5 times
focal length of lens used which was 200 mm. Drop-size
test sections in Figure 3 was designed such that the width
of the box is not up to 300 mm.Vrignetting is a
phenomenon where scattered light escapes from the
collection angle i.e. the spray do not diffract light at such a
high angle that the light does not illuminate the Fourier
lens. The effect is underestimation of small drop
population because they have greatest diffracted light
angle.
Multiple light scattering occurs when the measuring


Paper No


open,










Ointe~neal pre..ur~e l


Figure 3: Schematics of the test section


Water is taken from a storage tank and pumped through a
bank of calibrated rotameters to monitor the flow rate into
mixer. Bronkhorst EL-Flow, a dynamic mass flow
controller supplemented with gas rotameters was used to
regulate gas flux into the two-phase mixer. The mixer
consisted of an annular section into which air was
introduced. Water emerged into the annulus through a
series of 3mm holes on the wall of the capped central pipe.
This mixer was mounted at the bottom of the pipe 3 10 pipe
diameters from section where the conductance probes are
located. Two pressure taps separated by a distance of 82
pipe diameters were connected to either side of a
Rosemount differential pressure cell, located 230 pipe
diameter from the mixer, were used to monitor the pressure
drop in the system. The liquid film was extracted via a
19mm internal diameter, 350mm long acrylic pipe in to
which holes had been drilled to give 80% open area.
Beyond the liquid extractor, only the droplet-laden gas core
flows through the chamber which admits laser beam to
illuminate the flow and allows scattered light to emerge
without any distortion.. The pipe outlet is connected to a
separator, the air being returned to the compressor, the
liquid flowing back to the storage tank.

Instrumentation
Drop size measurements were carried out using a laser
light scattering technique. The particular instrument
employed was a Malvemn Spraytec which provides time
resolved volume-based drop-size distribution and
concentration information from the analysis of the angular
distribution of light scattering resulting from the
interaction between the drops and the laser beam.
The instrument mathematical inversion process employs
both patented Lorenz-Mie algorithms (an improvement
over Fraunhofer's principle) and a multiple scattering
algorithm to reconstruct scattered light profile to generate
drop size distribution with improved accuracy. Lorenz-Mie
theory accounts for the contribution of the angular light



































































SLtquid superficialvelocity (m/s)



* a


** m
+ m



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


_dI '~ (2)

Where 6 = film thickness, [mm]; d = pipe diameter;
eg = cross sectional averaged void fraction, [-].

Typical time traces of circumferentially averaged film
thickness, entrained fraction (drop concentration) and
pressure drop are shown in Figure 4, 5 and 6. Thought there
are very clear flow structures visible in the film signal, there
are fluctuations present in the other signals.


Paper No


volume contains a high number of drops either because the
spray density is high or because the measuring volume is
large. The reduction of the mean diameter is a consequence
of the overestimation of the small drop population. It has
widely reported that light multiple scattering affects the
measurement when the transmission is less than 40% and
introduces a bias that depends on the transmission and on
spray characteristics.
The ratio of the diffracted light intensity to the incident
light intensity provides the obscuration of the measurement.
The experiments were carefully controlled such that light
obscuration did not greater than 20% i.e. transmission =
100%-obscuration. The Spraytec multiple light algorithms
helped correct multiple scattering effects.
The Spraytec can be synchronized with other
instrumentation using a trigger system which allows
simultaneous data acquisition with other instrumentation
(conductance probes, differential pressure cell). The
Spraytec was operated in flash mode. In the present
application the Fourier transform lens had a focal length of
200 mm. The range of drop sizes that could be studied
was 0.5-460 microns. The instrument employs a 1 mW
He/Ne laser.
Cross-sectional view of the conductance probe is shown in
Figure 4. The thickness of each electrode is 0.5mm with a
separation distance of 1.7mm. The probes are connected to
electric circuit, essentially a Wheatstone bridge. The
voltage response has a unique relationship with phase
distribution as established by calibration. Void fraction
(film thickness) is recorded from this resistance-phase
distribution relationship.


0.5

0.4
0-3
o,

0.1

O


0.2

S0.15

0.1
^ ^


0 0.2 0.4 0.6 0.8 1
Time (s)
Figure 5: Examples of time series for film thickness and
drop concentration. Gas superficial velocity = 32 m/s;
liquid superficial velocity = 0.15 m/s.






a- 5.7



~5.6


5.5
0 1 2 34 5 6
Time (s)
Figure 6: Example of time series of pressure drop

Mean 17/m thickness


Acrylic resin
body


Pipe diameter


Electrodes


Direction of flow
Figure 4: Cross sectional view of ring-type conductance
probes as used to measure void fraction

The measurements from the probes and the DP cell were
acquired using a PC installed with NI DAQ card.
Calibration procedures for the DP cell and conductance
probe are detailed in Kaji (2007). Data was obtained a 1
k(Hz for 6 sec.

Results
Two series of simultaneous measurements were carried out.
In the first, the gas superficial velocity was varied between
13 and 43 m/s at liquid superficial velocities of 0.05 and
0.15 m/s. In the second, the gas velocity was kept constant
at 14 m/s for liquid superficial velocities between 0.03 and
0.18 m/s. In addition, measurements were made using the
ring probes at further flow rates.
Void fraction times series obtained with by the conductance
probes is converted to film thickness using equation (2).


,. Vl

0.2



S0.05
o


0 5 10 15 20 25 30 35 40 45
Gas superficial velocity (m/s)
Figure 7: Film thickness variation with gas superficial
velocity for liquid superficial velocities of 0.05 and
0.15m/s.








































SIqol suer clal veoc,?( ms







-* .

*+s**
0 10 20 30 40 5(
Gas superficial velocity (m/s)


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

concentration is strong function of gas velocity and gas
density. As gas velocity increases the flow structures
increases. Wave traversing the gas-liquid interface traps gas
bubbles into the liquid film. Density difference causes the
bubbles to migrate and agglomerate near the wave crest
causing increase in interfacial shear stress. Gravity
drainage, gas-stream shear and bubble expansion causes
liquid membrane to gets thinner. Eventually, bubble bursts
forming numerous droplets and develops vortices. The
newly formed droplets cause the gas core density to
increase and expand. This continues until film becomes
thinner and can no longer shed droplet.
The flow rate corresponding to a liquid superficial velocity
of 0.15m/s produces higher droplet concentrations and
hence higher entrained fraction.

The concentration data shown in Figure 8 have been
converted to entrained fraction using equation (1) above in
which gas superficial velocity was substituted for the drop
velocity. Values were obtained which agree well with
previous data from a pipe of a similar diameter measured by
Azzopardi et al. (1991). The data shows excellent
agreement especially at lower liquid superficial velocity.
However, the differences in the data from the two sources
becomes noticeable at higher gas superficial velocity, i.e.,
gas superficial velocities >40 m/s.


Paper No


Figure 7 shows that if the liquid superficial velocity is kept
constant and the gas superficial velocity is increased, the
time-averaged film thickness decreases monotonically.

An interesting hydrodynamic phenomenon occurs around
gas superficial velocity = 21m/s. This is visible in Figure 7
as an inflection. Visual observation shows that the film
becomes more stable and axi-symmetrical. This transition
was picked up by all instrumentations used in the data
acquisition. The possible reason for this transition is the
influence of gravitational acceleration on the liquid
drop-outs or the entrained fraction. Geraci (2005) has
reported that gravitational acceleration influences annular
flow. It seems influence of gravity increases disturbance
waves due to the acceleration of the liquid phase in the
opposite direction to the fluid motion McGillivray &
Gabriel. (2002). The influence of gravity created an
unstable, chaotic film before the transition.
Film thickness drops at the transition boundary around gas
superficial velocity = 21m/s. After the transition, it recovers
behaving linearly decreasing with increase in gas superficial
velocity for both liquid superficial velocity of 0.15m/s. This
trend in the average film thickness behavior with increasing
gas and liquid superficial velocity is in good agreement with
previous studies on air-water annular flow. Kaji (2007)
reported this behavior to be as a result of change in film
thickness with axial distance. Kaji (2007) claimed that for
gas superficial velocity > 12m/s, film thickness increases
with axial distance up to about 100 pipe diameters then
decreases asymptotically.
The standard deviation of the film thickness is seen to
decrease with increasing gas superficial velocity.
McGillivray & Gabriel (2002) used standard deviation of
the liquid film thickness to categorize waves in annular
two-phase flow into huge and disturbance waves. They
characterized huge wave as having large standard deviation.
In the present data the standard deviation decreases as film
thickness decreases with increase gas superficial velocity,
becomes indistinguishable after gas superficial velocity =
30m/s, gets to a turning point around gas superficial
velocity = 36m/s. After gas superficial velocity = 36m/s,
the film thickness has reached a limiting value of 0.02
mm.That point might be linked with the condition of
maximum entrainment. Ripple dominates the gas-film
interface after the point of maximum entrainment.
McGillivray & Gabriel (2002) did not specify boundary
conditions for the huge and disturbance waves based on
deviation of the film thickness from the mean. Therefore,
using the findings in this study we can conclude that huge
wave transverses the gas liquid interface under the gravity
and this dominance ceases after gas superficial velocity =
21m/s. This is reasonable as the wave is characterized by
large amplitude typical of huge wave before transition to
another regime after gas superficial velocity = 21m/s. After
gas superficial velocity = 21m/s, wave amplitude becomes
smaller, decreasing with increasing gas superficial velocity.

Drop concentration
The concentration of the liquid droplets emanated from the
liquid film is shown in Figure 8 with increase in gas
superficial velocity. The figure reveals drop concentration
increases monotonically with increasing gas superficial
velocity at constant liquid superficial velocity. Drop


0.3

S0.25

-90.2

% 0.15

S0.1

S0.05

a


Figure 8: Drop concentration variation with increase gas
superficial velocity


Discussion
As well as drop concentration, information was obtained on
the distribution of sizes of drops. This can be summarized
through a mean diameter. As with previous work in this
area, there was an inverse relationship with gas superficial
velocity. There was a small effect of liquid superficial
velocity. The present data are compared, as mass median
diameter with earlier data taken on a pipe of the same
diameter by Azzopardi et al. (1991). That work also
employed a laser light scattering instrument. However,
though state of the art in those days, the instrument that was
used employed a coarser technique to extract the drop size
distribution from the angular variation of scattered light. A
simple optimization technique was employed to determine
best fit values of the two parameters of the equation
proposed by Rosin & Rammler (1933). The present
instrument calculates the relative volumetric fractions in a






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


R,,(kAr) =IT z [x(t) x] [x(t+ kr) x] dt : r< T

(3)
where T is the sampling duration, kdr is the time delay, z

is the interrogating time delay and x x=)d

The Power Spectrum Density is then obtained from:

Exf)= AT-R,(0)+ R,,(kAr)w(4kAr)cos(2x/Mr)az

2 k=1(4)

where w(kdz) is a windowing function. Windowing
functions help to suppress the spectrum leakage which
mostly comes out as the side lobes at the high frequency
end of the spectrum. By using appropriate windowing
function the frequencies contributing the system becomes
clear. In initial analysis carried out here, a basic cosine
windowing function was used,



Figure 11 shows examples of the Power Spectral density for
both film thickness and drop concentration taken at a gas
superficial velocity of 32 m/s and a liquid superficial
velocity of 0.15 m/s. These both show a peak, the most
likely frequency,


Paper No


number of size ranges. As seen in Figure 9 there is good
agreement between the two data sets.
400

350 -
L quid superficial l elocit) (m/s)
30o woo me is ISonzopard at er al
S250
S200




50 9


80


20 40 60
Gas superficial velocity (m/s)


Figure 9: Comparison of drop sizes from present work and
previous measurements on a similar diameter pipe.

The time varying drop size values can be examined further
in both amplitude and frequency space. The amplitude
variation is carried out using the Probability Density
Function. This is the frequency of occurrence of each
mean drop size time series. PDFs were generated from
time-series of MMD for a series of gas superficial velocities
at a liquid superficial velocity, liquid superficial velocity of
0.05m/s as shown in Figure 10. An interesting feature is
that for gas superficial velocities greater than 30 m/s, the
PDF of drop size changes from multiple-peaked to
single-peaked. The possible explanation for this behavior is
that after superficial velocity of 30m/s, the drops are solely
from disturbance waves, whilst below this gas velocity they
could arise from both huge and disturbance waves.


01


0.01


0.001


0.0001


1 10

Frequency (Hz)


Figure 11: Examples of Power Spectral Densities for both
film thickness and drop concentration at gas superficial
velocity of 32 m/s and a liquid superficial velocity of 0.15


If the characteristic frequencies for drops are plotted against
gas superficial velocity, Figure 12, it can be seen that there
is a great deal of scatter for the lower liquid superficial
velocity at lower gas superficial velocities. This might not
be surprising as the concentration of drops in this range is
very low as shown in Figure 8. Therefore these results
might be taken as less reliable. Nevertheless, the
characteristic frequencies of the fluctuations in drop
concentration are seen to increase with both gas and liquid
velocities.


Gas superficial velocity, mis


Mass median diameter, pm


Figure 10: Changes to Probability Density Function after
transition to mist flow as Do (MMD) decreases

The frequency characteristics of the times series can be
obtained using Power Spectrum analysis. Here, Power
Spectrum Densities (PSD) have been obtained by using the
Fourier transform of the auto covariance functions. Since
the auto covariance function has no phase lag, a discrete
cosine transform can be applied.
The auto covariance function of a signal x(t) is given by:












Liquid superfical vclocity (m/s)










. . .. . *
0 10 20 30 40 54
Gas superficial velocity (m/s)


Liquid superficial velocity (m s)


-~~~ *s n









0 10 20 30 40 50
Gas superficial velocity (m/s)


.
*


~iquid superticial velocity (m's)
40.05 O.15 OAl70pardib & halley (1980)


0 10 20 3(
Drop frequency (Hz)


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


Paper No


30

25

S20


S15



o


30

25

C20


a,15



o


Figure 14: Drop-wave frequency relationship


Figure 12:
frequency


Effect of gas superficial velocity drop


Frequency information has also been obtained for the film
thickness data. Here it is more obvious that this
frequency is that of disturbance waves on the film surface.
Again, this frequency increases with increases in both gas
and liquid flow rates as shown in Figure 13.


10



c.

a,
e
5
E
f
e


S 005 Liquid superlicial velocity
mo.1s (m/s)
Gas superticlal velocity = 14 rn/s
**



*~**


*'r*




0.1
Lockhart-Martinelli parameter


30




S20



a,10



0


Figure 15: Relationship between the dimensionless wave
frequency and the Lockhart-Martinelli parameter (the
square root of the ratio of the superficial momentum fluxes
of hiquid and gas).

That the frequency of fluctuations in drop concentration, fD,
should be less than the frequency of disturbance waves, fw,
is a puzzle. Examination of high speed cine/video
footage taken looking axially down the pipe would lead
one to expect several drop creation events per wave, i.e.,
D ~W. The results reported by Azzopardi & Whalley
(1980) showed three events for one wave. However, this
was a solitary wave and is the its frequency obtained.
Those workers overcame the problem by determining the
equivalent liquid flow rate at wave inception. They let
the instanteous flow rate, i be

M Mb +P' (6)

where Mb is the base film flow rate, Pi is the liquid
density, V is the injected volume and At is the time period
over which inject took place.


Figure 13: Effect of gas and liquid superficial velocities on
the frequencies of disturbance waves on the film interface.

Unlike the characteristic frequencies of the fluctuations in
drop concentration, there is a significant data base of the
frequencies of disturbance waves, Azzopardi (1997, 2006).
It has been show that data from a number of very different
fluid pairs helium/water, steam water at 70 bar as well as
air/water are well correlated by use of a dimensionless
frequency. The Strouhal number (frequency times pipe
diameter divided by the liquid superficial velocity) has
been found to be inversely proportional to the
Lockhart-Martinelli parameter. This implies that the
frequency is directly proportional to the gas superficial
velocity but that the effect of liquid superficial velocity is a
minor effect. Data from the present experiments, when
plotted in this matter shows the self-same trend.
If drop frequency is plotted against wave frequency, Figure
14, it is seen that on the whole the latter are higher. This
ties in with the limited prior datum reported by Azzopardi
and Whalley (1980).






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

Published in 'Basic Mechanisms in Two Phase Flow and
Heat Transfer (1 98 0) .

Azzopardi, B.J., Freeman, G & King, D.J. Drop sizes and
deposition in annular two phase flow. UKAEA Report
AERE R9634 (1980).

Azzopardi, B.J., Picarcey, A. & Jepson, D.M. Drop size
measurements for annular two-phase flow in a 20 mm
diameter vertical tube. Experiments in Fluids, Vol. 11,
191-197 (1991).

Azzopardi, B.J. & Teixeira, J.C.F. Detailed measurements
of vertical annular two phase flow Part I: drop velocities
and sizes. J. Fluids Eng., Vol. 116, 792-795 (1994).

Azzopardi, B.J. Drops in annular Two-phase flow. Int. J
Multiphase Flow, Vol. 24, S1-S53 (1997).

Azzopardi, B.J. & Zaidi, S.H. Determination of entrained
fraction in vertical annular flow. J. Fluids Eng, Vol.
122,146-150 (2000).

Azzopardi, B.J. Gas-Liquid Flows. Begell House Inc., New
York (2006).

Corcoran, T.E., Hitron, R., Humphrey, W. & Chigier, N.
Optical measurement of nebulizer sprays: A quantitative
COmparison of diffraction, phase Doppler interferometry,
and time of flight techniques. J. Aerosol Sci., Vol. 3 1, 35-50
(2000).
Dumouchel, C., Yongyingsakthavorn, P. & Cousin J. Light
Multiple scattering correction of laser-diffraction spray
drop-size distribution measurements. Int. J. Multiphase
Flow, Vol.35, 277-287 (2009).

Fore, L.B. & Dukler, A.E. The distribution of drop size and
velocity in gas-liquid annular flow. Int. J. Multiphase Flow,
Vol. 21, 137-149 (1995).

Geraci, G Gas-liquid flows in inclined pipes and Venturi.
PhD Thesis, University of Nottingham (2005).
Hall Taylor, N.S., Hewitt, GF., & Lacey, P.M.C. The
motion and frequency of large disturbance waves in
annular two-phase flow of air-water mixtures. Chem. Eng.
Sci. Vol. 18, 537-552 (1963).
Hall Taylor, N.S., & Nedderman, R.M. The coalescence of
disturbance waves in annular two-phase flow. Chem. Eng.
Sci. Vol. 23, 551-564 (1968).

Kaji, R. Characteristics of two-phase structures and
transitions in vertical upflow. PhD Thesis, University of
Nottingham (2008).
McGillivray, R.M. & Gabriel, K.S. Annular flow film
characteristics in variable gravity. Ann. N.Y. Acad. Sci.,
Vol. 974, 306-315 (2002).

Simmons, M.J.H. & Hanratty, T.J. Droplet size
measurements in horizontal annular gas-liquid flows. Int. J.
Multiphase Flow, Vol. 27, 861-883 (2001).

Van't Westende, J.M.C., Kemp, H.K., Belt, R.J., Portela,
L.M., Mudde, R.F. & Oliemans, R.VA. On the role of
droplets in cocurrent annular and churn-annular flow. Int. J.
Multiphase Flow, Vol. 33, 595-615 (2007).
Wilkes, N.S., Azzopardi, B.J. & Thompson, C.P. Wave


Paper No


A possible explanation for the lower than expected
frequency of drops is that drops from individual events is
that drops from one atomization event become diffused
into those from other events as they pass along the pipe.
Each event probably produces a distribution of sizes.
Small drops are accelerated more rapidly and so arrive at
the measuring position earlier that the larger drops that are
harder to accelerate. The faster drops could catch up with
slower drops from a previous event.

It is noted that there is another type of event which might
be being picked up in the frequency analysis. It had been
reported by Hall Taylor et al. (1963), Hall Taylor and
Nedderman (1968), Wilkes et al. (1983) that the frequency
of disturbance waves falls from an initially high value to a
lower one higher up the vertical pipe. This was attributed
to the meeting and merging of waves. Though the waves
had a characteristic (mean) velocity, there was a
distribution about this mean and faster waves could catch
up with slower waves in front of them. The combined
wave would be much bigger than normal and so more
likely to be broken up to create drops. Wilkes et al.
(1983) estimated that the amount of entrainment from
these wave coalescence events could be half the total
entrainment. Perhaps it is the frequency of coalescence
events that is being reported as fD*

Conclusions
From the results and discussions presented above the
following conclusions can be drawn:
1. New, time-resolved drop size and concentration data
have been obtained simultaneously with film thickness
and pressure drop information. All these parameters
show fluctuations with time. Some, such as film
thickness, are more obviously periodic than others.
2. The time averaged values are in agreement with prior
data.
3. Examination of the time series in amplitude and
frequency space reveals interesting features. From the
probability density function of mass median diameter, it
is seen that there are distinct regions of large and smaller
mean drop sizes are evident are visible at lower gas
superficial velocities but that there is not this feature at
higher gas velocities. Determination of the most
characteristic frequencies shows that those for waves
tend to be higher than those for waves. Both increase
with increasing gas and liquid superficial velocities.


Acknowledgements

The authors would like to express their appreciations to Dr.
Paul Kippax and Malvern Instruments, UK, for the loan of
Spraytec and EPSRC Engineering Instrument Pool for the
loan of the high speed camera.

References
Al-Sarkhi, A. & Hanratty, T.J. Effect of pipe diameter on
the drop size in a horizontal annular gas-liquid flow. Int. J.
Multiphase Flow, Vol. 28, 1617-1629 (2002).

Azzopardi, B.J. & Whalley, P.B. Artificial waves in annular
two phase flow. ASME Winter Annual Meeting, Chicago,






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

coalescence and entrainment in vertical annular two-phase
flow. Int. J. Multiphase Flow, Vol. 9, 383-398 (1983).
Woodmansee, D.E. & Harrantty, T.J. Mechanisms for the
removal of droplets from a liquid surface by a parallel air
flow. Chem. Eng. Sci., Vol. 24, 299-307 (1969).

Zaidi, S.H., Altunbas, A. & Azzopardi, B.J. A comparative
study of phase Doppler and laser diffraction techniques to
investigate drop sizes in annular two-phase flow. Chem.
Eng. J., Vol. 71, 135-143 (1998).




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