14th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 07-10 July, 2008
Characterisation of instabilities on the interface of coaxial jets of immiscible
liquids with Laser Induced Fluorescence
Georgios Charalampous1, Yannis Hardalupas2, Alex Taylor3
1: Department of Mechanical Engineering, Imperial College, London, UK, [email protected]
2: Department of Mechanical Engineering, Imperial College, London, UK, [email protected]
3: Department of Mechanical Engineering, Imperial College, London, UK, [email protected]
Abstract The early stages of the destabilisation of a round jet by a coaxial flow of an immiscible liquid
within the bounds of an annulus are investigated in the vicinity of the central nozzle exit by visualising the
flow by means of Planar Laser Induced Fluorescence (PLIF). The instabilities that develop at the interface of
the two liquids close to the central nozzle exit are classified in three categories based on their spatial
characteristics as dilatational, Kelvin Helmholtz and short wave instabilities. It is shown that the wavelength
of these instabilities strongly correlates to the slip velocity between the two streams. The growth rate of the
mixing zone between the two liquids, as quantified by the distance at which the outer mixing zone boundary
attaches to the mixing chamber wall, is measured and it is shown to correlate well with the ratio of the two
fluid velocities. Comparison of the rate of growth of the mixing zone for two immiscible streams with the
rate of growth of the mixing zone for miscible liquids reveals very similar growth rates of the mixing zone
for non-recirculating flows, while the presence of a recirculation zone in the annular flow causes
discrepancies.
1. Introduction
The mixing of a liquid jet in the coflow of a second immiscible liquid within the bounds of an
annulus is of interest to many engineering applications such as chemical reactors and mixers where
the precise control of the mixing process is of critical importance. However, there is limited
experimental investigation of this process which can be approached in two stages; the
destabilisation of the central jet and the mixing of the products of atomisation.
The fundamental processes that are involved in the destabilisation of the jet have been investigated
in greater depth for injection of liquids in gaseous environments and it is accepted that the initial
destabilisation of the liquid jet is dependent on the velocity difference between the jet stream and
the surrounding environment. For the lowest possible slip velocities between the two streams, the
mechanism is well understood and explained by Plateau (1873) and Rayleigh (1879) and is caused
by surface tension forces that amplify minute pre-existing perturbations on the surface of the central
jet that expand axisymmetrically at regular intervals along the jet length. For greater velocity
differences between the two streams, pressure forces across the jet, caused by aerodynamic effects,
supplement the effect of the surface tension and decrease the interval between the instabilities. For
significant differences in the slip velocity, for example the destabilisation of a liquid jet by a very
fast coaxial gas stream (Eroglu et al. (1991); Hardalupas and Whitelaw (1994); Lasheras et al.
(2002); Varga et al. (2003); Marmottant and Villermaux (2004)), it is generally accepted that initial
perturbations on the surface of the central jet are amplified under the influence of shear to KelvinHelmholtz type instabilities, which are later destabilised by a Rayleigh-Taylor mechanism.
All the above literature has examined the atomisation process at conditions when the density ratio
between the central jet and annular flow fluids is very high. However, at high pressure
environments the density of the gas flow is high and, as a consequence, the liquid-to-gas density
ratio can acquire values below 10. Coaxial flows of two liquids, which have similar densities, lead
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14th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 07-10 July, 2008
to density ratios of the order of 1.5, which is close to the high pressure liquid-gas atomisation and,
as a consequence, it is interesting to examine the instabilities of the interface in liquid-liquid flows.
Furthermore, the mixing of the products of atomisation of the central jet by the annular stream,
when the process is within the bounds of a tube, has not been considered for immiscible liquids.
However, for confined coaxial jets of miscible liquids, the mixing process has been investigated at
depth (Craya and Curtet (1955); Becker et al. (1963); Hill (1965)) and it has been determined to
evolve in spatially separate regions along the length of the mixing chamber (Fig. 1, not to scale). In
a short distance (A) downstream the central nozzle exit, the exhausted central jet has a constant
velocity profile, while further downstream (zone (B)) the central jet diffuses and the corresponding
velocity profile grows and is considered to be self preserving. As the jet diffuses, it entrains fluid
from the annular stream. However, if the annular stream is depleted before the central jet attaches to
the walls of the chamber, fluid will be entrained from downstream creating a recirculation zone
(zone (C)). Finally, after the jet grows and attaches to the walls, it eventually becomes fully
developed (zone (D)).
A
B
C
D
Fig. 1 Flow development for confined coaxial jets of miscible liquids.
The criterion for the existence of recirculation zone in the flow within the mixing chamber is based
on the Craya-Curtet number which is calculated as
Ct =
Um
12
(U12 − U 22 ) α 2 + 0.5 (U 22 − U m2 ) 


(1)
where α is the ratio D1/D2 and U m = (U1 − U 2 ) α 2 + U 2 is the mean velocity of the mixed flow. A
recirculation zone occurs when Ct is below a critical value, which varies in the literature and is 0.7
according to Hill (1965), 0.8 according to Curtet (1958), 0.85 according to Becker et al. (1963) and
0.9 according to Barchilon and Courtet (1964). However, equ. (1) does not take into account the
density difference between the two streams or the presence of surface tension. This is an additional
interest for confined flows of different liquids.
It is the purpose of this paper to investigate the early stages of the destabilisation of the interface of
the central jet in the vicinity of the jet nozzle exit and the mixing process along the length of the
mixing chamber for confined coaxial jets of immiscible liquids with visualisation of the process 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. Additionally, the progress of mixing of
the central jet with the annular flow can be evaluated in terms of the growth rate of the mixing zone
of the two streams.
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14th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 07-10 July, 2008
2. Experimental Arrangement
The test section (Fig. 2) was manufactured from transparent acrylic for optical access and consists
of three compartments; a contraction, a mixing chamber section and an expansion chamber. Within
the contraction, which is axi-symmetric and delivers the annular flow, the nozzle of the central jet
(with an internal diameter of D1=3.3mm) is inserted and aligned co-axially and exhausts one nozzle
diameter upstream of the plane, where the contraction and the mixing section join. In the mixing
chamber, which is a straight tube of constant diameter (D2=3.6D1) that extends for 21D1, the breakup of the central jet and its mixing with the annular flow take place. At the end of the mixing
chamber, the expansion chamber slowly decelerates the mixed flow before it exits the test section.
Central Nozzle
Coaxial Inlet
Mixing
Chamber
Expansion
Chamber
Fig. 2 Geometry of the test section
The working fluid of the central jet is a kerosene-based hydrocarbon with physical properties
(density 800Kg/m3, viscosity 0.0017Ns/m and surface tension 0.0263N/m) similar to those of
kerosene, but substantially higher flash point and high optical clarity. The annular flow is water.
The flow circuit (Fig. 3) is arranged around the test section (J) with the flow exhausting upwards
into a large diameter acrylic tube (K). Two goals are achieved by mounting the test section
vertically. One is that axi-symmetric patterns that develop on the hydrocarbon fuel jet will not be
disturbed by the influence of gravity. The second is that, at the top of the acrylic tube, a drain
collects the mixed flow keeping the height of liquid in the acrylic tube constant and therefore fixing
the pressure at the exit of the test section at about 2m of H2O. Variations in the density of the liquid
in (K) due to the introduction of the hydrocarbon during the experiment are minimal (less than 3%
maximum) as the volume contained within (K) is substantial and the lighter hydrocarbon is
preferentially drained from the height of the column. The drained mixture of water and hydrocarbon
flows into tank (C) where it is left to settle so both liquids can be reclaimed and reused.
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14th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 07-10 July, 2008
C
K
B
J
D
A
L
I
H
D
F
E
D
D
G
F
Fig. 3 Experimental arrangement of flow circuit centered around the test section (J). Annular flow
supply part and mixing chamber are shown in blue. Hydrocarbon supply part is shown in yellow.
The water (shown in blue) and the hydrocarbon (shown in yellow) are delivered to the test section
from their respective tanks (A) and (B) by pumps (E) and (G) and their flow-rates are measured by
rotameters (H) and (I). The flow-rate of each liquid can be set independently to a range of desired
values by controlling valves (D) for water and (F) for the hydrocarbon. Additionally, a contraction
(L) of 9:1 area ratio attached to the base of the test section, ensures the uniformity of the annular
water flow that enters the test section.
For the visualisation of the flow, the water phase is doped with Rhodamine WT dye, which does not
readily dissolve in the hydrocarbon. As a result, when the flow is illuminated with the 2nd harmonic
of a Nd:YAG laser (532 nm), the water phase becomes luminous while the hydrocarbon remains
dark, making separation of the two phases and detection of their interface simple and ensuring good
contrast between the two phases. The short duration of the Nd:YAG pulse (5ns) guaranties
instantaneous imaging of the flow. A CCD camera recorded images of the flow with a resolution of
2048 x 2048. The imaging area was about 72mmx72mm and, considering the resolution of the
CCD, the spatial resolution of the acquired images was about 35µm x 35µm. The contribution of
scattered light to LIF images was suppressed by a long pass filter (Schott OG 570) placed in front
of the lens of the imaging camera.
The flow conditions under which the investigation was performed are summarised in Table 1 and
were achieved by controlling the flowrates of the central nozzle stream (Q1) and the coaxial stream
(Q2). The velocities of the two streams, U1 for the central nozzle stream and U2 for the coaxial flow,
are calculated as the cross section area averaged velocities at the plane of the nozzle exit. 17
combinations of central and annular flow rates were considered. From the physical properties and
the velocities of the liquids of the two streams, the Reynolds (Re) number at the central nozzle exit
Re =
ρ1 ⋅U1 ⋅ D1
µ1
(2)
that spans between 3215 and 19292 (ρ1 is the central jet liquid density and µ1 is the central jet liquid
dynamic viscosity ), and the Weber (We) number
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14th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 07-10 July, 2008
2
ρ ⋅ (U1 − U 2 ) ⋅ D1
We = 2
σ
(3)
ranging from 16 to 16417 (ρ2 is the annular stream liquid density and σ is the interfacial tension
between the to liquids) can be calculated which are typically used to scale the atomisation
observables (Lefebvre (1989); Eroglu et al. (1991)).
Additionally the ratio of the flow of momentum of the central to the annular stream
momentum flow ratio =
M 1 ρ1 ⋅ u12 ⋅ A1
=
M 2 ρ 2 ⋅ u22 ⋅ A2
(4)
is calculated that has also been shown be a good scaling parameter (Engelbert et al. (1995);
Lasheras et al. (1998)) and which for the range of flowrates of this investigation extends from 0.098
to 88. However, measurements are not possible for all combinations of the above parameters, since
the flowrates that are required for some conditions could not be attained.
Table 1 Examined conditions of flowrates of central and annular flows and resulting nondimensional flow parameters for immiscible liquids
Q1
Q2
U1-U2
U1/U2
(l/min)
(l/min)
(m/s)
1
2
1.6
6.1
1
5
1.2
2.4
1
10
0.4
1.2
2
5
3.1
4.9
2
10
2.3
2.4
2
15
1.5
1.6
2
20
0.7
1.2
3
5
5.0
7.3
3
20
2.7
1.8
4
20
4.6
2.4
5
2
9.4
30.6
5
10
8.1
6.1
5
20
6.6
3.1
6
2
11.4
36.7
6
6
10.7
12.2
6
12
9.8
6.1
6
20
8.5
3.7
ReL
We
M1/M2
3215
3215
3215
6431
6431
6431
6431
9646
9646
12861
16076
16076
16076
19292
19292
19292
19292
337
168
16
1220
673
288
64
3235
896
2693
11273
8428
5453
16417
14627
12137
9177
2.445
0.391
0.098
1.565
0.391
0.174
0.098
3.520
0.220
0.391
61.116
2.445
0.611
88.007
9.779
2.445
0.880
In all cases of mixing of immiscible liquids, for each flow condition a sample of 100 temporally
uncorrelated images was acquired. From the acquired images of each flow, the geometric
characteristics of the structures that developed on the surface of the central jet core due to the
interaction of the two streams were clearly detectable and digital enhancement of the images for the
detection of the interface of the two liquids was not required. The wavelength of the instabilities
that developed was measured directly on the images as the distance between the first two successive
well-defined crests or troughs. The mean value of the wavelength of the features that developed on
the jet core was determined from the standard deviation of each sample to be accurate within ±5%
of the mean value of the sample with a confidence level of 95%. From the average fluorescence
intensity of the images of each flow condition, the external boundary of the mixing zone of the two
streams was measured in the mean, by tracking the sharp change of the fluorescence intensity that
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14th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 07-10 July, 2008
exists at the boundary of the mixing zone and the annular stream.
In addition to the measurement of immiscible jets, the experiment was also conducted for a limited
number of cases with water in both streams in order to compare the resulting flows during the
mixing of immiscible and miscible liquids. The summary of flow conditions with water in both
streams is presented in Table 2 and conditions with recirculation zone (Ct<0.9) and no recirculation
zone (Ct>0.9) in the mixing chamber are considered.
Table 2 Examined water flowrates for central and annular flows and resulting non-dimensional
flow parameters for mixing of miscible liquids
Q1
Q2
U1-U2
U1/U2
(l/min)
(l/min)
(m/s)
7
4.2
13.0
20.6
7
8.3
12.4
10.3
7
12.5
11.7
6.9
7
16.7
11.0
5.2
7
20.8
10.4
4.1
ReL
Ct
M1/M2
45210
45210
45210
45210
45210
0.46
0.64
0.84
1.05
1.27
34.5
8.6
3.8
2.2
1.4
For miscible liquids a sample of 500 images was acquired for each flow condition. The processing
of the images of the fluorescence of the miscible liquids was performed in the same fashion as the
processing of the fluorescence images of immiscible liquids.
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14th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 07-10 July, 2008
3. Results
As the central jet flow exits from the nozzle and enters the mixing chamber, interaction with the
annular stream results to a number of forces acting on the interface of the jet. Primarily the central
jet is subjected to deceleration in the vertical direction due to shear from the slower moving coaxial
flow. In addition, due to the difference in the density between the two streams, the central jet is also
subject to buoyancy, which tends to accelerate the jet in the upward direction. Finally, a small
compressive force in the radial direction acts at the base of the central jet due to the deflection of
the slightly converging annular stream towards the vertical by column of the central jet. However,
even for the lowest slip velocities between the two streams, the shear force is expected to be much
more significant than the other two.
The action of the forces on the central jet leads to agitation of the interface and minute perturbations
can develop into large scale features that can be classified according to their morphology as
dilatational, Kelvin-Helmholtz and short wave type. Typical samples for each type can be observed
in Fig. 4 where the dye doped annular water stream that fluoresces under illumination by the laser
sheet can be observed as the bright flow component, while the unseeded hydrocarbon appears dark.
It should be noted that as the refractive index of water in the annular flow is lower than that of the
hydrocarbon of the central jet flow, lensing effects are unavoidable and for this reason the uniform
luminosity of the laser sheet that enters the test section from the right side of the figures, is
redistributed at the interface of the two fluids upon entering and exiting the central jet and, as a
consequence, on the left half of the test section illumination is not uniform. Nevertheless, for the
purpose of this investigation, the redistribution of the laser sheet intensity is more of a cosmetic
rather than a real problem.
The dependence of the type of features that develop on the interface of the central jet on the domain
of slip velocity (U1-U2) between the two streams and the velocity ratio (U1/U2) is presented in
Fig. 5. It is clear that the defining parameter for the development of features is the slip velocity
between the two streams. While more than one type of feature develops on the central jet core for
each flow condition, it is dilatational type features that grow primarily at low slip velocities. For
slip velocities between 2-4m/s (500<We<2000), Kelvin-Helmholtz features appear and at slip
velocities above 4m/s (We>2000) the features on the central jet interface are short wavelength
waves.
While the velocities at the interface of the two streams were not measured and therefore the fine
details of the processes that lead to the formation of these features on the jet core are not possible to
determine decidedly, the geometry of the central jet and its dependence on the slip velocity can be
used to conjecture the course of destabilisation.
For the lowest slip velocities close to the exit of the nozzle, waves of small amplitude and long
wavelength are formed (Fig. 4a). These waves grow along the length of the central jet in an
axisymmetric mode to form dilatations downstream. As the slip velocity between the two streams is
low in this mode, interfacial tension is expected to have a contribution to the mechanism of
destabilisation. The maximum wavelength of these waves is of the order of the diameter of the
nozzle exit for the lowest slip velocity between the two streams and the Rayleigh-Plateau
mechanism cannot be considered solely responsible as the wavelength due to solely this mechanism
is about 3 times the jet diameter. It is probable that a mixed mode due to surface tension and shear
between the two streams is responsible and results in the shortened instability wavelength. Further
downstream along the length of the central jet, where the amplitude of the dilatations becomes
sufficiently large, the rim of the dilatation which is more exposed to the annular flow is
preferentially decelerated relative to the core of the jet due to the shear between the two streams and
stretches in the upstream direction forming a membrane that envelops the jet core. The sequence of
such features is reminiscent of a stack of cups. Further downstream the membrane is destabilised
and breaks down to form droplets.
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14th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 07-10 July, 2008
As the slip velocity between the two streams increases, the primary waves on the surface of the
central jet at the exit of the nozzle continue to grow in an axi-symmetric mode. The process of
growth is similar for the case of lower slip velocities and the rim of the dilatations is retracted
upstream. However, in this case, the increased velocity difference between the two streams does not
result in rim stretching and subsequent enveloping of the core of the central jet but rather to the
rolling of the membrane and the formation of Kelvin-Helmholtz type structures (Fig. 4b). These
structures are inherently unstable and break down shortly downstream.
Finally, for the higher velocity differences between the two streams, the type of features that grow
on the interface of the central jet changes and only short wavelength waves of small amplitude are
observed (Fig. 4c). The axisymmetric development does not persist due to the increased amount of
shear and the dilatational growth of the initial waves is suppressed as the rim of the short waves is
sheared off before it has time to grow and acquire a large amplitude.
The wavelength of the features is not constant across the considered flow conditions. Two
approaches were followed for the scaling of the wavelength of the interface features. The first is
based on the slip velocity (U1-U2), which is characteristic of the Weber number and the second on
the velocity ratio (U1/U2) of the two streams, which is characteristic of the momentum ratio of the
two streams. From Fig. 6a, it can be observed that the magnitude of the mean wavelength
(normalised to the internal diameter of the central nozzle) on the interface of the central jet is
strongly correlated to the slip velocity between the two streams and follows a single trend with the
wavelength of the instabilities reducing with increasing slip velocity. However, the rate of decrease
is not constant across the range of slip velocities considered. Two different trends can be noticed.
At low slip velocities, where mainly the dilatational and Kelvin Helmholtz type features form, the
decrease of the wavelength is linear. At higher slip velocities, the effect of the slip velocity is
reduced and the wavelength of the instability at the central jet interface asymptotically approaches a
value between 0.2-0.3D1. For coaxial atomisation of a liquid jet by a fast coaxial gas stream, the
wavelength of the instability is found to be proportional to the thickness of the shear layer of the gas
stream (Marmottant and Villermaux (2004)). It is probable that the same principle applies to the
current flow, where the vorticity layer thickness is probably fixed by the thickness of the nozzle lip
at the higher flowrates. In contrast to the scaling of the surface wavelength to the slip velocity,
scaling with the velocity ratio does not result to a convincing correlation (Fig. 6b), since the
measurements do not follow a single trend. Some correlation appears to exist for low velocity
ratios. However, the correlation is weak since the measured wavelength changes considerably with
relatively minor changes of the velocity ratio. Moreover, if the larger values of the velocity ratio are
also considered, the same wavelength can be observed for a wide range of velocity ratios.
From the development of the flow along the length of the mixing chamber, it can be observed
(instantaneous and average images across the range of considered flows are presented in Fig. 7
through Fig. 9) that as the central jet breaks up, the original features that developed close to the
central nozzle exit collapse, entraining liquid from the annular stream and an expanding mixing
zone forms. However, observations within the mixing zone are problematic due to the dissimilar
refractive indices between the two streams, which cause the incident laser sheet to suffer from
deflection at the surface of the larger globules and diffusion at the surface of the smaller droplets,
that both attenuate the laser sheet intensity and obstruct the imaging of the illuminated plane. As the
dispersion of the two phases becomes finer and the interfacial surface increases, the effect is
enhanced. Due to the attenuation of the laser sheet intensity across the mixing zone, the
fluorescence intensity from the unmixed annular stream on the left side of the mixing zone is
decreased in comparison to the intensity of the fluorescence of the unmixed annular stream on the
right side of the mixing zone. Additionally, within the mixing zone, the scattering of the laser sheet
causes multiple passes of the laser illumination through the same volume leading to a significant
increase of the fluorescence intensity that can exceed even the fluorescence intensity of the unmixed
phase. Consequently, the mass fraction and the geometrical characteristics of the structures within
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14th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 07-10 July, 2008
the mixing zone cannot be evaluated.
a)
b)
c)
Fig. 4 Characteristic images of the instabilities that develop at the exit of the central nozzle a)
dilatational instability b) Kelvin Helmholtz instability and c) short wavelength instability
40
Velocity ratio
35
30
25
Dilations
KH
Short waves
20
15
10
5
0
0
2
4
6
8
10
12
Slip Velocity (m/sec)
Fig. 5 Distribution of features on the interface of the central jet on the slip velocity-velocity ratio
domain
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14th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 07-10 July, 2008
1.0
1.0
0.9
0.9
0.8
0.8
0.7
0.7
0.6
Dilations
KH
Short waves
0.5
0.4
λ/D
λ/D
0.6
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0.0
0
a)
Dilations
KH
Short waves
0.5
2
4
6
8
10
12
Slip Velocity (m/sec)
0
b)
10
20
30
40
Velocity ratio
Fig. 6 Mean wavelength of the instability of the central jet normalized by the inner diameter of the
nozzle as a function of a) U1-U2 and b) U1/U2
Nevertheless the boundary of the mixing zone can be decisively determined on the right side of the
images of the mixing chamber, since no deflection of the laser sheet or obstruction of the imaging
plane exists there, and from that the expansion rate of the mixing zone can be measured. In the
majority of flows, the boundary of the mixing zone was observed to expand linearly with distance
from the nozzle exit (as in Fig. 7 and Fig. 8). However, deviation from this regime was observed for
a small number of cases where the boundary of the mixing zone expanded swiftly to fill the crosssection of the mixing chamber within a short distance from the nozzle exit (as in Fig. 9). This was
observed only for the highest central to annular velocity ratios (above 10) and is believed that the
expansion of the mixing zone is caused by a recirculation zone that is formed in the annulus due to
the complete entrainment of the annular stream by the central jet before it attaches to the mixing
chamber walls as in the case of miscible liquids (Fig. 1). As a result of the depletion of the annular
flow, mixed fluid from downstream is entrained in the recirculation zone and consequently the
boundary of the mixing zone rapidly expands to the dimensions of the mixing chamber.
The growth rate of the mixing zone was quantified by the distance from the nozzle exit at which the
outer boundary of the mixing zone of the two streams attached to the mixing chamber walls. As
such, when the growth rate was large, the mixing zone attached to the mixing chamber walls within
a short distance from the central nozzle exit (which was about 4 central nozzle diameters for the
fastest growing mixing zone) and vice versa.
The dependency of the attachment length L, on the slip velocity and the velocity ratio of the two
streams can be observed in Fig. 10. In the case of the slip velocity (and therefore also the We
number), there is no convincing correlation between the two, since the measurements do not
collapse to a single trend (Fig. 10a) and appear to be rather insensitive of the magnitude of the slip
velocity. Scaling with the velocity ratio, however, resulted to an excellent reduction of the
measurements to a single trend with a negative dependence of the attachment length on the velocity
ratio. It is interesting to note that, while the mixing zone expands suddenly for high velocity ratios,
where a recirculation zone may be present, and grows at a constant rate for most other cases, all
attachment length measurements collapse on the same trend. A power law fitting revealed a
relationship of the attachment length to the inverse square root of the velocity ratio.
Comparison of the attachment length between the mixing of miscible and immiscible liquids shows
good agreement for the flows where the mixing zone does not expand suddenly. In Fig. 11 the
expansion of the mixing zone of two flows of similar velocity ratios and slip velocities but of
miscible (Fig. 11a) and immiscible (Fig. 11b) can be observed. The similarity between the
expansion of the mixing zone for the two types of liquids is apparent and despite the small increase
of the density of the central jet for miscible liquids, it can be seen that in both flows the central jet
grows at the same constant rate along the length of the mixing chamber, until it attaches to the wall
at about the same distance from the nozzle exit. The full set of attachment length measurements is
presented in Fig. 12. The collapse of the measurements of the two types of liquids on the same trend
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14th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 07-10 July, 2008
is remarkable at velocity ratios below 7. However when the velocity ratio, which is related to the Ct
number for the case of miscible liquids, exceeds the value of 7, the corresponding Ct number drops
below the critical value for formation of a recirculation zone (0.85). In this regime, a deviation from
the single trend manifests as the attachment length of miscible liquids deviates from the main trend
and its value reduces significantly. However, the cause of this discrepancy is not clear but it is
possible that in the case of immiscible liquids the dispersed central liquid jet does not respond in the
same way to the recirculation zone of the annular stream.
4. Conclusions
The process of destabilisation of a circular liquid jet of a hydrocarbon with density, viscosity and
surface tension similar to those of kerosene by the flow of a coaxial water stream within the bounds
of a confined geometry was investigated by means of laser induced fluorescence for a range of
central jet flowrates that result in a Reynolds number of the central jet between 3215 and 19292 and
Weber numbers between 16 and 16417.
It was determined that close to the nozzle exit three types of features form on the interface of the
central jet based on the difference between the cross section average velocities. At low slip
velocities (<2m/s or We<500), axisymmetric dilatational features were observed. For intermediate
slip velocities (2-4m/s or 500<We<2000), Kelvin Helmholtz type structures existed and at the
highest slip velocities (>4m/s or We>2000) only short wavelength waves developed on the jet
surface. The wavelength of these features, independently of their type, was observed to decrease
with the increase of the slip velocity until it converged to a constant value for slip velocities above
6m/s (We>4500).
The growth of the mixing zone, as quantified by the distance from the nozzle exit that the mixing
zone attached to the wall, was shown to be highly dependent on the ratio of the velocities of the
central jet and the annular stream and to scale well to its inverse square root. Comparison between
immiscible and miscible jets showed that the attachment length is the same at low velocity ratios
where a recirculation zone does not occur in the annular stream. When a recirculation zone is
formed, however, a steeper reduction of the attachment length for miscible liquid was shown to
exist.
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14th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 07-10 July, 2008
a)
b)
Fig. 7 Image of the break-up of the central jet in the coaxial flow in the mixing chamber
(Q1=1 l/min, Q2=10 l/min, U1-U2=0.4m/s, U1/U2=1.2) a) instantaneous image b) mean image
a)
b)
Fig. 8 Image of the break-up of the central jet in the coaxial flow in the mixing chamber
(Q1=6 l/min, Q2=12 l/min, U1-U2= 9.8 m/s, U1/U2=6.1) a) instantaneous image b) mean image
a)
b)
Fig. 9 Image of the break-up of the central jet in the coaxial flow in the mixing chamber
(Q1=6 l/min, Q2=2 l/min, U1-U2=11.4 m/s, U1/U2=36.7) a) instantaneous image b) mean image
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14th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 07-10 July, 2008
100
Dilations
KH
Short Waves
10
L/D
L/D
100
1
Dilations
KH
Short waves
10
1
0
2
4
6
8
10
12
1.E+00
Slip velocity (m/s)
a)
1.E+01
1.E+02
Velocity Ratio
b)
Fig. 10 Mean attachment length of the boundary of the mixing region to the wall of the mixing
chamber normalized by the inner diameter of the nozzle as a function of a) U1-U2 and b) U1/U2
a)
b)
Fig. 11 Comparison of mixing for miscible (a) and immiscible (b) liquids for similar velocity ratios
in the case of a) U1-U2=11.7m/s, U1/U2=6.9 and b) U1-U2=9.8m/s, U1/U2=6.1
L/D
100
Immiscible
Miscible
10
1
1.0
10.0
100.0
Velocity Ratio
Fig. 12 Attachment length of the boundary of the mixing region to the wall of the mixing chamber
normalized by the inner diameter of the nozzle as a function of the velocity ratio U1/U2 of the two
streams for immiscible (cyan squares) and miscible (yellow triangles) liquids
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14th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 07-10 July, 2008
References
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