Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 2.7.3 - Destabilization modes of confined coaxial liquid jets
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 Material Information
Title: 2.7.3 - Destabilization modes of confined coaxial liquid jets Interfacial Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Charalampous, G.
Hardalupas, Y.
Taylor, A.M.K.P.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: confined jets
coaxial jets
liquid in liquid breakup
 Notes
Abstract: The morphology of a round liquid jet in a coaxial flow of an immiscible liquid was investigated within the bounds of a circular annulus and in the vicinity of the nozzle exit. The jet geometry was visualised in the central plane of the annulus by means of Planar Laser Induced Fluorescence (PLIF) that allowed preferential imaging of only one phase. Two flow regimes were considered: (a) the central liquid jet is accelerated and (b) the central liquid jet is decelerated with distance from the nozzle exit due to the momentum transfer between the two liquid streams. A wide range of modes of destabilisation of the central jet was observed in both regimes, which include blocked flow, dripping flow, dilatational, sinusoidal, Kelvin Helmholtz and short wave instabilities. The modes were classified in terms of the Weber number of the central jet, Momentum Ratio of the two streams and the Reynolds number of the central jet. The classification was successful by introducing a sign in front of the Weber number, which indicates if the central liquid jet accelerates or decelerates. The conventional definition of the Weber number of Weber (1931), which cannot take into account the acceleration or deceleration of the liquid jet, could not classify properly the different modes.
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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Resource Identifier: 273-Charalampous-ICMF2010.pdf

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

Destabilization modes of confined coaxial liquid jets


Georgios Charalampous*, Yannis Hardalupas* and A.M.K.P. Taylor*

Imperial College London, Department of Mechanical Engineering,
Exhibition Rd, London, SW7 2AZ, U.K

Keywords: confined jets, coaxial jets, liquid in liquid breakup

Abstract

The morphology of a round liquid jet in a coaxial flow of an immiscible liquid was investigated within the bounds of a circular
annulus and in the vicinity of the nozzle exit. The jet geometry was visualised in the central plane of the annulus by means of
Planar Laser Induced Fluorescence (PLIF) that allowed preferential imaging of only one phase. Two flow regimes were
considered: (a) the central liquid jet is accelerated and (b) the central liquid jet is decelerated with distance from the nozzle exit
due to the momentum transfer between the two liquid streams. A wide range of modes of destabilisation of the central jet was
observed in both regimes, which include blocked flow, dripping flow, dilatational, sinusoidal, Kelvin Helmholtz and short
wave instabilities. The modes were classified in terms of the Weber number of the central jet, Momentum Ratio of the two
streams and the Reynolds number of the central jet. The classification was successful by introducing a sign in front of the
Weber number, which indicates if the central liquid jet accelerates or decelerates. The conventional definition of the Weber
number of Weber (1931), which cannot take into account the acceleration or deceleration of the liquid jet, could not classify
properly the different modes.


Introduction

The atomisation of a round liquid jet injected in an
environment of an immiscible fluid has been the focus of
many investigations (e.g. Lin and Reitz (1998), Lasheras
and Hopfinger (2 i" i 1)). The interaction of the two fluids
determines the shape and dispersion of the two phases as
well as the size of the droplets of the minority phase in the
environment of the majority phase, all of which are
important when such processes are implemented in
practical applications.
The atomisation process takes place in stages,
beginning with the initial destabilisation of the straight
liquid jet column that is followed by detachment of liquid
from it. A number of modes of destabilisation of the liquid
jet have been demonstrated (Lin and Reitz (1998), Lasheras
and Hopfinger (2i I" I )) that depend on the relative velocity
between the liquid jet and the surrounding environment,
which in practical applications is determined by the
implementation of the atomisation process.
Research has mainly focused on atomising liquid jets
in gaseous surrounding environments in which two
processes have been mostly considered. In the first, a
relatively slow moving central liquid jet is atomised by a
high speed coaxial gas stream and has been studied
extensively (Eroglu et al. (1991), Farago and Chigier
(1992), Engelbert et al. (1995), Lasheras et al. (1998),
Varga (t21' ), Marmottant and Villermaux (t i2"4)). In the
second, a high speed liquid jet is destabilised in a quiescent
gas and has also been extensively studied (Reitz and
Bracco (1982), Wu et al. (1991), Wu and Faeth (1993),
Hiroyasu (2 I"' ), Sallam et al. (21 12)). Research in these
types of flow has been focused on liquid jets in gaseous
environments, which is of interest to applications such as
fuel atomisation where the quality of atomization will
determine the characteristics of combustion. The ratio of
the densities of the two working fluids has traditionally
been of the order of 1000:1.


In contrast, for liquid jets in liquid environments, there
has been experimental work on the breakup of a liquid
column in a quiescent liquid environment (Webster and
Longmire (2001), Milosevic and Longmire 2I iii2)), which
is under low shear between the two streams. However,
experimental work on the destabilization of round liquid
jets by a coaxial liquid stream where density ratios are in
the region of 1:1 under high shear could not be found. This
type of flow is also important. In mixers, for example, the
destabilization of the central jet will determine the quality
of mixing of the two phases, which will increase the
process efficiency. Also, in chemical reactors the rate of
mixing will determine the speed of chemical reaction. In
addition, the atomisation of liquid in a high pressure gas
stream can lead to density ratios of the two working liquids
of the order of 10:1. Therefore, experiments with two
liquids with density ratios close to 1:1 may approximate
the physics of the atomisation process at high gas pressures.
This process can also be approached in two stages; the
destabilisation of the central jet and the mixing of the
products of atomisation.
It is the purpose of this paper to investigate the
morphology of the liquid jet in the vicinity of the jet nozzle
exit, as it becomes destabilised by the coaxial stream of an
immiscible liquid. By confining the two streams within a
tubular chamber, the relative velocity of the two streams
can be controlled and its variation measured with distance
from the nozzle exit. As a consequence, momentum
transfer from one liquid stream to the other can lead to
conditions where the central liquid jet can be accelerating
or decelerating with distance from the nozzle exit. The
shape of the central jet structure is determined by
visualisation of the contour of the liquid-liquid interface by
means of Planar Laser Induced Fluorescence (PLIF). In
such a way, the spatial characteristics of the instabilities
that develop at the interface between the two liquids close
to the central nozzle exit can be evaluated and the
mechanism of break-up determined.






Paper No


Nomenclature


Diameter (m)
Momentum flow ratio
Weber number
Reynolds number
Speed (m s-1)


Greek letters
p. viscosity (Pa s)
a surface tension (N m-1)
Subsripts
1 Oil
2 Water

Experimental Facility

This investigation is focused on the interaction of a
circular jet with the parallel flow of an immiscible liquid
within a confined chamber of circular cross section. The jet
flow was provided by a long nozzle with an internal
diameter of Di=3.3mm at the nozzle exit. The nozzle was
inserted into a purpose-built tubular test chamber that was
manufactured to accommodate the nozzle coaxially and
guide the annular flow in parallel to the central jet (Figure
1). The chamber was made of acrylic to permit optical
access within and consists of three tubular coaxial
compartments. In the first compartment, which is a
contraction, the annular flow is accelerated and the nozzle
is inserted and aligned coaxially with the axis of the
chamber. The tip of the nozzle exhausts one nozzle
diameter upstream of the plane, where the contraction and
the next compartment meet. The two parallel flowing
liquids are delivered to the next compartment which is a
cylinder of constant diameter of 12mm (3.6D1) and extends
for about 21D1. In this compartment, the interaction of the
two parallel flowing liquid streams is observed. There is a
series of taps along the length of this compartment to
measure the pressure downstream of the nozzle exit but
they where not used in this investigation. The final
compartment is a conical expansion compartment with
length 44mm and ending to a diameter of 20mm, where the
flow is decelerated before it exits the test chamber.

Central Nozzle _____

Contraction
compartment Mixing Expansion
S- Compartment compartment

Figure 1: Geometry of the test chamber and the inlet flow
of the coaxial jets.

The liquid supplied at the central jet flow is an oil
(Clairsol 350, which is kerosene-based) with density
800Kg/m3 and viscosity 0.0017Ns/m2 and the liquid at the
annular flow is water with density 1000Kg/m3 and
viscosity 0.001Ns/m2. Therefore, the resulting density ratio
is 0.8. The two fluids have insignificant miscibility and
separate easily when not agitated. Therefore, a sharp


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

interface forms between the two. A flow circuit, Figure 2,
was built around the test chamber (J), which is positioned
vertically and exhausts upwards in a vertical column (K)
that is 2m in length and 280mm internal diameter. This
approach has two advantages. One is that the features that
develop on the oil -water interface are not disturbed in the
horizontal direction by the influence of gravity. The second
is that the height of liquid in the system is kept constant by
a drain at the top of the vertical column. Since the volume
of the tube is filled with water at the beginning of the
experiment and the oil from the jet is buoyant and rises to
the top where it is drained, the oil concentration in the
column does not exceed 3%. Therefore, the pressure at the
exit of the test chamber is always constant at about 2m of
H20.
The water and oil components of the flow circuit are
shown in blue and yellow respectively. Storage tanks (A)
for water and (B) for oil have a capacity of about 5001 each
and their contents are pumped in the test chamber by
pumps (E) and (G). The flow rate of each liquid is
monitored by rotameter (H) for water and (I) for oil and is
adjusted by a set of controlling valves (D) for water and (F)
for oil that either limit the flow to the test chamber or
return excess flow back to the storage tanks. In addition, a
contraction (L) of 9:1 area ratio is attached to the base of
the test chamber to ensure the uniformity of the velocity
profile of the annular water flow that enters the test
chamber. The mixed flow at the exit of the vertical column
(J) was drained to tank (C), where the two phases were left
to separate overnight so that they could be reused.


Figure 2: Experimental arrangement of flow circuit of the
coaxial jets, which is centred on the transparent test
chamber (J). Water circuit is shown in blue and oil circuit
in yellow.

The distinction of the two streams in the mixing
chamber was performed by visualization of only the water
phase. Rhodamine WT dye was used to dope the water in
tank (A), while the oil phase remained un-doped.






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


Interaction of the two liquids did not result in dye transfer
to the oil phase, since Rhodamine WT does not readily
dissolve in oil. The beam of the 2nd harmonic of a
Nd:YAG laser (532 nm), was formed to a laser sheet by a
series of spherical and cylindrical lenses in order to
illuminate the central plane of the mixing compartment in
the test chamber. The fluorescence dye in the water was
excited by the laser light and, as a consequence, water
became luminous, while the un-doped fuel phase remained
dark. The good contrast between the two phases allowed
the separation of the two liquids, while the short duration
of the Nd:YAG pulse (5ns) guarantied the lack of motion
blurring in the acquired images. A 2048x2048 pixel camera
(MegaPlus ES4) was used to capture images of the
fluorescence intensity emitted from the water flow. The
considerable amount of scattered light from the interface of
the two liquids was suppressed in the images by a long
pass filter (Schott OG 570) placed in front of the camera
lens.
Samples of at least 100 temporally uncorrelated
images were acquired for each test condition. The geometry
of the central oil jet was clearly visible in most of the tested
flow conditions. Since the purpose of this investigation is
to determine the morphology of the oil jet, no correction
for the laser sheet intensity profile, lensing effects due to
the different indices of refraction of the two liquids, or
background was required. Also, for the highest
decelerations of the central oil jet, where the mixing of the
two streams was intense, the number of droplets that
dispersed in the mixing chamber obstructed the
visualization of the full length of the oil jet. Nevertheless,
there was always a sufficient length of unobstructed jet
close to the nozzle exit to draw conclusions on the type of
instabilities that developed in each case.
Both accelerating and decelerating central jets were
considered, which occurred due to momentum transfer
between the two liquid streams. The characteristic velocity
U1 of the central jet stream and U2 of the coaxial flow are
calculated as area averaged velocities at the cross section of
the nozzle exit, using the measured volumetric flowrates.
The ranges of the velocities considered here are between
0.24m/s and 11.7m/s for U1 and between Om/s and 6.4m/s
for U2.
The morphology of the central jet is considered in
terms of the Reynolds number (Re), the Weber number
(We) and the momentum ratio (MR) of the two streams.
These parameters have been extensively used to
characterise the characteristics of liquid jets destabilised in
a gaseous environment (Lefebvre (1989), Eroglu et al.
(1991), Engelbert et al. (1995); Lasheras et al. (1998)).
The value of Re was based on the diameter of the
central nozzle exit Di:


Re= U, D,
Re =


2 (U,-U2) D,


where P2 is the annular stream liquid density and a is the
interfacial tension between the two liquids. The Weber
number was artificially considered as negative when the
momentum of the annular flow was higher than the
momentum of the central oil jet. This approach is novel and
attempts to recognize the change of the diameter of the
liquid jet, which Weber (1931) did not, in order to provide
a common approach for the characteristics of jets exposed
to stagnant or fast moving surrounding fluid. In this way, it
was possible to differentiate between cases with
accelerating or decelerating central liquid jet and the Weber
number spanned the range between -4787 to 16417. This
range of We numbers included conditions where no
hydrodynamic effects between the two streams occur
(We=0) and conditions where the hydrodynamic effects
dominate in the destabilisation of the oil jet for the largest
values of We.
The ratio of the momentum of the annular to the
momentum of the central stream is:


MR =2
"I2


p2 U2. A2
P U2 -A
p, U2 A,


and varies between 0.0 to 11175, which practically
represents stationary annular flow of water for MR=0 to a
combined flow that does not respond to the oil jet
momentum for the highest water flow rates.
The full range of combinations of Re, We and MR of
this investigations is summarised in Figure 3 and table 1
and supplements the flow conditions investigated earlier by
Charalampous et al. (2" i'), which considered only
decelerating jets.


18000
16000
14000
12000
S 1000
8000
6000
4000
2000


5000 0 5000 10000 15000 20000
We


Figure 3: Range of experimental conditions


and spans between 389 and 19292 (pi is the central jet
liquid density and pC is the central jet liquid dynamic
viscosity). This range is sufficient to include both laminar
and turbulent jets. The Weber (We) number is:


Table 1: Summary of examined flow conditions
ReL We_ if
389 7 0.000


-66
-234
-1107
-2624


251.454
698.484
2793.936
6286.356


Paper No


I
- I

- I *1
I
-

**
-






Paper No


Table 1: Summary of examined flow conditions
ReL We i_ I
389 -4787 11175.744
1305 79 0.000
1305 -3 22.335
1305 -82 62.040
1305 -729 248.162
1305 -2022 558.364
1305 -3960 992.648
2225 231 0.000
2225 19 7.688
2225 -8 21.356
2225 -430 85.423
2225 -1497 192.202
2225 -3209 341.692
2836 375 0.000
2836 74 4.733
2836 2 13.146
2836 -274 52.584
2836 -1192 118.313
2836 -2754 210.334
3447 554 0.000
3447 163 3.204
3447 31 8.899
3447 -153 35.596
3447 -921 80.090
3447 -2334 142.383
4058 768 0.000
4058 287 2.312
4058 95 6.421
4058 -68 25.684
4058 -685 57.790
4058 -1948 102.737
6431 1220 0.639
6431 673 2.557
6431 288 5.752
6431 64 10.227
9646 3235 0.284
9646 896 4.545
12861 2693 2.557
16076 11273 0.016
16076 8428 0.409
16076 5453 1.636
19292 16417 0.011
19292 14627 0.102
19292 12137 0.409
19292 9177 1.136

Results and Discussion

As the central jet leaves the nozzle, a number of forces
are acting upon it. These include the shear force due to the
difference of the velocities of the two streams, the
interfacial tension force due to the preferential affinity of
each phase with itself, the buoyancy force due to the
difference in density between the two liquids and a
compressive force at the nozzle exit due to the conical
contraction that accelerates the annular flow. The sum of
these forces, cause the morphology of the central liquid jet
to development in various radically different modes,
determined by the flow rates of the oil and the water
streams. Nine modes of development were observed and
classified as:


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


a) Dripping flow. In this type of flow the central jet flows
in a straight column (Figure 4). The oil column is
segmented in a line of droplets of approximately the
same diameter in the same fashion as water dripping
from a tap. Satellite droplets of small diameter are also
observed. The predominant parameter that determines
the occurrence of this type of flow is the Re number.
This mode was observed only for jets with Re=389
(the lowest considered here) and for a range of We
between -234 and 7. The most plausible explanation
for this type of flow is that the slow moving laminar
central jet, under the influence of interfacial tension
breaks predominantly into single droplets of the same
diameter by a Rayleigh-Plateau type of mechanism.
For We numbers that are increasingly negative (Figure
4 right), it is evident from the thinning of the central
diameter that the jet is accelerated but the overall flow
pattern does not appear to change.


Figure 4: Example of mode of development of the central
oil jet in the coaxial flow of water: Dripping flow (Left,
Re=389, We=7, MR=0, Right, Re=389, We=-66, MR=62).
Note that the diameter of the annular section is 12mm.

b) Blocked flow. In this type of flow most of the water in
the mixing compartment of the test chamber becomes
displaced by unmixed oil (Figure 5) downstream of the
nozzle exit. This type of flow is observed for Re>389
and only when the annular water stream is stopped,
which corresponds to a water to oil momentum ratio of
MR=0 and We>0. The We number is also the
maximum attainable for each Re. With no flow of
water, the buoyancy force is not sufficient to remove
the oil from the mixing compartment faster than the
rate by which it is introduced. As a result, a lump of oil
is formed that fills the mixing compartment. Increasing
the Re number causes the blocked flow to move closer
the oil nozzle up to Re=2225, where the blockage
occurs directly at the nozzle exit.





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


Figure 5: Example of mode of development of the central
oil jet in the coaxial flow of water: Blocked flow (Left,
Re=1305, We=79, MR=0, Right, Re=2225, We=231,
MR=0). Note that the diameter of the annular section is
12mm.

c) Straight jet. In this mode, the central jet develops in a
straight column without showing significant features
along its length (Figure 6). This mode presents two
sub-types, both of which occur for MR<120. In the
first sub-type, the diameter of the central jet remains
about the same as the nozzle diameter (Figure 6, left).
This occurs when the We number is close to 0
(velocities of both streams are about equal) and the
shear force between the two is not sufficient to cause
hydrodynamic effects to perturb the central jet. As a
result, the two streams move in parallel with very slow
interaction with each other. Dilatational features along
the jet length that could develop from the
Rayleigh-Plateau mechanism do not manifest in the
imaged region. It is likely that due to the velocity of
the central jet, the residence time in the mixing
compartment is too small for such features to develop
within the length of the imaged region. The straight
profile of the central jet also demonstrates that there
are no flow pulsations from the supply pumps and the
flow in the channel is smooth. In the second sub-type,
the We number becomes moderately negative, i.e. ~
-80, and the central jet is accelerated. The acceleration
causes the thinning of the central jet diameter
downstream (Figure 6, right) until it becomes constant,
suggesting that the two streams have attained the same
velocity. Since the water momentum is always much
higher than the oil momentum (MR>15), the oil jet is
accelerated quickly to the water stream velocity and
the shear between the two stream becomes close to 0
for most of the length of the jet, which explains the
absence of Kelvin-Helmholtz type instabilities.


Figure 6: Example of mode of development of the central
oil jet in the coaxial flow of water: Straight jet (Left,
Re=1305, We=-3, MR=22, Right, Re=1305, We=-82,
MR=62). Note that the diameter of the annular section is
12mm.

d) Sinusoidal jet. In this regime, which was observed in
the region of We around -1000 for Re up to 1305, the
central jet develops in a sinusoidal fashion as in Figure
7 with wavelength of the order of the nozzle diameter.
The diameter of the central jet is smaller than the
nozzle internal diameter with the decrease of the
diameter of the jet depending on We. The waves persist
for most of the length of the mixing compartment. The
exact mode of instability could not be definitely
distinguished between helical and planar oscillations,
since only a 2D cross section of the central jet was
imaged. However, the sinusoidal shape of the liquid jet
persisted in the acquired images, suggesting the
presence of helical jet type instability. As for the case
of straight jets, the diameter of the central jet is
thinning quickly in the near nozzle region to attain a
constant diameter within 2-3 nozzle diameters
downstream. For cases where the continuity of the
central jet was interrupted within the imaged region, a
single trail of droplets was produced. The evolution of
the central jet along its length points to the presence of
an additional force that caused the initial sinusoidal
destabilisation by interfacial tension forces. This is
made noticeable be the phase shift between the waves
on each side of the central jet length. Close to the
nozzle exit, the waves on either side of the jet are in
phase and form the overall sinusoidal jet shape.
However, in the region of droplet formation, there is a
phase shift between the waves, which can be attributed
to the influence of surface tension.


Paper No






Paper No


Figure 7: Example of mode of development of the central
oil jet in the coaxial flow of water: Sinusoidal accelerated
jet (Left, Re=1305, We=-729, MR=248, Right, Re=389,
We=-1107, MR=2793). Note that the diameter of the
annular section is 12mm.

e) Unstable jet. This type of jet development covers a
wide range of accelerated jets for MR>120 and
We<-1500. In this mode, the oil stream is perturbed
with irregular features and typical dimensions less than
the diameter of the nozzle (Figure 8). The overall
evolution of the central jet is irregular and evolves
mostly in a straight path, with sporadic cases of sinus
development. The primary destabilisation mechanism
is of hydrodynamic nature, as this type of flow is
observed only for We number below -1500, where the
shear between the two streams is considerable.
Increasing the Reynolds number, while maintaining the
same We, causes the central jet to become less
perturbed, which can be explained by the more
energetic central stream becoming more insensitive to
the same level of shear from the coaxial flow.


Figure 9: Example of mode of development of the central
oil jet in the coaxial flow of water: atomised jet (Re=389,
We=-4787, MR=11175). Note that the diameter of the
annular section is 12mm.

g) Cups. When the We>0 and Re<4058, the shear
between the central oil and the jet streams is
decelerated. The central oil jet core close to the nozzle
forms waves on the surface of the oil jet, which can
appear as dilatations (Figure 10) or sinusoidal waves
(Figure 11). In both cases the wavelength is of the
order of the nozzle diameter. The exposed rim of these
features is stretched in the direction of the nozzle due
to the slower moving water stream to form a curtain
and envelope the faster moving jet core. The resulting
geometry is reminiscent of stacked cups. This
geometry is inherently unstable and disintegrates
within a distance of a few nozzle diameters after the
first cups are formed.


Figure 8: Example of mode of development of the central
oil jet in the coaxial flow of water: Unstable jet (Left,
Re=3447, We=-2334, MR=142, Right, Re=1305,
We=-2022, MR=558). Note that the diameter of the


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

annular section is 12mm.

f) Atomised jet. This is the extreme case of the unstable
jet developed in the case of Re=389 and We=-4787
and MR=11175. For this condition, the central oil jet is
disintegrated by the annular water stream in the
proximity of the nozzle exit (Figure 9) and it is
reminiscent of the coaxial air blast atomisation. The
diameter of the atomised droplets is smaller than the
nozzle diameter. While the development of the droplet
path is not consistent, there are occurrences, (Figure 9,
Right) where a sinus droplet path is observed.





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


Figure 10: Example of mode of development of the
central oil jet in the coaxial flow of water: 'Cups' from
dilatational jet (Left, Re=3215, We=16, MR=23, Right,
Re=3215, We=168, MR=2,5). Note that the diameter of
the annular section is 12mm.


Figure 11: Example of mode of development of the
central oil jet in the coaxial flow of water: Cups from
sinusoidal jet (Left, Re=3447, We=163, MR=7, Right,
Re=4058, We=287, MR=2.3). Note that the diameter of
the annular section is 12mm.

h) Kelvin Helmholtz. By increasing the We over 337 and
the Re over 4058, the decelerated jet development
changes from 'cups' to Kelvin-Helmholtz type features
along the jet length (Figure 12). The initial
development of the central oil jet is essentially the
same in both cases, with dilatations along the oil jet
with amplitude close to the nozzle diameter and
stretched layers of oil forming from their decelerated
rims. However, in this mode, the stretched oil
membrane does not engulf the jet core upstream, but
rolls within itself to form Kelvin-Helmholtz type
structures. As in the case of the 'cup' structures, the
Kelvin Helmholtz structures are not stable and
disintegrate to irregular lumps of oil.


Figure 12: Example of mode of development of the
central oil jet in the coaxial flow of water:
Kelvin-Helmholtz (Left, Re=6431, We=673, MR=2.5,
Right, Re=6431, We=1220, MR=0.6). Note that the
diameter of the annular section is 12mm.

i) Short waves. When the We and the Re numbers
increase above 3235 and 12861 a singular mode
appears. The energetic central oil jet and the rapid
deceleration of the central jet do not allow large scale
features to develop on its surface. In contrast, waves of
short wavelength and amplitude, initiate close to the
nozzle exit. Almost immediately, liquid is stripped
from the short waves on the surface of the oil jet
(Figure 13). The evolution of the oil jet beyond this
point is difficult to determine, because the droplets that
are produced are relatively fine and dense and obstruct
the remaining length of the mixing compartment. It is
arguable that the stripping of oil is mostly limited to
the surface of the oil jet in the initial stages of
deceleration and the jet core persists continuous
downstream. This process should persist until the jet
disintegrates completely to fine droplets before the two
streams attain the same velocity. Otherwise, if the
velocities of the two phases equalise before full
disintegration, interfacial tension forces take over to
form lumps of oil from the remaining jet.


Paper No






Paper No


Figure 13: Example of mode of development of the
central oil jet in the coaxial flow of water: short waves
(Left, Re=19292, We=9177, MR=1.1, Right, Re=16076,
We=11273, MR=0.016). Note that the diameter of the
annular section is 12mm.

The overall map of the modes that were observed for
the range of Re, We and MR of this investigation is
presented in Figures 13-15. The vertical dashed line
designates We=0, where there is no acceleration or
deceleration of the central jet, with negative We
considering accelerated central jets and positive We
considering decelerated central jets. The classification of
the modes described above is more consistent, if it is made
based on We when we artificially add a positive or negative
sign. This is because the primary distinction between the
various modes is whether the central jet is accelerated or
decelerated, which we artificially included in We. Re does
not contain any information on the acceleration or the
deceleration of the central jet. The acceleration or
deceleration of the central jet does exist in the momentum
ratio, in the ratio of U2/U1 which is greater than unity for
accelerated central jets and lower than unity for decelerated
central jets. Considering the density and the area ratios
between the two streams, which are constant in this
investigation, U2/U1=l corresponds to MR=15.28 and can
also be used to distinguish directly the regimes of
accelerating/decelerating central liquid jet. However, MR is
less flexible than We, if the effects of the area or density
ratios are also investigated, which is not an issue with We
and for this reason We will be the principle parameter for
the characterisation of the central jet morphology. However,
We number is not sufficient to fully characterized the flow
and Re or MR need to be used.
The morphology of the central jet is classified in nine
categories from the observations of this investigation, but it
should be noted that the transition from one mode to the
other is progressive rather than sudden and overlapping
features of neighboring modes at various degrees can be
observed in the boundary regions.
For We<0, the MR is the criterion for defining
blocked flow, which occurs when the water flow is stopped.
This is expressed as MR=0. The only exemption to the rule
is when MR=0 and Re<398 where the dripping flow
regime takes place. This regime was observed only for
Re=398 and for -234 appears for We<0 and MR < 120. It is not clear, however, if
this correlation is indicative of the mechanism that results
in the increased jet stability. A possible explanation is that
up to a value of MR-120 the central jet has enough
momentum so that is not perturbed by the momentum of
the annular flow. For We<-1500 and MR>120, the central
jet becomes unstable and when MR becomes less than
10000, an atomisation type flow takes over. An exemption
to the irregular destabilisation of the jet occurs at We
around -1000 and for Re<1305, where the central jet takes
a sinus form. For decelerating jets (We>0), the momentum
ratio becomes less relevant. 'Cup' type of jet development
is observed for We up to about 337, Kelvin-Helmholtz
features are observed up to a We of 3235. For higher We
only short waves developed on the jet surface.
In order to demonstrate the contribution of the concept of


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

negative Weber number, which we have artificially
introduced, we also present the maps for the mode of
instability of the liquid jet as a function of Weber number
without any sign in front, as defined by Weber (1931), in
figures 17 and 18. In both figures there is significant
overlapping of modes that are clearly distinct when the
acceleration (white labels) and deceleration (pink labels) of
the central jet is not included in We. This can cause
confusion in the classification of the modes. To highlight
the importance of the sign in We, a high speed jet that is
injected and decelerated in a quiescent environment can be
considered. The We number will be high but the result will
be a blocked flow due to the rapid increase of the jet
diameter from the rapid deceleration. If the same jet is
considered but now in a significantly faster moving coaxial
flow that results in the same We, a completely different
mode will develop where the jet diameter is thinning,
which could be straight or it could be an atomising jet.


3000 -

2500-

2000
2000 -


ht


'4



4 \


MR
8000
5000
2000
1000
500
100
50
O.


-4000 -2000 0


Figure 14: Morphology of central oil jet in the We-Re-MR
domain in the region of Re from 0 to 3000. Note that
negative We number corresponds to accelerating central
liquid jet.


4000



3500


S1

- .
,




-\
-


-2000 -1000
We


I ,- MR
10000
8000
5000
2000
1000
500
100
50
o-


Figure 15: Morphology of central oil jet in the We-Re-MR
domain in the region of Re from 2500 to 4500. Note that
negative We number corresponds to accelerating central
liquid jet.


1Soo

1000






Paper No


-' I ~



4


2


I . I I


MR
500
300
100
50
20
10
05
00


'-5000 0 5000 10000 15000 20000
We


Figure 16: Morphology of central oil jet in the We-Re-MR
domain in the region of Re from 4000 to 20000. Note that
negative We number corresponds to accelerating central
liquid jet.


MR
10000
8000
5000
:2000
1000
500
100
50


Figure 17: Morphology of central oil jet in the We-Re-MR
domain in the region of Re from 0 to 3000. Using the
conventional definition of We (without the artificially
introduced sign) causes overlapping of different modes of
jet morphology that were distinct when considering
positive (pink label) and negative (white label) We.


MR
10000
8000
5000
2000
1000
500
100


Figure 18: Morphology of central oil jet in the We-Re-MR
domain in the region of Re from 2500 to 4500 Using the
conventional definition of We (without the artificially
introduced sign) causes overlapping of different modes of


11.111111

11111111


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

jet morphology that were distinct when considering
positive (pink label) and negative (white label) We.



Conclusions

The morphology of the development of a circular oil
jet surrounded by a coaxial flow of a water stream was
investigated in the bounds of a tubular chamber by means
of planar laser induced fluorescence. The flow conditions
considered involved both accelerated and decelerated
central jets with distance from nozzle exit with
389 momentum ratios of 0 a novel approach was introduced and the Weber number
was artificially considered as negative when the central jet
was accelerated, which is different from the conventional
approach of Weber (1931). The results have demonstrated
that without this approach for the We number that considers
the acceleration/deceleration of the central liquid jet, the
destabilisation modes will overlap and the characterisation
will fail. The nine modes of the central oil jet development
that where were observed are summarised as:

a) Dripping flow: -234 b) Blocked flow: We>0, MR=0 and Re>398
c) Straight flow: We<0 and MR<120
d) Sinusoidal flow: We--1000 and Re<1305.
e) Unstable jet flow: -4500 120 f) Atomised jet flow: We<-4500 and MR<-10000
g) Cup type features: 00
h) Kelvin-Helmholtz features for We<3235 and MR>0
i) Short waves for We>3235 and MR>0

The boundaries of these zones are not completely clear as a
transition between the various modes takes place in a
continuous rather than an abrupt way.

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


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