Research Article Time Resolved PIV Investigation on the Skin

Hindawi Publishing Corporation
Advances in Mechanical Engineering
Article ID 901421
Research Article
Time Resolved PIV Investigation on the Skin Friction Reduction
Mechanism of Outer-Layer Vertical Blades Array
Seong Hyeon Park,1 Nam Hyun An,2 Hyun Sik Yoon,3 Hyun Park,3
Ho Hwan Chun,3 and Inwon Lee3
1
Department of Naval Architecture and Ocean Engineering, Pusan National University, Busan 609-735, Republic of Korea
Department of Shipbuilding and Marine Engineering, Koje College, Gyeongsangnam-do 656-701, Republic of Korea
3
Global Core Research Center for Ships and Offshore Plants (GCRC-SOP), Pusan National University,
Busan 609-735, Republic of Korea
2
Correspondence should be addressed to Inwon Lee; [email protected]
Received 23 April 2014; Revised 12 September 2014; Accepted 13 September 2014
Academic Editor: Feng-Chen Li
Copyright © Seong Hyeon Park et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The drag reducing efficiency of the outer-layer vertical blades, which were first devised by Hutchins (2003), have been demonstrated
by the recent towing tank measurements. From the drag measurement of flat plate with various vertical blades arrays by Park et
al. (2011), a maximum 9.6% of reduction of total drag was achieved. The scale of blade geometry is found to be weakly correlated
with outer variable of boundary layer. The drag reduction of 2.8% has been also confirmed by the model ship test by An et al.
(2014). With a view to enabling the identification of drag reduction mechanism of the outer-layer vertical blades, detailed flow field
measurements have been performed using 2D time resolved PIV in this study. It is found that the skin friction reduction effect is
varied according to the spanwise position, with 2.73% and 7.95% drag reduction in the blade plane and the blade-in-between plane,
respectively. The influence of vertical blades array upon the characteristics of the turbulent coherent structures was analyzed by
POD method. It is observed that the vortical structures are cut and deformed by blades array and the skin frictional reduction is
closely associated with the subsequent evolution of turbulent structures.
1. Introduction
The reduction of frictional drag of turbulent boundary layer
is of great importance for the fuel economy of ship. Along
with the development of hull form optimization technique,
the wave-making resistance is less than 20% of the total
drag of most modern ships. Therefore, the advantage from
the reduction of the remaining frictional drag would be
enormous. The fuel consumption of global ocean shipping
in 2003 was estimated 2.1 billion barrel/year [1], which
corresponds to approximately 200 billion US$/year. Thus,
10% reduction of frictional drag, with the propulsive power
being estimated to be 90% of total power consumption, would
lead to saving of approximately 14 billion US$/year.
The skin frictional drag is closely associated with the
coherent structures, for example, hairpin vortices in the turbulent boundary layer flow. Various control strategies toward
the attenuation of the drag-inducing flow structure have
been proposed during several decades. From the viewpoint
of reliability, the passive techniques such as riblet [2, 3],
compliant coating [4], and LEBU (Large Eddy BreakUp
device) are more suitable for the marine application. Hefner
et al. [5] conducted the experiments with LEBU to reduce the
skin friction downstream of the LEBU devices and achieved
24% of drag reduction compared to undisturbed flat plate
levels. The LEBU devices directly interact with and change the
large eddy structures, thus interrupting the production loop
and reducing the bursting events causing surface stress.
Recently, Hutchins [6] used the array of thin vertical
plates in the turbulent boundary layer. This array chops
off large structures, thereby disconnecting the link between
outer and inner structures. The height and the spanwise
packing (the spacing between each plate) were varied to find
optimal values. Maximum skin friction reduction amounted
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Advances in Mechanical Engineering
20 mm
12 mm
Figure 1: Circulating water tunnel and outer-layer vertical blades installed in the test section.
to 30%. However, these results do not necessarily imply the
usefulness of this device in real application. This is because
only the reduction of local skin friction downstream of
the device was quantified. The device drag associated with
the momentum deficit was not investigated in detail. In
case of LEBU, the device drag usually exceeds the reduced
skin friction, thereby severely restricting the applicability. A
couple of towing tank measurements of a flat plate and a ship
model with blades array have been conducted to assess the
total drag reduction capability. Park et al. [7] showed a 9.6%
reduction of total drag for flat plate. For a KVLCC ship model,
a 2.8% total drag reduction has been reported by An et al. [8].
In both studies, the drag reduction efficiency appeared to be
correlated with the outer scaling based on the boundary layer
thickness. This implies that the present outer-layer vertical
blades array is more plausible in terms of the applications to
such high Reynolds number flows as the flow around ship
hull.
With a view to enabling the identification of drag reduction mechanism, a detailed flow field measurements have
been performed using 2D time resolved PIV in this study.
The time-mean velocity profiles and turbulence quantities
are compared between the baseline case and the blade case.
The influence of vertical blades array upon the turbulent
coherent structures is scrutinized in 𝑥𝑦-planes as well as 𝑥𝑧planes. The POD analyses based on the unsteady flow field in
both planes are employed to substantiate the changes of the
coherent structures due to the vertical blades array.
2. Experimental Methods
2.1. PIV Measurement Setup. The PIV measurement in this
study was performed in the circulating water tunnel displayed
in Figure 1. The test section is a 2-dimensional channel with
the cross section of 0.4 m (width) × 0.16 m (height). Water
flow in the test section is driven by a centrifugal pump. The
flow speed is controlled by adjusting the rotating speed of the
pump by the inverter. A magnetic flow meter was employed to
monitor the flow rate. In this study, the average flow velocity
𝑈𝑀, which is defined by dividing volume flow rate by the cross
sectional area, was set to 0.534 m/s.
The 2D time-resolved PIV system (Dantec Dynamics)
consisted of high repetition rate Nd:YAG laser, high-speed
CMOS camera, and synchronizer. The illuminating laser was
a Lee diode-pumped Nd:YAG laser (LDP-100MQG) with output wavelength of 532 nm, variable repetition rate from 10 Hz
to 20 kHz, and pulse energy of 11 mJ. The high-speed camera
was a 10 bit resolution NanoSense Mk. III CMOS camera
with a maximum frame rate of 1040 Hz, a pixel resolution of
1,280 × 1,024, and internal flash memory of 2 GByte. This
memory capacity allowed successive acquisition of 500 frame
pairs with the maximum frame resolution of 1,280 × 1,024
pixels. Hollow glass beads with a diameter of 10 𝜇m had been
added in the water reservoir prior to the measurement.
Profile of time-mean velocity for the baseline, undisturbed fully-developed channel flow was measured by the
PIV system. The parameters of the baseline channel flow are
Advances in Mechanical Engineering
3
Table 1: Parameters for the baseline case without blades array.
𝑈𝑀 (m/s)
0.534
𝑢𝜏 (m/s)
0.0252
𝛿 (mm)
80.0
𝐶𝑓 × 10
4.440
3
Re𝜏
2,104
listed in Table 1. The local wall shear stress 𝜏𝑤 was calculated
by using the CPT (Computational Preston Tube) method
from the mean velocity profile, which was first introduced by
Nitsche et al. [9]. This method is basically to fit the measured
velocity profile onto the canonical velocity profile in turbulent
boundary layer of Szablewski [10] as follows:
𝑢+
𝑦+
= ∫ ((2 (1 + 𝐾3 𝑦+ ) 𝑑𝑦+ )
0
{
{
2
× (1 + {1 + 4(𝐾1 𝑦+ ) (1 + 𝐾3 𝑦+ )
{
{
× [1 − exp ((−𝑦+ √1 + 𝐾3 𝑦+ )
[
2
0.5
−1
}
}
−1
× (𝐾2 ) ) ] } ) ) .
}
]}
(1)
Here, 𝐾1 corresponds to the von Karman constant, 𝐾2 to the
van Driest damping factor, and 𝐾3 = (]/𝜌𝑢𝜏3 )(𝑑𝑝/𝑑𝑥) being
the dimensionless pressure parameter. Compared with the
Clauser plot method, this method is not affected by subjective
selection of the extent for the logarithmic region, thereby
giving more robust estimation of 𝜏𝑤 . This was verified as a
useful tool to estimate the skin friction in a wide variety of
nonequilibrium turbulent boundary layer flows [11].
Figure 1 also demonstrates the outer-layer blades installed
in the test section of the circulating water tunnel. Here,
the height and the spanwise packing were set to 20 mm
and 12 mm, respectively. These values correspond to the
nondimensional heights of ℎ/𝛿 = 0.177 (ℎ+ = 385) and
nondimensional spanwise packings of 𝑧/𝛿 = 0.106 (𝑧+ =
231) based on the half-channel height 𝛿 and the friction
velocity 𝑢𝜏 for the undisturbed baseline case. Although the
nondimensional height of ℎ/𝛿 = 0.177 is less than the optimal
range found in the preceding studies of Park et al. [7] and An
et al. [8], the height of the blade is high enough to extend to
the outer-layer flow, thereby affecting the flow field.
The PIV measurements were performed in two measurement plane setups, 𝑥𝑦-planes (0 ≤ 𝑥/ℎ ≤ 32, 𝑧 = 0,
6 mm) and 𝑥𝑧-planes (0 ≤ 𝑥/ℎ ≤ 32, 𝑦 = 1, 4, 9 mm).
The field of view had dimensions of 90 mm by 75 mm, with
the plane oriented parallel to the mean flow direction, and
this yielded 78 by 60 velocity vectors after processing with
50% overlap. 4,000 PIV realizations were used to compute
the mean velocity profile. The analysis of PIV measurement
uncertainty described in Scarano and Riethmuller [12] was
employed based on the formula 𝜀𝜇 = 𝑍𝐶𝜎/𝜇√𝑁, where 𝑍𝐶 is
the confidence coefficients 𝜇 and 𝜎 are the time-mean and the
standard deviation of the measured velocity. The uncertainty
for the time-mean streamwise velocity 𝑈 was estimated to be
7% using a 95% confidence interval.
As depicted in Figure 2, the 𝑥𝑦-planes with 𝑧 = 0 mm
correspond to the in-blade plane, while the 𝑥𝑦-planes with
𝑧 = 6 mm being the midblade plane. It is worthwhile
to mention that the flow behind the blades array would
exhibit a significant three-dimensionality, that is, the change
of flow field depending on the spanwise location relative to
blade. Therefore, the two spanwise locations are selected to
investigate such three-dimensionality. The 𝑥𝑧-planes were
located at three heights from the wall, 𝑦 = 1 mm (𝑦+ = 20),
𝑦 = 4 mm (𝑦+ = 80), and 𝑦 = 9 mm (𝑦+ = 180). Thus,
these heights were set for the investigation in the inner layer
(𝑦+ = 20) and outer layer (𝑦+ = 80 and 180).
2.2. POD Analysis Method. The POD is a well-known technique determining an optimal basis for the reconstruction
of a data set. Since introduced by Karhunen [13], this
technique has been extensively employed for the extraction
and identification of the coherent structures [14]. The basis
function obtained from POD analysis of a spatial function represents a dominant structure. For a spatiotemporal
velocity field 𝑢(𝑥,⃗ 𝑡), POD determines orthonormal functions
⃗ 𝑗 = 1, 2, . . ., such that the projection of the velocity
𝜑𝑗 (𝑥),
field onto the first 𝑛 functions 𝑢̂(𝑥,⃗ 𝑡) = ∑𝑛𝑗=1 𝑎𝑗 (𝑡) 𝜑𝑗 (𝑥)⃗
minimizes the square error of the projection 𝐸, defined by
2
⃗ ⟩. The functions 𝜑𝑗 (𝑥)⃗ are
𝐸 = ⟨‖𝑢(𝑥,⃗ 𝑡) − ∑𝑛𝑗=1 𝑎𝑗 (𝑡)𝜑𝑗 (𝑥)‖
obtained by solving the integral equation
∫ 𝑅 (𝑥,⃗ 𝑥⃗∗ ) 𝜑 (𝑥⃗∗ ) 𝑑𝑥⃗∗ = 𝜆𝜑 (𝑥)⃗ ,
(2)
where 𝑅(𝑥,⃗ 𝑥⃗∗ ) = ⟨𝑢(𝑥)⃗ 𝑢(𝑥⃗∗ )⟩ is the autocorrelation of
the velocity. The above equation is again an eigenvalue
problem with the integration variable being 𝑥⃗∗ . Solving this
⃗ 𝑗 = 1, 2, . . . , 𝑛. For
equation gives 𝑛 eigenfunctions 𝜑𝑗 (𝑥),
a function with two-dimensional spatial dependence, direct
numerical calculation of the above integral equation requires
considerable amount of calculation time. The method of
snapshots proposed by Sirovich [15] leads to a dramatic saving
in computational effort in computing the eigenfunctions. In
this study, the method of snapshots has been employed.
3. Results
3.1. Time-Mean Statistics and Unsteady PIV Measurement
Results. From the time-mean velocity profiles measured
in 𝑥𝑦-planes, the local wall shear stress 𝜏𝑤 and friction
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Advances in Mechanical Engineering
12 mm
L = 1460 mm
Field of view
A = 270 mm
y
z = 0 mm
B = 1190 mm
x = 90 mm, y = 70 mm
z = 6 mm
x
L
A
B
xz-plane (9 mm)
xy-plane
Chamber
xz-plane (4 mm)
xz-plane (1 mm)
Contraction
y
Flow
Blades
z
x
Flowmeter
Laser sheet
Inverter
Centrifugal pump
Test
section
CMOS cam
1,024 × 1,280
Nd: YAG laser
Synchronizer
PC
Figure 2: Measurement domain and schematic diagram of PIV.
velocity 𝑢𝜏 = √𝜏𝑤 /𝜌 are estimated as a function of 𝑥, the
downstream distance from the trailing edge of the blade.
The local shear stress 𝜏𝑤 (𝑥) is then nondimensionalized as
a local skin frictional coefficient 𝐶𝑓 (𝑥) = 𝜏𝑤 (𝑥)/0.5𝜌𝑈𝑚2 .
Figure 3 presents the streamwise development in two spanwise measurement locations. For comparison, the baseline
skin friction value without blades is designated as a horizontal
solid line. It is found that the Z06 plane (midblade plane)
is noted predominantly by skin friction reduction, whilst
the Z00 plane (in-blade plane) shows local skin friction
augmentation regions. The average skin friction reduction
rates are calculated as 7.95% for the Z06 plane and 2.73%
for the Z00 plane, respectively. Also it is revealed that the
streamwise local skin friction distributions at two spanwise
locations exhibit negative correlation. It is worth mentioning
that momentum deficit is expected downstream of blade in
Z00 plane, whilst the Z06 plane is not associated with it.
Despite the higher momentum in Z06 plane, the skin friction
becomes smaller in the average. This suggests that the skin
friction reduction is mainly attributable to the constraint
Advances in Mechanical Engineering
5
0.0055
12 mm
0.005
Cf
Z00 Z06
0.0045
0.004
0.0035
10
0
20
30
x/h
Baseline
Z00
Z06
Figure 3: Streamwise development of local skin friction coefficient.
25
0.6
U/u𝜏
U (m/s)
0.5
0.4
0.3
0.2
0
10
20
y (mm)
x/h = 0.50
x/h = 0.75
x/h = 1.00
x/h = 1.25
x/h = 1.50
30
40
x/h = 2.00
x/h = 2.50
x/h = 3.00
x/h = 4.00
x/h = 5.00
(a)
20
15
10
102
yu𝜏 /
x/h = 0.50
x/h = 0.75
x/h = 1.00
x/h = 1.25
x/h = 1.50
x/h = 2.00
103
x/h = 2.50
x/h = 3.00
x/h = 4.00
x/h = 5.00
Log law
(b)
Figure 4: Mean velocity profiles measured in Z00 plane; (a) dimensional plot, (b) nondimensional plot.
of spanwise motion of the coherent structures between the
blades, which is expected in the Z06 plane.
Figures 4 and 5 show the profiles of time mean streamwise
velocity in the Z00 and Z06 planes, respectively. The velocity
profiles in the Z00 plane (Figure 4) exhibit hollows near the
edge of the blade 𝑦 = 20 mm, which almost disappear at
𝑥/ℎ = 5. These are associated with the wake of the blade.
On the other hand, such hollow is not observed from the
velocity profiles in the Z06 plane (Figure 5). The profiles of
the streamwise turbulence intensities √𝑢󸀠2 /𝑈𝑚 in the Z00
and Z06 planes are plotted in Figures 6 and 7, respectively. In
Z00 plane (Figure 6(a)), the streamwise turbulence intensity
becomes larger than the baseline case just after the blade
𝑥/ℎ = 0.5. This is caused by the vortices in blade wake.
The increase of turbulent energy, however, does not persist
in further downstream region and the streamwise turbulence intensity becomes slightly smaller than the baseline
case. Similarly, in Z06 plane (Figure 7(a)), the streamwise
turbulence intensity shows increase over the baseline case
and then subsequent decrease downstream. The wall-normal
turbulence intensity, plotted in Figures 6(b) and 7(b), presents
similar behavior with more discernible reduction from the
baseline case. The most significant reduction is observable
in the Reynolds stress in Figures 6(c) and 7(c). It is notable
that the Reynolds stress becomes minimum near the edge of
the blade 𝑦/ℎ = 1.0 in the Z00 plane, whilst there exists a
local maximum of the Reynolds stress at 𝑦/ℎ = 1.0 in the
Z06 plane. The decrease in the Reynolds stress implies the
attenuation of the turbulence activities, which is in support
of the skin friction reduction.
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Advances in Mechanical Engineering
25
0.6
20
U/u𝜏
U (m/s)
0.5
0.4
0.3
0.2
0
10
20
y (mm)
30
15
10
40
102
103
yu𝜏 /
x/h = 2.00
x/h = 2.50
x/h = 3.00
x/h = 4.00
x/h = 5.00
x/h = 0.50
x/h = 0.75
x/h = 1.00
x/h = 1.25
x/h = 1.50
x/h = 2.50
x/h = 3.00
x/h = 4.00
x/h = 5.00
Log law
x/h = 0.50
x/h = 0.75
x/h = 1.00
x/h = 1.25
x/h = 1.50
x/h = 2.00
(a)
(b)
Figure 5: Mean velocity profiles measured in Z06 plane; (a) dimensional plot, (b) nondimensional plot.
0.06
0.15
󳰀
rms
/Um
󳰀
urms
/Um
0.2
0.1
0.05
0
0
0.5
1
1.5
y/h
2
2.5
0.04
0.02
0
3
0
0.5
x/h = 5.00
x/h = 7.00
x/h = 9.00
x/h = 11.00
x/h = 15.00
Without blade
x/h = 0.50
x/h = 1.00
x/h = 2.00
x/h = 3.00
x/h = 4.00
1.5
y/h
Without blade
x/h = 0.50
x/h = 1.00
x/h = 2.00
x/h = 3.00
x/h = 4.00
(a)
2
Reynolds stress/Um
1
2
2.5
3
x/h = 5.00
x/h = 7.00
x/h = 9.00
x/h = 11.00
x/h = 15.00
(b)
0.002
0.0015
0.001
0.0005
00
0.5
1
1.5
y/h
Without blade
x/h = 0.50
x/h = 1.00
x/h = 2.00
x/h = 3.00
x/h = 4.00
2
2.5
3
x/h = 5.00
x/h = 7.00
x/h = 9.00
x/h = 11.00
x/h = 15.00
(c)
Figure 6: Turbulence intensity profiles in Z00 plane; (a)√𝑢󸀠2 /𝑈𝑚 , (b)√V󸀠2 /𝑈𝑚 , and (c) −𝑢󸀠 V󸀠 /𝑈𝑚2 .
Advances in Mechanical Engineering
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0.06
0.15
󳰀
rms
/Um
󳰀
urms
/Um
0.2
0.1
0.05
0
0
0.5
1
1.5
y/h
2
2.5
0.04
0.02
0
3
0
0.5
x/h = 5.00
x/h = 7.00
x/h = 9.00
x/h = 11.00
x/h = 15.00
Without blade
x/h = 0.50
x/h = 1.00
x/h = 2.00
x/h = 3.00
x/h = 4.00
1.5
y/h
Without blade
x/h = 0.50
x/h = 1.00
x/h = 2.00
x/h = 3.00
x/h = 4.00
(a)
2
Reynolds stress /Um
1
2
2.5
3
x/h = 5.00
x/h = 7.00
x/h = 9.00
x/h = 11.00
x/h = 15.00
(b)
0.002
0.0015
0.001
0.0005
0
0
0.5
1
1.5
y/h
Without blade
x/h = 0.50
x/h = 1.00
x/h = 2.00
x/h = 3.00
x/h = 4.00
2
2.5
3
x/h = 5.00
x/h = 7.00
x/h = 9.00
x/h = 11.00
x/h = 15.00
(c)
Figure 7: Turbulence intensity profiles in Z06 plane; (a)√𝑢󸀠2 /𝑈𝑚 , (b)√V󸀠2 /𝑈𝑚 , and (c) −𝑢󸀠 V󸀠 /𝑈𝑚2 .
Figure 8 displays the plots of instantaneous velocity
vectors and the contours of spanwise vorticity 𝜔𝑧 for the
baseline case and the blade case in Z06 plane in comparison.
Here, the volumetric mean velocity 𝑈𝑀 has been subtracted
from the streamwise velocity to exhibit coherent structures
convecting downstream. Figures 8(a) and 8(b) are both
clearly characterized by such features of coherent structures
as the concentrated spanwise vorticity in the shear layer,
ejection/sweep motion, and so forth. There is hardly found a
qualitative change in the coherent structures observed in 𝑥𝑦
plane due to the presence of blade.
Figure 9 through Figure 11 illustrate the instantaneous
flow field viewed from the above, that is, in the 𝑥𝑧 plane
at varying distance from the wall. Here, the velocity vector
plots of (𝑢󸀠 , 𝑤󸀠 ) and contour plots of the streamwise velocity
fluctuations 𝑢󸀠 are given for baseline case and blade case.
The red-colored contours designates high-speed streamwise
velocity region, while blue ones correspond to low speed
regions. These plots enable the comparison of flow structures
at respective flow region. Figure 9 compares the flow field at
𝑦 = 1 mm (𝑦+ = 20) which corresponds to the buffer layer.
The baseline case in Figure 9(a) is spotted with red (highspeed) streaks and blue (low-speed) streaks, which is a clear
indication of the near wall turbulent flow features. The blade
case in Figure 9(b) shows essentially similar characteristics
as those in Figure 9(a) with some minor change of extended
low speed streaks. From this observation, it is suggested that
the near-wall turbulent structures are seldom changed by the
vertical blades. This is consistent that the spanwise distance
between blades in this case is over 200 in wall unit, which
is wider than the spanwise spacing of the near wall streaky
structures.
The instantaneous flow structure observed in the 𝑥𝑧plane of the outer layer (𝑦+ = 80) is compared in Figure 10.
It is first found that the streaks are grown both in length
and width in the baseline case in Figure 10(a). Adrian et al.
[16] described the coherent structure as the nested packet of
hairpin vortices, not evenly distributed individual hairpins.
The extended streak is attributable to the packet of hairpin
vortices. On the contrary, the blade case in Figure 10(b)
exhibits contours which are torn apart. It is conjectured that
the presence of blade interrupts the growth of the large
Advances in Mechanical Engineering
t = 0.000 s
1250
y+
1000
750
500
250
0
0
300 600 900 1200 1500 1800
0.09
0.08
0.06
0.05
0.04
0.03
0.01
0.00
−0.01
−0.03
−0.04
−0.05
−0.06
−0.08
−0.09
1500
1250
1000
y+
1500
0.09
0.08
0.06
0.05
0.04
0.03
0.01
0.00
−0.01
−0.03
−0.04
−0.05
−0.06
−0.08
−0.09
𝜔+z
t = 0.000 s
750
500
250
0
0
x+
𝜔+z
8
300 600 900 1200 1500 1800
x+
10u𝜏
10u𝜏
(a)
(b)
Figure 8: Vector plot and spanwise vorticity plot in 𝑥𝑦-plane; (a) without blade, (b) with blade (Z06 plane).
t = 0.010 s
t = 0.010 s
6.00
6.00
2000
4.00
0.00
z+
2.00
1000
−2.00
500
0
4.00
1500
u󳰀 /u𝜏
z+
1500
500
−6.00
500
1000
x+
0.00
1000
−2.00
−4.00
0
2.00
u󳰀 /u𝜏
2000
0
1500
−4.00
−6.00
0
500
1000
x+
1500
10u𝜏
10u𝜏
(a)
(b)
Figure 9: Vector plot and contour plot of streamwise velocity fluctuation in 𝑥𝑧-plane at 𝑦 = 1 mm (𝑦+ = 20); (a) without blade, (b) with
blade.
t = 0.010 s
t = 0.010 s
6.00
6.00
4.00
4.00
−2.00
500
0.00
z+
0.00
2.00
1000
−2.00
500
−4.00
−6.00
0
500
x+
10u𝜏
1000
u󳰀 /u𝜏
2.00
1000
u󳰀 /u𝜏
z+
1500
0
1500
−4.00
0
−6.00
0
500
x+
1000
10u𝜏
(a)
(b)
Figure 10: Vector plot and contour plot of streamwise velocity fluctuation in 𝑥𝑧-plane at 𝑦 = 4 mm (𝑦+ = 80); (a) without blade, (b) with
blade.
Advances in Mechanical Engineering
9
t = 0.010 s
t = 0.010 s
6.00
4.00
0.00
−2.00
500
−2.00
500
−4.00
0
2.00
1000
z+
z+
0.00
u󳰀 /u𝜏
2.00
1000
6.00
1500
4.00
−4.00
−6.00
0
500
x+
0
1000
u󳰀 /u𝜏
1500
−6.00
0
500
1000
x+
10u𝜏
10u𝜏
(a)
(b)
10−4
0
10−1
10−2
10−3
10−4
0
Eigenvalue (baseline)
Eigenvalue (Z00)
Eigenvalue (Z06)
Cumulative sum of energy (baseline)
Cumulative sum of energy (Z00)
Cumulative sum of energy (Z06)
100
90
80
70
60
50
40
30
20
10
0
50 100 150 200 250 300 350 400
Mode
Eigenvalue (baseline)
Eigenvalue (Y09)
Cumulative sum of energy (baseline)
Cumulative sum of energy (Y09)
(b)
(a)
Figure 12: Eigenvalue versus eigenmode; (a) 𝑥𝑦 plane, (b) 𝑥𝑧 plane.
4
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900
y+
0
600
−2
300
−4
0
5
10
15
tuavr /L
20
400
0.4u𝜏
(a) 1st Eigen mode (15.8%)
Figure 13: Continued.
800
x+
1200
1600
Cumulative sum of energy (%)
10−3
100
90
80
70
60
50
40
30
20
10
0
50 100 150 200 250 300 350 400
Mode
Eigenvalue
10−2
a1 (t) × 1000
Eigenvalue
10
−1
Cumulative sum of energy (%)
Figure 11: Vector plot and contour plot of streamwise velocity fluctuation in 𝑥𝑧-plane at 𝑦 = 9 mm (𝑦+ = 180); (a) without blade, (b) with
blade.
10
Advances in Mechanical Engineering
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2
900
0
y+
a2 (t) × 1000
4
600
−2
300
−4
0
5
10
15
tuavr /L
20
400
800
x+
1200
1600
1200
1600
1200
1600
1200
1600
0.4u𝜏
(b) 2nd Eigen mode (7.6%)
1200
2
900
0
y+
a3 (t) × 1000
4
600
−2
300
−4
0
5
10
15
tuavr /L
400
20
800
x+
0.4u𝜏
(c) 3rd Eigen mode (5.2%)
1200
2
900
0
y+
a4 (t) × 1000
4
600
−2
300
−4
0
5
10
15
tuavr /L
400
20
800
x+
0.4u𝜏
(d) 4th Eigen mode (4.4%)
1200
2
900
0
y+
a5 (t) × 1000
4
−2
600
300
−4
0
5
10
15
tuavr /L
20
400
0.4u𝜏
(e) 5th Eigen mode (2.9%)
Figure 13: Continued.
800
x+
Advances in Mechanical Engineering
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1200
2
900
0
y+
a6 (t) × 1000
4
600
−2
300
−4
0
5
10
15
tuavr /L
20
400
800
1200
1600
x+
0.4u𝜏
(f) 6th Eigen mode (2.4%)
4
1500
2
1200
0
900
y+
a1 (t) × 1000
Figure 13: POD coefficient and POD mode vector of baseline case in 𝑥𝑦 plane, baseline case; (a) 1st mode, (b) 2nd mode, (c) 3rd mode, (d)
4th mode, (e) 5th mode, and (f) 6th mode.
600
−2
300
−4
0
5
10
15
tuavr /L
20
400
800
1200
x+
1600
2000
800
1200
x+
1600
2000
0.4u𝜏
4
1500
2
1200
0
900
y+
a2 (t) × 1000
(a) 1st Eigen mode (10.4%)
600
−2
300
−4
0
5
10
15
tuavr /L
20
400
0.4u𝜏
(b) 2nd Eigen mode (8.2%)
Figure 14: Continued.
Advances in Mechanical Engineering
4
1500
2
1200
0
900
y+
a3 (t) × 1000
12
600
−2
300
−4
0
5
10
15
tuavr /L
400
20
800
1200
1600
2000
800
1200
x+
1600
2000
800
1200
x+
1600
2000
800
1200
x+
1600
2000
x+
0.4u𝜏
4
1500
2
1200
0
900
y+
a4 (t) × 1000
(c) 3rd Eigen mode (5.2%)
600
−2
300
−4
0
5
10
15
tuavr /L
400
20
0.4u𝜏
4
1500
2
1200
0
900
y+
a5 (t) × 1000
(d) 4th Eigen mode (4.0%)
600
−2
300
−4
0
5
10
15
tuavr /L
400
20
0.4u𝜏
4
1500
2
1200
0
900
y+
a6 (t) × 1000
(e) 5th Eigen mode (3.5%)
600
−2
300
−4
0
5
10
15
tuavr /L
20
400
0.4u𝜏
(f) 6th Eigen mode (2.7%)
Figure 14: POD coefficient and POD mode vector of blade case in 𝑥𝑦 plane, blade case in Z00 plane; (a) 1st mode, (b) 2nd mode, (c) 3rd
mode, (d) 4th mode, (e) 5th mode, and (f) 6th mode.
13
4
1500
2
1200
0
900
y+
a1 (t) × 1000
Advances in Mechanical Engineering
600
−2
300
−4
0
5
10
15
tuavr /L
400
20
800
1200
x+
1600
2000
800
1200
x+
1600
2000
0.4u𝜏
4
1500
2
1200
0
900
y+
a2 (t) × 1000
(a) 1st Eigen mode (27%)
600
−2
300
−4
0
5
10
15
tuavr /L
400
20
0.4u𝜏
4
1500
2
1200
0
900
y+
a3 (t) × 1000
(b) 2nd Eigen mode (9.8%)
600
−2
300
−4
0
5
10
15
tuavr /L
400
20
800
1200
1600
2000
1200
1600
2000
x+
0.4u𝜏
4
1500
2
1200
0
y+
a4 (t) × 1000
(c) 3rd Eigen mode (4.5%)
900
600
−2
300
−4
0
5
10
15
tuavr /L
20
400
0.4u𝜏
(d) 4th Eigen mode (4.0%)
Figure 15: Continued.
800
x+
Advances in Mechanical Engineering
4
1500
2
1200
0
900
y+
a5 (t) × 1000
14
600
−2
300
−4
0
5
10
15
tuavr /L
400
20
800
1200
x+
1600
1200
1600
2000
0.4u𝜏
4
1500
2
1200
0
900
y+
a6 (t) × 1000
(e) 5th Eigen mode (2.1%)
600
−2
300
−4
0
5
10
15
tuavr /L
20
400
800
2000
x+
0.4u𝜏
(f) 6th Eigen mode (1.9%)
Figure 15: POD coefficient and POD mode vector of blade case in 𝑥𝑦 plane, blade case in Z06 plane; (a) 1st mode, (b) 2nd mode, (c) 3rd
mode, (d) 4th mode, (e) 5th mode, and (f) 6th mode.
scale turbulent structures primarily in the outer layer. The
suppression of the coherent structure growth in outer layer
by the blade becomes even more pronounced in Figure 11 at
𝑦 = 9 mm (𝑦+ = 180). Along with the growth of the streak,
there is found a significant spanwise velocity in the baseline case (in Figure 11(a)). However, the flow field for
the blade case in Figure 11(b) remains unchanged from
that observed in inner layers, hardly showing any significant spanwise motion. In summary, the present vertical
blades array is found to suppress the growth of outerlayer turbulent coherent structures by shredding them and
blocking the spanwise momentum transfer in the outer
layer.
3.2. POD Analysis Results. The eigenvalue of each mode in
POD analysis results represents the energy share of corresponding mode. Figure 12 displays eigenvalues and cumulative energy sum of baseline flow in comparison with those
for the blade cases (𝑥𝑦-Z00, 𝑥𝑦-Z06). The energy shares of
the 1st and 2nd mode for the baseline flow appear to be
15.8% and 7.6%, respectively. The cumulative sum of energy
up to 9th mode is 43.7% of the total energy. In the case of
𝑥𝑦-Z00, the 1st and 2nd modes take 10.4% and 8.2% and
the cumulative sum up to 9th modes contains 39.5% of the
total energy. This implies that the less amount of energy is
occupied by the lower order modes for the blade case. On
the other hand, lower order modes become more dominant
in the midblade plane (𝑥𝑦-Z06); 27.0% for the 1st mode and
cumulative sum up to 9th mode being 53.6%. From these
lower order energy distributions, it can be stated that the
evolution of coherent structures is interrupted by the blades
in the blade plane, whilst it is promoted in the midblade plane.
It is worthwhile to mention that the present POD analysis
was performed for the initial flow region just downstream
of the vertical blades, that is, 0 ≤ 𝑥/ℎ ≤ 4. Therefore, the
promotion of coherent structures for Z06 plane is responsible
for the initial skin friction increase observed on Figure 3. In
the meantime, in the case of 𝑥𝑧-plane observations shown
in Figure 12(b), cumulative energy sum of blade case (𝑥𝑧Y09) is lower than that of baseline flow. This implies that the
evolution of coherent structures is generally impeded by the
presence of the vertical blades array.
Advances in Mechanical Engineering
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1500
1200
2
0
z+
a1 (t) × 1000
4
900
600
−2
300
−4
0
5
10
tuavr /L
15
400
800
1200
800
1200
800
1200
x+
0.4u𝜏
(a) 1st Eigen mode (10.6%)
1500
4
1200
a2 (t) × 1000
2
z+
0
900
600
−2
300
−4
0
5
10
tuavr /L
15
400
x+
0.4u𝜏
(b) 2nd Eigen mode (6.7%)
1500
1200
2
0
z+
a3 (t) × 1000
4
900
600
−2
300
−4
0
5
10
tuavr /L
15
400
x+
0.4u𝜏
(c) 3rd Eigen mode (6.3%)
1500
1200
2
0
z+
a4 (t) × 1000
4
900
600
−2
300
−4
0
5
10
tuavr /L
15
400
x+
0.4u𝜏
(d) 4th Eigen mode (4.2%)
Figure 16: Continued.
800
1200
16
Advances in Mechanical Engineering
1500
1200
2
0
z+
a5 (t) × 1000
4
900
600
−2
300
−4
0
5
10
tuavr /L
400
15
x+
800
1200
800
1200
0.4u𝜏
(e) 5th Eigen mode (3.1%)
1500
1200
2
0
z+
a6 (t) × 1000
4
900
600
−2
300
−4
0
5
10
tuavr /L
400
15
x+
0.4u𝜏
(f) 6th Eigen mode (3.0%)
Figure 16: POD coefficient and POD mode vector of baseline case in 𝑥𝑧-plane, baseline case; (a) 1st mode, (b) 2nd mode, (c) 3rd mode, (d)
4th mode, (e) 5th mode, and (f) 6th mode.
Figures 13∼15 show time histories of POD coefficients
𝑎𝑗 (𝑡) and POD modes up to 6th lower order in the case of
baseline flow, 𝑥𝑦-Z00 and 𝑥𝑦-Z06 cases, respectively. The
3rd through 6th modes in 𝑥𝑦-Z00 case in Figure 14 become
different from those for the baseline flow in Figure 13. This is
consistent with the change of coherent structure due to the
interaction of flow between the blades.
Figures 16 and 17 compare POD modes of baseline flow
with those of blade case (𝑥𝑧-Y09) observed in 𝑥𝑧-plane. A
closer inspection indicates that the spanwise velocity component of the POD modes are suppressed for the blade case (𝑥𝑧Y09) compared with the baseline case. This again manifests
the skin friction reduction mechanism of vertical plates
array, the constriction of spanwise motion, and consequent
attenuation of coherent structures of the flow.
4. Conclusions
In this study, an experimental investigation has been conducted to investigate the drag reduction mechanism of the
outer-layer vertical blades array using a time-resolved 2D
PIV. Turbulent flow modification effect by blades array
has been revealed from the unsteady flow field measurement results from the PIV. The POD (Proper Orthogonal
Decomposition) analyses based on the unsteady flow field
in both planes are employed to substantiate the changes of
the coherent structures due to the vertical blades array. The
skin frictional reduction effect exhibited different behaviors
at different spanwise location; the blade plane (Z00 plane) and
the blade-in-between plane (Z06) showed 2.73% and 7.95%
drag reduction effect, respectively. Decrease in the turbulence
quantities, particularly the reduction of Reynolds stress, was
noted for the blade case. Whilst the turbulent flow field
measured in 𝑥𝑦 plane remained unchanged, those measured
in 𝑥𝑧 planes significant changes in the outer layer. The
instantaneous flow field and the POD modes indicated that
the spanwise momentum transfer and consequent growth
in the outer layer are hindered by the blades array, thereby
attenuating the coherent structure of turbulent flows. In the
previous study of Park et al. [7], the outer scaling is found
to give better collapse of drag reduction efficiency 𝐶𝐹 /𝐶𝐹0 .
This observation is in support of the outer-scaling of drag
reduction effect found in Park et al. [7].
Conflict of Interests
The authors declare that there is no conflict of interests
regarding the publication of this paper.
17
4
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2
1200
0
900
z+
a1 (t) × 1000
Advances in Mechanical Engineering
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−2
300
−4
0
5
10
tuavr /L
400
15
x+
800
1200
800
1200
800
1200
800
1200
0.4u𝜏
4
1500
2
1200
0
900
z+
a2 (t) × 1000
(a) 1st Eigen mode (11.3%)
600
−2
300
−4
0
5
10
tuavr /L
15
400
x+
0.4u𝜏
4
1500
2
1200
0
900
z+
a3 (t) × 1000
(b) 2nd Eigen mode (6.6%)
600
−2
300
−4
0
5
10
tuavr /L
15
400
x+
0.4u𝜏
4
1500
2
1200
0
900
z+
a4 (t) × 1000
(c) 3rd Eigen mode (4.8%)
600
−2
300
−4
0
5
10
tuavr /L
15
400
x+
0.4u𝜏
(d) 4th Eigen mode (4.0%)
Figure 17: Continued.
Advances in Mechanical Engineering
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1500
2
1200
0
900
z+
a5 (t) × 1000
18
600
−2
300
−4
0
5
10
tuavr /L
15
400
x+
800
1200
800
1200
0.4u𝜏
4
1500
2
1200
0
900
z+
a6 (t) × 1000
(e) 5th Eigen mode (2.8%)
600
−2
300
−4
0
5
10
tuavr /L
15
400
x+
0.4u𝜏
(f) 6th Eigen mode (2.3%)
Figure 17: POD coefficient and POD mode vector of baseline case in 𝑥𝑧-plane, blade case; (a) 1st mode, (b) 2nd mode, (c) 3rd mode, (d) 4th
mode, (e) 5th mode, and (f) 6th mode.
Acknowledgments
This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government
(MSIP) through GCRC-SOP (no. 2011-0030013) and Industrial Strategic Technology Development Program (Grant no.
10038606) funded by the Ministry of Trade, Industry and
Energy (MOTIE, Korea).
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