biomimetics
Article
Laser Ablating Biomimetic Periodic Array Fish Scale Surface for
Drag Reduction
Dengke Chen 1, * , Bowen Zhang 1 , Haifeng Zhang 1 , Zheng Shangguan 1 , Chenggang Sun 2 , Xianxian Cui 3 ,
Xiaolin Liu 3 , Zehui Zhao 3 , Guang Liu 4 and Huawei Chen 3,5, *
1
2
3
4
5
*
Citation: Chen, D.; Zhang, B.; Zhang,
H.; Shangguan, Z.; Sun, C.; Cui, X.;
College of Transportation, Ludong University, Yantai 264025, China
Shandong Laboratory of Advanced Materials and Green Manufacturing at Yantai, Yantai 264006, China
School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China
College of Mechanical Engineering, Hebei University of Science & Technology, Shijiazhuang 050091, China
Advanced Innovation Center for Biomedical Engineering, Beihang University, Beijing 100191, China
Correspondence: chendk@ldu.edu.cn (D.C.); chenhw75@buaa.edu.cn (H.C.)
Abstract: Reducing resistance to surface friction is challenging in the field of engineering. Natural
biological systems have evolved unique functional surfaces or special physiological functions to adapt
to their complex environments over centuries. Among these biological wonders, fish, one of the oldest
in the vertebrate group, have garnered attention due to their exceptional fluid dynamics capabilities.
Fish skin has inspired innovation in reducing surface friction due to its unique structures and material
properties. Herein, drawing inspiration from the unique properties of fish scales, a periodic array of
fish scales was fabricated by laser ablation on a polished aluminum template. The morphology of the
biomimetic fish scale surface was characterized using scanning electron microscopy and a white-light
interfering profilometer. Drag reduction performance was measured in a closed circulating water
tunnel. The maximum drag reduction was 10.26% at a Reynolds number of 39,532, and the drag
reduction performance gradually decreased with an increase in the distance between fish scales.
The mechanism of the biomimetic drag reduction surface was analyzed using computational fluid
dynamics. Streamwise vortices were generated at the valley of the biomimetic fish scale, replacing
sliding friction with rolling friction. These results are expected to provide a foundation for in-depth
analysis of the hydrodynamic performance of fish and serve as new inspiration for drag reduction
and antifouling.
Liu, X.; Zhao, Z.; Liu, G.; Chen, H.
Laser Ablating Biomimetic Periodic
Keywords: laser ablating; fish scale; drag reduction; simulation; vortices
Array Fish Scale Surface for Drag
Reduction. Biomimetics 2024, 9, 415.
https://doi.org/10.3390/
biomimetics9070415
Academic Editor: Luciano Afferrante
Received: 3 June 2024
Revised: 3 July 2024
Accepted: 4 July 2024
Published: 7 July 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
1. Introduction
Resistance reduction to surface friction is challenging in a viscous fluid and has
attracted considerable attention from researchers in the last few decades [1]. Both active and passive methods have been examined to reduce surface friction [2–4]. Because
the active drag reduction method requires external energy consumption [5], the passive
drag reduction method is trending owing to its lack of external energy consumption over
time [6]. Physical creatures have evolved unique surface structural features and physiological functions throughout evolution. Therefore, natural organisms are a source of
innovative inspirations for understanding passive drag reduction. Fish are among the most
ancient species of the major vertebrate groups; they are a typical representative of excellent
fluid dynamics adaptation to a complex environment [7–10], which can be attributed to
both their physiological structure and the unique structure and material properties of the
fish skin. Fish skin is a multi-layered system comprising mucus, epidermis, fish scale,
and dermis layers from the outer to inner side. Fish scales embedded in a flexible dermis
layer serve several functions, such as ensuring resistance to external attacks [11,12] and
ion exchange [13]. The drag reduction performance of the fish scale has been examined
in recent years. Among aquatic creatures, micro-denticles of sharkskin stand out for their
Biomimetics 2024, 9, 415. https://doi.org/10.3390/biomimetics9070415
https://www.mdpi.com/journal/biomimetics
Biomimetics 2024, 9, 415
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unique structure, conferring exceptional drag reduction and antifouling properties [14,15].
However, not all fish possess these specialized structures. Several fish species exhibit
cycloid scales, which have recently garnered attention for their potential role in reducing
drag [16–19]. Certain cycloid-like fish scales have demonstrated drag reduction performance in complex ocean environments.
The drag reduction performance of biomimetic cycloid scale surfaces has been examined in several studies. Wu et al. examined the effect of “water trapping” on drag reduction
by crescent microstructures, drawing inspiration from the scales of Ctenopharyngodon Idella.
The biomimetic surface formed a fluid lubrication film, effectively reducing skin friction
drag [20]. Muthuramalingam et al. examined the effect of biomimetic fish scale arrays to
reduce drag and reported the formation of high–low speed stripes on the surface, which
can delay the boundary transition from laminar to turbulence [17]. Biomimetic fish scales
mimicking Carassius auratus were fabricated by coating technology for drag reduction [21].
Some studies have employed the laser ablating method as an inexpensive way to fabricate
biomimetic functional surfaces. The results suggest that the biomimetic surfaces exhibit
different drag reduction performances under various flow conditions [22–24]. For instance,
Xue et al. developed a fish-skin-inspired Janus hydrogel coating and reported a drag reduction ratio of 38.5% [25]. Chen et al. fabricated biomimetic gradient flexible fish skin with
a passive dynamic micro-roughness exhibiting a drag reduction ratio of 13.8% [26]. The
nanosecond pulse laser ablation-chemical etching (LACE) process proposed by Liu et al.
can be used to prepare patterned superhydrophobic surfaces with microstructures that
are orientation-controllable and can be reliably applied to drag reduction and water repellency fields [27]. These biomimetic cycloid fish scale surfaces exhibited a drag reduction
effect; however, the influence of fish scale array spacing on drag reduction in relevant
papers is rarely reported. Therefore, we fabricated an array of biomimetic fish scales with
different spacings and examined the drag reduction performance at different incoming
flow velocities.
In this study, five biomimetic periodic array fish scale surfaces with different spacings
were fabricated on an aluminum (Al) template using the femtosecond laser method. The
morphological characteristics of biomimetic fish scale surfaces were characterized using
scanning electron microscopy (SEM) and three-dimensional (3D) white-light confocal
microscopy devices. Drag reduction performances of the biomimetic fish scale surfaces
were examined in a closed circulating water tunnel. A drag reduction of 10.26% was
obtained at Reynolds number (Re) = 39,532. The computational fluid dynamics (CFDs)
method was employed to elucidate the drag reduction mechanism, and the results showed
the generation of streamwise vortices on the valley of the fish scale. Thus, the unique
hydrodynamic characteristics of the periodic array of the fish scale surface can provide a
theoretical reference for understanding the excellent dynamic properties of fish.
2. Materials and Methods
2.1. Materials
Albacore tuna was purchased from a seafood market and stored in a freezer before
experimentation. A polished Al template measuring 50 × 30 × 1 mm3 was purchased
from the Chaosheng metal market and cleaned using ethanol in an ultrasonicator (CR-020S,
Yantai Zhichuang Micro Technic Co., Ltd., Yantai, China). The contact angle (CA) was
determined using deionized water at 20 ◦ C, and the droplet volume was 7 µL. Ethanol
(analytical grade) and polydimethylsiloxane (PDMS) were obtained from Beijing Chemical
Works (Beijing, China) and Sigma-Aldrich Trading Co., Ltd. (Shanghai, China)., respectively.
All chemicals were used as received without further processing.
2.2. Biomimetic Prototype and Model Extraction
In this study, Albacore tuna was the biomimetic prototype. Albacore tuna is known for
its high nutritional value and lifelong swimming abilities, with sustained swimming speeds
in excess of 1.5 m/s (0.6 body length s−1 ) [28]. The excellent hydrodynamic properties of
Biomimetics 2024, 9, x FOR PEER REVIEW
Biomimetics 2024, 9, 415
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2.2. Biomimetic Prototype and Model Extraction
3 of 12
In this study, Albacore tuna was the biomimetic prototype. Albacore tuna is known
for its high nutritional value and lifelong swimming abilities, with sustained swimming
speeds in excess of 1.5 m/s (0.6 body length s−1) [28]. The excellent hydrodynamic proper‐
tunaties
areofattributed
to its streamlined
body and
structure
andand
material
properties
tuna are attributed
to its streamlined
bodythe
andunique
the unique
structure
material
of its
skin. Tuna
five layers,
outer
inner:
mucus,
flexible
epidermis,
properties
of itsskin
skin.comprises
Tuna skin comprises
fivefrom
layers,
from to
outer
to inner:
mucus,
flexible
fish scale,
andfiber
collagen
Thefish
hardscale
fish scale
layer
is coveredby
bya flexible
fishepidermis,
scale, dermis,
anddermis,
collagen
[4].fiber
The[4].
hard
layer
is covered
a flexiblelayer
epidermis
layer and embedded
in the dermis
as shown
in Figure
The
epidermis
and embedded
in the dermis
layer, layer,
as shown
in Figure
1a.1a.
The
fish scales
fishAlbacore
scales of the
Albacore
tuna
in the micro‐dimension
(as the
are the
denticlesembedded
em‐
of the
tuna
are not
inare
thenot
micro-dimension
(as are
denticles
in
bedded in sharkskin); instead, they are in the millimeter range. The fish scales are ar‐
sharkskin);
instead, they are in the millimeter range. The fish scales are arranged in a
ranged in a periodic overlapping pattern, and the posterior region is exposed. This ex‐
periodic
overlapping pattern, and the posterior region is exposed. This exposed area is
posed area is shaped like a fan (yellow dotted box), as shown in Figure 1b. The length of
shaped
like
a fan
dotted
box),
as along
shown
Figure 1b.
The length
exposed area
the exposed
area(yellow
of the fish
scale is
longer
theinspanwise
direction,
unlike of
thethe
stream‐
of the
fish
scale isand
longer
along
the of
spanwise
direction,
unlike the
direction,
and
wise
direction,
the line
shape
the transition
area between
fish streamwise
scales is arched.
A
the line
shape of
the transition
area between
fishscales
scaleswas
is arched.
biomimetic
with
biomimetic
surface
with a periodic
array of fish
designedAbased
on theirsurface
ar‐
rangement
andof
morphology
studying
the fishbased
scale characteristics
and the arrangement
a periodic
array
fish scalesbywas
designed
on their arrangement
and morphology
of tuna skin.
by studying
the fish scale characteristics and the arrangement of tuna skin.
Figure
Albacore tuna
tuna and
arrangement
of fish
(a) Albacore
and different
layers.
(b)
Figure
1. 1.
Albacore
andthe
the
arrangement
ofscales.
fish scales.
(a) tuna
Albacore
tuna and
different
layers.
Fish scale arrangement.
(b) Fish scale arrangement.
Sample Preparation
2.3. 2.3.
Sample
Preparation
Firstly, the shape of the biomimetic periodic array fish scale was designed and drawn
Firstly, the shape of the biomimetic periodic array fish scale was designed and drawn
using CAXA CAD software. The biomimetic periodic array fish scale surface with differ‐
using
CAD
software.
The curves,
biomimetic
periodic
fishadjacent
scale surface
with5 different
entCAXA
spacings
comprised
multiple
and the
spacingarray
between
curves was
spacings
comprised
multiple
curves,
and
the
spacing
between
adjacent
curves
was 5 µm.
μm. The initial spacing of the fish scale pattern was 42 μm and then gradually increased
Thetoinitial
spacing
of in
the
fish 2a.
scale
pattern
42 µm
then
gradually
to
994 μm,
as shown
Figure
Secondly,
anwas
Al plate
was and
cleaned
using
ethanol inincreased
an
ultrasonicator
for
20
min
and
dried
at
25
°C.
A
femtosecond
laser
device
(HR‐PT‐Orien,
994 µm, as shown in Figure 2a. Secondly, an Al plate was cleaned using ethanol in an
◦ C. A femtosecond
Yantai, China)
was
fabricate
biomimetic
fish scale surfaces
following
de‐
ultrasonicator
for
20employed
min andtodried
at 25
laser
device the
(HR-PT-Orien,
signed curve. The Al plate was placed directly below the laser head, and the distance be‐
Yantai, China) was employed to fabricate biomimetic fish scale surfaces following the
tween the laser source and the sample surface was 152 mm. The laser parameters were set
designed curve. The Al plate was placed directly below the laser head, and the distance
as follows: the pulse duration was set at 1 ps and the processing frequency was 100 kHz.
between
the energy
laser source
and the
surface
152 mm. The
laser parameters
were
The pulse
and current
weresample
set at 200
μJ andwas
3 A, respectively,
whereas
the scan‐
set as
follows:
the
pulse
duration
was
set
at
1
ps
and
the
processing
frequency
was
100
kHz.
ning speed was set at 500 mm/s. Each curve was scanned 30 times. Finally, the Al samples
Thefabricated
pulse energy
and
current
were
set
at
200
µJ
and
3
A,
respectively,
whereas
the
scanning
were ultrasonically cleaned and dried in a normal atmospheric environment.
Positive
scale surfaces
were obtained
using a 30
template
speed
was biomimetic
set at 500fish
mm/s.
Each curve
was scanned
times.replication
Finally, method
the Al samples
with
PDMS.
The
ratio
of
PDMS
to
curing
agent
was
10:1.
Curing
was
performed
at 80
°C
fabricated were ultrasonically cleaned and dried in a normal atmospheric
environment.
for
2
h,
followed
by
demolding
the
cured
PDMS
from
the
Al
template.
The
preparation
Positive biomimetic fish scale surfaces were obtained using a template replication method
process is shown in Figure 2b.
◦
with PDMS. The ratio of PDMS to curing agent was 10:1. Curing was performed at 80 C
4 of 13
for 2 h, followed by demolding the cured PDMS from the Al template. The preparation
process is shown in Figure 2b.
Biomimetics 2024, 9, x FOR PEER REVIEW
Figure 2. (a) Biomimetic fish scale pattern surfaces and (b) schematic of the preparation of biomimetic
fish scale surfaces. Figure 2. (a) Biomimetic fish scale pattern surfaces and (b) schematic of the preparation of biomi‐
metic fish scale surfaces.
2.4. Sample Characterization
A biomimetic fish scale surface was successfully prepared on an Al template. The
whole size of the fabricated samples measured 50 × 15 mm2 (as shown in Supplementary
Figure S1). An ultra‐depth field microscope (KEYENCE, VHX‐970F, Osaka,Japan) was
Biomimetics 2024, 9, 415
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Figure 2. (a) Biomimetic fish scale pattern surfaces and (b) schematic of the preparation of biomi‐
2.4. Sample
Characterization
metic fish scale surfaces.
A biomimetic fish scale surface was successfully prepared on an Al template. The
Sample Characterization
whole2.4.
size
of the fabricated samples measured 50 × 15 mm2 (as shown in Supplementary
A
fish scalefield
surface
was successfully
prepared on
an Al template.
The Japan) was
Figure S1). biomimetic
An ultra-depth
microscope
(KEYENCE,
VHX-970F,
Osaka,
whole size of the fabricated samples measured 50 × 15 mm2 (as shown in Supplementary
employed
characterize
the field
two-dimensional
(2D) morphology
of the biomimetic
fish scale
FiguretoS1).
An ultra‐depth
microscope (KEYENCE,
VHX‐970F, Osaka,Japan)
was
surface
(Figure
3a).
The
biomimetic
fish
scales
were
successfully
fabricated
and
exhibited
a
employed to characterize the two‐dimensional (2D) morphology of the biomimetic fish
scale
surface
(Figure 3a).
fishillustrate
scales were
fabricated
ex‐
periodic
array
structure
on The
the biomimetic
Al plate. To
thesuccessfully
microstructure,
theand
positive
template
a periodic
array
structure
the Al plate.by
Togold
illustrate
the microstructure,
the pos‐
of thehibited
biomimetic
fish
scale
wason
processed
spraying
and characterized
using an
itive template of the biomimetic fish scale was processed by gold spraying and character‐
scanning electron microscope (SEM; Hitachi, SU8010, Osaka, Japan). The results are shown
ized using an scanning electron microscope (SEM; Hitachi, SU8010, Osaka, Japan). The
in Figure
3b.areThe
surface
roughness
of the
biomimetic
scale surface
and the
results
shown
in Figure
3b. The surface
roughness
of the fish
biomimetic
fish scale increased,
surface
microstructures
exhibited
an irregular
porosity
feature.porosity
The irregular
micro-/nanostructures
increased, and
the microstructures
exhibited
an irregular
feature. The
irregular
micro‐/nanostructures
were obtainedlaser
usingbeam.
a high‐energy laser beam.
were obtained
using a high-energy
3. Characteristics
the biomimetic
fishfish
scales.
(a) Optical
images ofimages
the biomimetic
scale
FigureFigure
3. Characteristics
ofofthe
biomimetic
scales.
(a) Optical
of the fish
biomimetic
fish scale
surface with different spacings. (b) SEM images under different magnifications.
surface with different spacings. (b) SEM images under different magnifications.
The 3D morphology of the biomimetic fish scales was determined using a white-light
interfering profilometer (DVM6A, Berlin, Germany). The results are shown in Figure 4a–e.
The average height of the fish scale was 25 ± 3 µm and the spacing of these five biomimetic
fish scales was different. The surface roughness of the biomimetic fish scales considerably
increased after femtosecond laser processing, and the variation in surface roughness is
supplied in Supplementary Figure S2. Generally, the surface wettability of a surface with
micro-/nanostructures processed by laser often changes [27]. The contact angle (CA)
increased with laser processing as micro- or nanostructures exhibited superhydrophobic
properties. However, the CAs of biomimetic fish scale surfaces did not exhibit a superhydrophobic peculiarity and were within 114 ± 2◦ for all biomimetic surfaces (Figure 4f).
Our results suggest that the arrangement of the fish scales is the only factor affecting
drag reduction.
2.5. Drag Measurement
A closed circulating water tunnel was employed to measure the total drag force of
smooth and biomimetic fish scale surfaces. Figure 5 shows the schematic of the closed
circulating water tunnel and test section. Fabricated PDMS samples were placed in a groove
of the mold, and the direction of the biomimetic fish scale was parallel to that of the flow.
The fabricated PDMS smooth surface had no biomimetic fish scale. The mold was rigidly
connected to a stress–strain sensor, a unidirectional force device having an accuracy of
0.01 mN and a measuring range of 0–20 N, to measure the total drag force of the biomimetic
fish scale surface and placed in the middle of the test section. The stress–strain sensor was
a one-way force device, which means that the deformation only can be generated in the
Biomimetics 2024, 9, 415
5 of 12
fluid flow direction. The accuracy of the stress–strain sensor was evaluated according to
the voltage signal generated by weights of 0, 50, 100, and 200 g before the test. The test
section comprised transparent acrylic and the total length was 1500 mm. The width (w)
and height (h) of the test sections were 80 and 80 mm, respectively. The total drag force of
biomimetic fish scale surfaces was measured at different incoming flow velocities (0.5, 1,
1.5, and 2 m/s). Tap water was the working media and the velocity of water was controlled
using a variable frequency driver. The water inlet remained open and excess tap water
was2024,
discharged
the overflow port to limit the operating temperature of the 5tap
Biomimetics
9, x FOR PEER through
REVIEW
of 13
water. The temperature of the water was monitored using a thermometer and the tap water
temperature was maintained at 25 ± 2 ◦ C, to exclude the effect of water temperature on
TheMultiple
3D morphology
of the biomimetic
fish scales
was determined
white‐light
the experimental results.
honeycomb
turbulators
were
set at the using
inletachest
to
interfering profilometer (DVM6A, Germany). The results are shown in Figure 4a–e. The
stabilize the flow field
and reduce the turbulence intensity. The Reynolds (Re) number
average height of the fish scale was 25 ± 3 μm and the spacing of these five biomimetic
corresponding to the
different
was
calculated
using
following
formula:
fish
scales wasvelocities
different. The
surface
roughness
of thethe
biomimetic
fish scales
considerably
increased after femtosecond laser processing, and the variation in surface roughness is
Re =
ρUD/u
supplied in Supplementary
Figure
S2. Generally, the surface wettability of a surface (1)
with
micro‐/nanostructures processed by laser often changes [27]. The contact angle (CA) in‐
laser processing
micro‐velocity,
or nanostructures
exhibited
superhydrophobic
where ρ, U, D, andcreased
u are with
the water
density,asflow
hydraulic
diameter,
and the
However,
thehydraulic
CAs of biomimetic
fish scale
did not exhibit
a super‐
dynamic viscosity, properties.
respectively.
The
diameter
wassurfaces
determined
as follows:
hydrophobic peculiarity and were within 114 ± 2° for all biomimetic surfaces (Figure 4f).
D = 2wh/(w + h). The
calculated Re numbers were 39,532, 79,065, 118,598, and 158,130,
Our results suggest that the arrangement of the fish scales is the only factor affecting drag
indicating fully turbulent
flow in the test section (Recritical = 2300).
reduction.
Biomimetics 2024, 9, x FOR PEER REVIEW
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temperature of the tap water. The temperature of the water was monitored using a ther‐
mometer and the tap water temperature was maintained at 25 ± 2 °C, to exclude the effect
of water temperature on the experimental results. Multiple honeycomb turbulators were
set at the inlet chest to stabilize the flow field and reduce the turbulence intensity. The
Reynolds (Re) number corresponding to the different velocities was calculated using the
following formula:
Re = ρUD/u
(1)
where ρ, U, D, and u are the water density, flow velocity, hydraulic diameter, and the
dynamic viscosity, respectively. The hydraulic diameter was determined as follows: D =
2wh/(wFigure
+ h). The
calculated and
Re morphology
numbers
were
39,532,
79,065,
118,598,
and
158,130,
indicat‐
Figure 4. Three-dimensional
morphology
contact angle
of the
biomimetic
fish surface.
(a) (a)
FS-1,
4. Three‐dimensional
and contact
angle
of the biomimetic
fish surface.
FS‐1,
(b)
FS‐2,
(c)
FS‐3,
(d)
FS‐4,
(e)
FS‐5,
and
(f)
contact
angle.
ing
fully
turbulent
flow
in
the
test
section
(Re
critical
=
2300).
(b) FS-2, (c) FS-3, (d) FS-4, (e) FS-5, and (f) contact angle.
2.5. Drag Measurement
A closed circulating water tunnel was employed to measure the total drag force of
smooth and biomimetic fish scale surfaces. Figure 5 shows the schematic of the closed
circulating water tunnel and test section. Fabricated PDMS samples were placed in a
groove of the mold, and the direction of the biomimetic fish scale was parallel to that of
the flow. The fabricated PDMS smooth surface had no biomimetic fish scale. The mold
was rigidly connected to a stress–strain sensor, a unidirectional force device having an
accuracy of 0.01 mN and a measuring range of 0–20 N, to measure the total drag force of
the biomimetic fish scale surface and placed in the middle of the test section. The stress–
strain sensor was a one‐way force device, which means that the deformation only can be
generated in the fluid flow direction. The accuracy of the stress–strain sensor was evalu‐
ated according to the voltage signal generated by weights of 0, 50, 100, and 200 g before
the test. The test section comprised transparent acrylic and the total length was 1500 mm.
The width (w) and height (h) of the test sections were 80 and 80 mm, respectively. The
total drag force of biomimetic fish scale surfaces was measured at different incoming flow
velocities (0.5, 1, 1.5, and 2 m/s). Tap water was the working media and the velocity of
Figure 5.
of circulating
the closed
water
tunnel.
(a)
3D
diagram
of the
water
tunnel.
water
controlled
usingcirculating
awater
variable
frequency
driver.
The
water
inlet
remained
open (b)
Figure 5. Schematic
ofSchematic
thewas
closed
tunnel.
(a) 3D
diagram
of the
water
tunnel.
Schematic
of
the
biomimetic
surface
and
stress–strain
sensor
installation.
and
excess
tap
water
was
discharged
through
the
overflow
port
to
limit
the
operating
(b) Schematic of the biomimetic surface and stress–strain sensor installation.
3. Drag Reduction
The total drag force of the biomimetic fish scale surfaces was measured and all bio‐
mimetic samples were tested thrice. The average value was considered as the final value.
The total drag force of the smooth surface at different Re values was measured and con‐
sidered the contrast value (Figure S3). The drag reduction rate was calculated as per Equa‐
Biomimetics 2024, 9, 415
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3. Drag Reduction
The total drag force of the biomimetic fish scale surfaces was measured and all
biomimetic samples were tested thrice. The average value was considered as the final
value. The total drag force of the smooth surface at different Re values was measured and
considered the contrast value (Figure S3). The drag reduction rate was calculated as per
Equation (2):
F
− Fbiomimetic
Dragreduction (DR%) = smooth
× 100%
(2)
Fsmooth
where Fsmooth and Fbiomimetic are the total drag force of the smooth surface and biomimetic
fish scale surface, respectively. Figure 6a shows the total drag force of the smooth and
biomimetic surfaces. The resulting error bar is extremely small compared to the ordinate
value and cannot be obviously seen in Figure 6a. The results showed that the total drag
force significantly increased with Re for all surfaces, with the total drag force of the smooth
surface being the greatest and that of the FS-1 surface being the least. Furthermore, the
total drag force gradually increased as the fish scale spacing increased, approaching the
drag force value of the smooth surface. The drag reduction rate of the biomimetic fish scale
surface was obtained using Formula (2) (Figure 6b). The best drag reduction performance
Biomimetics 2024, 9, x FOR PEER REVIEW
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of the biomimetic fish scale surface was FS-1 at Re = 39,532, and the drag reduction rate
gradually decreased with an increase in spacing under the same Re numbers. The maximum
value DR of FS-1 was 10.26% at Re = 39,532.
Figure
6. Results
of test.
(a) Total
dragdrag
forceforce
for biomimetic
fish scale
different
Re numbers.
(b) Drag(b)
Figure
6. Results
of test.
(a) Total
for biomimetic
fishatscale
at different
Re numbers.
coefficient
of
the
biomimetic
fish
scale
surface.
(c)
Drag
reduction
rate.
Drag coefficient of the biomimetic fish scale surface. (c) Drag reduction rate.
4. Mechanism
4. Mechanism
4.1. Simulation Model
4.1. Simulation Model
The CFD method was employed to calculate the fluid flow of the biomimetic fish
The CFD
method
was employed
to calculate
thereduction
fluid flowinofthe
the
biomimetic
fish
scales near
the wall
to elucidate
the mechanism
of drag
biomimetic
fish
scales
near
the
wall
to
elucidate
the
mechanism
of
drag
reduction
in
the
biomimetic
fish
scale surface in turbulent flow. First, the numerical simulation models of the biomimetic
scale surface in turbulent flow. First, the numerical simulation models of the biomimetic
fish scale and fluid domain were established (Figure 7a,b). Setting reasonable and accurate
boundary conditions and calculation methods was critical to the calculation. The bound‐
ary conditions were defined such that the inlet used was the velocity inlet, the outlet used
was the outflow boundary condition, the upper and biomimetic fish scale surfaces were
Biomimetics 2024, 9, 415
7 of 12
fish scale and fluid domain were established (Figure 7a,b). Setting reasonable and accurate
boundary conditions and calculation methods was critical to the calculation. The boundary
conditions were defined such that the inlet used was the velocity inlet, the outlet used
was the outflow boundary condition, the upper and biomimetic fish scale surfaces were
in the no-slip boundary condition, and the wall and outlet used were in the periodic
boundary conditions (Figure 7a). The fluid domain is shown Figure 7b. Reasonable fluid
domain size was important for calculations. Therefore, the size of the fluid domain was
Lx × Ly × Lz = 16H ′ × 4H ′ × 2H ′ , where H ′ represents the half-width of the fluid domain
channel. The height of the fluid domain must exceed ten times h of the biomimetic fish
scale to prevent interference with the flow field near the fish scale wall. A transition zone
(8H ′ ) was established between the biomimetic fish scale surface and the inlet to ensure a
smooth transition in fluid flow. The working fluid was water flowing horizontally along
the x-direction (streamwise direction). The inlet velocity ranged from 0 to 2 m/s. Fluent
meshing (2021 R1) was employed to generate a polyhexcore grid (Figure 7c). A non-uniform
boundary layer of gird was applied on the biomimetic fish scale surface in the wall-normal
Biomimetics 2024, 9, x FOR PEER REVIEW
8 of 13
direction to obtain the precision flow field near the biomimetic fish scale wall. The first layer
grid distance was obtained using a y+ calculator and was 2.3 × 10−5 m. The grid spacing
increased from the walls by an aspect ratio of 1.1 with 10 boundary layers. The schematic
schematic
of the biomimetic
fish scale
surface
with a non‐uniform
boundary
layer is illus‐
of
the biomimetic
fish scale surface
with
a non-uniform
boundary
layer is illustrated
in
trated
in
Figure
7d.
Figure 7d.
Figure 7. Simulation model and boundary conditions. (a) Boundary conditions for the numerical
Figure 7. Simulation model and boundary conditions. (a) Boundary conditions for the numerical
simulation of the biomimetic fish scale surface. (b) Computational domain for the numerical simu‐
simulation of the biomimetic fish scale surface. (b) Computational domain for the numerical simulalation of the biomimetic fish scale surface. (c) Polyhexcore grid of the biomimetic fish scale domain.
tion
of thedomain
biomimetic
fish scale
surface.layer.
(c) Polyhexcore grid of the biomimetic fish scale domain.
a boundary
(d) Fluid
grid with
(d) Fluid domain grid with a boundary layer.
The Large Eddy Simulation (LES) turbulent model and wall‐adapting local eddy‐vis‐
The Large Eddy Simulation (LES) turbulent model and wall-adapting local eddycosity subgrid‐scale model were used to analyze the flow field characteristic [29–31]. De‐
viscosity subgrid-scale model were used to analyze the flow field characteristic [29–31].
spite the complexity of the turbulent flow in the test section, it satisfies the basic governing
Despite the complexity of the turbulent flow in the test section, it satisfies the basic govequations of fluid mechanics. The incompressible Navier–Stokes equation can be ex‐
erning equations of fluid mechanics. The incompressible Navier–Stokes equation can be
pressed as follows:
expressed as follows:
ϑuϑu
i i
= =0,0,
(3)
(3)
ϑxϑx
i i
ϑui u j
ϑui
1 ϑp
ϑ2 ui
1 ϑp + v ϑ2 ui
+ ϑui ϑu
=i u−
+ fi
j
+
=-ρ ϑxi + v ϑxi ϑx
+f
ϑt
ϑx
ϑt j ϑx
ϑx ϑx ji
ρ ϑx
j
i
i
j
(4)
(4)
where ui is the velocity components of a fluid in different directions; xi is the spatial co‐
ordinate in different directions; t is the time; ρ is the fluid density; p is the pressure of the
fluid; v is the viscosity of the fluid; and fi represents the volume force per unit mass acting
on a fluid element in different directions. Pressure−velocity coupling was modeled by the
pressure implicit in the splitting of the operator’s algorithm. The momentum equation
was discretized using bounded central differencing, and the time term was solved by a
Biomimetics 2024, 9, 415
8 of 12
where ui is the velocity components of a fluid in different directions; xi is the spatial
coordinate in different directions; t is the time; ρ is the fluid density; p is the pressure of the
fluid; v is the viscosity of the fluid; and fi represents the volume force per unit mass acting
on a fluid element in different directions. Pressure−velocity coupling was modeled by the
pressure implicit in the splitting of the operator’s algorithm. The momentum equation
was discretized using bounded central differencing, and the time term was solved by
a second-order implicit method for higher accuracy. Appropriate boundary conditions
and grids were established to ensure convergent and consistent results throughout the
simulation. Therefore, the independence validation of grid density on the area–weight
wall shear stress was analyzed, as shown in Figure 8. The shear stress of the biomimetic
Biomimetics 2024, 9, x FOR PEER REVIEWperiodic array fish scale surface stabilized when the grid number reached 1,245,006
9 of 13 at a
velocity of 2.5 m/s. Thus, the number of grid elements should not be less than 1,245,006 in
the simulation. When the residual values of continuity, x-velocity, y-velocity, and z-velocity
were less than 1 × 10−3 , the calculation result was considered convergent.
Figure
8. Independence
validation
of grid
the grid
density.
Figure
8. Independence
validation
of the
density.
4.2. Flow Characteristics
4.2. Flow Characteristics
The flow field characteristics near the wall were important to reveal the drag reduction
The flow field
characteristics
wallTherefore,
were important
to reveal
the were
drag reduc‐
mechanism
of the
biomimeticnear
fish the
scale.
simulation
results
processed
tionusing
mechanism
of
the
biomimetic
fish
scale.
Therefore,
simulation
results
were
processed
Fluent post-processing software, and the velocity vector of the biomimetic fish scale
using
Fluentwas
post‐processing
and the velocity
vector
of the
biomimetic
scaleand
surface
obtained. Thesoftware,
velocity magnitude
vectors
of FS-1
and
FS-2 were fish
selected
surface
was
obtained.
The
velocity
magnitude
vectors
of
FS‐1
and
FS‐2
were
selected
and the
processed to explain why the drag reduction performance of FS-1 was the best, and
processed
to
explain
why
the
drag
reduction
performance
of
FS‐1
was
the
best,
and
thescale
drag reduction effect gradually decreased with an increase in the spacing of the fish
drag(Figure
reduction
effect
gradually
decreased
with
an
increase
in
the
spacing
of
the
fish
scale
9). The incoming flow near the biomimetic fish scale wall was divided into two parts
(Figure
9).the
The
incoming
flow
biomimetic
fish scale
divided
intoalong
two the
when
spacing
of the
fishnear
scalethe
was
the least (FS-1):
onewall
part was
directly
flowed
parts
when the spacing
the fish
scale was
the least
partthe
directly
flowed
along to
streamwise
directionof(pink
arrows),
and this
fluid(FS‐1):
movedone
along
streamwise
direction
the streamwise
(pink arrows),
and this
fluid
along theblue
streamwise
direc- 9a).
the midpointdirection
of the downstream
cycloid
of the
fishmoved
scale (Enlarged
box in Figure
tion When
to thethis
midpoint
of
the
downstream
cycloid
of
the
fish
scale
(Enlarged
blue
box
indue
part of the fluid moved to the trough of the downstream cycloid, it was lifted
Figure
9a).
When
this
part
of
the
fluid
moved
to
the
trough
of
the
downstream
cycloid,
to the effect of the fish scale structure, which reduced the normal velocity gradient,itthus
wasdecreasing
lifted due to
effect
of the
fish scaleThe
structure,
which
reduced
normal velocity
thethe
wall
friction
resistance.
other part
flows
along the upstream
cycloid of
gradient,
thus
decreasing
the (enlarged
wall friction
resistance.
The other
part part
flows
the up‐fluid
the fish
scale
(red arrows)
green
box in Figure
9a). This
ofalong
the flowing
stream
thetwo
fishparts.
scale (red
arrows)
in Figure
9a). This part
wascycloid
dividedofinto
The first
part (enlarged
of the fluidgreen
flow box
moved
to the upstream
cycloid
of the
flowing
fluid
was
into
two Another
parts. The
first
of theflow
fluidalso
flowparticipated
moved to in
and
merged
with
thedivided
incoming
flow.
part
ofpart
the fluid
the upstream
cycloid
merged
with the
incoming
Another
of of
thethe
fluid
flow
the flow along
theand
upstream
cycloid,
and
vortices flow.
formed
on the part
valley
biomimetic
alsofish
participated
in theto
flow
along
the upstream
cycloid, with
and vortices
formed on
valley the
scale, leading
sliding
friction
being replaced
rolling friction.
In the
addition,
high–low
velocity
were formed
on the
biomimetic
fish scalewith
surface
duefriction.
to the fluid
of the
biomimetic
fish stripes
scale, leading
to sliding
friction
being replaced
rolling
dividingthe
and
mergingvelocity
with the
incoming
flow (Figure
The formed
velocity
stripes
In addition,
high–low
stripes
were formed
on the9b).
biomimetic
fish scale
surface
directly
associated
with
the path
of the
flow. The
part (pink
arrows)
flowed
duewere
to the
fluid dividing
and
merging
with
thefluid
incoming
flowfirst
(Figure
9b). The
formed
directly
along
the directly
streamwise
direction,
and
the
velocity
was
significantly
velocity
stripes
were
associated
with
the
path
of themagnitude
fluid flow.vector
The first
part
(pink
larger
than
those
in
the
other
positions.
The
second
part
(red
arrows)
participated
in the
arrows) flowed directly along the streamwise direction, and the velocity magnitude vector
formation
of
the
vortices
and
merged
with
the
incoming
flow.
Therefore,
this
special
was significantly larger than those in the other positions. The second part (red arrows)flow
participated in the formation of the vortices and merged with the incoming flow. There‐
fore, this special flow weakened the velocity magnitude along the streamwise direction,
as indicated by the velocity magnitude vector of this part of the merged fluid being
smaller than that of the first part. This is the direct reason for the function of the delay
transition of high–low velocity stripes and the high–low velocity stripes, which further
Biomimetics 2024, 9, 415
9 of 12
weakened the velocity magnitude along the streamwise direction, as indicated by the
velocity magnitude vector of this part of the merged fluid being smaller than that of the first
part. This is the direct reason for the function of the delay transition of high–low velocity
stripes and the high–low velocity stripes, which further reduced the drag [17]. However,
Biomimetics 2024, 9, x FOR PEER REVIEW
10 of 13
the number of vortices was not related to the increase in the spacing of the fish scales, and
they mostly flowed along the streamwise direction, as shown in Figure 9b.
Figure 9. The velocity magnitude vector of the biomimetic fish scale. (a) Velocity magnitude vector
Figure 9. The velocity magnitude vector of the biomimetic fish scale. (a) Velocity magnitude
of FS‐1 and a fluid flow magnified drawing. (b) Velocity magnitude vector of FS‐2 and a magnified
vector
of FS-1 and a fluid flow magnified drawing. (b) Velocity magnitude vector of FS-2 and a
drawing.
magnified drawing.
Remarkably, when the incoming fluid flowed along the upstream cycloid of FS‐1, the
Remarkably, when the incoming fluid flowed along the upstream cycloid of FS-1,
flowing fluid moved to the tip of the fish scale. Owing to the hindrance of the fluid by the
the flowing fluid moved to the tip of the fish scale. Owing to the hindrance of the fluid
fish scale, some fluid mixed with the incoming flow. However, this mixed fluid did not
by the fish scale, some fluid mixed with the incoming flow. However, this mixed fluid
form a high‐velocity stripe. Nevertheless, the other part generated streamwise vortices
did not form a high-velocity stripe. Nevertheless, the other part generated streamwise
under the influence of the unique biomimetic fish scale. Four cross sections along stream‐
vortices under the influence of the unique biomimetic fish scale. Four cross sections along
wise direction were established on the biomimetic fish scale surface to reveal the charac‐
streamwise direction were established on the biomimetic fish scale surface to reveal the
teristics of the flow field near the fish scale wall (Figure 10a). Cross section 1 as the nar‐
characteristics of the flow field near the fish scale wall (Figure 10a). Cross section 1 as the
rowest tip of a fish scale, cross sections 2 and 3 as the middle position of the cycloid, and
narrowest tip of a fish scale, cross sections 2 and 3 as the middle position of the cycloid, and
cross section 4 at the middle position of the adjacent two fish scales. As described above,
with the fluid flow moving along the cycloid to the tip‐region‐adjacent fish scales, a large
streamwise vortex was generated (Figure 10b, the enlarged box was the velocity pathline).
Streamwise vortices were generated on the valley of the fish scale along the cycloid, which
can be observed in cross sections 2 and 3, as shown in Figure 10c,d. Interestingly, a couple
of streamwise vortices formed at the valley of the adjacent fish scale along the streamwise
Biomimetics 2024, 9, 415
10 of 12
cross section 4 at the middle position of the adjacent two fish scales. As described above,
with the fluid flow moving along the cycloid to the tip-region-adjacent fish scales, a large
streamwise vortex was generated (Figure 10b, the enlarged box was the velocity pathline).
Streamwise vortices were generated on the valley of the fish scale along the cycloid, which
Biomimetics 2024, 9, x FOR PEER REVIEW
13
can be observed in cross sections 2 and 3, as shown in Figure 10c,d. Interestingly,11a of
couple
of streamwise vortices formed at the valley of the adjacent fish scale along the streamwise
direction, as shown in Figure 10e. In contrast, the streamwise vortices were not generated
adjacent fish
mobile
fluid
of of
on the adjacent
fish scale
scale of
ofFS‐2
FS-2in
incross
crosssection
section1,1,which
whichwas
wasthe
themost
most
mobile
fluid
part two,
two, and
anddirectly
directlymerged
mergedwith
withthe
theincoming
incoming
flow.
However,
streamwise
vortices
part
flow.
However,
streamwise
vortices
were
were generated
the valley
of the biomimetic
fishasscale,
asinshown
in Supplementary
generated
on theon
valley
of the biomimetic
fish scale,
shown
Supplementary
Figure S4a.
Figure
S4a. Intwo
the sections,
other twothe
sections,
the flow
field characteristics
were roughly
to as
In
the other
flow field
characteristics
were roughly
similarsimilar
to FS-1,
FS‐1, asinshown
in Supplementary
FigureThese
4b,c. streamwise
These streamwise
acted
as rolling
shown
Supplementary
Figure S4b,c.
vorticesvortices
acted as
rolling
bearings
bearings
the drag
frictionthe
between
the biomimetic
fish scale
surface
water
to
reduceto
thereduce
drag friction
between
biomimetic
fish scale surface
and
water and
[32–34].
The
[32–34].
The
number
of
streamwise
vortices
of
the
FS‐1
was
highest
in
all
biomimetic
fish
number of streamwise vortices of the FS-1 was highest in all biomimetic fish scale surfaces;
scale surfaces;
FS‐1
showed
the best drag
reduction performance.
In biomimetic
addition,
therefore,
FS-1 therefore,
showed the
best
drag reduction
performance.
In addition, the
the
biomimetic
fish
scale
unit
cells
changed
the
wall
pressure
distribution,
and
a peak
fish scale unit cells changed the wall pressure distribution, and a peak pressure point
was
pressure
point
was
formed
in
front
of
the
biomimetic
fish
scale
unit
cells
(upstream
side);
formed in front of the biomimetic fish scale unit cells (upstream side); the difference
in the
the difference
in the pressure
distribution
in the
fish
scales became
pressure
distribution
in the space
between the
fishspace
scalesbetween
became the
more
tangible
[32,34], as
more tangible
[32,34],
shown
in Figure
10f. as shown in Figure 10f.
Figure 10.
10. Velocity
fish
scale
surface.
(a)(a)
Position
Figure
Velocity magnitude
magnitudevector
vectorand
andpathlines
pathlinesfor
forthe
thebiomimetic
biomimetic
fish
scale
surface.
Position
diagram of the cross section on the biomimetic fish scale. (b) Streamwise vortices at section 1. (c–e)
diagram of the cross section on the biomimetic fish scale. (b) Streamwise vortices at section 1.
Vortices at cross sections 2, 3, and 4, respectively. (f) The distribution of the FS‐1 surface.
(c–e) Vortices at cross sections 2, 3, and 4, respectively. (f) The distribution of the FS-1 surface.
5. Conclusions
In summary, the unique fish scale structure of Albacore tuna was used as the biomi‐
metic prototype and a biomimetic periodic array fish scale surface was designed in this
study. The biomimetic fish scale surface was fabricated using a femtosecond laser device.
The features of the morphology of the biomimetic fish scale were characterized using SEM
Biomimetics 2024, 9, 415
11 of 12
5. Conclusions
In summary, the unique fish scale structure of Albacore tuna was used as the biomimetic
prototype and a biomimetic periodic array fish scale surface was designed in this study.
The biomimetic fish scale surface was fabricated using a femtosecond laser device. The
features of the morphology of the biomimetic fish scale were characterized using SEM and a
white-light interfering profilometer. The characterization results showed that the height of
the biomimetic fish scale prepared at the same level and the surface roughness considerably
increased. The drag reduction performance of the biomimetic fish scale surfaces was
measured in a circulating water tunnel. The FS-1 surface showed the maximum drag
reduction rate of 10.26% at Re = 39,532. The mechanism of action of the biomimetic fish
scale was revealed using the CFD method. Rolling bearings replaced the sliding friction,
which led to the biomimetic fish scale exerting a drag reduction effect. These results can
serve as a foundation for an in-depth analysis of the hydrodynamic performance of fish
and a novel inspiration for drag reduction and antifouling.
Supplementary Materials: The following supporting information can be downloaded at: https://
www.mdpi.com/article/10.3390/biomimetics9070415/s1, Figure S1: Bionic fish scale surface fabricated
on Al template; Figure S2: Diagram of section position and the height variation trend. Figure S3: Total
drag force of smooth surface at different velocities; Figure S4: Streamwise vortices of FS-2 surface at
different cross sections.
Author Contributions: Conceptualization, B.Z. and H.Z.; methodology, Z.S.; software, B.Z.; validation,
H.Z; formal analysis, C.S.; investigation, X.L.; resources, X.C.; data curation, Z.Z.; writing—original
draft preparation, B.Z.; writing—review and editing, H.Z.; visualization, Z.S.; supervision, D.C.; project
administration, D.C.; funding acquisition, D.C., G.L. and H.C. All authors have read and agreed to the
published version of the manuscript.
Funding: This work was supported by the National Natural Science Foundation of China (Grant
nos. 52305311, 52205297, 51935001, 51725501, and T2121003), and project ZR2023QE018 supported by
Shandong Provincial Natural Science Foundation.
Institutional Review Board Statement: Not applicable.
Data Availability Statement: The data that support the findings of this study are available from the
corresponding author upon reasonable request.
Conflicts of Interest: The authors declare that they have no known competing financial interests or
personal relationships that could appear to have influenced the work reported in this paper.
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