PHYSICS OF FLUIDS 20, 101510 共2008兲
Does the sailfish skin reduce the skin friction like the shark skin?
Woong Sagong, Chulkyu Kim, Sangho Choi, Woo-Pyung Jeon, and Haecheon Choia兲
School of Mechanical and Aerospace Engineering, Seoul National University,
Seoul 151-744, South Korea
共Received 5 February 2008; accepted 22 May 2008; published online 31 October 2008兲
The sailfish is the fastest sea animal, reaching its maximum speed of 110 km/h. On its skin, a
number of V-shaped protrusions pointing downstream exist. Thus, in the present study, the
possibility of reducing the skin friction using its shape is investigated in a turbulent boundary layer.
We perform a parametric study by varying the height and width of the protrusion, the spanwise and
streamwise spacings between adjacent ones, and their overall distribution pattern, respectively. Each
protrusion induces a pair of streamwise vortices, producing low and high shear stresses at its center
and side locations, respectively. These vortices also interact with those induced from adjacent
protrusions. As a result, the drag is either increased or unchanged for most of the cases considered.
Some of these cases show that the skin friction itself is reduced but the total drag including the form
drag on the protrusion is larger than that of a smooth surface. In a few cases, the drag is decreased
only slightly 共⬃1%兲 but this amount is within the experimental uncertainty. Since the shape of
present protrusions is similar to that used by Sirovich and Karlsson 关Nature 共London兲 388, 753
共1997兲兴 where V-shaped protrusions pointing upstream were considered, we perform another set of
experiments following their study. However, we do not obtain any drag reduction even with random
distribution of those V-shaped protrusions. © 2008 American Institute of Physics.
关DOI: 10.1063/1.3005861兴
I. INTRODUCTION
Skin-friction reduction in a turbulent boundary layer is
one of the important issues for various engineering applications such as vehicles, aircraft, ships, and fuel pipelines.
Many control methods1–6 have been suggested so far to reduce the skin friction in a turbulent boundary layer, but most
of them are active ones that require many feedback sensors
and actuators or significant amount of power input. The riblet
共v-grooved surface兲,6 similar to the denticles on the shark
skin, has been regarded as the most successful passive device, which reduces the skin friction up to 8% as compared
to a smooth surface. Nevertheless, the practical implementation of the riblet has been hampered by its small size. For
example, the tip-to-tip spanwise spacing of riblets is only O
共10 ␮m兲 when the riblets are applied to a commercial airplane for skin-friction reduction. With this small size, the
riblet-valley area is easily filled by dust in the air, resulting in
no drag reduction. Therefore, one needs a device having
scales larger than that of riblets for the reduction in skin
friction, but no such device has ever been found except that
of Sirovich and Karlsson.7
The sailfish is the fastest among all the sea animals,
reaching its maximum speed of 110 km/h,8 whereas the
maximum speed of sharks is 50 km/h. Biologists have studied the sailfish due to its peculiar overall shape as well as its
amazing speed. The sailfish folds its sail-like dorsal fin into
the body for fast swimming. The role of its dorsal fin is to
a兲
Author to whom correspondence should be addressed. Electronic mail:
[email protected]. Also at the Center for Turbulence and Flow Control Research, Institute of Advanced Machinery and Design, Seoul National University, Seoul 151-744, South Korea.
1070-6631/2008/20共10兲/101510/10/$23.00
ensure high maneuverability9 or to work as a brake by increasing drag.10 Ovchinnikov11 argued that the bill of the
sailfish generates turbulence earlier in the boundary layer
even at very low speeds and delays separation. Walters12
suggested that the sailfish skin could function as a compliant
wall, similar to the role of the dolphin skin.13 This hypothesis
was based on the existence of oil-filled canals in the skin of
sailfish. He also suggested that the sailfish could reduce the
drag by redistributing fluid from high to low pressure regions
through the pore-canal system on its skin, called dynamic
damping, but this mechanism does not work in a turbulent
boundary layer.14 Ovchinnikov15 observed gas bubbles on
the sailfish skin and speculated that the sailfish could decrease the drag by trapping air within its skin. These hypotheses have been suggested to explain the fast swimming ability of the sailfish but have not been proven yet.
Recently, we caught a sailfish from the South China Sea
to observe its skin more precisely and confirmed that there
exist large 共compared to the size of riblets兲 V-shaped protrusions pointing downstream on its skin, similar to
Nakamura’s16 description. Quite surprisingly, these protrusions are similar in shape but opposite in direction to those
used by Sirovich and Karlsson,7 with which they obtained
about 10% reduction in skin friction.
Therefore, in the present study, we investigate the possibility of skin-friction reduction in a turbulent boundary layer
using V-shaped protrusions existing on the sailfish skin
through both wind-tunnel experiment and direct numerical
simulation. We perform a parametric study by varying the
height and width of the protrusion, the spanwise and streamwise spacings between adjacent ones, and the overall distribution pattern 共i.e., parallel, staggered, or random distribu-
20, 101510-1
© 2008 American Institute of Physics
Downloaded 29 Jul 2010 to 147.46.120.125. Redistribution subject to AIP license or copyright; see http://pof.aip.org/pof/copyright.jsp
101510-2
Phys. Fluids 20, 101510 共2008兲
Sagong et al.
tion of the protrusions兲, respectively. We also conduct
another set of experiment and numerical simulation to examine the drag-reducing performance of the passive device used
by Sirovich and Karlsson.7
II. EXPERIMENTAL SETUP AND NUMERICAL DETAILS
The sailfish 共Istiophorus platypterus兲 shown in Fig. 1共a兲
is 2.25 m long and has a long and slender bill, a sail-like
dorsal fin, and a lunate caudal fin. On its skin, there are
hundreds of V-shaped protrusions pointing downstream 关Fig.
1共b兲兴. We caught this sailfish in the South China Sea with the
help of Korea Game Fish Association. We caught a total of
eight sailfishes and then released seven after observing their
skins on the boat. One sailfish was brought back to Korea for
further investigation and stuffed at Korea Research Center of
Maritime Animals for the preservation of the skin in good
condition. We measure the characteristic lengths of the protrusions. The mean values of their spanwise width 共W兲,
streamwise length 共L兲, and wall-normal height 共H兲 are
W = 1.8 mm, L = 4.7 mm, and H = O 共0.1 mm兲, respectively
关Fig. 2共a兲兴. Shown also in Fig. 2共a兲 are three different alignments of protrusions: parallel, staggered, and random, respectively. In the present study, the ratio of width to length
(a )
flow
(b )
FIG. 1. Sailfish: 共a兲 overall shape; 共b兲 skin.
u∞
W
H
Sz
α
L
Sx
<random>
<staggered>
<parallel>
FIG. 2. Experimental setup: 共a兲 schematic of the protrusions placed on a flat plate 共parallel, staggered, and
random distributions兲; 共b兲 schematic of the wind tunnel
and floating element apparatus.
(a )
y
z
test plate
x
trip wire
air bearing
micrometer
u∞
wind tunnel
test section
loadcell
floating element apparatus
(b )
Downloaded 29 Jul 2010 to 147.46.120.125. Redistribution subject to AIP license or copyright; see http://pof.aip.org/pof/copyright.jsp
Phys. Fluids 20, 101510 共2008兲
Does the sailfish skin reduce the skin friction
⌬D共%兲 = 共D − D0兲/D0 ⫻ 100,
共1兲
where s+ = su␶ / ␯, u␶ is the wall-shear velocity, and D and D0
are the drags with and without riblets, respectively. Again,
the present results agree well with the previous ones,6,23 confirming the accuracy of the present drag measurement.
We also perform direct numerical simulation to investigate the flow over V-shaped protrusions. An immersed
6
5
C f x 1000
共W / L兲 and angle 共␣兲 are fixed to be 0.383 and 53°, respectively, following direct measurement of the sailfish skin. The
parameters considered are the width 共W兲 and height 共H兲 of
each protrusion, the streamwise and spanwise spacings between adjacent ones 共Sx and Sz兲, and the overall distribution
pattern 共parallel, staggered, and random, respectively兲. Here,
the random distribution pattern is obtained from the parallel
pattern by random shifts of rows following the approach
made by Sirovich and Karlsson.7 For each set of parameters,
we directly measure the drag of the test plate 关Fig. 2共b兲兴. We
consider more than 170 configurations but only some of the
results are shown in this paper.
The experiment is conducted in an open-circuit suctiontype wind tunnel. The length of the test section is 2 m 共x兲,
the
cross-sectional
area
of
the
entrance
is
0.3 m 共y兲 ⫻ 0.4 m 共z兲, and that of the exit is slightly expanded 共0.3⫻ 0.42 m2兲 to obtain zero pressure gradient.
Here, x, y, and z denote the streamwise, vertical, and spanwise directions, respectively. The uniformity of mean
streamwise velocity and the turbulent intensity at 20 m/s are
both within 0.5%. The free-stream velocities 共u⬁兲 are from
15 to 30 m/s and the corresponding Reynolds numbers
共Re␪ = u⬁␪ / ␯兲 are from 4400 to 8300, where ␪ is the momentum thickness right before the test plate, and ␯ is the kinematic viscosity. The size of the test plate is 598 mm 共x兲
⫻ 298 mm 共z兲, corresponding to about 30 000 共x兲
⫻ 15 000 共z兲 in wall unit at u⬁ = 20 m / s 共here, the wallshear velocity u␶ right before the test plate is used兲. The flow
above the test plate shows the characteristics of the fully
turbulent boundary layer profile. Given u⬁, Re␪ slightly varies along the test plate: e.g., at u⬁ = 20 m / s, Re␪ ⬇ 5600 right
before the test plate and 6400 at the end location of the plate.
The skin friction on the test plate is measured using the floating element apparatus as shown in Fig. 2共b兲. The test plate is
supported by four air bearings. We minimize errors caused
from the misalignment between the test plate and bottom
wall of the test section by positioning the plate precisely
using a micrometer installed under each corner of the plate.
Also the air leakage near the gap between the test plate and
bottom wall is prevented by sealing up the floating element
apparatus. The skin friction is measured using a loadcell
共LC4001-G120, AND兲, and the repeatability error in the
force measurement is ⫾1.5%. For example, the drag force on
the test plate is 0.125⫾ 0.0018 N at u⬁ = 20 m / s.
For the verification of the present experimental setup, we
measure the drags on the smooth and riblet surfaces, respectively, and compare them with the data available in the literature. Figure 3共a兲 shows the skin-friction coefficient 共C f 兲
on the smooth surface. The present C f agrees well with the
previous ones.17–22 Figure 3共b兲 shows the drag variation
共⌬D兲 with the riblet tip-to-tip spacing 共s兲,
4
3
2
1
103
104
Re θ
(a )
20
0.4mm
15
0.35mm
10
D (%)
101510-3
5
0
s+
-5
h+
-10
0
(b )
10
20
30
40
50
s+
FIG. 3. Drag measurements in a turbulent boundary layer: 共a兲 skin-friction
coefficient on the smooth surface; 共b兲 drag on the riblet surface with the
tip-to-tip spacing 共s+兲: 共a兲 -----, Schlichting 共Ref. 17兲; —, Fernholz and
Finley 共Ref. 18兲; 䉮, Hites et al. 共Ref. 19兲; 䊊, Österlund et al. 共Ref. 20兲; 〫,
Purtell et al. 共Ref. 21兲; 䊐, Smits et al. 共Ref. 22兲; 쎲, present study. 共b兲 䊊,
Walsh 共h = s = 0.25 mm兲 共Ref. 6兲; 䊐, Walsh 共h = s = 0.51 mm兲 共Ref. 6兲; 䉮,
Bechert et al. 共h = 2.63 mm and s = 3.04 mm兲 共Ref. 23兲; 䉭, Bechert et al.
共h = 5.28 mm and s = 6.1 mm兲 共Ref. 23兲; 쎲, present study 共experiment, h
= 0.35 mm and s = 0.4 mm兲; 䊏, present study 共simulation, h+ = s+ = 10兲; 䉲,
present study 共simulation, h+ = 17 and s+ = 20兲. Shown in the inset in 共b兲 is
the actual riblet surface measured using a laser displacement sensor.
boundary method24 is used to represent the protrusions in the
Cartesian coordinate system. In the framework of this
method, the governing equations for the unsteady incompressible viscous flow become
1 ⳵2
⳵ ui
⳵
⳵p
u iu j = −
+
ui + f i ,
+
⳵t ⳵xj
⳵ xi Re ⳵ x j ⳵ x j
共2兲
⳵ ui
− q = 0,
⳵ xi
共3兲
where xi is the Cartesian coordinates, ui is the corresponding
velocity component, p is the pressure, f i is the momentum
forcing, and q is the mass source/sink.24 A second-order
semi-implicit fractional step method is used in time, and a
second-order central difference method is used in space. The
flow considered here is turbulent channel flow, and the upper
and lower walls of the channel are the flat plates without and
Downloaded 29 Jul 2010 to 147.46.120.125. Redistribution subject to AIP license or copyright; see http://pof.aip.org/pof/copyright.jsp
101510-4
y
Phys. Fluids 20, 101510 共2008兲
Sagong et al.
Ly
flow
x
z
Lx
Lz
change of only about 3%. The computational results are averaged over 500␦ / Ul.
For the verification of numerical method used in this
study, we performed two direct numerical simulations of
flows over riblets with 共h+ , s+兲 = 共10, 10兲 and 共17,20兲, respectively. The results are given in Fig. 3共b兲 together with those
from the present and other previous experiments, showing
excellent agreement with experimental data and confirming
the accuracy of the present simulation.
III. RESULTS AND DISCUSSION
FIG. 4. Schematic of the computational domain.
with V-shaped protrusions, respectively 共Fig. 4兲. A periodic
boundary condition is used in the streamwise and spanwise
directions and no-slip condition is applied to both the upper
and lower walls. All variables are nondimensionalized by the
channel half-height 共␦兲 and laminar centerline velocity 共Ul兲.
The Reynolds number considered is Re= Ul␦ / ␯ = 4200 共Re␶
= u␶␦ / ␯ ⯝ 180兲. A constant volume flux is imposed, Q
= 兰AcudA = 32 AcUl, throughout the computation, where Ac is
the cross-sectional area of the channel and u is the streamwise velocity.
For numerical simulation, we consider 15 cases of
V-shaped protrusions having W / L = 0.383 and ␣ = 53°. For all
the cases considered, the computational domain sizes are
larger than a minimal flow unit.25 The domain size and the
number of grid points vary depending on the size of the
protrusions, the streamwise and spanwise spacings between
adjacent ones, and their distribution pattern. For example, the
domain size is 5␦ 共x兲 ⫻ 2␦ 共y兲 ⫻ 3.9␦ 共z兲 and the number of
grid points is 160 共x兲 ⫻ 132 共y兲 ⫻ 128 共z兲 for the case of
H+ = 8, W+ = 174, Sz / W = 4, Sx / L = 2, and parallel distribution.
Uniform grids are used in the spanwise direction, while nonuniform grids are used in the streamwise and wall-normal
+
= 4,
directions. The grid spacings in wall unit are ⌬xmin
+
+
+
+
⌬xmax = 13.5, ⌬y min = 0.4, ⌬y max = 6.5, and ⌬z = 5.4. An additional computation with more grid points of 224 共x兲
⫻ 160 共y兲 ⫻ 256 共z兲 and further grid clustering near the protrusion for the case described above results in the total-drag
In Table I, we show the parameter ranges of protrusion
height 共H兲 and width 共W兲 adopted for the present experiment
and numerical simulation, together with those of sailfish and
those of Sirovich and Karlsson7 and Sirovich et al.28 The
values of u␶ and ␪ for the sailfish are obtained using the
seventh power law of mean velocity in a turbulent boundary
layer. Since the boundary layer thickness grows along the
body of the sailfish, the nondimensional height and width of
the protrusion existing on the sailfish skin also change. For
example, at the cruise speed of 2 m/s, H+ ⬇ 8.4 共H / ␪
⬇ 0.07兲 and W+ ⬇ 150 共W / ␪ ⬇ 1.21兲 right behind the gill and
H+ ⬇ 7.6 共H / ␪ ⬇ 0.03兲 and W+ ⬇ 136 共W / ␪ ⬇ 0.54兲 near the
caudal peduncle. Hence, in Table I, the nondimensional values of H and W for the case of the sailfish are taken at the
center of the sailfish body. The ranges of H+, W+, H / ␪, and
W / ␪ considered in the present study cover the values associated with the sailfish except those of H+ ⬇ 90 or W+
⬇ 1650. However, as shown in below, the cases with H+
⬇ 90 or W+ ⬇ 1650 should increase the drag significantly or
result in no change in drag, respectively.
Figures 5共a兲 and 5共b兲 show the variations in drag with
the height and width of the protrusion, respectively, from the
present experiment. Here, the drag includes the form drag on
the protrusion. The drag increases more with bigger height
共H+兲 and with smaller width 共W+兲 when other parameters are
fixed. With decreasing height and increasing width, the drag
converges to that without the protrusion. In Fig. 5共b兲, the
drag slightly decreases by 1% for the cases of H+ = 6.1, but
this amount of drag reduction is within the experimental un-
TABLE I. Comparison of nondimensionalized protrusion parameters 共H and W兲.
Present study
Experiment
Sailfish
Max. speed
共⯝30 m / s兲b
Cruise speed
共⯝2 m / s兲a
H 共mm兲
H+
H/␪
W 共mm兲
W+
W/␪
0.1
8
0.047
90
0.08
1.8
145
0.84
1650
1.45
Min.
Max.
Min.
Max.
0.05
2
0.01
1.7
65
0.39
0.32
25
0.08
6.8
500
1.64
¯
4
0.26
¯
44
2.81
¯
16
1.02
¯
261
16.7
a
c
b
d
References 26 and 27.
Reference 8.
Simulation
Sirovich
and Karlssonc
Sirovich et al.d
5–6
0.25
5
200
9.1
182
Reference 7.
Reference 28.
Downloaded 29 Jul 2010 to 147.46.120.125. Redistribution subject to AIP license or copyright; see http://pof.aip.org/pof/copyright.jsp
101510-5
Phys. Fluids 20, 101510 共2008兲
Does the sailfish skin reduce the skin friction
15
D (%)
10
5
0
-5
0
5
10
(a )
H+
15
20
25
15
D (%)
10
5
0
-5
0
(b )
100
200
300
W+
400
500
600
FIG. 5. Variations in drag with the 共a兲 height and 共b兲 width of protrusion: 共a兲
䊐, 共W+ , Sz / W , Sx / L , pattern兲 = 共85, 2 , 1.5, S兲; 䉭, 共103, 2, 1.5, P兲; 䊊, 共103, 2,
1.5, S兲; 〫, 共103, 3, 1.5, P兲; 䉮, 共125, 3, 1.5, P兲; 䉱, 共131, 2, 2, S兲; 䉲, 共171,
2, 2, S兲; 쎲, 共207, 2, 2, S兲; ⽧, 共250, 2, 2, S兲. 共b兲 䊊,
共H+ , Sz / W , Sx / L , pattern兲 = 共7.3, 2 , 2 , S兲; 䉭, 共8.1, 2, 2, S兲; 䊐, 共9.8, 2, 2, S兲;
䉮, 共11.7, 2, 2, S兲; 〫, 共12.5, 2, 2, S兲; 쎲, 共6.1, 4, 2, S兲; 䊏, 共9.8, 4, 2, S兲; 䉲,
共11.7, 4, 2, S兲; ⽧, 共12.5, 4, 2, S兲. Here, P and S denote the parallel and
staggered distribution patterns of protrusions, respectively.
certainty 共⫾1.5%兲. There might be a possibility of drag reduction using smaller values of H+ than 6.1, but Fig. 5共a兲
indicates that very small values of H+ 共⬍5兲 result in nearly
no change in the drag. Therefore, it seems clear that these
V-shaped protrusions do not reduce the drag in a flat-plate
boundary layer.
We perform direct numerical simulations to see how the
flow is modified by the protrusion. Figure 6 shows the mean
cross-flow vectors 共v , w兲 at the middle of the protrusion and
the contours of the mean shear-stress variation at the wall for
the cases of H+ = 4 and 8 共W+ = 87, Sz / W = 3, Sx / L = 2, and
parallel distribution pattern兲. Here, the shear-stress variation
is defined as 共du / dy 兩protrusion − du / dy 兩smooth兲 / du / dy 兩smooth. As
shown, this V-shaped protrusion generates a pair of mean
streamwise vortices. Upward and downward motions induced by these vortices produce low and high shear stresses
at the center and sides of the protrusion, respectively. At
H+ = 4, these vortices are weak and thus the shear-stress
variation is small. At H+ = 8, these vortices become stronger
and larger, and the shear-stress variation is evident. Overall,
the skin friction increases by 0% and 5%, respectively, for
H+ = 4 and 8 as compared to that of the smooth surface. The
protrusion also possesses its own form drag that becomes
larger with increasing height. The amounts of drag increase
due to the form drag are 2% and 5% for H+ = 4 and 8,
respectively.
Figure 7 shows the mean cross-flow vectors 共v , w兲 at the
middle of the protrusion and the contours of mean shearstress variation at the wall for the cases of W+ = 87 and 174
共H+ = 8, Sz / W = 3, Sx / L = 2, and parallel distribution pattern兲.
Besides the main pair vortices, secondary pair vortices exist
between adjacent protrusions at W+ = 174. The upward and
downward motions become stronger at W+ = 87 owing to the
interaction between the vortices generated from adjacent protrusions. They decrease the skin friction at the center region
of the protrusion and increase it at the sides, respectively.
The overall skin friction increases by 0% and 5% for W+
= 174 and 87, respectively. On the other hand, the amounts of
drag increase due to the form drag are 3% and 5% for W+
= 174 and 87, respectively.
Figures 8共a兲 and 8共b兲 show the variations in drag with
the spanwise and streamwise spacings between the adjacent
protrusions, respectively, from the present experiment. The
drag increases more with smaller spanwise and streamwise
spacings when other parameters are kept constant. It is also
expected that there is no change in drag when Sx and Sz
become large. Figure 9 shows the mean cross-flow vectors
共v , w兲 at the middle of the protrusion and the contours of
mean shear-stress variation on the wall for the cases of
Sz / W = 3 and 1.14 共H+ = 8, W+ = 87, Sx / L = 2, and parallel distribution pattern兲 from numerical simulation. It is clear that
pair vortices generated from each protrusion interact more
with those from adjacent protrusions and become stronger
when the spanwise spacing becomes smaller. Thus, the skin
frictions increase by 5% and 12% for Sz / W = 3 and 1.14,
respectively. The form drag also increases more at smaller
spanwise spacings. A similar trend is observed as the streamwise spacing varies 共not shown here兲.
Figure 10 shows the variation in drag with the distribution pattern of protrusions for eight different cases. The drag
increases for all the cases investigated no matter how the
protrusions are distributed on the flat plate. There seems to
be only small differences in drag variation between the staggered and random distributions. The protrusions distributed
in the parallel pattern increase drag more than those in the
staggered and random patterns when the streamwise and
spanwise spacings are small. In the parallel pattern, when
they travel downstream, pair vortices generated from a protrusion meet other pair vortices having the same senses of
rotation. Thus, the increase in the drag caused by pair vortices is maintained in the downstream location. On the other
hand, in the staggered pattern, the senses of rotation of upstream and downstream pair vortices are opposite to each
other, so the vortices become weaker than those in the parallel pattern and thus the drag increases less significantly in
the staggered pattern 共when the streamwise and spanwise
spacings are not large兲. This behavior is clearly observed
Downloaded 29 Jul 2010 to 147.46.120.125. Redistribution subject to AIP license or copyright; see http://pof.aip.org/pof/copyright.jsp
101510-6
Phys. Fluids 20, 101510 共2008兲
Sagong et al.
0.5u τ
0
0
0
0.10
1
0. 4
0
0
0
0
-0
.4
0
-0.10
0
0.5
0.10
0
0
0.5
1
1.5
2
FIG. 6. Mean cross-flow vectors
共v , w兲 at the middle of protrusion 共left兲
and contours of mean shear-stress
variation on the wall 共right兲 for the
case of 共W+ , Sz / W , Sx / L , pattern兲
= 共87, 3 , 2 , parallel兲: 共a兲 H+ = 4; 共b兲
H+ = 8.
(a )
0
0.5u τ
0
0.40
0
-0.30
-0.
30
1
0.40
0
0.20
0.40
z
0
0
0.5
(b )
-0.40
-0.40
0.5
y
0.20
0.40
z
1
1.5
2
x
As mentioned in Sec. I, the present V-shaped protrusion
is quite similar in shape but opposite in direction to that used
by Sirovich and Karlsson.7 They showed that their V-shaped
protrusions pointing upstream 关Fig. 12共a兲兴 reduce the drag by
10% when they are placed randomly on a flat plate but increase it in the parallel distribution. On the other hand,
Bechert29 performed oil-channel experiments with the same
protrusions as those used by Sirovich and Karlsson7 but did
not obtain any drag reduction from direct force measurement. Monti et al.30 conducted a similar experiment in a
turbulent boundary layer. They claimed that drag reduction
up to 30% was obtained in a narrow range of Reynolds num-
from the result of numerical simulation in Fig. 11. In Fig.
11共b兲, in the staggered pattern, the skin friction decreases by
5% but the form drag increases by 16%, resulting in net-drag
increase. However, when the protrusions are sparsely spaced,
the drag variation is nearly insensitive to the distribution
pattern because the pair vortices generated from each protrusion do not interact much with those from others.
In addition, we change the angle ␣ of protrusion 关Fig.
2共a兲兴 from ␣ = 53° to 28°, 90°, and 180°, respectively, and
measure the drags for 12 different combinations of W+, H+,
Sz / W, and Sx / L. However, all of them produce increase or
nearly no change in the drag.
0
0
0.5u τ
2 0.10
0.40
0.20
0
-0.40
0
0
-0.10
-0.40
-0.10
0.10
1
0.20
0.40
0
0
0
2
4
FIG. 7. Mean cross-flow vectors
共v , w兲 at the middle of protrusion 共left兲
and contours of mean shear-stress
variation on the wall 共right兲 for the
case
of
共H+ , Sz / W , Sx / L , pattern兲
= 共8 , 3 , 2 , parallel兲: 共a兲 W+ = 174; 共b兲
W+ = 87.
(a )
0
0
0.10
0
-0.40
-0.40
0.5u τ
2
0.10
0.10
0
0
0
1
y
z
0.20
-0.40
0.40
-0.30
0.40
0.20
0.10
0
z
x
2
0.10
-0.40
4
(b )
Downloaded 29 Jul 2010 to 147.46.120.125. Redistribution subject to AIP license or copyright; see http://pof.aip.org/pof/copyright.jsp
101510-7
Phys. Fluids 20, 101510 共2008兲
Does the sailfish skin reduce the skin friction
15
10
D(%)
D(%)
10
5
5
0
0
-5
-5
1
2
3
4
5
6
parallel
7
FIG. 10. Variation in drag with the distribution pattern of protrusions 共parallel, staggered, and random兲: 쎲, 共H+ , W+ , Sz / W , Sx / L兲 = 共6.3, 107, 2 , 1兲; 䊊,
共7:3, 124, 2, 1兲; 䉲, 共5.0, 85, 1.14, 1.5兲; 䉮, 共6.3, 107, 1.14, 1.5兲; 䊏, 共4.6, 66,
2, 1.5兲; 䊐, 共6.0, 85, 2, 1.5兲; 䉱, 共6.0, 85, 3, 1.5兲; 䉭, 共7.3, 103, 3, 1.5兲.
10
bers. However, in that study, the drag was not directly measured but was evaluated using the Karman integral equation
based on the mean velocity measurement. Therefore, to confirm the result of Sirovich and Karlsson,7 we perform another
set of experiments on these protrusions following their study.
The shape and size of protrusions described in their
studies7,28 are shown in Fig. 12共a兲. Since the protrusion
thickness 共t兲 is not reported in their studies, we consider
three different thicknesses, t+ = 20, 30, and 40, respectively.
The result of drag measurement is shown in Fig. 12共b兲 with
three different distribution patterns. As shown, the drag increases for all the cases considered unlike their result and is
rather insensitive to the protrusion thickness. Also, the staggered and random distributions increase the drag, although
the amount of drag increase is smaller than that of parallel
distribution.
We perform two other direct numerical simulations for
5
0
-5
0
1
2
3
4
Sx / L
(b )
FIG. 8. Variations in drag with the 共a兲 spanwise and 共b兲 streamwise spacings: 共a兲 䊊, 共H+ , W+ , Sx / L , pattern兲 = 共6.0, 85, 1 , S兲; 䉭, 共7.3, 103, 1, S兲; 䉮,
共8.8, 124, 1, S兲; 䊏, 共6.2, 131, 2, S兲; ⽧, 共6.2, 197, 2, S兲; 䉱, 共8.0, 171, 2, S兲;
쎲, 共8.0, 256, 2, S兲; 䉲, 共11.7, 249, 2, S兲. 共b兲 䊊, 共H+ , W+ , Sz / W , pattern兲
= 共4.6, 66, 2 , S兲; 䊐, 共6.0, 85, 2, S兲; 䉮, 共7.3, 103, 2, S兲; 〫, 共8.0, 256, 2, S兲;
䉭, 共8.8, 124, 2, S兲; 丣 , 共9.7, 310, 2, S兲; 䉲, 共7.3, 103, 3, S兲; 䉱, 共8.8, 124, 3,
S兲. Here, S denotes the staggered distribution pattern.
0
0
0.10
0
-0.40
-0.40
2
0.5u τ
0.10
0.10
0
0
0
1
0.20
-0.40
0.20
0.40
-0.30
0.40
0.10
-0.40
0.10
0
2
4
(a )
0.5u τ
-0.40
-0.20
0
2
0.40
-0.40
0
-0.20
1
z
z
-0.40
0
0.40
-0.40
0.40
0.40
-0.40
0
0.40
0
x
2
FIG. 9. Mean cross-flow vectors
共v , w兲 at the middle of protrusion 共left兲
and contours of mean shear-stress
variation on the wall 共right兲 for the
case
of
共H+ , W+ , Sx / L , pattern兲
= 共8 , 87, 2 , parallel兲: 共a兲 Sz / W = 3; 共b兲
Sz / W = 1.14.
-0.40
0
0.40
-0.20
y
random
Pattern
15
D(%)
staggered
Sz / W
(a )
4
(b )
Downloaded 29 Jul 2010 to 147.46.120.125. Redistribution subject to AIP license or copyright; see http://pof.aip.org/pof/copyright.jsp
101510-8
Phys. Fluids 20, 101510 共2008兲
Sagong et al.
0.5u τ
-0.40
-0.20
0.40
0
2
-0.40
-0.20
0.40
-0.40
0
0.40
0.40
0
1
-0.40
0
-0.20
-0.40
0.40
-0.40
0
0.40
0
2
4
FIG. 11. Mean cross-flow vectors
共v , w兲 at the middle of protrusion 共left兲
and contours of mean shear-stress
variation on the wall 共right兲 for
the case of 共H+ , W+ , Sz / W , Sx / L兲
= 共8 , 87, 1.14, 2兲: 共a兲 parallel; 共b兲
staggered.
(a )
0.5u τ
2
-0.40
0
-0.30
-0.30
0
0.40
-0.40
0
y
z
z
-0.40
0.40
-0.40
0
1
0.40
0
0.40
0
0.40
-0.30
-0.40
0.40
0
-0.4
0.40
-0.40
2
x
4
(b )
u∞
Sz
e
L
W
t
Sx
Sirovich and
Karlsson 7
Sirovich et al.
W+
200
182
L+
-
200
H+
5~6
5
Sz+
260
270
Sx+
300
278
e+
130
135
28
(a )
FIG. 12. Experiment using the
V-shaped protrusions suggested by
Sirovich and Karlsson 共Ref. 7兲 and
Sirovich et al. 共Ref. 28兲: 共a兲 schematic
and size of the protrusions; 共b兲 variation in drag with the distribution pattern. 共b兲 䊊, t+ = 20; 쎲, 30; 䉭, 40.
15
D(%)
10
5
0
-5
(b )
parallel
staggered
random
Pattern
Downloaded 29 Jul 2010 to 147.46.120.125. Redistribution subject to AIP license or copyright; see http://pof.aip.org/pof/copyright.jsp
101510-9
Phys. Fluids 20, 101510 共2008兲
Does the sailfish skin reduce the skin friction
0
0.5u τ
0
0.40
0
0.40
0.40
0.40
2
-0.10
-0.10
-0.40
1
0.40
-0.10
-0.10
-0.40
0
-0.40
0
0
0.40
0.40
4
2
6
(a )
-0.40
-0.40
0
0.20
0.5u τ
0
0.20
-0.40
2
FIG. 13. Direct numerical simulation
using the V-shaped protrusions
共t+ = 20兲 suggested by Sirovich and
Karlsson 共Ref. 7兲 and Sirovich et al.
共Ref. 28兲: 共a兲 parallel; 共b兲 staggered.
Shown are the mean cross-flow vectors 共v , w兲 at the middle of protrusion
共left兲 and contours of mean shearstress variation on the wall 共right兲.
0.20
-0.40
-0.40
1
y
z
z
0
0.20
0
0.20
x
021
0
4
6
(b )
the cases of parallel and staggered distributions 共t+ = 20兲 to
confirm our experimental results. As shown in Fig. 13 共left
column兲, the V-shaped protrusion pointing upstream also
generates a pair of streamwise vortices but the senses of
rotation are opposite to those from the protrusion pointing
downstream, showing high and low skin frictions on its center and sides, respectively 关Fig. 13 共right column兲兴. The
streamwise vortices are relatively weak because the protrusion height is only 5 in wall unit. The skin friction increases
by 3% for the parallel distribution but decreases by 3% for
the staggered one, which is similar to what we observe from
our V-shaped protrusion. However, the net drag still increases by 5% even with the staggered distribution due to the
form drag on each protrusion.
IV. CONCLUSIONS
Motivated by the fastest sea animal, the sailfish, reaching
its maximum speed of 110 km/h, we observed the skin of a
sailfish in detail hoping that we might have similar or more
skin-friction reduction than that from the shark skin, the riblet. We found that there exist many V-shaped protrusions on
the sailfish skin and their sizes in inner and outer scales are
much larger than those of riblets. Therefore, in the present
study, we investigated the possibility of reducing skin friction in a turbulent boundary layer using the V-shaped protrusions found on the sailfish skin. We performed both the
wind-tunnel experiment and direct numerical simulation.
The parameters needed to consider were the height,
width, and length of each protrusion, the streamwise and
spanwise spacings between the adjacent ones, and the overall
distribution patterns such as parallel, staggered, and random
distributions of protrusions. The drag force was directly measured using floating element and load cell. More than 170
different cases were tested to see if these protrusions might
reduce the skin friction on a flat plate. All the cases investigated showed drag increase or negligible drag reduction considering the errors of force measurement. Each protrusion
located on a flat plate induced a pair of streamwise vortices,
producing low and high skin frictions at the center and sides
of the protrusion, respectively. These vortices interacted
more vigorously with those from adjacent protrusions when
the spacings between adjacent protrusions were small, resulting in higher drag increases. In some cases, a staggered 共or
random兲 distribution of the protrusions reduced the skin friction itself because a pair of streamwise vortices generated
from a protrusion met another pair of streamwise vortices,
having opposite senses of rotation, from a downstream protrusion and became weak through the vortical interaction.
However, even in this case, the net drag increased due to the
form drag on the protrusions.
Actual scales of sailfish are rounded at the corners and
blended to the body surface smoothly 共see Fig. 1兲. Therefore,
the role of smooth edges on the drag-reduction performance
seems to be an important issue. However, reproduction of
actual sailfish scales on the test plate whose size is 298
⫻ 598 mm2 is very difficult due to the geometric complexity
and the large size of the test plate. Thus, we considered a
simpler geometry, triangular protrusions, instead of present
V-shaped ones. We tested 12 different sets of triangular protrusions with sharp and smooth edges, respectively. The
drags of the plate with smooth-edged protrusions were either
smaller 共by maximum 3%兲 than or nearly the same as those
with sharp-edged ones, but they are still larger than that of a
flat plate without protrusions. It may be interesting to see if
the V-shaped protrusions with smooth edges reduce the drag
as compared to the flat plate without protrusions.
Quite surprisingly, the present V-shaped protrusions observed from the sailfish skin 共V-shaped protrusions pointing
downstream兲 are very similar in shape but opposite in direction to those 共V-shaped protrusions pointing upstream兲 suggested by Sirovich and Karlsson7 for drag reduction. To confirm this experimental result, we performed another set of
experiments and direct numerical simulations using the same
protrusions as theirs. The V-shaped protrusion pointing upstream also generated a pair of streamwise vortices, but the
senses of rotation were the opposite to those from the one
pointing downstream. Thus, the high and low skin frictions
Downloaded 29 Jul 2010 to 147.46.120.125. Redistribution subject to AIP license or copyright; see http://pof.aip.org/pof/copyright.jsp
101510-10
occurred at the center and sides of the protrusion, respectively. As was observed from the case of protrusions pointing
downstream, the skin friction itself decreased through the
interaction between the upstream and downstream pair of
vortices when the protrusions were placed in a staggered 共or
random兲 pattern, but the net drag increased again due to the
form drag on the protrusions.
The roles of the sailfish skin have been conjectured as a
compliant wall,12 a dynamic damping system,12 or a trap for
air within its skin.15 It seems clear from the present study
that these protrusions do not directly reduce the drag in a
turbulent boundary layer. Another possibility of drag reduction using the present shape is the form-drag reduction
through the main separation delay. It was suggested that the
bill of sailfish generates turbulence and the body of sailfish is
completely immersed in a turbulent boundary layer even at a
low speed. Therefore, it should be interesting to investigate
that the present V-shaped protrusions are effective in delaying turbulent separation through the generation of streamwise vortices and enhanced near-wall momentum.
ACKNOWLEDGMENTS
This paper is presented at the 60th Birthday Workshop
celebrating John Kim’s contribution to fundamental turbulence physics and control. We dedicate this paper to John
Kim. This work is supported by the National Research Laboratory Program of the Korean Ministry of Education, Science
and Technology through KOSEF 共Grant No. ROA-2006-00010180-0兲.
1
Phys. Fluids 20, 101510 共2008兲
Sagong et al.
H. Choi, P. Moin, and J. Kim, “Active turbulence control for drag reduction in wall-bounded flows,” J. Fluid Mech. 262, 75 共1994兲.
2
Y. Du and G. E. Karniadakis, “Suppressing wall turbulence by means of a
transverse traveling wave,” Science 288, 1230 共2000兲.
3
W. J. Jung, N. Mangiavacchi, and R. Akhavan, “Suppression of turbulence
in wall-bounded flows by high frequency spanwise oscillations,” Phys.
Fluids A 4, 1605 共1992兲.
4
S. Kang and H. Choi, “Active wall motions for skin-friction drag reduction,” Phys. Fluids 12, 3301 共2000兲.
5
C. Lee, J. Kim, and H. Choi, “Suboptimal control of turbulent channel
flow for drag reduction,” J. Fluid Mech. 358, 245 共1998兲.
6
M. J. Walsh, “Turbulent boundary layer drag reduction using riblets,”
AIAA Paper No. 1982-0169, 1982.
7
L. Sirovich and S. Karlsson, “Turbulent drag reduction by passive mechanism,” Nature 共London兲 388, 753 共1997兲.
8
F. W. Lane, “How fast do fish swim?” Ctry. Life 90, 534 共1941兲.
9
V. V. Ovchinnikov, “On the functional significance of the dorsal fin of the
sailfish-Histiophorus americanus,” Vopr. Ikhtiol. 7, 194 共1967兲.
10
Y. G. Aleyev, Nekton 共Junk, The Hague, 1977兲.
11
V. V. Ovchinnikov, “Turbulence in the boundary layer as a method for
reducing the resistance of certain fish on movement,” Biophysics 共Engl.
Transl.兲 11, 186 共1966兲.
12
V. Walters, “Body form and swimming performance in the scombroid
fishes,” Am. Zool. 2, 143 共1962兲.
13
M. O. Kramer, “Boundary layer stabilization by distributed damping,” J.
Am. Soc. Nav. Eng. 72, 25 共1960兲.
14
P. W. Webb, “Hydrodynamics and energetics of fish propulsion,” Bull. Fish. Res. Board Can. 190, 1 共1975兲.
15
See National Technical Information Service Document No. TT-71-50011
共V. V. Ovchinnikov, “Swordfishes and billfishes in the Atlantic Ocean—
ecology and functional morphology,” Atlantic Science Research Institute
of Fisheries and Oceanography Report, Kalingrad, USSR, 1971; translated
from Russian by the Israel Program for Scientific Translation, Jerusalem兲.
Copies may be ordered from the National Technical Information Service,
Springfield, VA.
16
I. Nakamura, “FAO species catalogue. Vol. 5. Billfishes of the world. An
annotated and illustrated catalogue of marlins, sailfishes, spearfishes, and
swordfishes known to date,” FAO Fish Synop. 5, 65 共1985兲.
17
H. Schlichting, Boundary-Layer Theory 共McGraw-Hill, New York, 1979兲.
18
H. H. Fernholz and P. J. Finley, “The incompressible zero-pressuregradient turbulent boundary layer: An assessment of the data,” Prog.
Aerosp. Sci. 32, 245 共1996兲.
19
M. Hites, H. Nagib, and C. Wark, “Velocity and wall shear-stress measurements in high-Reynolds-number turbulent boundary layers,” AIAA
Paper No. 1997-1873, 1997.
20
J. M. Österlund, A. V. Johansson, H. M. Nagib, and M. H. Hites, “A note
on the overlap region in turbulent boundary layers,” Phys. Fluids 12, 1
共2000兲.
21
L. P. Purtell, P. S. Klebanoff, and F. T. Buckley, “Turbulent boundary layer
at low Reynolds number,” Phys. Fluids 24, 802 共1981兲.
22
A. J. Smits, N. Matheson, and P. N. Joubert, “Low-Reynolds-number turbulent boundary layers in zero and favorable pressure gradients,” J. Ship
Res. 27, 147 共1983兲.
23
D. W. Bechert, M. Bruse, W. Hage, J. G. T. van der Hoeven, and G.
Hoppe, “Experiments on drag-reducing surfaces and their optimization
with an adjustable geometry,” J. Fluid Mech. 338, 59 共1997兲.
24
J. Kim, D. Kim, and H. Choi, “An immersed-boundary finite-volume
method for simulations of flow in complex geometries,” J. Comput. Phys.
171, 132 共2001兲.
25
J. Jiménez and P. Moin, “The minimal flow unit in near-wall turbulence,”
J. Fluid Mech. 225, 213 共1991兲.
26
B. A. Block, D. Booth, and F. G. Carey, “Direct measurement of swimming speeds and depth of blue marlin,” J. Exp. Biol. 166, 267 共1992兲.
27
J. P. Hoolihan, “Horizontal and vertical movements of sailfish 共Istiophorus
platypterus兲 in the Arabian Gulf, determined by ultrasonic and pop-up
satellite tagging,” Mar. Biol. 共Berlin兲 146, 1015 共2005兲.
28
L. Sirovich, E. Levich, L. Y. Bronicki, and S. Karlsson, U.S. Patent No.
5,833,389 共10 November 1998兲.
29
D. W. Bechert, “Passive control methods: Riblets, vortex generators and
self-activating flaps,” in Proceedings of the IUTAM Symposium on Mechanics of Passive and Active Flow Control, edited by G. E. A. Meier and
P. R. Viswanath 共Kluwer, Amsterdam, 1999兲, pp. 107–108.
30
R. Monti, S. De Ponte, and E. Levich, “Effects on the resistance and on
the separation of V shapes passive manipulators in a turbulent boundary
layer,” in Proceedings of the CEAS/DragNet European Drag Reduction
Conference, edited by P. Thiede 共Springer, Berlin, 2001兲, pp. 286–293.
Downloaded 29 Jul 2010 to 147.46.120.125. Redistribution subject to AIP license or copyright; see http://pof.aip.org/pof/copyright.jsp