Experimental Thermal and Fluid Science 32 (2008) 1548–1563
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Experimental Thermal and Fluid Science
journal homepage: www.elsevier.com/locate/etfs
A swirling jet under the influence of a coaxial flow
A. Giannadakis, K. Perrakis, Th. Panidis *
University of Patras, Department of Mechanical Engineering and Aeronautics, Laboratory of Applied Thermodynamics, Greece
a r t i c l e
i n f o
Article history:
Received 16 October 2007
Received in revised form 30 March 2008
Accepted 28 April 2008
Keywords:
Swirling jets
Coaxial flow
Vortex breakdown
DPIV
a b s t r a c t
The recirculating flow field generated by a swirling jet and a coaxial annular stream entering a pipe is
investigated with the use of 2D-DPIV. Parametric change of inlet flow rates (constant tangential injection
with change of annular flow and vice versa) is being considered in order to study the mean and turbulent
flow field. A recirculation bubble stabilized close to the swirler exit is the dominating feature of the interaction between the inner swirling jet and the annular stream. Results are discussed in terms of bubble
topology and dynamics on the basis of a modified Rossby number that appears to describe the trends
of the complex flow field.
Ó 2008 Elsevier Inc. All rights reserved.
1. Introduction
Swirl flows have been widely used in combustion systems as
they enhance mixing between fuel and oxidant and flame stabilization. Introducing swirl in jet flows causes large-scale effects such
as jet growth, entrainment and decay. Strongly swirling flows impose radial and axial pressure gradients generating an internal
toroidal recirculation zone, which acts like an aerodynamic blockage similar to that of the well studied ‘‘bluff body” case. This phenomenon, known as ‘‘vortex breakdown”, has been described by
Leibovich [1] as a ‘‘disturbance characterized by the formation of
an internal stagnation point on the vortex axis, followed by reversed flow in a region of limited extent”. The complex structure
of vortex breakdown has been a challenging issue for experimentalists over the past few decades. Several review-papers [2–5]
and books [6,7] focusing on experimental, numerical and theoretical work regarding vortex breakdown have outlined the multitude
of approaches pursuing our understanding of this complex phenomenon. Recently, Lucca-Negro and Doherty [8] presented an
extensive guide to vortex breakdown literature.
Numerous efforts focusing on the visualization of the vortex
breakdown flow field [9,10] have been reported providing qualitative data on the structure of vortex breakdown. Sarpkaya observed
three basic modes of vortex breakdown by conducting visual
experiments, namely: double helix, spiral and bubble type (axisymmetric). He also observed that for the bubble type vortex
breakdown a toroidal vortex ring, whose axis gyrates at a regular
* Corresponding author. Tel.: +30 2610997242; fax: +30 2610997271.
E-mail address: [email protected] (Th. Panidis).
0894-1777/$ - see front matter Ó 2008 Elsevier Inc. All rights reserved.
doi:10.1016/j.expthermflusci.2008.04.010
frequency about the axis of the bubble, is formed at the downstream half of the bubble. Sarpkaya explained the fluid exchange
that takes place between the recirculation bubble and the outer
flow through the vortex ring as a simultaneous filling and emptying process that is possibly due to pressure instabilities in the wake
of the bubble. Later measurements with the use of Laser Doppler
Anemometry [11] and Particle Tracking Velocimetry [12] provided
more detailed data about the mean properties of the recirculating
flow field. Brücker and Althaus confirmed Sarpkaya’s observation
on the existence of an inclined vortex ring gyrating around the
vortex axis, which plays a dominant role on the fluid exchange
between the recirculation bubble and the ambient flow. They also
provided information regarding the mean three-dimensional
structure of the recirculating bubble. Turbulent properties of recirculating swirl flows have been studied by several experimentalists
[13–18], focusing on the influence of the flow field topology on
fluid transport and mixing and the characteristics of the precessing
vortex core. Up to now, rather limited data has been presented,
regarding the turbulent flow field created by coaxial jets with inner
and/or outer swirl [19–22].
The development of numerical tools, over the last two decades,
has provided important additional information on the structure of
vortex breakdown and on the identification of the parameters
affecting its occurrence and development [23–31]. However, relatively few studies have been reported, correlating numerical with
experimental results [32–36].
Research on vortex breakdown phenomena has led to a parallel
research on the critical parameters that could determine whether
vortex breakdown will occur. The definition of non-dimensional
parameters, mainly based on the correlation of axial and azimuthal
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A. Giannadakis et al. / Experimental Thermal and Fluid Science 32 (2008) 1548–1563
Nomenclature
Q
r*
R
Rex,i
Rex,0
Rex,i
Ro
mean statistical divergence
vertical distance between recirculation zones centres
(m)
swirl orifice diameter, Ri = Di/2 (m)
pipe diameter, R0 = D0/2 (m)
time between laser pulses (s)
transverse bubble length (vortex ring diameter) (m)
04
x
flatness value of longitudinal velocity, F U x ¼ puffiffiffiffiffiffi
(–)
4
u02
x
bubble longitudinal length (m)
length of interrogation area (m)
annular mass flow rate (kg/s)
tangential mass flow rate (kg/s)
mass flow ratio m = Ma/Mt (–)
R r
RR
recirculating mass flow ratio, m ¼ 0 U x r dr= r0 U x r dr
(–)
volumetric flow rate (m3/s)
distance of zero Ux contour line from vortex axis (m)
ratio of the radial to the tangential velocity, R = Uh/Ux (–)
Reynolds number based on Ux,i, Rex,i = Ux,iDi/v (–)
Reynolds number based on Ux,0, Rex,0 = Ux,0(D0 Di)/v (–)
Reynolds number based on Uh,i, Rex,i = Uh,i Di/v (–)
U ðx ÞU ðx Þ
Rossby number: Ro ¼ x;0 U0h;i ðx0x;iÞ 0 (–)
S
S*
swirl number (–) (see definition in Table 1)
2U ðx Þ
swirl ratio: S ¼ U x;ih;iðx00Þ (–)
SUx
x
skewness value of longitudinal
velocity,
SUx ¼ pffiffiffiffi
ffi3 (–)
pffiffiffiffiffiffiffiffiffiffiffi
ffi
u02
02
x
u02
x þur
turbulence intensity, TI ¼ pffiffiffiffiffiffiffiffiffiffiffi
(–)
2
2
Di
D0
dt
DVR
F Ux
LB
LIA
Ma
Mt
m
m*
TI
U, V, W
Ur
u03
U x þU r
Cartesian velocity components
mean radial velocity (m/s)
Ri
R Ri
U x U h r2 dr
S ¼ 0 RR 2
Ri
S¼
Ri
S ¼ 23
0
U x r dr
R1
U U r2 dr
R 10 2x h1 2
0
Mattingly et al. [20]
ðqU x þqux þðpp1 ÞÞr dr
0
ðU x 2U h Þr dr
Di
D0
2 tanðaÞ
1
Di
D0
Ux,0
qffiffiffiffiffiffi
u02
x
Reynolds stress component (m2/s2)
mean tangential velocity (m/s)
swirlingR jet spatially mean tangential velocity,
R
U h;i ¼ 2 0 i U h r dr=R2i ðm=sÞ
Cartesian coordinates
polar coordinates
longitudinal distance of the recirculation zone centre
from the jet’s exit mouth (m)
longitudinal distance of the vortex ring axis from jet’s
exit mouth, xCRZ ¼ ðxCRZð1Þ þ xCRZð2Þ Þ=2 (m)
longitudinal distance from jet’s exit mouth, where inlet
conditions are set, x0 = 0.25Di (m)
vertical position of longitudinal axis (m)
u0x u0r
Uh
Uh,i
x, y, z
x, r, h
xCRZ
xCRZ
x0
yc
Greek letters
d
laser sheet thickness (m)
f
velocity ratio, f = Ux,0/Ux,i (–)
U
mean value of i samples
X
circulation number (–)
Xx
mean axial vorticity (1/s)
Xhffiffiffiffiffiffiffiffi
mean azimuthal vorticity (1/s)
q
RMS value of azimuthal vorticity (1/s)
vortex breakdown occurs, X is the circulation number and R the ratio of the radial to tangential velocities in the inflow region. The
correlation is good over a wide range of Re (5 102–105) although
‘‘departures are evident for very high circulation numbers”. In the
case of more complex flow fields, such as wing tip or leading edge
vortices, a correlation between Reynolds and Rossby number has
been proposed as more appropriate to explain flow attributes, such
as vortex breakdown initiation [23,5]. A critical Rossby number value for Re P 250 is Ro 0.65.
However, all approaches are highly dependent on the inlet
velocity profile. Fitzgerald et al. [37], following the work done by
Billant et al. [38], proposed the calculation of a swirl ratio critical
3.5
Ben-Yoshua (1993)
Champagne-Kromat (2000)
Giannadakis etal (2007)
3.0
2.5
2.0
1.5
1.0
Ivanic [45]
0.5
Ribeiro [41], Champagne [21]
0.0
3
1
RMS value of radial velocity (m/s)
mean longitudinal velocity (m/s)
swirling jet spatially mean longitudinal velocity,
U x;i ¼ 4Q i =pD2i (m/s)
annular flow spatially mean longitudinal velocity,
U x;0 ¼ 4Q 0 =pðD20 D2i Þ (m/s)
RMS value of longitudinal velocity (m/s)
x02h
velocities or momenta, has been an issue of scientific interest that
has often led to different approaches and criteria for vortex breakdown prediction.
Swirl number (S) is a parameter often used to describe the
behavior of swirling jets. The definition of swirl number varies in
the literature as it depends strongly on the means of swirl generation (rotating nozzles, guide vanes, tangential injectors, etc.). Calculation of swirl number (or ratio) is based either on the
comparison of the axial flux of swirl momentum to that of the axial
momentum or on the ratio of characteristic velocity scales of the
flow field such as a tangential velocity to an axial velocity (geometric swirl number). A commonly used critical value for vortex breakdown initiation is S = 0.57. For the case of tangentially injected
swirl flows, the tangential to the total momentum flux ratio has
been employed as a similarity parameter [14,27] as it is not possible to control the axial momentum flux independently. In Table 1,
several approaches of swirl number definition are presented.
Escudier and Zehnder [4] proposed a simple criterion for the
occurrence of vortex breakdown at a fixed location in a tube:
ReB X3R1; where ReB is the pipe Reynolds number at which
Table 1
Swirl number calculation approaches
R Ri
qðU x U h þu0x u0h Þr2 dr
S ¼ R R0 2
02
qffiffiffiffiffiffi
u02
r
Ux
Ux,i
Swirl ratio (S*)
a
DCRZ
0
Gupta [6], Heitor [13]
10
20
30
40
50
60
70
Mass flow ratio (m)
Fig. 1. Validity confirmation of swirl ratio calculation according to Fitzgerald [37].
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A. Giannadakis et al. / Experimental Thermal and Fluid Science 32 (2008) 1548–1563
Tangential Injectors
Annular flow
inlet
Annular gap
Circular
Screens
Swirl Nozzle
(a) Side view of the Test Rig
(b) Front view
(c) Rear view of the swirler device
(d) Side view of the swirler device
Fig. 2. Experimental facility description.
for the initiation of vortex breakdown which is independent of the
velocity profiles as it is defined by the ratio of the mass flow averaged azimuthal velocity to the averaged axial velocity. The definition of this swirl ratio is similar to that proposed by Marliani et al.
[16]. Its critical value is in the range of S* 1.2–1.3 with
S ¼
2U h;i ðx0 Þ
U x;i ðx0 Þ
ð1Þ
where Uh,i is the swirling jet spatially mean tangential velocity and
Ux,i is the swirling jet spatially mean longitudinal velocity.
The authors confirmed the validity of this swirl ratio (Fig. 1) for
the case of coaxial jets with outer swirl [39,21] and inner
swirl [40]. The swirl ratio proposed by Fitzgerald et al. is in
average 2.6 times higher than that calculated by Champagne and
Kromat due to the different approaches in swirl number
definition.
Still, predicting vortex breakdown is not by itself adequate to
characterize the mean and turbulent features of the recirculating
flow field. Moreover, in the case of coaxial jets, with or without
swirl, previous studies [41–43,21,44] have shown that the flow
field created is strongly affected not only by the velocity or mass
flow ratio of the jets but also by the absolute values of the jets’
velocities or the velocity jump (DU = Ux,0 Ux,i) between the two
streams. For the case of coaxial swirling jets it is apparent that
the interaction between the shear layers (mainly azimuthal and
400
Ω z =(dV/dx-dU/dy)
400
Ω x =(dW/dy-dV/dz)
300
Ω =-dU/dr
θ
-1
200
Vorticity(1/s)
Vorticity (1/s)
Ω x =r d(rUθ)/dr
100
0
0
-400
-100
-200
-800
-5
0
5
10
15
20
25
r (mm)
Fig. 3a. Axisymmetry evaluation for Xx.
30
35
40
0
5
10
15
20
25
r (mm)
Fig. 3b. Axisymmetry evaluation for Xh.
30
35
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A. Giannadakis et al. / Experimental Thermal and Fluid Science 32 (2008) 1548–1563
Table 2
Mean PIV divergence error evaluation
Pairs of images
Ux (%)
Ur (%)
Xh (%)
qffiffiffiffiffiffi
u02
x (%)
qffiffiffiffiffiffi
u02
r (%)
qffiffiffiffiffiffiffiffi
500–1000
1000–1500
1500–2000
2.83
2.48
1.25
111.02
13.28
5.86
8.00
4.84
3.42
1.94
1.09
0.75
1.88
1.13
0.81
2.43
1.37
0.96
x02
h (%)
u0x u0r (%)
SU x (%)
F U x (%)
25.46
10.08
5.24
5.58
3.47
2.37
5.14
3.18
2.02
2. Experimental setup
y
Stagnation
2.1. Experimental facility
x
xCRZ(1)
Zone
The experimental facility (Fig. 2) consists of a slightly diverging
conical swirler (3%) with Di = 28 mm exit diameter and a coaxial
annular duct from which parallel flow is introduced into the chamber. The test chamber consists of a 400 mm long Plexiglas tube of
D0 = 100 mm inner diameter. At the inlet of the test chamber an
annular gap between the swirling nozzle and the annular duct exists, due to the wall thickness of the swirling nozzle (1.5 mm).
Swirl is produced through tangential injection of air into the swirling nozzle. Four tangential injectors of 4 mm inner diameter are located five nozzle diameters upstream (140 mm) from the jet exit. A
centrifugal blower supplies the tangential flow, whiles a centrifugal fan feeds the annular flow. Homogenization of the annular flow
is achieved with the use of circular screens.
DCRZ D
VR
Bubble
Nose
Bubble
aft
xCRZ(2)
LB
Fig. 4. Recirculation bubble topology (test case f).
2.2. Measurement technique
axial) is the key to understand the features of such a complex flow
field [22].
In this work mean and turbulent characteristics of the recirculating flowfield generated by a swirling jet under the influence of
a coaxial stream are discussed, laying emphasis on the structure
of the recirculation bubble and its effect on the interaction and
mixing of the two streams. Analysis of the experimental results
is based on a modified Rossby number, defined as the ratio of the
jets’ velocity jump – or velocity deficit – to the mass flow averaged
swirl velocity, which appears to describe the trends and characteristic features of the recirculating flow field.
Ro ¼
U x;0 ðx0 Þ U x;i ðx0 Þ
U h;i ðx0 Þ
2.2.1. General description of the DPIV system and experimental setup
2D Digital Particle Image Velocimetry is used to monitor the
flow field. The measurement equipment consisted of a Flowsense
2M CCD Camera (1600 1200, 15 Hz acquisition rate) and two
Quantel pulsed lasers (30 mJ). Both the CCD Camera and the laser
were mounted on a 3D traversing mechanism (0.1 mm step accuracy), aligned to the test rig. Longitudinal and transverse planar
cuts along and normal to the swirl axis are used for flow field
monitoring.
2.2.2. Time control and illumination setup
Regulation of the time interval between laser pulses (dt) is
based on the bulk velocity of the flow field and the length of the
interrogation area that is being monitored (LIA). As swirling flows
ð2Þ
where Ux,0 is the annular flow spatially mean longitudinal velocity.
Table 3
Inlet conditions
Test case
Mt (kg/s)
Ma (kg/s)
m (–)
Ux,i (m/s)
Ux,0 (m/s)
Uh,i (m/s)
Rex,i (–)
Rex,0 (–)
Rex,i (–)
S (–)
f (–)
Ro (–)
a
b
c
d
e
f
1.35E03
1.19E03
9.76E04
1.35E03
1.19E03
9.76E04
2.61E02
2.61E02
2.61E02
3.49E02
3.49E02
3.49E02
19.35
22.04
26.79
25.79
29.39
35.71
1.80
1.58
1.30
1.80
1.58
1.30
3.00
3.00
3.00
4.00
4.00
4.00
1.90
1.49
1.20
1.51
1.36
1.33
1668
2928
1205
1668
2928
1205
13898
13898
13898
18531
18531
18531
3521
2761
2224
2798
2520
2465
2.11
1.89
1.85
1.68
1.72
2.05
1.67
1.9
2.31
2.22
2.53
3.08
0.63
0.95
1.41
1.46
1.78
2.03
Table 4
Recirculation bubble length scales
Test case
DCRZ
Di
DVR
Di
xRCZ
Di
LB
Di
xCRZ
DCRZ
xCRZ
DVR
LB
DCRZ
LB
DVR
(a)
(b)
(c)
(d)
(e)
(f)
0.51
0.54
0.58
0.59
0.63
0.64
0.61 ± 5%
0.71
0.76
0.82
0.82
0.84
0.86
0.79 ± 4%
1.25
1.14
1.07
1.00
0.93
0.89
1.11 ± 9%
1.90
1.80
1.68
1.64
1.50
1.39
1.65 ± 9%
2.45
2.17
1.84
1.69
1.52
1.39
1.85 ± 14%
3.73
3.35
2.90
2.78
2.45
2.17
2.88 ± 12%
1.76
1.55
1.30
1.22
1.11
1.03
1.33 ± 15%
2.68
2.39
2.05
2.00
1.78
1.62
2.1 ± 14%
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A. Giannadakis et al. / Experimental Thermal and Fluid Science 32 (2008) 1548–1563
are three dimensional the light sheet thickness (d) has to be
regulated accordingly. Taking into consideration the Nyquist criterion, the following conditions have to be satisfied for the measurement control volume for longitudinal measurements:
LIA
U
d P 4W dt
dt 6 0:25
ð3Þ
where U and W are the reference velocity components on the laser
sheet plane and normal to it, respectively.
In the case of cross sectional measurements the criteria are inversed as far as the velocities are concerned. Satisfying both of the
criteria is a task that, for the case of high swirl flows, results into
the weakening of the laser sheet illumination strength and thus
introduces errors in image capturing. For the present experiments
such errors are dealt with in a satisfying manner for the longitudinal
Fig. 5. Contours of mean longitudinal velocity Ux (m/s).
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A. Giannadakis et al. / Experimental Thermal and Fluid Science 32 (2008) 1548–1563
and transverse measurements, since U and W are of the same order
of magnitude.
In order to diminish reflection effects, the swirl orifice and half
the test chamber are smoothly colored black.
2.2.3. Seeding particles
Droplets of 4 lm mean diameter are used as seeding particles,
generated by an OMRON nebulizer, with adjustable air-flow and
nebulization rate. Homogeneity of particle concentration is
achieved by seeding both the annular and the tangential inlets.
2.2.4. Image post processing and evaluation of results
Post-processing of the images is accomplished by subtracting a
static image (with no seeding particles) from the seeded images in
order to remove white noise produced by reflections. Additionally,
low-pass filters are applied on the subtracted images.
Raw vector data of the flow field is produced with the use of
adaptive correlation processing. Each frame is divided into interrogation windows, fixed at 32 32 pixels with 25% overlap. Mean
and turbulent statistics from raw vector data are calculated with
the use of a home developed code.
Two thousand pairs of images for each test case are acquired in
order to evaluate the mean and turbulent flow field. The criterion
for the amount of images needed was the convergence of the evaluation output for every additional five hundred pairs of images. In
Table 2 a typical result of the mean statistical divergence resulting
from the increase in image pair samples by 500 is shown
(a = kUi+500j jUik/jUi+500j). Results show good convergence of
the measured values with errors varying from 0.7% to 5.86%. Maximum divergence observed for Ur is due to the fact that it takes
small values (near zero) and thus when normalized it produces relatively large percentage error.
DPIV measurements at the inlet of the test rig, supplying only
the annular flow, showed a symmetric flow field with no secondary
flows, ensuring thus that coaxiallity and homogenization of the
annular flow is achieved at a satisfying level. Hot wire measurements of this flow field with an X probe further validated the symmetry of the annular flow which presented a turbulence intensity
of 1.5 % [41] at the inlet of the test chamber. Measured velocities
at all test cases satisfy continuity with a maximum divergence error of 10%.
For further evaluation of the experimental results, axisymmetry
is checked for both measurement planes by comparing the axisymmetric terms of the vorticity components calculated using the
measured velocity distributions in polar coordinates with the directly measured vorticity:
3.1. Basic topology description of the recirculation bubble
In Fig. 4, the characteristic length scales of the recirculation
bubble are defined, based on the measured streak line plot of test
case f, depicting the main features of the flow field. The internal
structure of bubble vortex breakdown is characterized by the formation of two counter-rotating recirculation zones and the existence of a stagnation zone (Ux = 0). The stagnation zone passes
through the centers of the recirculation zones and defines the limits of the bubble on the vortex axis (bubble nose and aft). The recirculation zones constitute a planar cut of a vortex ring which
gyrates around an axis almost parallel to the longitudinal axis of
the flow and an azimuthal defined by the vortex ring core. Small
asymmetries are observable in all test cases, despite the efforts
to eliminate them. Since these asymmetries are not consistent
(e.g. the longitudinal distance in the x-direction between the upper
and the lower center of the recirculation zones is at times positive
or negative) they should not be attributed to secondary effects due
to misalignment but rather to secondary effects due to inlet
conditions.
The recirculation bubble geometry is strongly influenced by inlet conditions. Comparison of length scales (Table 4) shows that increase of tangential flow rate (comparing cases a–b–c and d–e–f)
results in a positive shift of the bubble aft position ðLDBi Þ and an elonB
, symbols are defined in Fig. 4 and in
gation of the bubble shape (DLVR
the nomenclature). On the other hand, increase in the annular flow
rate (comparing cases a–d, b–e and c–f) leads to negative shift of
the bubble aft position and widening of the recirculation bubble.
Vortex ring length scales follow the same trends as the recircula). Comparing all test cases from a to f
tion bubble (see xDRCZi and DxCRZ
CRZ
it is seen that an increase in the proposed Rossby number results
in the widening of the recirculation bubble and an upstream shift
of its aft. This observation along with that of Escudier and Zehnder
[4] who noted that increase of swirl causes breakdown to occur upstream, provide evidence that in the case of coaxial flows the swirl
parameter is not by itself adequate to describe the recirculating
flow regime. This is more clearly shown in the following section,
where the influence of the proposed Rossby number on the recirculating trend of the flow is discussed.
3.2. Mean flow field
As seen in Fig. 5, depicting the mean longitudinal velocity contours (Ux), only for test case d a closed bubble shape is formed. The
bubble interior is in all test cases characterized by negative velocities. ‘‘Zero” longitudinal and radial velocity values (Uxc = 0 and
1 oðU h rÞ
oU x
; xh axisymmetric vorticity terms
r or
or
oW oV
oV oU
xx ¼
; xz ¼
measured vorticity terms
oy
oz
ox oy
xx 0.020
Ro=2.03
Ro=1.78
Ro=1.46
Ro=1.41
Ro=0.95
Ro=0.63
0.018
0.016
ð4Þ
0.014
Comparison (Fig. 3) between the calculated axisymmetric terms
and the measured vorticity components shows that the mean flow
field is almost axisymmetric and that the location of the vortex axis
center is correctly estimated.
0.012
m*
0.010
xB
0.008
0.006
0.004
3. Experimental results
In Table 3 the experimental conditions corresponding to the six
test cases considered using three tangential and two annular mass
flow rates are presented. Inlet conditions are calculated from the
experimental data according to Ivanic [45] and Fitzgerald et al.
[37], at a distance x0 = x/Di = 0.25.
0.002
0.000
-0.002
-1.0
-0.5
0.0
0.5
(x-xCRZ)/Di
Fig. 6. Recirculation mass flow ratio.
1.0
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A. Giannadakis et al. / Experimental Thermal and Fluid Science 32 (2008) 1548–1563
Fig. 7. Contours of mean radial velocity Ur (m/s).
Urc = 0) are observed at the centers of the recirculation zone (vortex ring core center). This observation is in agreement with the static nature of the vortex ring [6]. While keeping Ux,0 constant (case
a–b–c and d–e–f), the flow field’s tendency to recirculate increases
with the velocity jump (DU = Ux,0 Ux,i). This relates to previous
work on coaxial jets without swirl [44], where it was found that
for velocity ratio higher than a specific limit (f > 8) the outer jet begins to penetrate upstream on the inner jet axis imposing a pres-
sure deficit which leads to recirculation. In general swirl is
expected to intensify the recirculation trend of a jet. However, in
the present experiments the rotation of the internal stream and
the associated centrifugal forces seem to inhibit the penetration
of the outer flow towards the inner jet axis leading to decreased
recirculation. The swirler’s exit mouth sets the reference location
for the stabilization of the recirculation bubble. The proposed
Rossby number takes into account these effects, related to the
A. Giannadakis et al. / Experimental Thermal and Fluid Science 32 (2008) 1548–1563
interaction of a longitudinal and an azimuthal shear layer and appears to describe the observed trends. The recirculation mass flow
R r
RR
ratio ðm ¼ 0 U x r dr= r 0 U x r drÞ depicted in Fig. 6 shows explicitly
this agreement as it increases with Rossby number. Maximum values of m* occur at the vortex ring core plane and scale almost linearly with the Rossby number.
Contours of the mean radial velocity (Ur) component (Fig. 7)
show how the flow travels around the recirculation bubble. Bubble
1555
interior is characterized by low radial velocities. Within the bubble,
fore and aft the vortex ring core, relatively high radial velocities
indicate the recirculation pattern. In the downstream boundary
of the bubble, the combined effect of the expanding flow around
the bubble and the flow entering the bubble results to high radial
velocities.
Mean azimuthal vorticity (Xh) contours (Fig. 8) show the interaction of the shear layer, created by the swirling jet and the
Fig. 8. Contours of mean azimuthal vorticity Xh (1/s).
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A. Giannadakis et al. / Experimental Thermal and Fluid Science 32 (2008) 1548–1563
Fig. 9. Contours of
annular flow, with the rotating vortex ring. Maximum values of Xh
increase with the Rossby number and are observed in two
regions:
(i) The first and stronger one is located at the jet exit, where the
shear layer between the two flows is formed.
(ii) The second is located at the position of the vortex ring core
due to the rotation of the vortex ring.
qffiffiffiffiffiffi
u02
x (m/s).
The interior of the recirculation bubble is characterized by low
azimuthal vorticity values in the upstream region, close to the
swirling nozzle and higher ones in the region between the vortex
ring core and the bubble’s aft, due to fluid exchange between the
recirculation bubble and the outer flow. Increase of Rossby number
results into the widening of the latter region.
The increase in azimuthal vorticity values has also been correlated by Althaus et al. [7] with the upstream displacement of the
A. Giannadakis et al. / Experimental Thermal and Fluid Science 32 (2008) 1548–1563
Fig. 10. Contours of
recirculation bubble, as it has been discussed earlier in the bubble
topology section, illustrating the ability of the proposed Rossby
number to describe the flow field’s trends.
3.3. Turbulent flow field
of longitudinal and radial RMS velocities
qContours
qffiffiffiffiffiffi
ffiffiffiffiffiffi
, presented in Figs. 9 and 10, show the effect of
u02
u02
x and
r
1557
qffiffiffiffiffiffi
u02
r (m/s).
the recirculation bubble on q
the
ffiffiffiffiffiffiturbulent
qffiffiffiffiffiffi dynamics of the coaxial
flow field. Intense values of u02
u02
x and
r occur in the shear layer
between the outer flow and the recirculation bubble, while maxima are located at the vortex ring core plane (bubble–annular flow
interaction) and the bubble aft (wake flow region), respectively.
Furthermore, their intensity is increased with the Rossby number.
As expected, the interior of the recirculating bubble is characterized by lower values of turbulent kinetic energy [10]. Contours of
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A. Giannadakis et al. / Experimental Thermal and Fluid Science 32 (2008) 1548–1563
pffiffiffiffiffiffiffiffiffiffiffi
02
u02
x þur
Fig. 11. Contours of turbulence intensity TI ¼ pffiffiffiffiffiffiffiffiffiffiffi
.
2
2
U x þU r
qffiffiffiffiffiffi
u02
x form a low value ‘tail’ at the recirculation bubble aft depicting
the effect of the aft stagnation zone on fluid flowing
inside
p
ffiffiffiffiffiffiffiffiffiffiffiand
out02
u02
x þur
p
ffiffiffiffiffiffiffiffiffiffi
ffi
is obside the bubble. High turbulence intensity TI ¼
2
2
U x þU r
served at the periphery of the recirculation bubble (Fig. 11). In
the central region of the bubble an elliptic zone of low turbulence
intensity is formed. This zone corresponds to the high recirculating
velocities zone observed in the longitudinal mean velocities con-
tour (Fig. 4). The area occupied by this zone increases
qffiffiffiffiffiffiffiffi with the
Rossby number. Azimuthal vorticity fluctuations ð x02
h Þ maxima
(Fig. 12) show the strong interaction of the vortex ring with the
outer flow. An interesting feature of vorticity fluctuations is the
fact that its maxima are located between the first and the second
region of maximum mean vorticity, depicting the strong effect of
the vortex ring on flow turbulence dynamics and a diffusion-like
A. Giannadakis et al. / Experimental Thermal and Fluid Science 32 (2008) 1548–1563
Fig. 12. Contours of turbulent azimuthal vorticity
process from the shear q
layer
ffiffiffiffiffiffi to the vortex ring. Topology of
qffiffiffiffiffiffiffiffi
x02h is
quite similar to that of
Intense turbulence mixing via the u0x u0r
Reynolds stresses component (Fig. 13) between the swirling jet
and the annular flow is initiated in the shear layer close to the vortex ring core plane occupying a broader area in the aft shear layer
where fluid exchange between the outer flow and the bubble takes
place. Inside the bubble, local maxima are located in the vortex
u02
x .
1559
pffiffiffiffiffiffiffiffi
x02h (1/s).
ring core due to fluid recirculation. Shear stresses increase with
Rossby number.
Longitudinal velocity skewness (SUx ) contours (Fig. 14) depict
values close to zero (indicating a symmetric probability density
function, pdf) within the area of the bubble. Zero value contour
moves towards the bubble fore with the Rossby number. A similar
trend is observed in the longitudinal velocity flatness (F U x )
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A. Giannadakis et al. / Experimental Thermal and Fluid Science 32 (2008) 1548–1563
Fig. 13. Contours of Reynolds stresses u0x u0r (m/s)2.
contours (Fig. 15) within the bubble. The area surrounded by the
value 3.0 contour level (typical value for normal pdf) is getting larger and moves towards the bubble fore with the Rossby number.
The shear layer developing at the bubble boundaries is characterized by skewness
qffiffiffiffiffiffi and flatness values of 0 and 3, respectively, along
with high u02
x values. Intermittent presence of fluid parcels penetrating from the high velocity outer stream to the lower velocity
inner stream result to positive skewness values on the low velocity
side of the shear layer whereas the inverse mechanism results to
negative values on the high velocity side. These effects also lead
to increased flatness values on both sides of the shear layer.
4. Conclusions
The near flow field of a recirculating swirling jet interacting
with an annular flow was studied with the use of 2D DPIV. A
A. Giannadakis et al. / Experimental Thermal and Fluid Science 32 (2008) 1548–1563
1561
Fig. 14. Contours of SUx .
modified Rossby number has been proposed which appears to
describe the flow trends adequately. Length scale characteristics of the recirculating bubble scale with the Rossby number.
Increase of Ro results to the widening of the bubble and an
upstream shift of its aft. Results of the mean and turbulent
flow field demonstrate the important role of the recirculation
bubble on flow dynamics and the mixing process between
the swirling jet and the annular flow. High recirculating veloc-
ities are observed at the central area of the bubble, the amplitude of which increases with the Rossby number. The bubble
interior is characterized by low turbulent dynamics. Vorticity
diffusion from the shear layer to the vortex ring results to
theqcreation
of a second region of high Xh and high values
ffiffiffiffiffiffiffiffi
x02h at the vortex ring core plane. Skewness and flatness
of
contour diagrams indicate a normal velocity pdf distribution
in the bubble interior. Change of sign in skewness values and
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A. Giannadakis et al. / Experimental Thermal and Fluid Science 32 (2008) 1548–1563
Fig. 15. Contours of F U x .
high flatness values depict the intense momentum transfer between the two streams in the shear layer. Characteristics of
mean and turbulent flow field depict two zones in the flow
field. The first one is dominated by the recirculation bubble
and the vortex ring dynamics while the second one is located
downstream the aft of the bubble acquiring wake flow characteristics. The modified Rossby number, relating the azimuthal
with the axial shear layer influence on the flow field, appears
to describe the flow field’s trends and recirculation bubble
topology in a satisfying manner.
Acknowledgements
The support of the European Social Fund (ESF), Operational Program for Educational and Vocational Training II (EPEAEK II), and
particularly the Program HERAKLITOS, is gratefully acknowledged.
A. Giannadakis et al. / Experimental Thermal and Fluid Science 32 (2008) 1548–1563
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