Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 10.1.3 - Investigation of the void fraction, bubble size and velocity in divergence geometry
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00243
 Material Information
Title: 10.1.3 - Investigation of the void fraction, bubble size and velocity in divergence geometry Bubbly Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Kourakos, V.
Deniz, E.
Rambaud, P.
Chabane, S.
Buchlin, J.-M.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: singularity
void fraction
bubble diameter
bubble velocity
two-phase flow
slip ratio
optical probe
 Notes
Abstract: Two-phase flow, especially, gas-liquid flow is extensively used in industrial applications such as power generation units, heating systems etc. These systems often include complex geometries composed by singularities like expansion, contraction, bends, orifices and valves. Another system consisting of such kind of singularities is safety valve. Single-phase flow entering the safety valve can turn into two-phase flow while it is passing through different cross-sections which can be considered as several singular geometries. Thus, the two-phase flow features through these singularities should be considered for a proper design of the valve under two-phase flow regime. In this paper, flow visualization is performed with a high-speed camera to observe the two-phase air-water flow before, through and after a smooth enlargement of σ=0.64 and an opening angle of 9°. Moreover, horizontal and vertical void fraction distributions are obtained by means of dual optical probe measurements. The bubble size distribution, the Sauter mean diameter and the local bubble velocity are deduced as well. A novel method to predict the slip ratio through the processing of the optical probe measurements is proposed. The paper will provide a detailed discussion about the influence of the gaseous phase and the singularity on the void fraction distribution. An important influence of the pipe enlargement on the void fraction and bubble velocity is concluded especially for the lowest volumetric qualities. Additionally, higher bubble diameter is found in the downstream section possibly due to bubble coalescence and expansion of air.
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: VID00243
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: 1013-Kourakos-ICMF2010.pdf

Full Text

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


Investigation of the void fraction, bubble size and velocities in divergence geometry


Vasilios Kourakos*, Emrah Deniz:, Patrick Rambaud*, Said Chabanet and Jean-Marie Buchlin*


von Karman Institute for Fluid Dynamics, Rhode-St-Genese, B-1640, Belgium
tCentre Technique des Industries MWcaniques, Nantes, France
presently at Istanbul Technical University, Istanbul, Turkey

kourakos(givki.ac.be


Keywords: singularity, void fraction, bubble diameter, bubble velocity, two-phase flow, slip ratio, optical probe




Abstract

Two-phase flow, especially, gas-liquid flow is extensively used in industrial applications such as power generation units,
heating systems etc. These systems often include complex geometries composed by singularities like expansion, contraction,
bends, orifices and valves. Another system consisting of such kind of singularities is safety valve. Single-phase flow entering
the safety valve can turn into two-phase flow while it is passing through different cross-sections which can be considered as
several singular geometries. Thus, the two-phase flow features through these singularities should be considered for a proper
design of the valve under two-phase flow regime.
In this paper, flow visualization is performed with a high-speed camera to observe the two-phase air-water flow before,
through and after a smooth enlargement of a=0.64 and an opening angle of 9. Moreover, horizontal and vertical void fraction
distributions are obtained by means of dual optical probe measurements. The bubble size distribution, the Sauter mean
diameter and the local bubble velocity are deduced as well. A novel method to predict the slip ratio through the processing of
the optical probe measurements is proposed. The paper will provide a detailed discussion about the influence of the gaseous
phase and the singularity on the void fraction distribution. An important influence of the pipe enlargement on the void fraction
and bubble velocity is concluded especially for the lowest volumetric qualities. Additionally, higher bubble diameter is found
in the downstream section possibly due to bubble coalescence and expansion of air.


Introduction

Several studies have been performed in multiphase flow in
presence of geometrical singularities. However, since the
phenomena occurring are very complex, the published data,
models adopted and physical analysis still don't appear
adequate. The presence of more than one phase from one
hand and from the other hand, the change of section will
enhance the difficulties of studying this topic. Therefore,
although it is an old subject, its investigation seems still
very challenging.
Singular geometries have been considered by several
researchers. Schmidt & Friedel (1996, 1997) have studied
sudden expansions and contractions in duct areas. They
have established a new model to calculate the two-phase
pressure change caused by the singularity. The model is
tested using air-water, aqueous glycerol, watery calcium
nitrate and refrigerant R-12 experimental data. The new
model is found to be accurate enough to be used in
engineering applications.
Aloui et al. (1996, 1999) have carried out experiments in
axisymmetric sudden expansion geometries and determined
the void fraction, bubble size and velocities. Flow
visualization has proved that bubbly flow changes from a
dissymmetric configuration to a symmetric one above


certain values of the volumetric quality.
M. Fossa et al. (1998, 2002) concentrated their study in the
void fraction measurements and phase distribution for
horizontal sudden contraction. An air-water mixture was
investigated with pipe inner diameters 70/60 and 70/36 mm.
They have concluded that the characteristics of the flow
restriction deeply modify the flow structure upstream and
downstream the discontinuity. They have studied thin and
thick orifices as well for a=0.73 and 0.54 and remarked an
increase of the void fraction of almost 50 % compared to
straight pipe values.
W. H. Achmed et al. (2007, 2008) have focused their
interest in the flow structure and pressure losses in sudden
expansions. The working fluids were air and oil and the area
ratios a=0.0625 and 0.25. They have concluded that the
phase redistribution immediately downstream of the
expansion and the developing length are strongly dependent
on the upstream flow pattern and the sudden expansion area
ratio. Additionally, the pressure recovery was found to be
dependent both on the wall shear stress and the wall
pressure in the developing region immediately downstream
of the expansion.
Bertola (2002, 2004) has conducted experiments in
horizontal abrupt area contraction with diameters of 80 and
60 mm for upstream-downstream sections respectively






Paper No


using a single-fiber optical probe. The water flow rate tested
was 3 kg/s and the volumetric qualities of air varied
between 0.2 and 0.8. These measurements have allowed to
acquire a cross sectional average void fraction by numerical
integration of the local values. A considerable change in the
distribution of the two phases is observed due to the
convergence section.
Kourakos et al. (2009) have considered both smooth and
sudden expansion and contraction geometries. The surface
area ratios tested varied from 0.43 to 0.65, the opening
angles from 50 to 10 0 and the volumetric qualities ranged
from 0 to 30 %. They have determined the singular pressure
change and proposed an adapted correlation of Jannsen &
Kervinen (1966) model that predicts the singular pressure
change in two-phase flow for different opening angles.

In the present article, characteristics of air-water flow
through a horizontal channel having smooth expansion are
investigated experimentally. An essential quantity to be
determined for identifying the flow structure in two-phase
flow is the local void fraction. This is measured in vertical
and horizontal plane upstream and downstream the
expansion. A dual optical probe is used for this purpose and
the bubble velocity and diameter are also given by the
measurements. Visualization has been performed to obtain a
qualitative result and to compare with the optical probe
measurements.

Nomenclature

A area (m2)
d upstream diameter (mm)
D downstream diameter (mm)
Ax distance between two tips (pm)
g gravitational constant (ms-1)
G mass velocity (Kgm-2'-1)
P pressure (Nm-2)
Q water flow rate (l/s)
PDF Probability Density Function (-)
S slip ratio (-)
t time (s)
T time of probe measurement (s)
U axial velocity (m/s)
V radial velocity (m/s)
x axial distance (mm)
y radial distance (mm)
z distance normal to xy system (mm)
Greek letters
a void fraction (-)
3 volumetric quality (-)
a surface area ratio (A1/A2)


Subsril
1
2
20
30
32
acq.
b
flight
gas
L
peak


pts
upstream
downstream
surface mean
volume mean
Sauter mean
acquisition of results of probe
bubble
movement from one tip of the probe to the other
gas is meeting the probe
liquid
quantity at the peak of the diagram


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

Experimental Facility and conditions

An experimental facility that allows measurements of void
fraction, bubble diameter and velocity upstream and
downstream a divergence section is built. The surface area
ratio is a=0.64 for 32 and 40 mm inner diameter of the pipes
upstream and downstream respectively. The opening angle
of the enlargement is 9. A general schematic of the facility
is presented in Figure 1.
The two-phase mixture consists of air and water. A
centrifugal pump (1) with a maximum capacity of 18 m3/h is
sucking water from a reservoir and the rotational speed of
the motor of the pump is controlled with a frequency
inverter. During the experiments, an air release valve (7)
connected to the tank is kept continuously open to the
atmosphere to avoid bubbles entering the circuit. A by pass
valve (8) is used to prevent facility from water hammer
phenomenon. An electronic flow meter is used to measure
the water flow rate (2); the maximum capacity of the flow
meter is 18 m3/h. The maximum desired flow rate is around
11 m3/h.
The setup consisted of a calming length (3) of 60 upstream
pipe diameters to assure a fully developed flow after the
bend and before the singularity. Close to the test section, the
injection of the air is performed through a gas injector (4) as
indicated in Figure 1. The gas injector has four rows with a
total of 28 holes of 1 mm diameter each. A regulation valve
(5) controls the air that is supplied from a compressor. The
air flow rate is measured by an electronic flow meter (6). A
draining valve is also located at the bottom of the reservoir.


Figure 1: Experimental setup

The uncertainty related to the flow rate measurements is:
0.5-1.10% (for 100-10% of the scale of the range of the
measurement respectively). The uncertainty related to the
void fraction measurements is estimated to a maximum of
16 %. The test section consists of a box made in Polymethyl
Methachrylate (PMMA) which is filled with water to
decrease the optical aberration effect. In Figure 2, a
schematic of the test section is presented. The void fraction,
bubble size and velocity are measured with a dual optical
probe at a location situated at 6 tube diameters upstream and
downstream the singularity. Profiles are obtained in the
horizontal and vertical plane with the directions indicated in
the figure.
In Table 1, the conditions of the tests performed are given.
The flow rates of water vary from 2-4.7 l/s, the volumetric
qualities were up to 40 % and the different positions of the
measurements are specified.


Pump
Electronic water flow meter
Calming length
Air injector
Regulation valve
Electronic air flow meter
Pressure regulation valve
By pass vave






Paper No


Figure 2: Test section-measurement
orientation

Table 1: Test matrix


positions and flow


TEST Probe Visualization
Q [l/s] 2.5 2 4.7
[-] 6, 9, 14 1-40
d [mm] 32 32
D [mm] 40 40
-6d -Id
Measurement Singu
positions Singularity
positions
+6d +1d

Results and Discussion

A dual optical probe, manufactured in the French company
RBI, is used to acquire information about the void fraction,
bubble size and velocity. In Figure 3 the working principle
of the probe is briefly explained. The probe is made out of
Sapphire with two 30 microns tips. The latter ones are small
enough to be able to measure small bubbles which should
however be bigger than 30 microns. A distance of 0.91 mm
separates the two tips. The laser beam when the probe is in
air is reflected at the tip of the probe and the signal is
acquired through an acquisition box while when the probe is
in water the beam is refracted inside water. Thus, the time
for which the probe meets a bubble or water is recorded and
a time step diagram is extracted as it is illustrated in Figure
3.


Sapphire probe
Laser beam Water







Bubble

AT
Voltage

Two tips
measuring at
two different points


Figure 3: Working principle of the optical probe


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

Void fraction-bubble size and velocity-slip ratio

The flow rate of water studied during the optical probe
measurements is Q=2.5 1/s. The volumetric qualities are 6, 9
and 14 %. The acquisition time for each measurement point
is tacq=1 minute; this value was found sufficient after
acquiring measurements for different acquisition times
between 30 sec and 3 minutes. The profiles are structured
with 16 points of measurement for the upstream diameter
and 20 points for the downstream (2 mm step for both
cases). The error in the positioning of the probe due to the
transversal mechanism moving the probe is estimated to
0.2 mm. However, there is an important uncertainty in the
determination of the location of the probe caused by the risk
of breaking the probe near the wall. Therefore, a mismatch
of the two type of profiles extracted has been observed
(horizontal-vertical).
The void fraction is defined as follows:


gas
T
acq


where Tgas is the total time for which gas is passing in front
of the probe and Tacq the total acquisition time.
A typical horizontal profile for the three different volumetric
qualities upstream and downstream the divergence in Figure
4 is shown. Hence, the influence of the singularity and the
volumetric quality on the void fraction distribution is
concluded. The shape of the profile significantly changes in
the downstream part where the air is concentrated mainly in
the center of the tube while in the upstream part the profile
seems more uniform with two maximum values noticed at
the two edges of the pipe i.e. left and right of the pipe. This
phenomenon becomes more important for higher volumetric
qualities. Additionally, the void fraction becomes higher
with increasing 3 but also after the cone. The latter is
possibly due to the coalescence of bubbles that are forming
pockets of air in the center of the tube.


Horizontal profiles


10 15 20
Void fraction [%]


Figure 4: Influence of the singularity and the volumetric
quality on the void fraction distribution (horizontal profile)

In Figure 5, vertical void fraction profiles are plotted against
radial position for different 3 before and after the pipe
enlargement. A stratification of the flow is noticed upstream
of the pipe especially for the lowest volumetric quality
(6 %). The void fraction also becomes higher in the
downstream part and the distribution of the void fraction


Time






Paper No


seems more uniform after the singularity although still the
highest amount of air is concentrated in the upper part of the
tube due to the buoyancy effect. Finally, we should point out
that the void fraction increase is more significant for the
case of highest volumetric qualities. Thus, the influence of
the expansion seems to be more important for the case of
lower air-water mixtures.

Vertical profiles


40 60
Void fraction [%]


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

and therefore determine the local slip ratio, since the bubble
velocity is known, is proposed. To obtain this quantity we
make the hypothesis that the smaller bubbles are following
the flow of water and consequently have the same velocity.
Hence, the signal is filtered at the threshold of a size of 300
microns bubbles as it is shown in Figure 6. For this value of
the bubble diameter, the local average velocity is extracted
and the slip ratio is estimated for each location.


Bubble diameter (mm)


Figure 5: Influence of the singularity and the volumetric
quality on the void fraction distribution (vertical profiles)

The optical probe provides also information about the
average bubble velocity, the mean Sauter diameter and the
bubble size distribution. The aforementioned measured
quantities will be discussed in detailed in this paragraph.
The average bubble velocity is given by:

Ax
Vb = T (2)
Fight

where Ax is the distance between the reference and the
secondary sensors and Tflght is an average transit time
required for the bubbles to move from the reference sensor
to the secondary sensor.
The Sauter mean diameter is given by the formula:


d3O3
302
D 32


Figure 6: Example of bubble size distribution diagram
with lognormal fit, peak diameter Dpeak identified and
filtering of bubble diameter at 300 microns

In Figure 7, the bubble size distribution is extracted in the
horizontal plane for upstream and downstream locations and
P=6 %. The most probable diameter Dpeak is indicated
together with the associated void fraction at the same
location.
From the plot, one can conclude that for the same position
i.e. the center of the tube (z/D=0.5), the maximum diameter
remains practically constant at 1 mm. A slightly higher
diameter is observed for the right side of the pipe
(z/D=0.84) for a similar local void fraction of 8 % while for
the left part, smaller diameter for low void fraction (1 %) is
measured. The influence of the singularity for this
volumetric quality doesn't seem very important.


p=6 % -6D-horizontal
=1.004 (a=0.76%)


-z/D=0.53


where d30 is the volume mean diameter denoting the
diameter of a monodispersed bubble equivalent to the actual
bubble in liquid volume and d20 is the surface mean
diameter representing the diameter of a monodispersed
bubble equivalent to the actual bubble in liquid surface.

The Sauter mean diameter is the diameter of a
monodispersed bubble for which the volume-surface ratio is
equal to that computed for the actual bubble.
In addition, the bubble size distribution in each
measurement position is deduced. In the graph representing
the bubble distribution, one can identify a maximum value
(the peak of the curve) which corresponds to the most
probable diameter. An example of such a diagram in the
upstream section, at the horizontal plane and the middle of
the pipe for p=14 %, is given in Figure 6. The maximum
diameter, called Dpeak, is specified. The log-normal
distribution is attempted for fitting with this case.
In this article, a novel way of estimating the liquid velocity


p=6 % +6D-horizontal


1.5 D =0.558 (a=1.11%)
D p =1.051 (,x=8.07%)
peak
1 e7 Dpeak=1.226 (,=7.54%)


S1 2 3 4 5


Bubble diameter [mm]


-z/D=0.26
-z/D=0.47
--z/D=0.84


6 7 8


Figure 7: Bubble size distribution in the horizontal plane
for p=6 % at upstream and downstream positions for
different locations in the pipe

In figure 8, a similar chart is presented for the case of
3=9 % and 3 positions in the pipe before and after the
enlargement. For both cases we can observe that the highest
diameters are towards the center which is in accordance to






Paper No


the horizontal void fraction profiles presented previously.
By comparing the equivalent positions upstream and
downstream, one can detect that the cone considerably alters
the distribution of the bubble population in the z direction
and this phenomenon seems stronger with increasing
volumetric quality. Moreover, at the center of the tube, the
Dpeak is two times higher in the downstream part compared
to the upstream section. This can possibly be explained by
coalescence of bubbles. The distribution seems not to
approach a lognormal fit for the case of the downstream
section at the center of the pipe. Contrary to the lower
volumetric quality, for this case, the singularity seems to
have a significant role in the bubble size distribution.


p=9 % -6D-horizontal
1.5 D e=0.806 (a=0.29%)
D eak=0.988 (a=1.14%)
uD 1 466 (a=1.11%)
EL.0.


1 2 3 4 5
Bubble diameter [mm]
P=9 % +6D-horizontal


-z/D=0.2
-z/D=0.53
--z/D=1


6 7 8


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

ones for horizontal void fraction profiles.
The bubble velocity Vb profiles are deduced and are
represented in Figures 11 and 12 for horizontal and vertical
section. In both plots, one can observe that some points are
missing. This is caused by the fact that, depending on the
conditions, the cross correlation has sometimes failed. Since
this value is estimated after the interpretation of the signal
of the two sensors of the probe, occasionally the software is
not capable to perform this operation.


Horizontal profiles


A


F AA

I A
E, n A -
A


I - N i -A
A A
A
4


S-6D-p=9%
* +6D-p=9%
S-6D-p=14%
A +6D-p=14%


1 2 3 4
Dsm [mm]


Bubble diameter [mm]


Figure 8: Bubble size distribution in the horizontal plane
for 3=9 % at upstream and downstream positions for
different locations in the pipe

Finally, the influence of the volumetric quality at the same
location (z/D=0.5) before and after the singularity is
examined in Figure 9. Both in the upstream and downstream
parts, the maximum Dpeak is found for the intermediate
volumetric quality (P=9 %). For 9 and 14 % of air, the curve
changes considerably after the singularity while for 6 % the
distribution remains practically the same.


-6D -z/D=0.5
) =1.004 (=0.76%)
pea D p=1.439 (a=3.85%)

,/PC Dpeak=1.466 (=1.110%)


-p=6 %
-P=9 %
-P=14%


8 10


Figure 10: Mean Sauter diameter profiles in the horizontal
plane before and after the singularity for several volumetric
qualities

Figure 11 points out the influence of the presence of the
singularity on the bubble velocity; the increase of pipe
diameter results in decreasing fluid velocity and thus Vb
becomes smaller after the cone. However, the influence of
increasing volumetric quality seems to affect more the
bubble velocity in the upstream part than in the downstream
and this can be explained by a higher mixing of the two
phases after the expansion (air and water).

Horizontal profiles
1 ---*-----------------A----------------------


0.4


0.2


0 1 2 3
Vb [m/s]


4 5 6


4 6
Bubble diameter [mm]


Figure 9: Influence of the volumetric quality on the bubble
size distribution at the center of the pipe upstream and
downstream the singularity

Another important quantity provided by the optical probe
measurements is the mean Sauter diameter D.m. This is
plotted against radial position in Figure 10 for different
volumetric qualities before and after the pipe enlargement.
The shape of the curve and the conclusions are similar to the


Figure 11: Bubble horizontal velocity profiles before and
after the singularity for several volumetric qualities

In Figure 12, vertical bubble velocity profiles are illustrated
and similar conclusions can be extracted. Moreover, in the
upper part of the pipe, bubble velocity is lower due to
buoyancy which pushes the bubbles up and therefore
coalescence occurs. As a result, smaller bubbles will remain
in the bottom part and will move with a higher velocity.
As already mentioned, by processing of the optical probe
results and making the proper assumptions one can deduce
the local liquid velocity and thus local slip ratio can be


A +6D-p=6%
A 0 -6D-p=9%
S - - +6D-p=9%
o A -6D-p=14%
Da A A +6D-p=14%
,* A
1 -IL - - - -- -



a-

EL
III


I I r__


____






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


calculated.
The slip ratio is defined as


S ='b
VL

where VL is the local water velocity


Vertical profiles


Figure 12:
before and
qualities


3
Vb [m/s]


Bubble velocity profiles in the vertical plane
after the singularity for several volumetric


Figures 13 and 14 demonstrate how the slip ratio evolves
along the pipe in the horizontal and vertical plane
respectively. Three different volumetric qualities and
upstream-downstream positions vary in the two plots. The
value of slip ratio is almost in every case higher than unity
which means that bubble velocity is higher than liquid
velocity. An average value of 1.15 for the slip ratio can be
extracted for all cases. Additionally, the value of S is higher
in the upstream section and to a certain extent decreases
downstream for the two lowest flow rates; P=6 and 9 %.
This leads to the conclusion that the singularity results in a
better mixing of bubbles. For the highest volumetric quality
(14 %) this behavior is inversed and the slip ratio becomes
slightly higher downstream. The deceleration of the two
fluids which affects more water than air, due to its higher
density, possibly leads to this phenomenon for the highest 3
for which the presence of the bubbles becomes more
important.


that there are always more bubbles passing through the
probe and the bubbles are typically bigger in the
downstream section for the same acquisition time.
Coalescence of bubbles and expansion of air is probably the
(4)
explanation of these two remarks.
The average of liquid velocity along the horizontal section
is calculated before and after the divergence and is plotted
against volumetric quality in Figure 15. At the same chart,
the nominal velocity given by the flow meter is specified
with a dotted line (3.11 m/s). Apparently, the increase of 3
S increases VL both upstream and downstream the
to enlargement. The slope of the curve is constant upstream
% and is sharper downstream for the lowest volumetric
S qualities and becomes more stable towards the highest
air-water mixture.


0.8-

0.6-

0.4-


Vertical profiles
m3 m



A .
Ata
~~~~- - ^ - - 6 -p 6


S O -6D-p=6%
0* +6D-p=6%
00 o0
S. . 6D-p=9%
I 4. +6D-p=9%
SU A -6D-p=14%
i -O A+6D-p=14%


Figure 14: Slip ratio profiles in the vertical plane before
and after the singularity for several volumetric qualities

Horizontal profiles
4| i-----------------------
-e--6D
3.8 +6D - - -
3.6 --- - -------
3.4 ------ --
> 23.2 -- i -
T 3F
> -- - - - - - - - -- - - - -
2.8 -------
2.6 - .... ---
2.4 *S--'- -


Horizontal profiles
A E3 PA


AN a 0 4
Bo A^

A A
A r-a 0 -6D-p=6%
"o *+6D-p=6%
flAD 6 -6D-p=9%
0 +6D-p=9%
m o A -6D-p=14%
oA A+6D-P=14%


Figure 13: Slip ratio profiles in the horizontal plane before
and after the singularity for several volumetric qualities

From the majority of the diagrams shown one can observe


9 10
P -]


11 12 13 14


Figure 15: Average liquid velocity versus volumetric
quality upstream and downstream the singularity

Flow visualization-flow chart

The determination of the flow regime is one of the most
important aspects when dealing with two-phase flow.
Therefore, flow regime maps have to be considered. A
common regime map is that proposed by Baker (1954). It
was established for horizontal flows in pipes of constant
cross section.
This campaign of visualization is performed, using a
high-speed camera, in the fully transparent setup. Four
different flow patterns are identified downstream of the
cone; Bubbly, Plug, Disperse and Annular flow. The flow
conditions for which these regimes were visualized are


Paper No






Paper No


reported in Figure 17 in the Baker flow regime map and a
picture of each pattern is illustrated.
Furthermore, we should draw attention to the fact that all
flow conditions calculated refer to the upstream position.
Indeed, for these test cases, the flow regime upstream the
singularity corresponds to bubbly flow (Baker map) while
downstream three additional flow patterns occur (plug,
disperse and annular).
Finally, in Figure 16, the flow structure given by
visualization is compared to the results obtained with the


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

optical probe in the upstream and downstream position for
three volumetric qualities; 6, 9 and 14 %. For this purpose,
void fraction profiles are plotted function of the radial
distance of the pipe. The accordance of the qualitative with
quantitative results is satisfactory. A considerable
stratification of the flow is remarked mainly above 9 % of
quality. In the downstream section, a formation of plugs of
air is noticed for the two highest air volume fractions.


11-


6 % air












9 % air


SIP~\ al

(0


F,


0c


14 % air S 0


;. r.


Upstream


7-
.-.......... - ----------- i--------------





--------..------.-------.-------.------
S : : '


7 40 s o V
Void fraction N]


1-----,---------------- -
----------|








20 40 60 8l 10 1
Voidf1ct1on1%]


------- I------------- ------------ ---- ---- -------
-- I|---=14


-A,
- - - - - --,- --.. . - - - - - --. -- - - - - --. - - --. .- -



20 40 60 80so 1
Void fraction l


Figure 16: Flow visualization upstream and downstream the divergence section-comparison with void fraction profiles


*10 DIperse Annular




1 8tratfled
1 -
Plug


0.1
1 10 100 1000
GLqp [kgn.mrs

Figure 17: Baker flow regime map (1954) v
flow regimes determined by flow visualizati


/ 1


Conclusions


ivO1 In this paper a divergence geometry of a=0.64 and an
AgK9 opening angle of 9 is extensively studied. Void fraction,
bubble size and velocity profiles in a horizontal and vertical
Bubb*y plane are extracted. A novel way of estimating the local
liquid velocity and therefore the slip ratio is proposed. The
Effect of the singularity and the volumetric quality are
investigated. It is concluded that the expansion affects more
ABubbly the void fraction for the lowest volumetric qualities.
*Dsperse Furthermore, the bubble diameter is higher on the
i Plug downstream section possibly due to bubble coalescence and
An'"na expansion of air. Deceleration due to geometrical expansion
loooo 100000 influences more water than air as a result of the difference
in densities, therefore a higher relative velocity of bubbles
to liquid is observed downstream for the maximum
vith the different volumetric quality. The opposite conclusion is stated for the
on. lowest air-water mixtures and this is possibly because of the


Downstream


0.8

0.6

-f,' "I
2q


- .- .-.-.- --------- .-- -- -------


20 40 60
Void fraction [%]


20 40 60
Void fractn WI


*IAGD-B-14%


80 100


}4


80 100






Paper No


minimal presence of the air phase.
Bubble size distribution analysis is performed as well. The
singularity seems to alter significantly the shape of the
bubble distribution. In the z direction along the pipe and
downstream the singularity an important change in the
maximum bubble diameter is observed while upstream there
is no considerable variation. However, for both cases, the
bubbles are more concentrated in the middle of the pipe and
Dpeak becomes higher at this location.
Flow visualization shows good agreement with the optical
probe measurements. Finally, a flow regime map is
established and is represented in the Baker (1956) flow map.

Acknowledgements

The support of the French company CETIM (Centre
Technique des Industries MWcaniques) situated in Nantes,
France is gratefully acknowledged.

References

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