Experiments in Fluids [Suppl.] S141±S157 Ó Springer-Verlag 2000
Particle image velocimetry and planar laser-induced fluorescence
measurements on lobed jet mixing flows
H. Hu, T. Kobayashi, T. Saga, S. Segawa, N. Taniguchi
Abstract An experimental investigation of the vortical and
turbulent structures in lobed jet mixing ¯ows was conducted. The techniques of planar laser-induced ¯uorescence (PLIF) and particle image velocimetry (PIV) were
used to accomplish ¯ow visualisation and velocity ®led
measurements of the lobed jet mixing ¯ows. Compared
with a conventional circular jet ¯ow, the lobed jet mixing
¯ows were found to have a shorter laminar region, a
smaller scale of spanwise Kelvin±Helmholtz vortices,
quicker transition to turbulence and earlier appearance of
small-scale vortical and turbulent structures. The intensive
mixing of the core jet ¯ow with ambient ¯ow was found to
concentrate within the ®rst two nozzle diameters in the
lobed jet mixing ¯ow. More rapid growth of the shear layer
at the near ®eld and quicker decay of the central line
velocity were also found in the lobed jet mixing ¯ow. All
these indicated a better mixing enhancement performance
of the lobed nozzle compared with the conventional circular nozzle in the near-®eld region.
Based on the PLIF and PIV results, two aspects of the
mechanism of mixing enhancement in a lobed jet mixing
¯ow were suggested. One is that a lobed nozzle can cause
big azimuthal perturbations in the jet ¯ow due to its
special geometry, and the streamwise vortices produced by
the lobed nozzle can enhanced the azimuthal perturbations. The ``cut and connect'' process of the large-scale
spanwise Kelvin±Helmholtz vortex rings was accelerated.
This is responsible for the avalanche of three-dimensional
and smaller-scale motions and the generation of high
turbulence. Another is that the ``stretch effect'' of
streamwise vortices generated by the lobed nozzle on the
spanwise Kelvin±Helmholtz vortical rings reduced the
scale of the spanwise Kelvin±Helmholtz vortices, which
also results in the creation of much small-scale intense
turbulence and enhances the mixing of the core jet ¯ow
with the ambient ¯ow.
H. Hu (&)1, T. Kobayashi, T. Saga, S. Segawa, N. Taniguchi
Institute of Industrial Science
University of Tokyo, 7-22-1 Roppongi
Minato-Ku, Tokyo 106-8558, Japan
Present address:
1
Turbulent Mixing and Unsteady Aerodynamics Laboratory
A22 Research Complex Engineering
Michigan State University
East Lansing, 48824, MI, USA
e-mail: huhui@egr.msu.edu
1
Introduction
A lobed nozzle, which consists of a splitter plate with a
convoluted trailing edge, is a promising ¯uid mechanic
device for ef®cient mixing of two co-¯ow streams with
different velocities, temperatures and/or species. This has
been paid a great deal of attention by many researchers in
recent years and has also been widely applied to aerospace
engineering. For example, in commercial aero-engines,
lobed nozzles have been used to reduce take-off jet noise
and speci®c fuel consumption (SFC) (Tillman and Presz
1993; Presz et al. 1994; Hu et al. 1996). In order to reduce
the infrared radiation signals of military aircraft to improve
their survivability in modern war, lobed nozzles have also
been used to enhance the mixing process of the high
temperature and high speed gas plume from air-engines
with ambient cold air (Power et al. 1994). More recently,
lobed nozzles have also emerged as an attractive approach
to enhancing mixing between fuel and air in combustion
chambers to improve the ef®ciency of combustion and
reduce the formation of pollutants (Smith et al. 1997).
In connection with the mechanism of the mixing
enhancement in lobed jet mixing ¯ow, Peterson (1982) was
the ®rst to measure the velocity and turbulent characteristics downstream of a lobed nozzle/mixer systematically
by using laser Doppler velocimetry (LDV). He concluded
that a lobed nozzle/mixer could cause large-scale streamwise vortices shed at the trailing edge of lobes. So, the
downstream of the ¯ow ®eld is embedded with many
arrays of large-scale streamwise vortices of alternating
sign, which are believed to be primarily responsible for the
enhanced mixing.
Much of the later work on lobed nozzles concentrated
on discovering the underlying physics of the lobed mixing
process. The work of Werle et al. (1987) and Eckerle et al.
(1990) suggested that the formation process of the largescale streamwise vortices in a lobed mixing ¯ow is an
inviscid one, which was proposed to take in three basic
steps: vortices form, intensify and rapidly break down into
small-scale turbulent structures.
Elliott et al. (1992) found that both the streamwise
vortices shed from lobed trailing edge and the increased
initial interfacial area associated with the lobe geometry
are signi®cant for increasing the mixing compared with
that occurring within conventional ¯at plate splitter. At a
velocity ratio close to 1.0, the increased mixing is due
mainly to the increased contact area, whereas the
streamwise vortices have a larger role at a velocity ratio of
2.0, and its importance rises as the velocity ratio increases.
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The study by McCormick and Bennett (1994) revealed
more details for the ¯ow patterns downstream of a lobed
mixer. Based on pulsed-laser sheet ¯ow visualization with
smoke and three-dimensional velocity measurements with
a hot ®lm anemometer (HFA), they suggested that the
interaction of Kelvin±Helmholtz (spanwise) vortices with
the streamwise vortices produces the high levels of mixing.
The streamwise vortices deform the spanwise vortices into
pinch-off structures and increase the stirring effect in the
mixing ¯ow. These result in the creation of intense smallscale turbulence and mixing.
In the work of the Belovich and Samimy (1997), a
summary of the results of the previous research showed
that the mixing process in a lobed mixing ¯ow is controlled by three primary elements. The ®rst is the
streamwise vortices generated in the mixing ¯ow due to
the lobed shape. The second is the increase in interfacial
area between the two ¯ows due to the special geometry of
the lobed structure, and the third is the Brown±Roshikotype structures occurring in any shear layer due to the
Kelvin±Helmholtz instability.
Although many important results have been obtained as
a result of these previous investigations, much work is still
needed to understand the ¯uid dynamic mechanism of
mixing enhancement in a lobed jet mixing ¯ow more
clearly. Especially in relation to research on the vortical
and turbulent structure changes in a lobed jet mixing ¯ow
compared with a conventional circular jet ¯ow, and the
mechanism of how the large-scale streamwise vortices
generated by a lobed nozzle enhance the jet ¯ow mixing
process. Meanwhile, most of the previous research was
conducted by using a Pitot probe, LDV or HFA, with
which it is very hard to reveal the vortical and turbulent
structures in a jet mixing ¯ow instantaneously and globally
due to the limitation of those experimental techniques. In
the present study, both planar laser-induced ¯uorescence
(PLIF) and particle image velocimetry (PIV) techniques
Fig. 1. The schematic of the experimental set-up
were used to research the lobed jet mixing ¯ow instantaneously and globally. By using the directly perceived ¯ow
visualization results and the quantitative velocity vector
®elds, the evolution and interaction characteristics of the
spanwise Kelvin±Helmholtz vortices and streamwise vortices in the lobed jet mixing ¯ow were studied. The physics
of the jet mixing ¯ow and mechanism of the mixing
enhancement in a lobed jet mixing ¯ow were also discussed based on the PLIF and PIV measurement results.
2
Experimental set-up
Figure 1 shows schematically the experimental set-up used
in the present research. The test nozzles (a lobed nozzle
and a baseline circular nozzle) were ®xed in the middle of
a water tank (600 mm ´ 600 mm ´ 1000 mm). Fluorescent dye (Rhodamine B) for PLIF and PIV tracers (polystyrene particles d = 20±30 lm, density 1.02) was
premixed with water in a jet supply tank, and the jet ¯ow
was supplied by a pump. The ¯ow rate of the jet ¯ow,
which was used to calculate the representative velocity and
Reynolds numbers, was measured by a ¯ow meter. A
cylindrical plenum chamber was installed upstream of the
test nozzles to insure that the turbulent levels of the core
jet ¯ows at the exit of test nozzles were less than 3%.
The pulsed laser sheet (thickness about 1.0 mm, duration of the pulsed illumination 6 ns) to illuminate the ¯ow
®eld for PLIF visualization and PIV measurement was
supplied by a double-pulsed Nd:YAG laser at a frequency
of 10 Hz and power of 200 mJ/pulse. For the PIV
measurement, the time interval between the two pulses can
be adjustable, which is about 2±5 ms for the present study.
1 K by 1 K CCD cameras (PIVCAM 10±30) were used to
capture the PLIF and PIV images. The double-pulsed
Nd:YAG laser and the CCD camera were connected to a
work station (host computer, RAM 1,024 MB, HD 20 GB)
via a synchronizer (TSI Laserpulse Synchronizer), which
controlled the timing of laser illumination and CCD
camera image acquisition.
Rhodamine B was used as the ¯uorescent dye in the
present research. The induced ¯uorescent light for PLIF
visualization and the scattered laser light for PIV
measurement were separated from each other by the
installation of high pass and low pass optical ®lters at
the head of the CCD cameras. A low concentration
Rhodamine B solution (0.5 mg/l) was used to insure that
the strength of ¯uorescent light was linear with the
concentration of the ¯uorescent dye and that the effect
of laser light attenuation was negligible as the laser light
sheet propagated through the ¯ow (Hu et al. 1999).
Rather than tracking individual particles, the crosscorrelation method (Willert and Gharib 1991) was used in
the present study for PIV image processing to obtain the
averaged displacement of the ensemble particles. The images were divided into 32 ´ 32 pixel interrogation windows, and 50% overlap grids were employed. The spatial
resolution of the PIV images for the present research case
is about 120 lm/pixel. The post-processing procedures,
including sub-pixel interpolation (Hu et al. 1998) and
spurious velocity deletion (Westerweel 1994) were used to
improve the accuracy of the PIV result.
Figure 2 shows the two nozzles used in the present
study: a baseline circular nozzle and a lobed nozzle with
six lobes. The height of the lobes is 15 mm (i.e.,
H = 15 mm) and the inner and outer lobe penetration
angles are about 22° and 14° respectively. The equivalent
diameters of the two nozzles at the exit are the same, i.e.
D = 40 mm. In the present study, the core jet velocities
(U0) were set at about 0.1 m/s and 0.2 m/s. The Reynolds
Fig. 2a±c. The test nozzles and three studied axial slices.
a Circular nozzle; b Lobed nozzle; c Three axial slices for the
lobed jet mixing ¯ow
numbers of the jet ¯ows, based on the nozzle exit diameter
and the core jet velocities, were about 3,000 and 6,000.
Compared with a circular jet ¯ow, the changes in the
turbulent and vortical structures in the lobed jet mixing
¯ow were investigated ®rst in three axial slices: the lobe
trough slice, the lobe peak slice and the lobe side slice
(Fig. 2c). Then, PLIF visualization and PIV measurements
were conducted at several cross sections for the lobed jet
mixing ¯ows and circular jet ¯ows.
For the PIV measurement results, the mean velocity
®elds, time-averaged streamwise vorticity distributions,
turbulent kinetic energy ®elds and in-plane turbulence
intensity distributions were used to analyze the mixing
characteristics of the lobed mixing ¯ows and circular jet
¯ows. The mean values were calculated based on the
average of 400 frames of PIV instantaneous velocity vector
®elds, which were obtained at a frequency of 10 Hz. The
uncertainty of the PIV instantaneous measurement results
in the present study should be less than 2%. The deviations
of the ensemble averaged values, such as turbulence energy, turbulent intensity and mean vorticity, based on the
400 frames of instantaneous PIV velocity ®elds for the
present study should be about 5%.
3
Results and discussion
3.1
In the axial slices
Figure 3 shows the PLIF visualization and PIV measurement results of a conventional circular jet ¯ow at the
Reynolds number of 6,000. For the circular jet ¯ow, a
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Fig. 3a±d. PLIF visualization and PIV measurement result in the circular jet mixing ¯ow (Re = 6,000). a PLIF visualization; b PIV instantaneous result; c mean velocity distribution;
d tubulent kinetic energy distribution
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laminar region downstream of the circular nozzle can be
seen clearly in the ¯ow ®eld. At the end of the laminar
region (X=D ˆ 1:5 2:0), spanwise Kelvin±Helmholtz
vortex rings were found to roll up. Pairing and combining
of these spanwise vortex rings and the jet ¯ow transition to
turbulence were found to conduct downstream
(X=D ˆ 4 6), much of which is out of the CCD camera
view of the present study. Neither small-scale vortices nor
turbulence structures can be found in the investigated
region (X=D < 3:0). The PLIF visualization result of the
circular jet ¯ow obtained in the present study is qualitatively similar to the result reported by Liepmann and
Gharib (1992).
Figure 3c and d shows the mean velocity distribution
and turbulent kinetic energy distribution in the circular jet
¯ow. In the present paper, the turbulent kinetic energy is
de®ned as:
K ˆ 12…u02 ‡ 2v02 †=U02
0
0
1†
as v and w have been assumed to be equivalent.
From the ®gures, it can be seen that the circular jet ¯ow
began to expand just after the spanwise Kelvin±Helmholtz
vortices rolled up downstream of X=D > 1:5. A potential
core region (the regions where the turbulent kinetic energy
value is less than 0.005 in Fig. 3d in the center of the jet
¯ow extended downstream of X=D > 3:0 for the circular
jet ¯ow, while the intensive mixing regions (the regions
where the turbulent kinetic energy values are greater than
0.025 in Fig. 3d) were found to appear downstream of
X=D > 2:0, and extended much farther downstream.
Figure 4 shows the PLIF visualization and PIV measurement results of the lobed jet mixing ¯ow in the axial
slice passing lobe trough. Compared with the circular jet
¯ow, the laminar region downstream of the lobed nozzle
trailing edge became much shorter in this axial slice, and
the spanwise Kelvin±Helmholtz vortices were found to roll
up almost from the trailing edge of the lobed nozzle. It is
also found that the sizes of these spanwise Kelvin±
Helmholtz vortices are much smaller compared with that
in the circular jet ¯ow. The spanwise Kelvin±Helmholtz
vortices increased their wavelength (due to vortex pairing)
and broke down, then the jet ¯ow transit to turbulence at
the downstream of X=D ˆ 1:0 with many small-scale
vortical and turbulent structures appeared in the ¯ow ®eld.
These results are consistent with the results observed by
McCormick and Bennett (1994) in a two-dimensional
lobed mixing layer.
From the mean velocity and turbulent kinetic energy
distribution at this axial slice (Fig. 4c and d), it can be seen
that the lobed jet mixing ¯ow began to expand almost from
the trailing edge of the lobed nozzle. The expansion rate
of the lobe jet mixing ¯ow was found to be bigger than that
in the circular jet ¯ow (Fig. 3c and d) at the ®rst two
diameters of the lobed nozzle. Unlike that in the circular jet
¯ow, the intensive mixing regions (the regions where the
turbulent kinetic energy values are greater than 0.025 in
Fig. 4d) were found to be concentrated downstream of
X=D < 2:0 in the lobe jet mixing ¯ow. The potential core
region (the region where turbulent kinetic energy value is
less than 0.005) at the center of the lobed jet mixing ¯ow was
much smaller and shorter than that in the circular jet ¯ow.
Figure 5 shows the PLIF ¯ow visualization and PIV
measurement results of the lobed jet mixing ¯ow in the
axial slice passing the lobe peak. The laminar region at the
exit of the lobed nozzle in this axial slice was not a straight
cylinder like that in the circular jet, and looked like an
expansive cut-off cone along the lobe peak instead.
Compared with that in the lobe trough slice, the laminar
region in the lobe peak axial slice was slightly longer
(X=D ˆ 0:5), but still much shorter than that in the circular jet ¯ow. This may be caused by the different thickness of the boundary layer at the exit of the lobed nozzle.
[The diffusion of the ¯ow at lobe peak passages may result
in the accumulation of the boundary layer, which was
veri®ed by the work of Brink and Foss (1993). The thicker
boundary layer at the lobe peak needs a longer streamwise
distance to roll-up the Kelvin±Helmholtz vortices (Hussain and Husain 1989)]. Downstream of X=D > 1:0, the
lobed jet ¯ow was found to transit to turbulence, and
many small-scale turbulent and vortical structures appeared in the ¯ow ®eld. As in the lobe trough slice discussed above, most intensive mixing regions were found
to be concentrated in the ®rst two diameters of the lobed
nozzle in the lobe peak slice. The potential core region at
the center of the lobed jet mixing ¯ow in this axial slice
was also much smaller and shorter than that in the circular jet ¯ow.
Figure 6 shows the PLIF ¯ow visualization and PIV
measurement results in the axial slice passing the lobe side
of the lobed jet mixing ¯ow. Some streak ¯ow structures
can be seen clearly downstream of the lobe structure
trailing edge in this axial slice. These streak structures
were the Kelvin±Helmholtz vortical tubes shed periodically
from the lobe training edge, which was observed and called
``normal vortex'' by McCormick and Bennett (1994).
Downstream of the location at about X=D < 1:0, the lobed
jet mixing ¯ow was found to transit to turbulence, and
small-scale vortical and turbulent structures were found to
appear in the ¯ow ®eld.
3.2
In the cross planes
Figure 7 shows the PLIF ¯ow visualization results of the
lobed jet mixing ¯ow in six cross planes. At the location of
X=D ˆ 0:25 (X=H ˆ 0:7, Fig. 7a), the existence of the
streamwise vortices in the form of six petal ``mushrooms''
at the lobe peaks can be seen clearly. The spanwise Kelvin±Helmholtz vortices rolled up earlier at the lobe
troughs were found to be six ``crescents'' at this cross
section.
As the streamwise distance increased to X=D ˆ 0:5
(X=H ˆ 1:3), the ``mushrooms'' at the lobe peak grew
(Fig. 7b), which indicated the intensi®cation of the
streamwise vortices generated by the lobed nozzle. As
the streamwise vortices distance increased to X=D ˆ 0:75
(X=H ˆ 2:0), the streamwise vortices generated by the
lobed nozzle in the form of a ``mushroom'' structure
kept on intensifying. Six new counter-rotating streamwise vortex pairs can be found at lobe troughs. Although
the existence of the horseshoe vortex structures in the
lobed mixing ¯ow had been suggested by Paterson (1982)
two decades ago, this is the best known visualization
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Fig. 4a±d. PLIF visualization and PIV measurement results of lobed jet mixing ¯ow in the lobe trough slice (Re = 6,000). a PLIF visualization; b PIV instantaneous result; c mean
velocity distribution; d tubulent kinetic energy distribution
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Fig. 5a±d. PLIF visualization and PIV measurement results of the lobed jet mixing ¯ow in the lobe peak slice (Re = 6,000). a PLIF visualization; b PIV instantaneous result; c mean
velocity distribution; d tubulent kinetic energy distribution
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Fig. 6a±d. PLIF visualization and PIV measurement results of the lobed jet mixing ¯ow in the lobe side slice (Re = 6,000). a PLIF visualization; b PIV instantaneous result; c mean
velocity distribution; d tubulent kinetic energy distribution
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Fig. 7a±f. PLIF visualization of the lobed jet mixing ¯ow in several cross planes (Re = 3,000). a X/D ˆ 0.25 (X/H ˆ 0.7); b X/D ˆ 0.5
(X/H ˆ 1.3); c X/D ˆ 0.75 (X/H ˆ 2.0); d X/D ˆ 1.0 (X/H ˆ 2.7); e X/D ˆ 1.5 (X/H ˆ 4.0); f X/D ˆ 2.0 (X/H ˆ 5.3)
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result and provides unquestionable evidence of their
existence.
At the location of X=D ˆ 1:0 (X=H ˆ 2:7, Fig. 7d), some
small-scale vortical and turbulent structures were found to
appear in the ¯ow, and the interaction between the
streamwise vortices and spanwise Kelvin±Helmholtz vortices made adjacent ``mushrooms'' merge with each other,
which may indicate a process whereby the streamwise
vortices deform the spanwise Kelvin±Helmholtz vortical
tube into pinch-off structures, suggested by McCormick
and Bennett (1993). At the location of X=D ˆ 1:5
(X=H ˆ 4:0, Fig. 7e) and X=D ˆ 2:0 (X=H ˆ 5:3, Fig. 7f),
the ``mushroom''-shaped structures almost disappeared
and the ¯ow was almost fully ®lled with small-scale turbulent and vortical structures.
However, for the circular jet mixing ¯ow at the same
Reynolds number level, the jet mixing ¯ow is still in this
laminar region at the location of X=D ˆ 1:0 (Fig. 8a). The
spanwise Kelvin±Helmholtz vortices began to roll up at the
location of X=D ˆ 2:0 (Fig. 8b). At the downstream location of X=D > 3:0 (Fig. 8c), streamwise vortices due to the
azimuthal instability (Liepmann and Gharib 1992) were
found to appear in the ¯ow ®eld. However, neither smallscale turbulent structures nor small-scale vortices can be
found in the ¯ow ®eld at these cross planes for the circular
jet ¯ow.
Figures 9±12 give the PIV measurement results at
four typical cross planes in the lobed jet mixing ¯ow. As
in the PLIF visualization results, the large-scale
streamwise vortices generated by the special geometry of
the lobe nozzle can be seen clearly both from the instantaneous velocity ®eld and the mean velocity ®eld at
the cross plane of X/D = 0.5 (X/H = 1.3, Fig. 9a
and b). Figure 9c and d shows the in-plane turbulence distribution and streamwise vorticity distribution
in this cross plane. In the present paper, in-plane
turbulence intensity and streamwise vorticity are
de®ned as:
Fig. 8a±c. PLIF visualization of the circular jet mixing ¯ow in
several cross planes (Re = 3,000). a X/D ˆ 1.0; b X/D ˆ 2.0;
c X/D ˆ 3.0
p
v02 ‡ w02 †=U0
D ow ov
-x ˆ
U0 oy oz
Tˆ
2†
3†
From Fig. 9c, it can be seen that the contours of in-plane
turbulence intensity were found to be in the same geometry as the lobed nozzle. Intensive mixing regions were
concentrated downstream of the lobe troughs, which may
be caused by the earlier rolling-up of the spanwise Kelvin±
Helmholtz vortices at the lobe troughs. From the
streamwise vorticity distribution shown in Fig. 9d, it can
be seen that each lobe can generate a pair of large-scale
streamwise vortices (the solid line indicate positive and
dashed line indicate negative). The sizes of the streamwise
vortices are equal to the height of the lobe structures,
which is consistent with the results of the previous research (Paterson 1982).
As the streamwise distance increased to X/D = 1.0 (X/
H = 2.7, Fig. 10), the instantaneous velocity ®eld was found
to be more turbulent than that at X/D = 0.5 (X/H = 1.3)
cross plane. However, the geometry of the lobed nozzles can
still be identi®ed from the PIV instantaneous velocity ®eld.
As in the PLIF visualization results, the streamwise horseshoe
vortices with a smaller scale at the lobe troughs can also be
seen from the mean velocity ®eld and streamwise vorticity
®eld besides the six large-scale streamwise vortices pairs
generated by the lobed nozzle. The intensive mixing regions
were found to expand outward and inward.
As the streamwise downstream increased to X/D = 1.5
(X/H = 4.0, Fig. 11) and X/D = 2.0 (X/H = 5.3, Fig. 12),
the instantaneous velocity ®elds became much more
turbulent, which indicates that more intensive mixing
occurs in these sections. The geometry of the lobed
nozzle can almost not be identi®ed from the instantaneous velocity ®elds. The large-scale streamwise vortices
generated by the lobed nozzle were found to break down
into many smaller vortices; the strength of the stream-
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Fig. 9a±d. PIV measurement results at X/D = 0.5 (X/H = 1.3) cross plane for the lobed jet mixing ¯ow (Re = 3,000). a instantaneous
velocity ®eld; b mean velocity ®eld; c in-plane turbulance intensity distribution; d mean streamwise vorticity distribution
wise vortices were also found to dissipated considerably,
which will be discussed later. The intensive mixing regions expanded inwards and outwards much more seriously at these locations, which almost fully ®lled the
window studied.
3.3
The decay of the streamwise vorticity xx
The streamwise vortices generated by the lobed nozzle has
been suggested to be the primary reason for the mixing
enhancement of lobed jet mixing ¯ows in the previous
research. In order to study the evolution of the streamwise
vortices in the lobed jet ¯ow, the decay of the maximum
value of the mean streamwise vorticity max (xx ) based on
the above PIV measurement results are shown in Fig. 13.
At the ®rst one diameter of the lobed jet ¯ow (X/D < 1.0,
X/H < 2.7), the maximum value of the mean streamwise
vorticity was found to be almost constant, which is about
one-third of the maximum value of the spanwise vorticity
at the nozzle exit plane. The streamwise vortices generated by the lobed nozzle were also found to grow and
intensify at this region (from the above PLIF visualization
and PIV measurement results). This may correspond to
the steps of the streamwise vortices formation and intensi®cation suggested by Werle et al. (1987) and Eckerle
et al. (1990). However, the maximum streamwise vorticity
was found to decay very rapidly in the region of 2.0 < X/
D < 1.0 (5.3 < X/H < 2.7). The PLIF and PIV results also
showed that the large-scale streamwise vortices generated
by the lobed nozzle broke down into many small-scale
vortices in this region, which may correspond to be
broken-down step of the streamwise vortices suggested by
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Fig. 10a±d. PIV measurement results at X/D = 1.0 (X/H = 2.7) cross plane for the lobed jet mixing ¯ow (Re = 3,000). a instantaneous
velocity ®eld; b mean velocity ®eld; c in-plane turbulance intensity distribution; d mean streamwise vorticity distribution
Werle et al. (1987) and Eckerle et al. (1990). Downstream
of X/D > 2.0 (X/H > 5.7), the streamwise vortices generated by the lobed nozzle were dissipated so seriously
that the strength of the maximum streamwise vorticity
was just about 1/4 1/5 of that at the exit of the lobed
nozzle.
the momentum entrained into the shear layer, is calculated
using following equation:
Z
Z
U†…U U2 †
U0 U†=U
hˆ
dy …4†
dy ˆ
DU
U0
where DU = U1 ) U2, U1 and U2 are velocities of the two
streams at the inlet of the mixing region, U is the local
velocity of the PIV ensemble averaged values, which are
3.4
shown in Figs. 3c, 4c and 5c. In the present study, U2 = 0,
Shear layer growth
U1 = U0 and DU = U1 = U0.
In order to give a more quantitative comparison of the
Since the existence of the long laminar regions
mixing characteristics in a lobed jet mixing ¯ow with a
conventional circular jet ¯ow, the growth of the shear layer downstream of the circular nozzle, the conventional
circular jet data remain constant for the ®rst diameter of
in terms of momentum thickness h are given in Fig. 14.
the test nozzle, and then grow linearly over the meaFollowing the de®nition of McCormick and Bennett
(1994), the momentum thickness h, which is a measure of surement range. However, for the lobed jet ¯ow, the
U1
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Fig. 11a±d. PIV measurement results at X/D = 1.5 (X/H = 4.0) cross plane for the lobed jet mixing ¯ow (Re = 3,000). a instantaneous
velocity ®eld; b mean velocity ®eld; c in-plane turbulance intensity distribution; d mean streamwise vorticity distribution
growth rate is very high for the ®rst one-lobed nozzle
diameter (X/D < 1.0, X/H < 2.7) in the lobe peak slice,
with a growth rate less than the circular jet farther
downstream. In the lobe trough slice of the lobed jet
mixing ¯ow, the lobed jet was found to grow at a medium rate, which is still higher than the circular jet for
the ®rst two lobed nozzle diameters (X/D < 2,
X/H < 5.7). These results are consistent with the decay of
the streamwise vorticity discussed previously. At the ®rst
two nozzle diameters (X/D < 2.0, X/H < 5.3), the largescale streamwise vortices generated by the lobed nozzle
enhance the mixing of the core jet ¯ow with the ambient
¯ow. Farther downstream (X/D > 3.0, X/H > 8.0), the
streamwise vortices dissipated and the momentum
transport was conducted via a conventional gradienttype turbulent mechanism as in the circular jet ¯ow, so
the momentum growth rate decreased. The growth
rate farther ®eld (X/D > 3.0) in the lobed jet mixing
¯ow is below that of the conventional circular jet ¯ow,
also consistent with the conclusion of McCormick and
Bennett (1994) in a two-dimensional lobed mixing
layer.
3.5
Central line velocity decay in the jet flow
A comparison of the central line velocity decay in the
conventional circular jet and the lobed jet mixing ¯ow is
shown in Fig. 15. The central line velocity of the circular
S154
Fig. 12a±d. PIV measurement results at X/D = 2.0 (X/H = 5.3) cross plane for the lobed jet mixing ¯ow (Re = 3,000). a instantaneous
velocity ®eld; b mean velocity ®eld; c in-plane turbulance intensity distribution; d mean streamwise vorticity distribution
jet ¯ow keeps almost constant in the region studied
(X/D < 4.0), which is consistent with the result that the
length of potential core region of a conventional circular
jet ¯ow ranges from about 4D to 6D (Hinze 1959). However, the central line velocity of the lobed jet mixing ¯ow
began to decay from the downstream X/D = 1.0, which is
also consistent with the lobed jet mixing ¯ow's transition
to turbulence downstream of X/D < 1.0 revealed in the
above PLIF and PIV results. This means that the length of
the potential core region in the lobed jet ¯ow is just
about a quarter to one-sixth of the conventional circular
jet ¯ow, which also indicates the mixing enhancement
performance of a lobed nozzle over a conventional circular
nozzle in the near-¯ow ®eld.
3.6
Mechanism of the mixing enhancement
in lobed jet mixing flow
Compared with a circular jet ¯ow, a lobed jet mixing ¯ow
was found to have a smaller scale of Kelvin±Helmholtz
vortices, an accelerated process of vortices pairing, and a
quicker transition to turbulence from the above PLIF visualization and PIV measurement results. More rapid
growth of the shear layer at the near ®eld and faster decay
of the central line velocity were also found in the lobed jet
mixing ¯ow. All these indicated the mixing enhancement
of a lobed jet mixing ¯ow over a circular jet ¯ow. However,
how did the lobed nozzles enhance ¯uid mixing in a lobed
mixing ¯ow? McCormick and Bennettt (1994) suggested
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Fig. 13. The decay of the mean streamwise vorticity in the lobed jet mixing ¯ow
that the interaction of Kelvin±Helmholtz vortices with
streamwise vortices generated by the lobed nozzles produces high levels of mixing, which is mainly responsible
for the enhanced mixing. Yet, they did not explain by what
means these processes were conducted.
It is well known that the mixing process of the jet ¯ow is
also the transportation process of the energy and vorticity
from large-scale vortices to small-scale vortices. For a
conventional circular jet ¯ow, it is well known that the
spanwise vortex rings would be rolled up ®rst due to the
Kelvin±Helmholtz instability (®rst instability) existing at
any shear layer. As the spanwise vortex rings move
downstream, they cannot be two-dimensional vortical
rings due to the self-interaction and cross-interaction
effects between these spanwise vortical rings (Fig. 16).
They will be the combinations of helical vortical tubes, i.e.,
toroidal vortical rings through the effect of an additional
instability (secondary instability or azimuthal helical
Fig. 14. The momentum
thickness development in the
circular jet ¯ow and lobed jet
mixing ¯ow (Re = 6,000)
Fig. 15. Central line velocity decay of the
circular jet ¯ow and lobed jet mixing ¯ow
(Re = 6,000)
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Fig. 16. Idealization of the vortical evolution in a circular jet ¯ow
conjectured by Hussain (1986)
instability), So, the two-dimensional spanwise vortex
rings caused by the Kelvin±Helmholtz instability will be
wrapped and develop into three-dimensional structures
through secondary instability. Undergoing interactions,
the large-scale toroidal vortical rings will be broken down
into many substructures through the ``cut and connect''
process (Hussain 1986), which may be responsible for the
avalanche of three-dimensional and smaller-scale motions
and for the generation of high turbulence and Reyolds
stress. However, the evolution of such a process will always
need quite a long streamwise distance to complete in a
conventional circular jet ¯ow.
For a lobed nozzle, because of its special geometry, it
can cause large perturbations along the azimuth of the jet
¯ow. For example, the ¯ow direction is different in the
lobe peaks and lobe troughs at the exit of the lobed nozzle.
The non-uniform momentum thickness of the boundary
layer along the azimuth of the jet ¯ow results in the rolling
up of Kelvin±Helmholtz vortices at different streamwise
distances in the lobe peaks and lobed troughs, which is
revealed in the PLIF visualization and PIV measurement
results. The streamwise vortices produced by the lobed
Fig. 17. Stretch effect of streamwise vortices on the spanwise
Kelvin±Helmholtz vortical tube
nozzle enlarge the azimuthal perturbations by means of
deformation of the Kelvin±Helmholtz vortical tubes into
pinch-off structures [suggested by McCormick and Bennett (1994), and also revealed in the PLIF visualization and
PIV measurements results]. All these enhance the earlier
creation of the complex three-dimensional vortices and
the secondary helical instability of the jet ¯ow. i.e., the
``toroidal effect'' of the spanwise vortical structures is enlarged, and then the ``cut and connect'' process of the
vortical rings is accelerated (which is the merge process of
the adjacent ``mushroom'' observed on the above PLIF
¯ow visualization in the cross plane). This means that the
process of a large-scale vortical structure breaking into a
smaller scale vortical structure is conducted more rapidly,
therefore, the mixing of the core jet ¯ow with ambient ¯ow
is enhanced, and the transition of jet ¯ow to turbulence
conducted very quickly.
Besides this, the interaction between the large-scale
streamwise vortices produced by a lobed nozzle and the
spanwise vortices caused by the Kelvin±Helmholtz instability also results in stretching of the spanwise vortical
rings (Fig. 17). According to the Helmholtz vorticity
conservation law, the scale of the vortices will be reduced
quickly when the vortices are stretched, which also results
in rapid reduction of the scale of the vortices. (This may be
the reason why the scale of the spanwise Kelvin±Helmholtz
vortices in the lobed jet ¯ows is smaller than that in the
circular jet ¯ow visualized in the PLIF results.) This also
results in the creation of much small-scale intense turbulence and the mixing enhancement of the core jet ¯ow with
the ambient ¯ow.
4
Conclusion
PLIF visualization and PIV measurement results revealed
the great differences in the turbulent and vortical structures in a lobed jet mixing ¯ow compared with those in a
circular jet ¯ow. The lobed jet mixing ¯ow was found to
have a shorter laminar instability region, a smaller scale of
the spanwise Kelvin±Helmholtz vortices, earlier appearance of the small-scale turbulent structures and a faster
transition to turbulence. More rapid growth of the shear
layer at the near ®eld and quicker decay of the central line
velocity were also found in the lobed jet mixing ¯ow. All
these indicated the mixing enhancement performances of a
lobed jet mixing ¯ow over a conventional circular jet ¯ow.
Based on the PLIF visualization and PIV measurement
results, two aspects of the mechanism of mixing enhancement of in a lobed jet mixing ¯ow are suggested: one
is that a lobed nozzle can cause azimuthal perturbations in
the jet ¯ow, and the streamwise vortices produced by the
lobed nozzle enhanced these azimuthal perturbations.
These accelerate the ``cut and connect'' process of the
large-scale spanwise Kelvin±Helmholtz vortex rings to
transfer the energy and vorticity from large-scale vortices
to small-scale vortices. Another is that the ``stretch effect''
of the streamwise vortices on the spanwise Kelvin±Helmholtz vortex tubes also accelerate the reduction of the scale
of the spanwise vortices. Both result in the creation of
much smaller-scale intense turbulence and mixing
enhancement of the core jet ¯ow with ambient ¯ow.
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