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Journal of Applied Fluid Mechanics, Vol. 10, No. 5, pp. 1475-1486, 2017.
Available online at www.jafmonline.net, ISSN 1735-3572, EISSN 1735-3645.
DOI: 10.18869/acadpub.jafm.73.242.27617
A Novel Method for Defining the Leeward Edge of the
Planar Jet in Crossflow
K. Zhao1,2, X. Yang2†, P. N. Okolo1,3, Z. Wu2, W. Zhang2 and G. J. Bennett1
1 Department of Mechanical and Manufacturing Engineering, Trinity College Dublin, University of Dublin,
Dublin, Republic of Ireland
2 College of Aerospace Science and Engineering, National University of Defence Technology, Changsha
410073, P. R.China
3 Energy and Power Technology Division, Department of Mechanical Engineering, University of Nigeria,
Nsukka, Nigeria
†Corresponding Author Email: nkyangxixiang@163.com
(Received January 19, 2017; accepted May 8, 2017)
ABSTRACT
To avoid the complexity of the edge definition by the half width, a new approach to defining the leeward edge
of the planar jet in crossflow is introduced in this paper. Particle Image Velocimetry (PIV) experiments were
performed to measure different flow regimes within the single jet and the dual jets configurations in crossflow.
Based on the experimental data acquired, a series of velocity profiles were extracted from the flow field. In
each profile, a velocity threshold was given to distinguish the regions sheltered and the regions not sheltered
by the planar jet. The boundary of these regions was accordingly recognized as the leeward edge. Furthermore,
fitting of the edge was carried out using a second order polynomial so as to enable a mathematical expression
of the leeward edge. An application of the proposed approach towards the flow induced noise reduction using
a planar jet is also discussed in this paper. In addition, the PIV frame assembly algorithm used in this study is
reported.
Keywords: Planar jet; Crossflow; Leeward edge; PIV; Flow-induced noise reduction.
NOMENCLATURE
D diameter of the tandem cylinders
P pitch of the tandem cylinders
U∞ speed of the crossflow
Uj2 speed of the upstream jet in the dual jets
configuration
Uj1 speed of the primary planar jet in the single
jet configuration and the dual jet
configuration
Um maximum speed of the local section in the
2D natural system
1. INTRODUCTION
The turbulent jet in crossflow is a fluid problem
related to many engineering problems, such as
internal cooling of turbine blades, wast water
discharge into the costal water, etc. Compared with
the round jets, the planar jet in crossflow (PJIC) has
attracted less attention due to the limited
applications. Recent studies by Oerlemans and Bruin
(2009), Zhao et al. (2017) have shown the suitability
of PJIC towards the reduction of flow-induced noise.
The application is foreseen to be the landing gear
noise reduction (Sijpkes and Wickerhoff 2004). The
basic idea is to insert a planar jet upstream to a bluff
body in order to deflect the crossflow. The bluff body
is targeted to be situated below the planar jet. This
enables the local flow speed to be significantly
reduced, thereby reducing the aerodynamic noise. To
optimise the configuration so as to achieve the
maximum noise reduction, the bluff body position is
referred to the leeward edge of the planar jet.
Therefore, a crucial defining of the leeward edge is
necessary.
In the study of the turbulent jet ejected in a quiescent
flow, e.g. the planar jet and the round jet, the edge
has been well discussed. Conventionally, the half jet
width is utilised to describe the spreading of the
turbulent jet. To be more specific, the half jet width
represents a typical length where the velocity is equal
to half of the trajectory velocity (Rajaratnam 1976).
The trajectory velocity is also the maximum velocity
K. Zhao et al. / JAFM, Vol. 10, No.5, pp. 1475-1486, 2017.
1476
in the local normal plane of the jet trajectory. In the
quiescent flow, the jet trajectory can be easily
tracked because it is coincident with the geometric
centreline. As such, the half width edge can be
identified by extracting velocity profiles in the
spanwise plane. Furthermore, it is found that the
spreading rate (or growth rate) of the jet half width
can be expressed as a linear expression depending on
the jet centreline axis (Kotsovinos 1976; Ramaprian
and Chandrasekhara 1985).
When the turbulent jet is ejected into a crossflow, it
bends over downstream due to the entrainment of
ambient fluid with crossflow momentum. Then the
jet merges with the crossflow and consequently a
new mainstream is formed (Rudman 1996; Morton
and Ibbetson 1996). In addition, if there exists
multiple jets, e.g, in a tandem configuration, the
bending curvature of each jet varies due to the shelter
from front jets (Lin and Sheu 1991; Tanaka 1974;
Yu, Ali, and Lee ). Likewise, the jet half width has
been applied in the research of PJIC (Haniu and
Ramaprian 1989; Smith and Mungal 1998; Persen,
iann, and Mazumdar 1993). To begin with, a 2D
natural system in PJIC is established. As shown in
Fig.1, the 2D system possess 2 axes, denoted as α and
β. α is the trajectory of the jet. After α is defined, the
normal plane of α, termed as local section
hereinafter, can be determined. In the 2D system, β
is coincident with the local section. As such, the
trajectory definition underlies the establishment of
the natural system. To date there are different
approaches in the jet trajectory definition: locus of
velocity maxima, scalar concentration maxima or
vorticity maxima in the local sections. Alternatively,
the time-averaged streamline originating at the jet
exit can be used as the jet trajectory (Mahesh 2013).
Fig. 1. 2D Natural system in PIC.
When the natural system is established, the half jet
width can be introduced. More specifically, as shown
in Fig.1, the edges are the locus of those points that
possess a velocity of half local maximum (um/2) in
the local sections. b11/2 and b21/2 represent the
windward and the leeward half width edges of the jet
respectively. Research work by Haniu and
Ramaprian (1989) achieved the best model to date
for the planar jet trajectory prediction. To be more
specific, in the absence of significant buoyancy
effects, an assumption was made that behaviour of
the jet only depends on its initial (kinematic)
momentum flux and the crossflow velocity.
Therefore, a dimensionless analysis of the relevant
variables can be conducted, which yields:
(1)
where lm is the momentum length scale for 2D jet,
expressed as
= w
1
U
2
/U
2j1
. w1 is width of the jet
slot. Based on the experiment data, Eq. 1 was
corrected and the model is written as:
=1.2
.
(2)
More importantly, compared to the measurement
from the same jet in quiescent flow (Ramaprian and
Chandrasekhara 1985), Haniu and Ramaprian (1989)
concluded that the spreading rate of the PJIC is
slightly higher. Since the spreading rate in quiescent
flow has been well modelled, the conclusion makes
it possible to predict the half width edge of the jet to
some extent. It is this prediction that is used in the
work by Oerlemans and Bruin (2009) to determine
the optimised position for the bluff body noise
reduction using a planar jet.
However, there are some limitations in the half width
edge, which are worth discussing. Firstly, on the edge
definition. All definitions of the jet edge are based on
the local section. The local section is achieved as the
normal plane to the jet trajectory. Meanwhile, the jet
trajectory is defined by the locus of the maxima in the
local section. As such, there is a suspect of the circular
definition. As mentioned above, there are different
definitions of the jet trajectory. When the trajectory is
defined as the time-averaged streamline that
originates from the centre of the jet outlet, the circular
definition can be broken up. This is because the
streamlines are calculated as those curves that are
tangent to the flow velocity field. Even so, another
limitation may come out that the local velocity
maxima is not situated on the trajectory. Secondly, on
the model. Experimental work conducted by Haniu
and Ramaprian (1989) utilised a water jet in a water
flume, both of which had extremely low speed (Uj1 =
0.3m/s and U∞=0.3m/s, 0.33m/s, and 0.5m/s).
Therefore, it necessitates more investigations when
the jet speed is much higher. One recent study by
Bennett
et al
. (2016) has found the model can well
capture the jet trajectory close to the outlet, but being
a quadratic curve, the model cannot capture the jet
further downstream. At last but not least, on the
application. As mentioned above, the model has been
applied for bluff body noise reduction. Therefore, the
bluff body was situated below the leeward half width
edge of the jet. It suggests that the impinging flow
speed to the bluff body can be up to half of the local
maximum. Reduction of the impinging speed to the
bluff body is the key to the noise reduction using the
air curtain, concluded by Oerlemans and Bruin (2009)
and Zhao
et al
. (2016). Half of the local maximum, to
some extent, is still high. Therefore, a more
reasonable definition of the leeward edge of the PJIC,
especially for noise reduction, is highly expected.
K. Zhao et al. / JAFM, Vol. 10, No.5, pp. 1475-1486, 2017.
1477
Fig. 2. Schematic of the experimental rig (not in
scale): I. microphone array; II. crossflow nozzle;
III. honeycomb layer in the jet plenum; IV.
endplate and its supporting aluminium
extrusion.
Fig. 3. Auto-spectrum of the wind tunnel
background noise.
In this paper, a novel method for defining the
leeward edge of the PJIC is proposed based on PIV
experiments, which can be used for the single jet and
the dual jets configurations in crossflow. Firstly, the
experimental facilities and instruments are
introduced. Then the proposed method is described
in a step-by-step process and the validation is
conducted with a series of experimental cases. The
corresponding application towards the flow-induced
noise reduction is reported. In addition, the PIV
frame assembly approach used in this study is
introduced.
2. E
XPERIMENTAL
S
ET
U
P
A
ND
M
ODELS
All experiments were conducted in a low speed 3/4
open-jet wind tunnel with a planar jet system.
Schematic of the entire rig is shown in Fig.2. In
addition, the tandem cylinders were selected as the
test body to generate the flow induced noise source.
Specifics of the experimental set-up are described in
this section.
2.1 Open-Jet Wind Tunnel
The 3/4 openjet wind tunnel was powered by a 5.5
kW centrifugal blower. The dimension of the nozzle
(Fig.2.II) is 1000mm long with an outlet size of
75mm×75mm. The outlet was mounted to be flush
with a horizontal end-plate. The crossflow coming
from the wind tunnel has been characterised by a
series of comprehensive measurement using Dantec
hot-wire anemometry in the work by Zhao et al.
(2016). The crossflow speed from the wind tunnel
can be up to 70m/s and the free stream turbulence
intensity is within 2% in the measurement window.
The acoustic performance of the wind tunnel was
also characterised using the microphone array
introduced in the following section. The auto-
spectrum of the background noise when U∞ =
50.45m/s is shown in Fig.3. It is found that the
background noise mainly concentrates in the
frequency range that is less than 1,000Hz and SPL
dramatically declines when the frequency is higher
than 1,000Hz. Therefore, the acoustic analysis in the
reminder of the paper will mainly focus on the
frequency range over 1,000Hz.
2.2 Planar Jet System
The planar jet system was operated by a 2.2 kW
centrifugal blower and a cubic plenum equipped with
jet nozzles. The blower was situated to be far from
the rig but a hose was between the blower and the
plenum, which helps to reduce the background noise.
The Plenum was 540 mm high with a horizontal
section of 424mm×424mm. One honeycomb layer
with the hexagonal grid of 6 mm edge length (Fig. 2.
III) was installed inside to uncouple the jet flow from
the blower. Baffles were installed to minimise
recirculation inside. All internal structures of the
plenum were designed to ensure low turbulence
intensity in the planar jet.
The number of the jet nozzles could be controlled to
be either one or two, depending on specific tests. For
the dual jets configuration, rectangular outlets were
managed parallel to each other. The span-wise length
of the jet nozzles were fixed at 100 mm, and the
streamwise width could be controlled as required, i.e.
10mm in this study. Therefore, the length/width ratio
was not greater than 10, which allows the regime to
be treated as 2D flow. In The lip of the jet nozzles
was flush with the end-plate. In the single-jet
configuration, jet velocity can be easily controlled by
managing the area of the blower inlet. Additionally,
in the dual jets configuration, since the mass flow
was supplied by the same plenum, the speed
difference between two jets was achieved by
installing a piece of metal mesh plate, with different
porosity, between the plenum and the jet nozzle.
Examples of the mesh are shown in Fig.4. Prior to
experiment, a variety of mesh porosity were tested in
attempt to calibrate the jet speed. In the calibration,
the jet speed was measured by FCO510
micromanometer supplied by Furness Controls. As
such, the velocities anticipated for both jets could be
attained.
Fig. 4. Examples of the mesh plate inside the
planar jet system.
K. Zhao et al. / JAFM, Vol. 10, No.5, pp. 1475-1486, 2017.
1478
2.3 Test Model
As mentioned earlier, the application of the leeward
definition edge definition on the flow induced noise
reduction was conducted. In the experimental tests,
tandem cylinders were used as the noise source,
shown in Fig.5.a. The diameter of the cylinders was
4mm. Previous studies (Zdravkovich 1985;
Zdravkovich 1987) concluded that specific values of
P/D can lead to different flow regimes. For instance,
for intermediate spacing 2.2−2.5 < P/D < 3.1 − 3.4
an intermittent shedding can be detected in the region
between two cylinders and the vortex shedding
mainly occurs on the rear cylinder. These complex
flow structures can result in substantial noise
production. Therefore, in this study, this regime was
selected and P/D was set to be equal to 3. The pitch
between two cylinders, P, was 12mm.
Figure 5.b illustrates the setup for the cylinders in the
acoustic tests of the single jet configuration. The
cylinders were supported by two blocks and the span
of the cylinders was much longer than the crossflow
width. This avoids the extra noise that is generated if
the crossflow blows the block. The relative position
of the cylinders is determined referred to the jet
leeward edge, which will be reported in the reminder
of this paper.
(a)
(b)
Fig. 5. Flow induced noise source: (a). tandem
cylinders; (b). set-up.
3. EXPERIMENTAL APPARATUS
3.1 PIV
PIV has been widely applied on the studies of jets (in
crossflow). For example, work by Camussi et al.
(2002), Camussi (2002), Koched et al. (2011),
Larsson et al. (2012). As previously stated, the
leeward edge definition discussed in this study is
based on PIV experiment. The arrangement of the
PIV measurement is depicted in Fig.6. The
instrument was equipped with a LaVision low-speed
PIV system with a 15 mJ New Wave Solo-II PIV
double pulsed Nd:YAG laser. The laser beam was
refocused and diverged by a set of lenses and
consequently, a laser sheet could be formed as sharp
as 0.3 mm, i.e. the measurement plane. he cross-flow
and jets were seeded using Pea Soup Oil Based
Smoke Generator PS31. Particle size in all tests were
in the range of 1.5µm. Image pairs were recorded
using a double exposure LaVision Flow-master 3
camera, with a maximum resolution of 1280×1280
pixels. The camera was attached beside the endplate,
which allowed the lens to remain parallel to the laser
sheet. Once the camera was focused, it could attain
image pairs with a frame size of 97.2 mm×96.9 mm
and the time delay between two paired images was 8
µs. However, the streamwise frame length, i.e. lw =
97.2 mm, was not adequate enough to capture the
development of the jet. Therefore, the PIV frame
assembly was conducted for the time-mean analysis
through the Davis software and an open access
toolbox in Matlab–PIVMat. More specifically, the
Davis software was used to control the PIV
instrument, capture and process the pair images. The
PIVMat supplied a coding environment in Matlab, in
which the post-process and PIV assembly were
carried out.
The PIV assembly begins with paired image
acquisition. In particular, there are two sampling
positions, i.e. C1 and C2 in Fig.6.a. The camera was
traversed and respectively situated at C1 and C2.
Therefore, two different frames could be achieved,
denoted as F1 and F2 and shown in Fig.6.b. It is
worth noting that the calibration was only conducted
at C1, which means the coordinate system in F1 is
correct. However, in F2, the scale of the coordinate
system is correct but the origin is not. This problem
will be fixed after the assembly. The translation
between C1 and C2 is denoted as lw − ∆l, which must
be smaller than lw. In this experiment lw − ∆l was
controlled to be 90mm. 400 paired images were
acquired at each position respectively. This number
of image pairs has been validated to be sufficient to
achieve the convergence in the mean quantities, and
the time consumption is at a moderate level. The raw
data were processed with multi-pass correlation of
32×32 (50%overlap) and 16×16 (25% overlap) in
Davis. The file extension of the processed data from
Davis is “.vc7”, which can be directly loaded in
Matlab using the PIVMat for the post-process.
The data loaded for each frame in Matlab, in effect,
are stored as the structure array. The core of the array
is two matrices and two vectors. These two matrices,
with a size of 85 × 107 in this study, contain the
velocity components in X and Y respectively. The
results were averaged to achieve the time-mean flow
field for those two frames. One example is shown in
Fig.7 (a) and (b). As the two matrices in each of the
two frames possess same structure, they are herein
denoted as one capital letter. In other word, one
capital letter is used to denote both matrices for X
and Y in the same frame. Therefore, and B¯ are for
the mean field in F1 and F2 respectively, expressed
as:
={
,,…,
,
}× (3)
K. Zhao et al. / JAFM, Vol. 10, No.5, pp. 1475-1486, 2017.
1479
Fig. 6. Schematic of the PIV set-up.
={
,
,…,
,
}
×
(4)
where α = 85 and β = 107. In the meantime, their
corresponding coordinates are provided in the two
vectors mentioned above, termed as the coordinate
vectors. These two vectors contain the position
information in two orthogonal directions, i.e. X and
Y. More specifically, 107 elements in X direction
and 85 elements in Y direction. Note that after the
camera traversed from C1 to C2, the coordinate
vectors will not vary with the camera position. Thus,
these coordinate vector can be denoted with same
symbols in both frames, i.e. Xβ and Yα for X and Y
respectively. Elements inside these coordinate
vectors are the real X and Y coordinates of each pixel
rather than the pixel indices. They can be written as:
=
,
,…,
,
(5)
=
,
,…,
,
(6)
The number of elements in the streamwise dimension
within ∆l, i.e. the number of the superposition
elements in each frame (n) , is calculated as:
n= ×
∆
(7)
where“[ ]” gives the round integer of the inside
value.
The new assembled frame is a combination of F1 and
F2 with removing the superposition in F2. Therefore,
the length of the new frame is as long as 2lw − ∆l and
the matrix size for the new assembled frame should
be as long as 2β − n. Because the rounding can
introduce uncertain error to the assembly. Therefore,
a coefficient is introduced for correction, denoted as
co. The value of co is dependent on continuity, which
can be any of 0, 1, 2, etc. As such, the new assembly
is as long as 2β−n+co. is used to term the assembled
matrix, written as:
={
,
,…,
,
,
,
,…,
,
}
×
(8)
(a)
(b)
Fig. 7. Example of the time-mean flow field in
different frames: (a). F1; (b). F2.
The assembled coordinate vectors for X axis can be
written as:
٫
=
,
,…,
,
,
,
2,…,
1
,
×
(9)
where δ is the interval between any two adjacent X
coordinates in Xβ. Note that δ is a constant once the
K. Zhao et al. / JAFM, Vol. 10, No.5, pp. 1475-1486, 2017.
1480
calibration has been carried out. Obviously, the
assembled coordinate vector for Y remains to be
same, i.e.
,
=
(10)
Then the assembly array including
,X’ and Y’ can
be achieved, which can be shown using PIVMat
(Fig.8).
Fig. 8. Example of the assembled frame (F1+F2).
This approach can be of good use when there is
limitation of the PIV instrument, e.g. shortage of the
camera number. Therefore, it is necessary to discuss
the quality of this assembled frame. As an assembly
of multiple frames, continuity plays an important
role. As mention earlier, the choice of co is subject
to continuity. Therefore, the variation of the
continuity with co can be a criteria to evaluate the
choice of co.
In the continuity analysis in this study, horizontal
velocity profiles are used. More specifically, it is
known that the joint is somewhere around x =
38.22mm, the uncertainty is attributed to the
rounding as well as the choice of co. Therefore, three
arbitrary horizontal profiles were extracted, all of
which start from x = 30mm and end at x = 40mm.
However, those profiles should be averted (c) from
being inside the area with high velocity gradient.
Therefore, those horizontal profiles with
y=18.61mm, y=28.11mm and y=70.88mm were
used. These velocity profiles are shown in Fig.9 with
different co. The junction inside each subfigure and
its adjacent positions have been high-lighted with a
rectangle. From the comparison between different
co, it is clear shown that the continuity of the speed
profile is affected by the value of co. The best
continuity for all three profiles occurs when co = 1.
Thus, in this study co was set to be equal to one.
3.2 Microphone Array
As mention earlier, the application of the jet lee-ward
edge definition on flow-induced noise reduction is
described in this paper to show the usefulness of this
approach. All acoustic measurements were
performed using the microphone array illustrated
earlier in Fig. 2.I.
As shown in Fig.10, the array consists of 25KE4
Sennheiser electret microphones. Those
microphones worked within 20-20,000Hz range and
each of them was equipped with an amplifier to
enhance the signal. The distribution of the
microphones is illustrated in Fig.11. This irregular
pattern was determined using beamforming
simulation. A large number of arbitrary pattern was
tested using a virtual monopole source, among which
the one with the best performance was selected. This
pattern also enables to reduce the typical spatial
aliasing of the regular one. Data were acquired using
National Instrument DAQ system NI PXI-1033. For
each test the sampling time and the sampling
frequency were 10s and 100kHz. Moreover, one
camera was installed in the array, which allowed the
noise localization to be based on the real cut-out of
the test platform from the top view.
Fig. 9. Continuity analysis of the frame
assembly:(a). co = 0; (b). co = 1, (c). co = 2.
Fig. 10. Microphone array.
K. Zhao et al. / JAFM, Vol. 10, No.5, pp. 1475-1486, 2017.
1481
Fig. 11. Arrangement of the microphones in the
array.
The acoustic data were processed to achieve overall
one third octave band spectra, which are the results
as an average of all microphones in the array.
Moreover, the conventional beamforming with
diagonal deletion was utilised to obtain the noise
map. Effects of sound refraction within the wind
tunnel shear layer was corrected for, using an Amiet
method (Amiet 1978).
4. L
EEWARD
E
DGE
D
EFINITION
In this section, the process of defining the jet lee-
ward edge is explained in detail.
4.1 Leeward Edge Extraction
The proposal of the method is based on PIV test
results. In this study a series of PIV tests with
different initial conditions were conducted, reported
in Tab.1. The jet speed was measured using FCO510
micromanometer. There are single jet configurations
and dual jets configurations. In the dual jets
experiment, the distance between centres of the jet
slots is 60mm. In addition, each has been distributed
a run number.
Table 1 PIV Test matrix of the planar jet in
crossflow
No.
U
(m/s)
1
w
(mm)
1j
U
(m/s)
2
w
(mm)
2j
U
(m/s)
S1 40.32 10 39.27 / /
S2 40.12 10 50.15 / /
S3 29.18 10 41.13 / /
S4 30.15 10 49.52 / /
D1 40.35 10 49.15 10 19.98
D2 40.10 10 50.02 10 30.18
D3 40.34 10 49.89 10 49.54
T1 40.56 10 40.45 / /
Figure12.a shows the mean velocity contour of S1.
Note that the X and Y axes have been normalised by
the width of the primary jet (w1). A number of
vertical probes were extracted to achieve the velocity
profile. These profiles were extracted from the mean
field of the flow, the one sigma uncertainty of those
profiles was found to be within 0.5%. For example,
three of these probes, P1, P2 and P3 are illustrated in
Fig.12.a and their corresponding velocity profiles are
reported in Fig.12.b. From those three profiles, it is
observed that P1 and P2 begin with a slow velocity
when y/w1 is low. When the height increases, both
profiles quickly reach a local maximum, i.e. 17m/s
for P1 at y/w1 = 0.3 and 8.5m/s for P2 at y/w1 = 1.2.
Subsequently, with y/w1 going higher and having
passed the local maximum, the velocity goes slower
and then starts to accelerate again until it reaches the
global maximum. By contrast, P3 does not display
the same trend. It begins with an increase from low
velocity and then fluctuates around 10m/s until y/w1
= 3. When the fluctuation ends, the velocity of P3
soars to the maximum. The characteristics of P1, P2
and P3 discussed above can be well explained in the
velocity contour. As depicted in Fig.12.a, both P1
and P2 penetrate a relative high speed region below
the planar jet. This is the reason why in the profiles
of P1 and P2, there is an obvious local maximum
when y/w1 is low. However, P3 is always outside the
high speed region. Thus, it does not have any obvious
reversed trend except increase and fluctuation.
(a)
(b)
Fig. 12. Velocity profiles extraction (a). examples
of the probes (P1, P2 and P3); (b). velocity
profiles of P1, P2 and P3.
Formation of the relative high speed region below
the jet can be attributed to the recirculation zone
induced by the planar jet (Jones and Wille 1996). As
schematically shown in Fig.1, a main recirculation
zone can be induced below the planar jet due to the
entrainment of the ambient fluid. Research on the
characterisation of the recirculation structure can be
found in previous studies by Pavageau et al. (2006),
Ahmed et al. (2008), etc. However, not much
information can be found on how much the
recirculation zone affects the bending of the planar
jet. The trend of P1, P2 and P3 suggests that
characteristics of the velocity profiles are subject to
the recirculation zone. Therefore, when the leeward
edge is defined, the effects from the recirculation
K. Zhao et al. / JAFM, Vol. 10, No.5, pp. 1475-1486, 2017.
1482
must be taken into account.
Proceeding further, a speed threshold is proposed.
More specifically, the maximum of each velocity
profile can be easily localised, marked with ‘Max’ in
Fig.12.b. As discussed earlier, when the planar jet is
used for the noise reduction, the bluff body should be
situated below the leeward edge, which allows the
local flow speed to be reduced. Thus, the leeward
edge is the boundary between the low speed region
and the high speed region. In other word, the
boundary between the sheltered region and the
unsheltered region. As such, it is directly related to
the velocity profile. A threshold can be used to
separate the region sheltered and the region not
sheltered by the jet, and the locus of the threshold
points in all profiles can be defined as the leeward
edge. In this study, an example of the threshold is
used, which is equal to one quarter of the maximum
velocity. The corresponding location of the threshold
points in P1, P2 and P3 are also marked in Fig.12.b.
Likewise, more profiles were extracted from the
velocity contour and all points with 0.25 maximum
velocity are marked and illustrated, which is Fig.13.
It is worth noting that in some profiles there are more
than one point with 0.25 maximum velocity. These
profiles mainly show up in the jet outlet proximity
and the very downstream field of this contour
window. It suggests that the flow field of these areas
are much more complicated than others. A possible
explanation can be the recirculation as well, which
can result in high velocity gradient in these areas.
However, the point with the highest y/w1 in each
profile can be easily localised. When all those points
are linked, illustrated in Fig.13, a curve will show up,
which is the leeward edge.
Fig. 13. Threshold points and the leeward edge
definition.
4.2 Leeward Edge Fitting
When applied towards the engineering use, the
leeward edge frequently requires a mathematical
expression. Considering it is characterised by a
parabolic shape, a second-order polynomial is
attempted to fit the leeward edge, which is written as:
=
=
+
(1 1)
The coefficients in Eq.11 are determined by the
experimental data. As shown in Fig.14.a, the scatter
illustrates data acquired from the PIV experiment.
The fitting curves are superimposed on the scatter.
Values of the coefficients in the polynomial are
reported in Tab. 2. It is observed that the fitting
curves are in good agreement with the experimental
data, except the point most downstream in S2.
(a)
(b) Fig. 14. Fitting of the primary jet leeward
edge:(a). single jet configurations; (b). dual jets
configurations.
This point can be eliminated as an abnormal point.
Therefore, the error range of the fitting is within
5%difference of y/w1 for each point.
Also, a second-order polynomial was attempted to fit
the primary jet leeward edge in the dual jets
configurations. Likewise, the comparison between
experimental data and fitting curves is depicted in
Fig.14.b The good agreement also confirms the
efficiency of fitting when applied to the dual jets in
cross flow.
Table 2 Coefficients of the second order
polynomial for the leeward edge fitting
No.
0
P
1
P
1
P
S1 0.029 0.72 -0.041
S2 -0.456 0.63 -0.041
S3 0.450 0.71 -0.028
S4 0.014 0.61 -0.034
D1 1.6 0.85 -0.044
D2 0.32 0.86 -0.036
D3 0.65 0.62 -0.033
4.3 Comments and discussions
This leeward edge definition introduced above can
be a good approach to easily extract the leeward edge
of the PJIC. Moreover, the fitting method allows the
leeward edge to be mathematical expressed, which
K. Zhao et al. / JAFM, Vol. 10, No.5, pp. 1475-1486, 2017.
1483
can contribute to the establishment of an semi-
empirical equation for the leeward edge.
However, there are a few uncertainties that should be
addressed. Firstly, the extraction of the leeward edge
is subject to the threshold value in the vertical
vertical profile (0.25 maximum in this study), which
suggests that the performance of this approach can
be highly affected by the threshold selection.
Therefore, it will be helpful to compare the variation
of the leeward edge between different threshold.
Secondly, this approach is highly dependent on the
accuracy of the measurement technology. In this
study, PIV, a global measurement technique was
used to achieve the leeward edge. Technically, other
anemometry apparatus, e.g. hot-wire and LDV, can
be also used. Therefore, a comparison between
different techniques is expected to contribute to a
further validation of this approach. Thirdly, this
approach has been attempted only for the single jet
and the dual jets configurations. It is worth
investigating whether this approach can be used for
the primary jet in the multiple jets configurations. In
addition, it is worth noting again that all assumptions
and based on 2D measurement and the impact of the
3D representation can be underestimated. Therefore,
an analysis of the effects from the third velocity
component is expected.
5. N
OISE
R
EDUCTION
U
SING
T
HE
P
LANAR
J
ET
An example of the flow-induced noise reduction using
the planar jet is reported, which utilises an optimised
position based on the leeward edge definition.
5.1 Shelter Optimization
As mentioned earlier, tandem cylinders were
adopted as the test object. Fig.15 illustrates the
relative position of the cylinders that is referred to
the leeward edge. a is the horizontal position of the
centre between two cylinders, and b is the top height
of the cylinders. In order to maximise the noise
reduction, an optimisation of a and b has been carried
out, which is described in the following.
Fig. 15. Schematic of the tandem cylinders
position.
It is known that the shelter to the tandem cylinders
supplied by the planer jet dominates the performance
of noise reduction. When a planar jet is used to
reduce the flow-induced noise, it is expected to use
the jet with the lowest speed to shelter the noise
source. This is because the jet can generate
substantial self-noise, i.e. jet noise (Tam 1998;
Munro and Ahuja 2003). The self-noise intensity is
positive correlated with the jet speed. The highest
shelter of a jet stays below the peak of the leeward
edge. Therefore, to use the jet with the lowest speed,
it is reasonable to place the cylinders below the peak
of the leeward edge so as to achieve maximum
shelter height.
In this study, Case T1 in Tab.1 was applied to
conduct the acoustic tests. To begin with, the leeward
edge was fitted based on the PIV data. The
experimental data, the fitted curve and the
corresponding equation are depicted in Fig.16.
Mathematically speaking, the peak of the leeward
edge stays where the derivative of the polynomial
equals to zero, i.e.d f ( wx1 )/d( wx1 ) = 0. The
corresponding location is written in Fig.16, i.e. (7.82
w1,1.62 w1). Therefore, as discussed earlier, a was
set to be equal to 7.82 w1, i.e. 78.2mm. This allows
the horizontal position of the tandem cylinder to
align with the peak of the jet leeward edge. As for b,
it is obvious that b ≤ 1.62 w1. Considering the
curvature of the leeward edge, a whole number was
used and in the subsequent test and b was made to be
16mm.
Fig. 16. Fitting of the leeward edge (T1).
Fig. 17. One third octave band spectra related to
the use of planar jet for flow induced noise
reduction.
5.2 Acoustic Performance
In the acoustic experiment, three configurations were
tested related to noise reduction, termed as BG, NP
and P. In BG the cylinders were removed and the
planar jet was turned off. This configuration was
carried out to measure the background noise, e.g.
power noise from the wind tunnel. In NP, the
cylinders were installed. This configuration aimed to
K. Zhao et al. / JAFM, Vol. 10, No.5, pp. 1475-1486, 2017.
1484
Fig. 18. Noise map at 7,000Hz (a). NP (b). P.
Fig. 19. Noise map at 14,000Hz (a). NP (b). P.
characterise the tandem cylinders noise. Note that in
BG and NP, since there was no planar jet, the nozzle
of the planar jet was removed and the outlet of the
planar had been sealed. This is because when blown
by the crossflow, the empty nozzle of the planar jet
can act as a cavity and generate substantial cavity
noise. In P, the planar jet was turned on to validate
the noise reduction.
Fig.17 shows the overall one third octave band
spectra of BG, NP and P in logarithm scale. In NP, it
is obvious that SPL is much higher than BG, which
means that the tandem cylinders can induce
substantial noise. Moreover, a main tone can be
found at 2,000Hz. This should correspond to the
vortex shedding that occurs in the downstream field
of the cylinders. When the planar jet is turned on in
P, the spectrum comparison between NP and P shows
that the cylinder noise can be significantly reduced.
In particular, the tone discussed above has been well
removed. More specifically, in the frequency of
2,000Hz, SPL can be reduced by 6.2dB, from 98.5dB
to 92.3dB. Therefore, it is concluded that the planar
jet can be of good use to reduce the flow-induced
noise. More importantly, it is validated that the
position optimisation can be based on the leeward
edge definition approach in this study.
However, it is also found that SPL of P is still much
higher than BG, which means that there are some
subsequent noise sources after the planar jet is turned
on. Moreover, it is found that in the bands between
11,220Hz and 17,780Hz, SPL of P is higher than NP,
which means the introduction of the planar jet can
make more noise than without the planar jet in these
bands. In order to localise these subsequent noise
source and explain the unexpected noise increase, the
noise maps of NP and P are shown in Fig.18 and
Fig.19, which corresponds to 7,000Hz and 14,000Hz
respectively. The background image shows the
picture taken by the array camera mentioned above.
From the reader’s view, the cylinders, the mass
blocks, the wind tunnel nozzle and the test platform
can be clearly observed. Note that as mentioned
K. Zhao et al. / JAFM, Vol. 10, No.5, pp. 1475-1486, 2017.
1485
earlier, the nozzle of the planar jet had been closed
in NP, therefore, the out-let of the planar jet can be
only found in the noise map of P. The coloured
contour describes the SPL distribution within the
beamforming measurement plane. Because of the
dynamic range difference, the colour bar scale was
set to be 10dB for Fig.18 and 8dB for Fig.19 to
highlight the main noise source at different
frequencies.
The noise maps of NP in both frequencies clearly
illustrate that SPL is centred at the middle of the
cylinders. This is where the vortex shedding mainly
occurs. Therefore, the noise maps are in agreement
with the spectra. When the planar jet is turned on, it
is observed in Fig.18.b that at 7,000Hz the SPL is
significantly reduced. The noise production is still
centred at the cylinders, however, not in the middle
but the side. This suggests that the subsequent noise
generation may depend on the curvature of the
crossflow deflected by the planar jet. By contrast,
Fig. 19.b shows that the subsequent main noise
source is displaced from the cylinders to the outlet of
the planar jet. It appears that no reduction is achieved
at 14,000Hz. This suggests that the planar jet self-
noise has become another subsequent main noise
source. As such, the SPL increase in the bands
between 11,220Hz and 17,780Hz, can be attributed
to the jet self-noise.
5.3 Discussions
In this section, with the position achieved from the
leeward edge definition approach described in this
study, the use of the planar jet towards the flow
induced-noise reduction has been discussed. It is
found that despite significant noise reduction, the
cylinders and the planar jet can be the subsequent
main noise source in different frequency ranges
respectively. In particular, in the high frequency
range, the jet self-noise substantially contributes to
the total noise emission and SPL can be higher than
without the planar jet. Therefore, this self-noise may
impede the implementation of the planarjet, which
necessitates the self-noise suppression. Moreover,
the leeward edge definition has been validated to be
able to find an optimised shelter to the tandem
cylinders. Therefore, due to the usefulness of this
approach, further investigations, especially with
more parametric analysis on this approach, are
expected.
6. CONCLUSIONS
In this paper, a novel approach to defining the lee-
ward edge of the planar jet in crossflow was
introduced. The approach was validated for the
single jet and the dual jets configurations in
crossflow. The application of this approach on the
flow induced-noise was discussed. In addition, the
algorithm of the PIV frame assembly was reported.
To define the leeward edge, the PIV assembly was
carried out to capture the jet development in the
crossflow. Based on the PIV data, the approach
adopted a threshold to distinguish those regions that
are sheltered and not sheltered by the planar jet in
each velocity profile. Therefore, the locus of those
threshold points was defined as the leeward edge.
Furthermore, it is validated that the second order
polynomial is able to fit the leeward edge of the
primary jet in the single jet and the dual jets con-
figurations. This fitting allows the leeward edge to be
mathematically expressed. The usefulness of this
approach was subsequently confirmed by an
application for the flow-induced noise reduction.
The shelter position aligning with the leeward edge
peak was found using the approach. The acoustic
tests showed that the flow induced noise of the
tandem cylinders at the shelter position can be
significantly reduced. Moreover, it is foreseen that a
semi-empirical equation of the leeward edge can be
achieved based on the mathematical expression in
this approach.
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