4th International Symposium on Particle Image Velocimetry
Göttingen, Germany, September 17-19, 2001
PIV’01 Paper 1020
Investigation of the Vortex Structures Downstream of a Lobed
Nozzle by Means of Dual-plane Stereoscopic PIV
Hui HU, Tetsuo SAGA, Toshio KOBAYASHI, Nobuyuki TANIGUCHI and Masashi YASUKI
Abstract In a continuing effect to study the mixing enhancement by large-scale streamwise vortices in lobed
mixing flows, an advanced PIV system named as dual-plane stereoscopic PIV system was used in the present study
to conduct simultaneous vorticity (all three components) measurement of an air jet exhausted from a lobed nozzle.
Unlike “classical” 2-D PIV system or conventional “single-plane” stereoscopic PIV system, the dual-plane
stereoscopic PIV system used in the present study can obtain the flow velocity (all three components) fields at two
spatially separated planes simultaneously. Therefore, it can provide the distributions of all the three components of
vorticity vectors instantaneously and simultaneously. The evolution and interaction characteristics of the large-scale
streamwise vortices and azimuthal Kelvin-Helmholtz vortices in the lobed jet mixing flow were revealed
instantaneously and quantitatively from the measurement results of the dual-plane stereoscopic PIV system. The
characteristics of the mixing process in the lobed jet mixing flow were analyzed based on the simultaneous
measurement results of the steamwise vorticity and azimuthal Kelvin-Helmholtz vorticity distributions.
1
Introduction
Lobed mixers/nozzles, which are essentially splitter plates with corrugated trailing edges, are fluid mechanic
devices used to augment mixing in a variety of applications. Such devices have been applied widely in turbofan
engine exhausts and ejectors to reduce take-off jet noise and Specific Fuel Consumption (SFC) (Kuchar et al. 1980,
Presz et al. 1994, Hu et al. 1999). More recently, lobed mixers/nozzles have also emerged as an attractive approach
for enhancing mixing between fuel and air in combustion chambers to improve the efficiency of combustion and
reduce the formation of pollutants (Smith et al.1997).
Due to the excellent mixing enhancement performance and widely potential applications of the lobed
mixers/nozzles, extensively studies about the mechanism by which lobed nozzles/mixers substantially enhance the
mixing have been conducted. Based on pressure, temperature, and velocity measurements of the flow field
downstream an axisymetric lobed nozzle, Paterson (1984) revealed the existence of large-scale streamwise vortices
due to the secondary flow in the lobed mixing flow induced by the special geometry of the lobed nozzle. Horseshoe
vortices with smaller scale were also found to exist at the lobe troughs. Although the contribution of these vortices
to the overall mixing process was not clear, the large-scale streamwise vortices were believed to be responsible for
the enhanced mixing because of their much greater size. Werle et al. (1987) and Eckerle et al. (1992) found that the
large-scale streamwise vortices in a lobed mixing flow follow a three-step process by which the streamwise
vortices form, intensify, and then break down. They also found that the breakdown of the vortices was
accompanied by a significant increase in turbulent mixing. Elliott et al. (1992) suggested that there are three
primary contributors to the mixing processes in lobed mixing flows. The first is the azimuthal vortices, which occur
in any free shear layers due to the Kelvin-Helmholtz instability. The secondary is the increased interfacial contact
area due to the convoluted trailing edge of the lobed mixer. The last element is the streamwise vortices produced by
the special geometry of the lobed mixer. Based on the pulsed-laser sheet flow visualization with smoke and threedimensional velocity measurements with Hot Film Anemometer, McCormick and Bennette (1994) suggested that it
is the interaction of the azimuthal Kelvin-Helmholtz vortices with the streamwise vortices produces the high levels
of mixing. As the azimuthal Kelvin- Helmholtz vortices shed from the trailing edge of lobed mixers, the
streamwise vortices deform them until they are eventually pinched off and subsequently broken down. Turbulence
measurements showed the regions of high-turbulence kinetic energy that were consistent with the flow
visualization of the pinch-off effect.
H. Hu , T. Saga, T. Kobayashi and N. Taniguchi, Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo, Japan
M. Yasuki, Industrial Instruments Department, SEIKA Corporation,1-5-3 Koraku, Bunkyo-ku, Tokyo Japan
Correspondence to:
Dr. Hui HU, present address: Turbulent Mixing and Unsteady Aerodynamics Laboratory, A22, Research Complex Engineering, Michigan State
University, East Lansing, 48824, Michigan. U.S.A. Fax: 1-517-353-7179, Email: huhui@egr.msu.edu
1
PIV’01 Paper 1020
Although the existence of unsteady vortices and turbulent structures in lobed mixing flows has been revealed in
those previous studies by qualitative flow visualization, the quantitative whole-field velocity and vorticity
distributions in lobed mixing flows have never been obtained until the recent work of the authors. In the earlier work
of the authors, both planar Laser Induced Fluorescence (LIF), classical two-dimensional Particle Image Velocimetry
(PIV) (Hu et al.200a,b) and conventional single-plane Stereoscopic PIV (Hu et al. 2001a) techniques were used to
study lobed jet mixing flows. By using the directly perceived LIF flow visualization images and quantitative
velocity, vorticity and turbulence intensity distributions of the PIV measurement results, the evolution and
interaction characteristics of various vortical and turbulent structures in the lobed jet mixing flows were discussed.
It is well known that the PIV measurement results from a classical two-dimensional PIV system or a
conventional single-plane stereoscopic PIV system can only provide one component of vorticity vectors normal to
the laser sheet plane instantaneously. In order to obtain all the three components of the vorticity vectors to reveal the
evolution and interaction characteristics of the large-scale streamwise and azimuthal Kelvin-Helmholtz vortices in
the lobed mixing more clearly and directly, an advanced PIV system named as dual-plane stereoscopic PIV system,
which can obtain the flow velocity (all three components) fields at two spatially separated planes simultaneously,
has been developed recently by the authors (Hu et al. 2001b). Since the dual-plane stereoscopic PIV system can
measure the velocity fields (all three components) at two spatially separated planes simultaneously, all the three
components of the vorticity vectors with various auto-correlation and cross-correlation coefficients of flow variables
can be obtained instantaneously and simultaneously as the measurement results of the dual-plane stereoscopic PIV
system (Hu et al. 2001b).
The main object of the present work is to gain insight into the evolution and interaction characteristics of various
vortices and turbulent structures in a lobed jet mixing flow. The characteristics of the mixing process in the lobed jet
mixing flow will be analyzed based on the simultaneous measurement results of the steamwise vorticity and
azimuthal Kelvin-Helmholtz vorticity fields obtained by using the dual-plane stereoscopic PIV system.
2
Experimental Setup
2.1
Dual-plane stereoscopic PIV system
It is well known that particle scattering can be either Mie scattering or Rayleigh scattering depending on the
relative diameter of the particle compared with the wavelength (λ) of the incident light. According to McCartney
(1976), Mie scattering is generally defined as scattering from particles which is greater than 1/10 of the incident
light wavelength (λ) and Rayleigh scattering is defined as scattering form particle with diameters less than 1/10λ.
In the Mie scattering regime, the scattering will have a dominant forward direction, and nonuniform “lobed”
scattering towards the sides. The scattering distributions will depend upon the particle size, incident light
wavelength and polarization. It should be mentioned that the polarization direction is conservative in the Mie
scattering regime if the incident light is linearly polarized, and the Mie scattering pattern tends to go nearly to zero
(due to depolarization) in the direction normal to the incident polarization direction (Elliott and Beutner, 1999). As
the same as Keahler and Kompenhance (1999), the dual-plane stereoscopic PIV system used in the present study
utilizes the polarization direction conservation characteristics of the Mie scattering to separate the light scattering
from the two illuminating laser sheets to achieve simultaneous stereoscopic PIV measurements at two spatially
separated planes.
Figure 1 shows the schematic set-up of the dual-plane stereoscopic PIV system used in the present study. Two
sets of widely used double-plused Nd:YAG lasers (New Wave, 50mJ/pulse) with additional optics (half wave plate,
mirrors, polarizer and cylinder lens) were used to set up the illumination system of the dual-plane stereoscopic PIV
system. The P-polarized laser beams from the double-pulsed Nd:YAG laser set A were turn into S-polarized light by
passing a half wave (λ/2)plate before they are combined with the P-polarized laser beams from the double-pulsed
Nd:YAG laser set B. The P-polarized laser beams from the laser set B transmit through the Polarizer cube, while the
S-polarized light from the double-pulsed Nd:YAG laser set A are reflected by the Polarizer cube. By adjusting the
angular and/or the location of the mirror #1, the laser beams from the laser set A and laser set B can be overlapped
or not. Passing through the cylindrical lens and reflected by mirror #2, the laser beams are expanded into two
paralleling laser sheets with orthogonal linear polarization to illuminate the studied flow field at two spatially
separated planes. In the present study, the thickness of the illuminating laser sheets is about 2.0mm, and the gap
between the centers of the two illuminated planes is adjusted as 2.0 mm.
For capturing the stereoscopic PIV images simultaneously at two measurement planes illuminated by the two
laser sheets with orthogonal linear polarization, two pairs of high-resolution cross-correlation CCD cameras (1K by
1K, TSI PIVCAM 10-30) were used to do stereoscopic PIV image recording. The two pairs of the high-resolution
CCD cameras were settled on an optical table with a pair of polarizing beam splitter cubes and two high reflectivity
2
PIV’01 Paper 1020
Half wave (λ/2) plate
Mirror #1
Double-pulsed
S-polarized laser beam
Mirror #2
cylinder lens
P-polarized
laser beam
Host computer
Nd:YAG Laser set A
Double-pulsed
Nd:YAG Laser set B
Polarizer cube
Laser sheet with
S-polarization direction
Laser sheet with P-polarization direction
Synchronizer
Measurement region
80mm by 80mm
Lobed nozzle
Polarizing beam splitter cubes Mirror #4
high-resolution
CCD camera 4
650mm
25 0
0
high-resolution
CCD camera 3
25
650mm
Mirror #3
high-resolution
CCD camera 2
high-resolution
CCD camera 1
Fig. 1. The schematic set-up of the dual-plane stereoscopic PIV system
mirrors installed in front of the cameras to separate the scattered light from the two illuminating laser sheets with
orthogonal linear polarization. The illuminating laser sheets with orthogonal linear polarization are scattered by the
tracer particles seeded in the objective fluid flow. Due to the polarization direction conservation characteristics of
the Mie scattering mentioned above, the scattered light from the P-polarized laser sheet will keep the P-polarization
direction and pass straight through the polarizing beam-splitter cubes and is detected by cameras 2 and 3. The
scattered light from the S-polarized laser sheet will still be S-polarization and emerge from the polarizing beam
splitter cubes at the right angles to the incident direction. Reflected by the two high reflectivity mirrors (mirror #3
and #4), the scattered S-polarized light is detected by the cameras 1 and 4.
In order to maximized the size of measurement window, the two pairs of high-resolution CCD cameras were
arranged in an angular displacement configuration. With the installation of tilt-axis mounts, the lenses and camera
bodies were adjusted to satisfy Scheimpflug condition (Prasad and Jensen, 1995 )to obtain focused particle images
everywhere in the image recording planes. In the present study, the distance between the illuminating laser sheet and
image recording planes of the CCD cameras is about 650mm, and the angle between the view axiles of the two
cameras is about 500. For such arrangement, the size of the stereoscopic PIV measurement window is about 80mm
by 80mm.
The CCD cameras and double-pulsed Nd:YAG laser sets were connected to a workstation (host computer) via a
synchronizer (TSI LaserPulse synchronizer), which controlled the timing of the laser sheet illumination and the
CCD camera data acquisition. In the present study, the time interval between the two pulsed illuminations was set as
30µs.
A general three-dimensional (3-D) in-situ calibration procedure was conducted in the present study to obtain the
mapping functions between the image planes and object planes (Soloff et al. 1997). A target plate (100mm by
100mm) with 100µm diameter dots spaced at interval of 2.5 mm was used for the in-situ calibration. The front
surface of the target plate was aligned with the center of the laser sheet and then calibration images were captured at
three locations across the depth of the laser sheets. The space interval between these locations was 0.5mm for the
present study. The mapping function used in the present study was taken to be a multi-dimensional polynomial,
which is fourth order for the directions (X and Y directions) paralleling the laser sheet plane and second order for
the direction (Z direction) normal to the laser sheet plane. The coefficients of the multi-dimensional polynomial
were determined from the calibration images by using least square method.
It should be mentioned that the present dual-plane stereoscopic PIV system uses the same polarization direction
separation method as Kaehler and Kompenhans (1999) to do the scattered light separation. The optical arrangement
of the illumination system and stereoscopic PIV image recording system of the present dual-plane stereoscopic PIV
are also quit similar to the so-called “multiple-plane stereo PIV system” developed by Kaehler and Kompenhans
(1999) and Kaehler (2000). In contrast to the 2-D calibration method used by Kaehler and Kompenhans (1999), the
general 3-D in-situ calibration procedure (Soloff et al. 1997) was used in the present study to determine the
relationships between the three-dimensional objective fields and the two-dimensional image planes. For the 2-D
calibration used by Kaehler and Kompenhans (1999), mapping functions are sought only to relate each two-
3
PIV’01 Paper 1020
dimensional image planes to the two-dimensional objective planes. For the velocity three-component reconstruction,
the recording geometric quantities, such as separation between lenses, objective distance, the angular orientation of
the camera axis to the object plane and so on, are still required as inputs explicitly in the reconstruction equations
(Willert, 1997). It should be noted that these quantities pertaining to the recording geometry may be difficult to
measure accurately and may introduce errors. Furthermore, if recording is accomplished through a liquid-air
interface, the reconstruction equations will need to be modified to account for the refraction at the interface (Prasad,
2000). The general 3-D in-situ calibration method used in the present study can incorporate all the parameters of
system geometry and optical arrangement automatically and do not need any explicit input for both position
mapping and velocity three-component reconstruction.
The two-dimensional particle image displacements in each image plane were calculated separately by using an
improved cross-correlation method, named as Hierarchical Recursive PIV (HR-PIV) method (Hu et al. 2000).
Compared with conventional cross-correlation based PIV image processing methods, the Hierarchical Recursive
PIV method has advantages in the spurious vector suppression and spatial resolution improvement of PIV result.
Since 32 pixel by 32 pixel windows were used for the final step of the recursive correlation operation, the spatial
resolution of the present stereoscopic PIV measurement is expected to be about 2mm×2mm×2mm. Finally, by using
the mapping functions obtained by the in-situ calibration and the two-dimensional displacements in the two image
planes, all three components of the velocity vectors in the illuminating laser sheet plane were reconstructed. Further
details about the optical set-up, in-situ calibration and image processing of the present dual-plane stereoscopic PIV
system can be obtained from Hu et al. (2001b).
2.2
Lobed Jet Mixing Flow and Experimental Apparatus
Figure 2(a) shows the geometry parameters of the lobed nozzle used in the present study. The lobed nozzle has
six lobes. The width of each lobes is 6mm and the height of each lobe is 15mm (H=15mm). The inner and outer
penetration angles of the lobed structures are about 220 and 140 respectively. The diameters of the lobed nozzles is
D=40mm.
Figure 2(b) shows the jet flow experimental rig used in the present study. The air jet was supplied by a
centrifugal compressor. A cylindrical plenum chamber with honeycomb structures in it was used for settling the
airflow. Through a convergent connection (contraction ratio is about 50:1), the airflow is exhausted from the test
nozzle. All the jet supply apparatus were installed on a two-dimensional translation mechanism so that the distance
between the exit plane of the lobed nozzle and the illuminating laser sheets can be changed by operating the twodimensional translation mechanism. The illumination system and image recording system are fixed during the
experiment, the measurements for the different cross planes of the lobed jet mixing flow were achieved by changing
the positions of the lobed nozzle. Therefore, all the measurements at the different cross-planes of the lobed jet
mixing flow can be conducted by doing the in-situ calibration procedure only once.
The velocity of the air jet exhausting from the test nozzle is adjustable. In the present study, the jet velocity (U0)
was set at about 20m/s. The Reynolds number of the jet flow, based on the lobed nozzle diameter (D) and the jet
velocity is about 60,000.
A seeding generator, which is composed by an air compressor and several Laskin nozzles (Melling, 1997), was
used to generate 1~5µm DEHS (Di-2-EthlHexyl-Sebact) droplets as tracer particles in the jet mixing flow. The
seeding DEHS droplet flow from the seeding generator are divided into two streams; one is used to seed the core jet
flow and another for the ambient air seeding.
X
Lobe peak
Centrifugal compressor
Test nozzle
inner penetration angle
outer penetration angle
Cylindrical
plenum chamber
Lobe trough
Convergent connection
Two-dimension translation mechanism
Lobe height
Y
Z
H=15mm
a. test lobed nozzle
b. The schematic of the experimental rig
Fig. 2, The test lobed nozzle and experimental rig used in the present study
4
PIV’01 Paper 1020
20 m/s
Y
20 m/s
Y
30
30
X
20
0
-10
-20
Y mm
10
W m/s
20.00
19.00
18.00
17.00
16.00
15.00
14.00
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
Z
X
20
10
0
Y mm
Z
-10
-20
-30
-30
-30
-30
-20
-20
-10
-10
0
Xm
m
0
10
Xm
m
20
30
10
20
30
a. instantaneous velocity field in Z=10mm cross plane b. simultaneous velocity field in Z=12mm cross plane
Fig. 3. A pair of typical instantaneous velocity fields obtained simultaneously by
using the dual-plane stereoscopic PIV system
3
Experimental results and discussions
Figure 3 gives a pair of typical instantaneous measurement results obtained simultaneously by the dual-plane
stereoscopic PIV system in two parallel cross planes (Z=10mm and Z=12mm) near the exit of lobed nozzle. Since
the characteristics of the mixing process in the lobed jet mixing flow revealed from the velocity distributions has
been discussed extensively in the earlier work of the authors (Hu et al., 2000a,b and 2001a), the majority of the
results and discussions given in the present paper will focus on the evolution and interaction characteristics of
various vortical and turbulent structures in the lobed jet mixing flow revealed from the simultaneous measurement
results of the streamwise vorticity and azimuthal vorticity fields.
According to the definition of vorticity vector, the three components of the normalized vorticity vectors in the
lobed jet mixing flow can be calculated by using following questions:
D ∂w ∂v
(
− )
U 0 ∂y ∂z
D ∂u ∂w
ϖy =
( − )
U 0 ∂z ∂x
D ∂v ∂u
ϖz =
( − )
U 0 ∂x ∂y
ϖx =
(1)
(2)
(3)
Where D is the diameter of the lobed nozzle, and U0 is the velocity of the jet flow at the test nozzle inlet. While,
u, v and w are the instantaneous velocity in X, Y and Z directions (Fig. 2).
It should be noted that the terms like
∂u
∂v
and
in the above equations can not be determeined from the
∂z
∂z
measurement result of a “classical” 2-D PIV system or a conventional “single-plane” stereoscopic PIV system.
Therefore, only the out-of-plane componet of the vorticity ϖ z with its direction normal to the illuminted laser plane
can be obtained instantanously.
Since the present dual-plane stereoscopic PIV system can measure the velocity fields at two illuminated planes
simultaneously, all the terms in the above vorticity definition equations can be calculated. Besides the out-of-plane
component componet ϖ z , the other two in-plane components of the vorticity vectors ( ϖ x and ϖ y ) can also be
obtained in either of the two illuminated planes with first-order approximation and in the central plane between the
two parallel illuminated planes with second-order approximation accuracy. By using the simultaneous measurement
results of the dual-plane stereoscopic PIV system in Z=10mm and Z=12mm cross planes (Fig. 3), all the three
components of the instantaneous vorticity vectors in the Z=10m cross plane were calculated. The results are shown
in the Fig.4(a), 4(b) and 4(c).
5
W m/s
20.00
19.00
18.00
17.00
16.00
15.00
14.00
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
PIV’01 Paper 1020
40
40
30
30
1
1
-7
-5 -9
11 -1
9
11
-1
3
-5-9
-3 1
3
1
5
7
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1
3
7
1
Y mm
3
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911 -5
31
-3
11
-3
5
1
-1
3 7
-5
5
1
1
-3
-20
0
20
40
-40
-20
0
20
X mm
40
X mm
a. instnatanous vorticity (X-component)
b. instnatanous vorticity (Y-component)
40
40
30
4.7.0
0
13.0
4.
0
15.06.0
6.0
16.
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7.0
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6.0
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119.8.0
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Y mm
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0.5
0.
5
5
-0.
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3.5
11
0.5
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2.
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181. .0
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8.
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8.0
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.0
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15.00
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190.0
0
13. .0 4.0
8
8.0
5.0
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-0
2.5
4.0
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8. 5.0
in-plane vorticity
12
-0
.5
-1.5
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7.0
14.0
13.0
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0.5
-1.5
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7.
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12.0 9.0
0.5
10
5.0
0.5
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4.50
3.50
2.50
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0.50
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-4.50
-2.5
-4.5
1.5
3 .5
2.5
Streamwise vorticity
.5
-0. -4.5
5
20
.0
1143.0
-4
1.5
-0.5
10
-0.5
5.0
5.0
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-1.
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1.
5
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5
1.
1.5
2.0
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07.023.0.105 7.0
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98.0 11
6.0
5.0 0
7.0
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1.
111
-
20
0.5
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30
Y mm
7
5
5
Y mm
53
1
7
53
9
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-3
-1
1
-3
7
11.00
9.00
7.00
5.00
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-7.00
-9.00
-11.00
-30
-40
-40
-3
1
3
-20
3
5
-1
1
-1
-30
Vorticity distribution
(Y-componet)
57
11
1
-1
-10
3 1
1
-3-1-5
-3
53
-5
-3-1 -7
1
-1
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1
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9
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7
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39
7
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11.00
9.00
7.00
5.00
3.00
1.00
-1.00
-3.00
-5.00
-7.00
-9.00
-11.00
-7
-5
1
-7
-9
-1
0
20
5
10
-3
-5 -7
3
Vorticity distribution
(X-componet)
-5
-3
20
5
-1
0 .0
9. 47.0
-30
-40
-20
0
20
-40
40
-40
-20
0
20
X mm
40
X mm
c. instantaneous streamwise vorticity (Z-component) distribution
d. instantaneous azimuthal (in-plan)vorticity distribution
40
40
30
30
In-plane vorticity
-20
0
20
-40
40
X mm
-40
-20
4.0
.0
118.0
74.0.5
9.0 8.5
5.5
4.5
6.5
5.0
45.5
.5
7.0
11.0
33
.5.0
6.0
2.0
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11
5.0 7.0 .0
3.53
8.5
7.0
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-40
5.0
7 4
8. .5 .05.5
6.522..5
0
4.03 097..05
11 7.
.85.
6
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12.0.5
10.5
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89.0. 6. 10.0
5 5
4
8.5.5
8.
0
5.0
Y mm
7.0
.5 .0
10 2
53.0
24...55 10.01 10.
7 4.0 0. 5
0
2.0
0
6.
3.0
-30
-40
33.5.
5.00
-3.5
0.5
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3.5
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3.0
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9.0
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.901.5
79.54.0 8. .59..55
5.0
17
5
6. .5 1
10
-10
5
-0.
-20
2.0
2.5
7.5 5.56.5
9.85
.
5. 2.04611.100
5
.20 .5 79.0
.5
7 .0
9.0.0 58. .5
4.5 811 1 53 0
6..552
.0.01.95. .05
5
5.85.0
2.
5
.5
-1
2.5
-0.5 -2
.5
5
5
0.
-1
.5
Y mm
-3.5
-1.5
-2.
5
5 9.
9. 10.5
5
9.
-
-10
5
0.
.0
33.655.0
.58.0 11.5
3 .0
6.0 4.0
3.5
8.0 5.575.5.20.5
8.5
6.5
5.5
7.0
4.0
22
.0.5
0
5
6.
8.0
0.5
10.5
11
.0
10.0
3.08.5
5.0
10
10.0
64.0.5
2.5
-0.5 0.5
4.5
.0
10
47.08.5.5
11.0
0
8. .0
5.534.0
2.0
-1.5
0
4.50
3.50
2.50
1.50
0.50
-0.50
-1.50
-2.50
-3.50
-4.50
2.0
-0.5
5
0.
.5
-0
10
20
Streamwise vorticity
12.00
11.50
11.00
10.50
10.00
9.50
9.00
8.50
8.00
7.50
7.00
6.50
6.00
5.50
5.00
4.50
4.00
3.50
3.00
2.50
2.00
5
33.0.
0
6.
0
7.
9.5
1.
5
4.56.0
9.
0
.5
.08 4.5
81.00
0
34. 59.0.0 1.95.5 6.0 .0
11
1
30 .0
7.5
6.5
6.5
.509. .05 .5 7.5
4.0.06 151.5
1.065. 54
110.0
9
7.0
.0
23.0
-4.5
3.5
20
5
1.
-1
.5
0.5
0
20
40
X mm
e. ensemble-averaged streamwise vorticity distribution f. ensemble-averaged azimuthal (in-plane)vorticity distribution
Fig 4. The streamwise and azimuthal vorticity distributions in the Z=10mm cross plane of the lobed jet mixing flow
As mentioned above, there are two kinds of vortices which are very important for the mixing process in lobed
mixing flows: One is the large-scale streamwise vortices generated by the special geometry of lobed nozzle, another
is the zaimuthal vortices rolled up at the interface of the shear layers due to the Kelvin-Helmholtz instability. For the
6
PIV’01 Paper 1020
large-scale streamwise vortices generated by the special trailing edge of the lobed nozzle, their existance were
revealed very clearly from the instantaneous streamwise vorticity distribution shown in Fig. 4(c). In order to reveal
the azimuthal vortices rolled up in the lobed mixing flows due to the Kelvin-Helmholtz instability, the x-component
and y-component of the vorticity vectors were combined into in-plane vorticity by using the following equation:
ϖ in − plane = ϖ x 2 + ϖ y 2
(4)
Based on the equation (4), the distribution of the azimutha (in-plane) vorticity in the Z=10mm cross-plane of
lobed jet mixing flow was calculated (Fig. 4(d)). As it is expected, the azimuthal Kelvin-Helmholtz vortex ring was
found to have the same geometry as the lobed trailing edge at the exit of the lobed nozzle.
It should be noted that although the existances of the streamwise vortices and the azimuthal Kelvin-Helmholtz
vortices in lobed mixing flow have been suggested in previous studies, the quantitative data about the distributions
of streamwise vorticity and azimulthal vorticity in lobed mixing flows have never been obtained due to the
limitation of the experimental techniques used in those previous studies. The measurement results obtained by the
present dual-plane stereoscopic PIV system are likely to be the first to reveal the streamwise vortices and the
azimuthal Kelvin-Helmholtz vortices in the lobed jet mixing flows instantaneously and simultaneously.
Based on the 200 frames of instantaneous measurement results, the ensemble-averaged streamwise vorticty and
azimuthal (in-plane) vorticity distributions in the lobed jet mixing flow at Z=10mm cross plane were calculated,
which are given in Fig. 4(e) and Fig. 4(f). Compared with the instantaneous streamwise and azimuthal vorticity
fields, the ensemble-averaged streawise and azimuthal vorticity fields were found to be much smoother. However,
they have almost the same distribution pattern and magnitude as their instantaneous counterparts, which indicate that
the generation of the streamwise vortices and azimuthal vortex ring at the exit of the lobed nozzle are quite steady.
40
40
-0.5
Y mm
0. 5
0.52.5
5
-0.
1.
5
- 0.
5
2.5
1.
5
1.5
2.
5
-1.5
0
-0.5 .5
-1.5
.5
-1
-40
40
2.5
0.5
-2.5
.5
5
-3.
5
20
-0.5
0.5
1 .5
-30
0
0.5
-10
-0.5
-20
4.50
3.50
2.50
1.50
0.50
-0.50
-1.50
-2.50
-3.50
-4.50
1.5
0.
5
0.
-40
-1. -0.
5
5
-20
0.5.5
-0
-30
-3
.5
Streamwise vorticity
-0
.5
-1.5
-1
3.5
-20
-2.5
2.5 0.
5
Y mm
3.
5
0.5
-0 2.5
.5
5
1.
.5
-1
5
4.
.5
-0
1.
5
1.5
-0.
5
10
0
5
-1.
5
-0.
-0.5
-10
-40
2.5
1..55 5
0 -0. 5
0.
0.5
-0.
-2.5 -0.5 5 1 .5
.5 0
0.5
1.5
-1.5
5
0.
-1.5
0
4.50
3.50
2.50
1.50
0.50
-0.50
-1.50
-2.50
-3.50
-4.50
-1.5
0.5
20
Streamwise vorticity
5
0.
-3.5
-1 .
5
-3.5
-0.5
1.5
0.5
1.5 3.5
10
30
-1.5
5
-0.
-1.5
20
3.
5
2.
5
0
1.5.5
30
-40
-20
0
X mm
20
40
X mm
a. instantaneous streamwise vorticity distribution
b. ensemble-averaged streamwise vorticity distribution
40
40
30
30
In-plane vorticity
4.5
5
3.
2.5
3.0
6.0
3.5
2.0
5.5
7.5
4.5
5
3.
30.5
5
3. 4.56.0.54
4.5
0 22 .5
2.5..00
5.5 6.0
3.5
3.53
3.0
.0 5.6.
00
4.5
4.5
Y mm
7.0
7.
0
4.0
56.08.0
2. 6
0 .5
5
5.0
2. 5.5 .0
5 4
.0
3.0
7 .0
5.0
4.
0
5.
0
7.0
65.0
8.0
7.
0
0
4.
2.
.0
10
11 1 6.0
9. 3
4.0 .00 .0
11.0
46..00
14 6
6.0 .0 1.0
2.0
4.0
0
4.
2.0 2.5
4.0
5.0
-20
3.5
5.0
3.0
2.5
-40
5
6.
Y mm
6.5
-40
40
5
0 5.
7.0
4.
4.5
5.5
2.5 22.5.0
6.0
8.0
2.0
3.5
5.5
4 .5
-30
4.5
6.7.0
5
4.5
20
8
3.756.5 .0
.06.58.0
0
2.
0
4.
5
5..5
6 ..05
55
.0
.53
33.50 6.5
3.5 .06.45
3.0
6
0
5.
3.
0
X mm
0
2.0
-20
5.0
0
467.0.0
0
8.5
5.
3.0 2.5
76.5.0
5.0 6.05.5
2.0
2 .5
8.56.5
6.5
4.0
5
4.5.5
5
3.
-20
5.0
7.04.5
4.0
2.0
-10
6.0
-40
5.
3.5
0 .0
7. 8
4.0
8.
0
9.
60.0
0
5
6. 0
3.35.
5.
0
10
7.5
8 .0
12.0
9.0
4.0
6.0
0.0.0
8.0 112 9.0
0
091. .0
7.1
-30
-40
0
4.
4.0
4.0
5 .0
.0
10
5.0
12.0
4.0
8.0
.0 6.0
0
10
9.
.0
6.
0
9.0
9.0
11
-20
5.0
7.0
5.
0
-10
15.00
14.00
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.
35.
0
12.00
11.50
11.00
10.50
10.00
9.50
9.00
8.50
8.00
7.50
7.00
6.50
6.00
5.50
5.00
4.50
4.00
3.50
3.00
2.50
2.00
2.0
4.0
5.0
7.0
11
.0
.0
56.0
10.0 .0
9.0 7
15
.00
14.
20
In-plane vorticity
0
14
6.
.0
.0
180.0.07
.102.01.0
98.0
1
0
8.0
5
0
6.
0
4..0
8
5.0
7.0
6. 9
0 .0
10
6.
2.5
2.0 .5
6 .0
4.0 5 .5
7.0 .0 .5 4
6 3 .5
3.5 33..054.5 5 5.0
2.5
8.
0
5.0
0 0
6. 6.
9.0
9.0
5.
0
4.09.0
4.0
20
0
7.
.0
3.5 3
0
20
40
X mm
c.instaneous azimuthal vorticity distribution
d. ensemble-averaged azimuthal vorticity distribution
Fig. 5. The measurement results of the dual-plane stereoscopic PIV system at Z=20mm (Z/D=0.50, Z/H=1.33) cross plane
7
PIV’01 Paper 1020
Figure 5 shows the simultaneous measurement results of the streamwise vorticity and azimuthal vorticity
distributions in the Z=20mm (Z/D=0.5, Z/H=1.33) cross plane of the lobed jet mixing flow. The six pairs of counterrotating streamwsie vortices generated by the lobed nozzle were found to be deformed in the instantaneous
streamwise vorticity field. Some of the large-scale streamwise vortices were even found to begin to break into
smaller vortices. Besides the six pairs of large-scale streamwise vortices corresponding to the six lobes, six pairs of
smaller and weaker streamwise vortices at the six lobe troughs can also be identified from the instantaneous
streamwise vorticity distributions. These smaller and weaker streamwise vortices at lobe troughs are called
horseshoe vortex structures by Paterson (1984), which has also been visualized clearly from the planar LIF flow
visualization results of the earlier work of the authors (Hu et al. 2000a,b). McCormick and Bennett (1994) also
proved the existence of such horseshoe vortex structures in a planar lobed mixing flow.
Compared with the instantaneous streamwise vorticity vorticity field, the ensemble-averaged streamwise
distribution was found to be much smoother. The six pairs of the large-scale streamwise vortices still can be seen
very clearly. However, the maximum magnitude of the ensemble-averaged streawise vorticity (4.0), is found to be a
bit smaller than that of its instantaneous counterpart, which is about 4.5. Since the present lobed jet mixing flow is a
free jet, it can also be seen that that the centers of the these large-scale streamwise vortices have spread outward as
they travel downstream. The same phenomena were also found in the LDV measurement results of Bleovich and
Samimy (1997)
The azimuthal vortex ring in this cross plane was also found to deform seriously. It is even torn into
disconnected vortex tubes at some breakdown points. The large azimuthal vortex-ring with the same geometry as the
trailing edge of the lobed nozzle can still be seen from the ensemble-averaged azimuthal vorticity distribution.
However, the maximum magnitude of the ensemble-averaged azimuthal vorticity (11.0), is found to be a bit smaller
than that of its instantaneous counterpart, which is about 15.0.
40
40
0.5
-0.
5
-1
.5
-2.
5
-1.5
20
-40
40
5
0.
-40
-20
0
20
X mm
a. instantaneous streamwise vorticity distribution
b. ensemble-averaged streamwise vorticity distribution
-30
20
3.5
2.0
2.5
3.5
-40
40
X mm
5
3.0
2.
4.0
3.5
3.5
2.5
3.0
2.5
2.5
3.0
2.0
5
2.5
2.0
3 .0 3
.0
2.5
2.5
2.0
3.5
2.0
2.0
Y mm
5.0
4.0
65.0
.0
33.5.0
2.
2.
0
6.0
2.0
4.0
5.0
4.0
6.0
4.0
4.0
3.0
46.0
.0
5.0
764..0.00
8 .0
2.0
3.5
3.5
3.5
0
3.5
2.0
0
2.
2.0
-10
-20
3.0 2.5
5.0 3.0
3.0
5.0
4.0
3.0
8.0
2.0
5
3.
4.
0
6.0
12.00
11.50
11.00
10.50
10.00
9.50
9.00
8.50
8.00
7.50
7.00
6.50
6.00
5.50
5.00
4.50
4.00
3.50
3.00
2.50
2.00
0
4.
-20
2.5
2.5
-40
4.0
5.0
0
6.
-30
0
4.
7 .0
7. 4.0
0
5.0
2.5
0
4.0
0
3.5
4.
6.0
6.0
-20
0
5.
0
2.
3.0
3.0
4.0
4.0
4.0
3 .0
4.0
6 .0
0
22.5.
10
2.5
5.0
5.0
-10
4.0
9.0
6.08.0
7.07.0 .0
5
15.00
14.00
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
5.0
6.0
5.0
20
In-plane vorticity
4.0
10.0 .0
14
0
5.0
4.
0
3.0
2.5
4.0
4.0
10
67. .0
0
2.0
0
6.
20
5
4.
2.5
4.0
In-plane vorticity
3.
5
30
3.5
4.
0
4.0
7.
0
6.
0
40
30
Y mm
40
X mm
40
-40
-0.5
-0.5
-1.5
.5
1.
5
0.5
-10
-0
-0.5
-1.5
.5
-0
1.5
0.
5
4.5
2.5
-0.5
1.5
-0-3
.5.5
-2.5
-0.5
0.5
-30
0
4.50
3.50
2.50
1.50
0.50
-0.50
-1.50
-2.50
-3.50
-4.50
1.5
0
5
0.
.5
Streamwise vorticity
-0.
5
-20
-2.5
-0
-0.5
0.5
-20
-0.5
-0.5
10
2.5
-0.5
-40
1.
5
2.5
-0.5
-1.5
-4.5
-2.5
-3.5 2.5
0.5
-0.5
-20
.5
-1
0.5
-1.5
-0.5
-1.5
0.5
0.5
0.5
2.5
2.5
3.5
5
-3.
1.
5
-10
-30
5
-1.
5
-1.
01.55
0.-51.5
.5
2.5
Y mm
5
.5
0. 1 0.5
-0.5
5
Y mm
.
-1
5
-1
5
- 3.
-1.
.5
-0
0
2.5
4.50
3.50
2.50
1.50
0.50
-0.50
-1.50
-2.50
-3.50
-4.50
0.5
2.5
-3.5
.5
-0
-0.5.5
-1
10
-40
20
Streamwise vorticity
1.5
0 .5
20
0.5
1.5
0.5
1.5
0. 5
-0
.5
.5
-0
0.5
-1
.5
30
0.5
-0.
5
.5
-4
30
-40
-20
0
4.0
3.0
0
2.
20
40
X mm
c. instantaneous azimuthal vorticity distribution
d. ensemble-averaged azimuthal vorticity distribution
Fig. 6. The measurement results of the dual-plane stereoscopic PIV system at Z=400mm(Z/D=1.0, Z/H=2.67) cross plane
8
PIV’01 Paper 1020
In the Z=40mm (Z/D=1.0, Z/H=2.67) cross plane, the six pairs of the large-scale streamwise vortices (Fig. 6(a))
were found to deform more seriously. More and more large-scale streamwise vortices were found to break into
smaller vortices. The adjunct streamwise vortices were found to merge with each other to form a vortex ring
structure in the lobe troughs. From the ensemble-averaged streamwise vorticity distributions shown on Fig. 6(b), the
six pairs of large-scale streamwise vortices were found to grow and expand radially. The strength of these ensembleaveraged streamwise vortices were found to decrease quite much with the maximum value of the ensemble-averaged
streamwise vorticity only about the half of that at the Z=10mm (Z/D=0.25, Z/H=0.67) cross plane.
From the instantaneous azimuthal vorticity distribution given in Fig. 6(c), it can be seen that the azimuthal
vorticity ring, which has the same geometry as the lobed nozzle trailing edge at the exit of the lobed nozzle, has
broken into many disconnected vortical tubes in this cross plane. The azimuthal tubes at the lobe troughs was found
to begin to reconnect again to form a new circular-ring-like-structure in the center of the jet flow. Same phenomena
have been revealed clearly form the planar LIF flow visualization images of the earlier work of the authors (Hu et al.
2000a,b).
McCormick and Bennett (1994) suggested that the streamwise vortices deform the azimuthal KelvinHelmholtz vortical tube into pinch-off structures due to the interaction between the streamwise vortices and
azimuthal Kelvin-Helmholtz vortices. Such pinched-off effect of the azimuthal vortex tubes can be seen very clear
and quantitatively from the ensemble-averaged azimuthal vorticity distribution given in the Fig. 6(d). The cutting of
the large azimuthal vortex ring and reconnecting of the azimuthal vortex tubes at the lobe troughs to form a new
circular-ring-liked-structure in the center of the lobed jet flow can also be seen from the ensemble-averaged
azimuthal vorticity distribution.
40
40
-1.5
-0.5
-0.
5
-0.5
.5
-0
-20
0.
5
0.5
0.5
0.5
-30
20
-40
40
0.5
0
5
-0.
0.5
-0.5
0.5
0.5
Y mm
0
-10
-0.5
-40
-20
0
X mm
20
c. instantaneous streamwise vorticity distribution
d. ensemble-averaged streamwise vorticity distribution
30
In-plane vorticity
2.5
2.5
2.
4.0
0 3.0
4.0
6.0
40
2.0
4.
0
-20
4 .0
4.0
-40
-20
0
3.0
3.0
2.0
2.5
2.
0
2.0
-30
0
4.
20
3.5
3.0
2.5
-20
5 .0
5.0
56.0.0
0
5.
-30
2.5
5
2.
-10
2.0
6.0
3.0
2.0
2.0
4.0
7.0
5.0
4.0
0
2.0
2.0
5.0
5.0
5.
0
4.
0
-10
10
2.0
4.0
.0
6.04
4.0
2.5
3.0
4.
6.0
0
5.0
5.0
7.0
5.0
6.0
0
6.0
4.
4.0
5.0
6.70.0
15.00
14.00
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
2.5
4.0
8.0
20
In-plane vorticity
4.0
4 .0
7.0
5.0
10
Y mm
6.0
Y mm
5.0
4.0
6.0
20
7.4.0
0
4.0
5.
06
.
0
30
-40
40
X mm
40
0
4.50
3.50
2.50
1.50
0.50
-0.50
-1.50
-2.50
-3.50
-4.50
0.5
-2.5
-20
-0.
5
0.5
2.
5
-0
.5
-0
1.5
-2.5
.5
-2.5
-1
.5
-1.
5
1.5
4.5
10
-0.5
5
0.
.5
2.
5
5
-1.
-0
-0.5
-3
.5
Streamwise vorticity
0.5
Y mm
-1.5
-0.5
5
10. .5
0.5
5
-2.
-3 0.5
.5 5.5
-1-.0 1.5
0.
5
5
-1.
5
4.50
3.50
2.50
1.50
0.50
-0.50
-1.50
-2.50
-3.50
-4.50
0.5
.
-1
5
-32.. -1.5 -3.5
5
5
2.5
1.
-1 .
5-0.5
-0.5.5
0
1.5
-40
0. 5
2.5
0.5
.5
-2
-0.5
-40
-0
.5
1.5
-4.5
0 .5
-30
5
-2.5
5
3.
1.5
-1.
35.
5
.5
-1
-0.5
-0.5
0.5
20
Streamwise vorticity
-1
.5
-0 .
1.5
-0.5
1.5
3.5
-4.5
0.5
1.5
0.5
1.5
2.5
-10
-20
-1
.5
-3.5
-0.5
5
2.
.5
0.5
1.5 -1.5
0.5
0.5
0
-0
0.5
-0.5
-2.5
30
-0.5
-1.
5
1.5
0 .5
10
-0.5
0.5
20
0.5
-1
.5
-0.5
-1 0.5
.5
0.5
-0.5
-0.5
5.5
-0-.0 3.5
1.5
0.5
4.5
2.5
0.5
30
-0.5
2.0
-40
40
X mm
-40
2.5
-20
0
20
40
X mm
e. instantaneous azimuthal vorticity distribution
f. ensemble-averaged azimuthal vorticity distribution
Fig. 7. The measurement results of the dual-plane stereoscopic PIV system at Z=60mm (Z/D=1.5, Z/H=4.0) cross plane
9
12.00
11.50
11.00
10.50
10.00
9.50
9.00
8.50
8.00
7.50
7.00
6.50
6.00
5.50
5.00
4.50
4.00
3.50
3.00
2.50
2.00
PIV’01 Paper 1020
As the downstream distance increased to Z=60mm (Z/D=1.5, Z/H=4.00), the six pairs of large-scale streamwise
vortices generated by the lobed nozzle could no longer be easily identified from the instantaneous streamwise
vorticity field shown in Fig. 7(a). Instead of large-scale streamwise vortices, many smaller streamwise vortices were
found in the flowfield. It means the large-scale streamwise vortices observed in the upstream cross planes have
broken down into many smaller streamwise vortices. It should be mentioned that the maximum vorticity of these
smaller streamwise vortices are found to be almost at the same level as their parent streamwise vortices in the
upstream cross planes.
From the ensemble-averaged streamwise vorticity distribution shown in Fig. 7(b), it can be seen that the largescale streamwise vortices revealed in the ensemble-averaged streamwise vorticity distributions of upstream cross
planes were also found to break down into smaller vortices. The strength of these ensemble-averaged streamwise
vortices decayed substantially, and the maximum value of the ensemble-averaged streamwise vorticity was found to
be only about one fourth of that at Z=10mm (Z/D=0.25, Z/H=0.67) cross plane.
The azimuthal vortex ring, which has the same geometry as the lobed nozzle trailing edge at the nozzle exit, was
found to break into many disconnected vortical tubes completely in this cross plane. A new circular-ring-likestructure due to the reconnecting of the azimuthal vortex tubes at the lobe troughs can be found in the center of the
jet flow, which is similar to the circlar azimuthal vortex ring in a circular jet flow. The circular-ring-like-structure in
the central of the jet flow can been seen more clear from the ensemble-averaged azimuthal vorticity distribution,
while the azimuthal vortex tubes corresponding to the lobed peaks were found to form six “crescents” in this cross
plane. Due to the intensive mixing between the core jet and ambient flow, the strength of the azimuthal vortices has
dissipated very much. The maximum value of the ensemble-averaged azimuthal vorticity was found to be only about
one fourth of that at the exit of the lobed nozzle.
40
40
1.5
1
3.5 .5
0.5
-2
.5
0.5
0.
5
1.5
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1.5
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5
Y mm
-1.5
.5
-0
.5
.5
-0
--10..5
5
5
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5
3.
0.5
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0.5
0.
5
5
1.
5
0
-30
.5
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-0
.5
.5
-0
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0
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3.50
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0.50
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-4.50
.5
5
5
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-0
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Y mm
Streamwise vorticity
-20
-0.5
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-40
5
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-30
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.
-0
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10.5.
5
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.5
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-20
2.5
5
-2.5
0.55
.
-1
0.5
-0.5
5 .
-1. -2
5
1.
-10
.5
-0
0.5
4.50
3.50
2.50
1.50
0.50
-0.50
-1.50
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-3.50
-4.50
5
0.
.55
20.
1.5
5
-4.
.5
-2.5
5
-0.
50
20
Streamwise vorticity
-0.
5
1.5
0.5
-0.5
.5
-3
0
-1.5
5
0.
0.
0.5
10
2.5
.5
-2
-1.5
-2.5
0.5
30
-0.5
20
0.
15.
5
2.5
-0.5
0.5
-1.5
1.5
-1.5
0.5
-0.5
2.5
0.5
30
2.5
1.5
20
-40
40
-40
-20
0
X mm
20
40
X mm
a. instantaneous streamwise vorticity distribution
b. ensemble-averaged streamwise vorticity distribution
40
40
30
30
2.0
12.00
11.50
11.00
10.50
10.00
9.50
9.00
8.50
8.00
7.50
7.00
6.50
6.00
5.50
5.00
4.50
4.00
3.50
3.00
2.50
2.00
4.0
4.0
4.
0
4.0
0
4.
4.
0
4.0
Y mm
2.5
-20
-30
0
6.
-40
2.0
2.0
-30
2.0
6.0
-20
-10
2.
5
7.0
12.0
4.0
8.0
5.0
2.5
0
3.0
0
5.
.0
05
5.
4.0
2.
0
10
5
2.
4.0
6.0 4
.06.0
0
65.
-10
15.00
14.00
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
2.0
5.0
4.0
Y mm
6.
0
5.0
6.0
4.0
0
20
In-plane vorticity
0
2.
9.0
10
5.06.0
8.0
5.0 74.0
.0
4.0
4.0 5.0
20
5.0
4.
0
In-plane vorticity
-40
-20
0
20
-40
40
X mm
-40
-20
0
20
40
X mm
c. instantaneous azimuthal vorticity distribution
d. ensemble-averaged azimuthal vorticity distribution
Fig. 8. The measurement results of the dual-plane stereoscopic PIV system at Z=80mm (Z/D=2.0, Z/H=5.33) cross plane
10
PIV’01 Paper 1020
As the downstream distance increases to Z=80mm (Z/D=2.0, Z/H=5.33), the lobed jet mixing flow was found to
be more and more turbulent. The smaller but not weaker streamwise vortices originated from the breakdown of the
large-scale streamwise vorticity generated by the lobed nozzle almost fully filled the measurement window (Fig. 8
(a)). Since these small-scale streamwise vortices is so unsteady and they appear in the flow field very randomly,
only very vague vortical structures can be identified from the ensemble-averaged streamwise vorticity distribution.
The ensemble-averaged streamwise vorticity distribution shown in Fig. 8(b) revealed that the ensemble-averaged
streamwise vortices have been dissipated so seriously that their stength is only about one tenth of that in Z=10mm
upstream cross plane.
Due to the intensive mixing between the core jet flow and ambient flow, the azimuthal vortices also dissipated
substantially. The six “crescents” formed by the azimuthal vortex tubes at the lobed peak regions almost disappeared
in the flow field, and only the circular-ring-like-structure in the center of the jet flow can be identified from the
ensemble-averaged azimuthal vorticity distribution with its strength dissipated substantially.
As the downstream distance increased to Z/D=3.0 (Z/H=8.0) (Fig.9), so many small-scale streamwise vortices
were found to appear in the lobed jet mixing flow that they almost fully filled the measurement window. The
maximum vorticity of these smaller instantaneous streamwise vortices was found to be still at the same level of their
parent streamwise vortices in upstream cross planes. Due to the serious dissipation, almost no apprent streamwise
vortices can be identified from the ensemble-averaged streamwise vorticty distribution any more.Up to this
downstream cross-palne, the azimuthal vortices also dissipated so seriously that even the circular-ring-like structure
at the center of the jet flow has been torn open.
40
40
0.5
1.5
0.5
0.5
0
0.
5
0
5
0.
-20
-30
.5
-1
0.
5
-20
Y mm
-0.5
-1
.5
0.5
-1
.5
.5
-0
-40
0.5
20
0.5
-0.5
-40
-0.5
4.50
3.50
2.50
1.50
0.50
-0.50
-1.50
-2.50
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-4.50
-10
-0.5
-0.55
0.
0.5
Streamwise vorticity
10
-0.5
0 .5
-2.5
2.5
0.5
-0.5
0.
5
0.5
-0.
5
-0 .
5
0.5
-0.5 0.5
-
12.5.5
5
-3 .
-30
0.
5
1.5
-0.5
-1.5 -0.5
0.5
-20
5
0. -1.5
-0.5
0.5
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-0.
5
0.5
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0.5
4.50
3.50
2.50
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0.50
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-4.50
-0.5
.5
1
-0.5
Y mm
0
5
-2.
-0.5
0.5
0.5
.5
-2
1.5
20
Streamwise vorticity
0.5
0.5
5
-0.
1.52
.5
-0.
.5 5
-1
10
5
0.
-0.5
-0.
5
30
.5
-00.5
20
-0.5
5
- 0.
.5
-0
0.
5
-1.5
0.5
1.5
30
-40
40
-40
-20
0
X mm
20
40
X mm
a. instantaneous streamwise vorticity distribution
b. ensemble-averaged streamwise vorticity distribution
40
40
30
30
In-plane vorticity
6.0
4.0
-20
2.5
-10
2.0
2.0
-20
-30
4.0
-30
0
2.5
-10
2.0
4.0
4.0
5.0
5.0
4.0
2.0
10
Y mm
6.0
0
15.00
14.00
13.00
12.00
11.00
10.00
9.00
8.00
7.00
6.00
5.00
4.00
4.
0
10
Y mm
20
In-plane vorticity
2.5
20
12.00
11.50
11.00
10.50
10.00
9.50
9.00
8.50
8.00
7.50
7.00
6.50
6.00
5.50
5.00
4.50
4.00
3.50
3.00
2.50
2.00
-40
-40
-20
0
20
-40
40
X mm
-40
-20
0
20
40
X mm
c. instantaneous azimuthal vorticity distribution
d. ensemble-averaged azimuthal vorticity distribution
Fig. 9. The measurement results of the dual-plane stereoscopic PIV system at Z=120mm (Z/D=3.0, Z/H=8.0) cross plane
11
PIV’01 Paper 1020
5
streamwise vorticity
azimuthal vorticity
10
4
3
streamwise vorticity
2
5
azimuthal vorticity
1
0
Z/H
Max (ϖstreamwise)
Max(ϖazimuthal)
15
0
0
Z/D 0
1
2
3
4
5
1
6
2
7
8
3
9
10
4
Fig.10. The decay of the ensemble-averaged streamwise vorticity and azimuthal vorticity in the lobed jet mixing flow
From the above instantaneous streamwise distributions in different downstream cross planes, it can be seen that
as the downstream distance increases, the size of the instantaneous streamwise vortices in the lobed jet mixing flow
became smaller and smaller. It means the large-scale streamwise vorticity generated by the lobed nozzle break into
smaller vortices as they travel downstream. However, the maximum vorticity values of the smaller vortices were
found to be almost at the same level as their parent streamwise vortices. These results suggest that the dissipation of
the large-scale streamwise vortices generated by the corrugated trailing edge of the lobed nozzle did not happen
abruptly, but rather appeared to be a gradual process. The large streamwise vortices were found to break down into
many smaller, but not weaker streamwise vortices as the downstream distance increasing. Thus, besides the mixing
enhancement at large scale, mixing at a finer scale could also be achieved in the lobed jet mixing flow. The result,
therefore, agrees well with those obtained by Milam et al. (1997)
The ensemble-averaged streamwise vorticity distribution can be used to indicate the overall effect of the special
geometry of the lobed nozzle on the mixing processes in the lobed jet mixing flows. The special geometry of the
lobed nozzle results in the generation of large-scale ensemble-averaged streamwise vortices in the lobed jet mixing
flow. The large-scale ensemble-averaged streamwise vortices revealed in the ensemble-averaged streamwise
vorticity distributions were found to grow up and expand radially within the first diameter, which may correspond to
the streamwise vortex formation and intensification steps suggested by Werle et. al. (1987)and Eckerle et al. (1990)
(Their LDV measurement results only revealed the ensemble-averaged streamwise vortices in a planar lobed mixing
flow). The large-scale ensemble-averaged streamwise vortices were found to break down into smaller vortices at
further downstream regions. Figure 10 gives the decay of the maximum value of the ensemble-averaged streamwise
vorticity in the lobed jet flow quantitatively. From the figure, it can be seen that at the first diameter of the test
nozzle, the ensemble-averaged streamwise vorticity decayed very rapidly. At downstream region of Z/D>1.0
(Z/D>2.67), the large-scale ensemble-averaged streamwise vortices were found to break down into many smaller
vortices, then the decay rate of the ensemble-averaged streamwise vorticity slows down. Further downstream
(Z/D>3.0, Z/H>8.0), the ensemble-averaged streamwise vorticity dissipated so seriously that the strength of the
streamwise vortices became about one tenth of that at lobed nozzle exit. This may indicate that the overall effect of
the special geometry of the lobed nozzle on the enhanced mixing process in the lobed jet flow has almost
disappeared at this downstream location.
For the azimuthal vortices in the lobed jet mixing flow, they were generated at the interface of the mixing
streams due to the Kelvin-Helmholtz instability existed at any shear layer. Therefore, the azimuthal vortex ring at
the nozzle exit has the same geometry as the lobed nozzle trailing edge. Due to the interaction between the
streamwise vortices, the azimuthal vortex ring deformed into pinched-off structures first, then broke down into
disconnected substructures as they travel downstream. The broken azimuthal vortex tube pieces at the lobed troughs
were found to reconnect with each other to form a new circular-ring-like-structure at the center of the lobed jet flow,
while the azimuthal vortex tubes corresponding to the lobed peaks were found to form six “crescents” structures.
The six “crescents” structures were found to dissipated out further downstream,, and only very indistinct circularring-like-structure can be found at the central of the jet mixing flow.
12
PIV’01 Paper 1020
The decay of the maximum value of the ensemble-averaged azimuthal vorticity in the lobed jet mixing flow is
also given in the Fig. 10. It should be noted that the decay profile of the azimuthal vorticity is very similar to that of
the streamwise vorticity. The ensemble-averaged azimuthal vorticity decay very rapidly winthin the first one
diameter of the lobe nozzle, then turns to be a more moderate rate further downstream. This may be explained by
that within the first one diameter of the test nozzle (Z/D<1.0, Z/H<2.67), due to the stirring effect of the large-scale
streamwise vortices revealed in the ensemble-averaged streamwise vorticity distributions, the core jet flow and
ambient flow mixed intensively. The velocity of the core jet flow decays very rapidly. Weaker and weaker shear
layer (lower velocity ratio) is expected in the lobed jet mixing flow as the downstream distance increases. Therefore,
the magnitude of the azimuthal vorticty decays very quickly within the first diamter of the lobed nozzle. In the
downstream region of 1.0<Z/D<2.0, the large-scale streamwise vortices were found to breake down into smaller
vortices, the strength of large-scale streamwise vortices generated by the special geometry of the lobed nozzle were
found to be dissipated very seriously, i.e, the stirring effect of the ensemble-averaged streamwise vortices weakened.
The velocity decay of the core jet flow slows down, therefore, the decay rate of the azimuthal vorticity is also found
to slow down. The ensemble-averaged streamwise vorticity dissipated so seriously further downstream that they
almost can not be indentified in the flow field anymore, and the enhancement mixing due to the stiring effect of
large-scale streamwise vortices has be finished, the mixing between the core jet flow and ambinet flow is expected
to ocurr at the same gradient-type mechanism as that for a circular jet flow, therefore, the azimuthal vorticity decay
very slowly and linearly as that in a circular jet flow.
4
Conclusions
In the present study, the streamwise vorticity and azimuthal vorticity distributions in a lobed jet mixing flow
were measured simultaneously by using a novel dual-plane stereoscoipic PIV system. The evolution and interaction
characteristics of various vortical structures in the lobed jet mixing flow were analyzed based on the simultaneous
vorticity measurement results of the dula-plane stereoscoipic PIV system. From the instantaneous streamwise
vorticity distributions of the lobed jet mixing flow, it can be seen that the large-scale streamwise vortices generated
by the corrugated trailing edge of the lobed nozzle break into smaller, but not weaker streamwise vortices gradually
as they travel downstream. It is proposed as the reason that a lobed nozzle can enhance both the large-scale mixing
and small-scale mixing in flow field as reported in previous studies. The overall effect of the lobed nozzle on mixing
process in the lobed jet flow was evaluated by analyzing the ensemble-averaged streamwise vorticity distributions.
The ensemble-averaged streamwise vortices in the lobed jet flow were found to expand radially within the first
diameter downstream, then break down into smaller and weaker vortice in the following region, as has been called
as the formation, intensification and breakdown processes by other researchers. The strength of the ensembleaveraged streamwise vorticity was found to decay very rapidly over the first one diameter of lobed nozzle, then
decay at a more moderate rate further downstream. The azimuthal vortex ring was found to have the same geometry
as the lobed nozzle trailing edge at the nozzle exit. Due to the interaction with the streamwise vortices, the azimuthal
vortex ring deformed into pinched-off structures first, then broke down into disconnected substructures as they
travel downstream. The broken azimuthal vortex tube pieces at the lobed troughs were found to reconnect with each
other to form a new circular-ring-like-structure in the center of the lobed jet flow, which is similar to the circularazimuthal-vortex-ring in a circular jet flow field. The azimuthal vortex tubes corresponding to the projections of the
lobe peaks were found to form six “crescents” structures. The six “crescents” structures were found to dissipated out
further downstream, and only very indistinct circular-ring-like-structure can be found in the center of the jet mixing
flow. The decay of the azimuthal vorticity in the lobed jet flow is found to be very similar to that of the streamwise
vorticity. The azimuthal vorticity decay very rapidly within the first one diameter of the lobe nozzle, then turns to be
a more moderate rate in the downstream region of 1.0<Z/D<2.0 (2.67>Z/H>5.33). The azimuthal vorticity decay
very slowly and linearly in the Z/D>2.0 downstream region,. These results indicate that the enhanced mixing
process caused by the special geometry of the lobed nozzle is almost finished within the first two diameters of the
lobed nozzle (first six lobe heights). The mixing between the core jet flow and ambient flow in the lobed jet mixing
flow further downstream will occur by the same gradient-type mechanism as that in a circular jet flow.
5
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14