Proceedings of the ASME 2011 Conference on Smart Materials, Adaptive Structures and Intelligent Systems
SMASIS2011
September 18-21, 2011, Phoenix, Arizona, USA
SMASIS2011- 4931
Fish Inspired Biomimetic Ionic Polymer Metal Composite Pectoral Fins Using
Labriform Propulsion
G. Karthigan
Sujoy Mukherjee
Ranjan Ganguli
Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India
ABSTRACT
Ionic polymer metal composites (IPMC) are a new class of
smart materials that have attractive characteristics such as
muscle like softness, low voltage and power consumption, and
good performance in aqueous environments. Thus, IPMC’s
provide promising application for biomimetic fish like
propulsion systems. In this paper, we design and analyze IPMC
underwater propulsor inspired from swimming of Labriform
fishes. Different fish species in nature are source of inspiration
for different biomimetic flapping IPMC fin design. Here, three
fish species with high performance flapping pectoral fin
locomotion is chosen and performance analysis of each fin
design is done to discover the better configurations for
engineering applications. In order to describe the behavior of an
active IPMC fin actuator in water, a complex hydrodynamic
function is used and structural model of the IPMC fin is
obtained by modifying the classical dynamic equation for a
slender beam. A quasi-steady blade element model that accounts
for unsteady phenomena such as added mass effects, dynamic
stall, and the cumulative Wagner effect is used to estimate the
hydrodynamic performance of the flapping rectangular shape
fin. Dynamic characteristics of IPMC actuated flapping fins
having the same size as the actual fins of three different fish
species, Gomphosus varius, Scarus frenatus and Sthethojulis
trilineata, are analyzed with numerical simulations. Finally, a
comparative study is performed to analyze the performance of
three different biomimetic IPMC flapping pectoral fins.
INTRODUCTION
Research focus on design and development of
biomimetic swimming systems for underwater vehicles are of
major interest these days [1]. The drive for this research arises
from the fact that the underwater vehicles that mimicking the
behavior of swimming life forms offers potentially superior
benefits in stealth, maneuverability and efficiency
characteristics compared to conventional propeller driven
underwater vehicles [2, 3]. Biomimetic swimming systems have
wide applications ranging from navy platforms for surveillance
and seabed sampling for mining or archaeology to other
underwater monitoring operations such as pollution detection,
video mapping and pipe inspection in the radiate area [4]. Some
biomimetic swimming systems are well adaptive for uncertain
and/or unstructured underwater environments such as littoral
zones in Great barrier reefs and Caribbean seas. However, the
conventional systems are limited in this field due to limited
space offered by traditional electro-mechanical actuators such
as motor which are difficult to shrink because of its
electromagnetic structure. Inspired by the speed, efficiency and
maneuverability of real fishes, fish like propulsion systems has
obtained great attention due to its compactness, high efficiency,
noiseless motions and great steering capability [5, 6].
Researchers have studied extensively to mimic such capabilities
using oscillating or undulating foils for propulsion [7]. Various
mechanical designs of fish like biomimetic propulsion systems
have also been proposed [8]. However, the mechanical
swimming structures that mimic the aquatic fish like propulsion
by means of rigid, oscillating plates or foils are driven by
servomotors, gears, bearings and other interfacing parts.
Therefore, these structures face the problems such as relatively
large structure, complex mechanisms, low efficiencies, noisy
biomimetic vehicles and excessive thermal energy generation.
Moreover, these biomimetic propulsion systems suffer from
large costs and less eco friendly systems [9].
At present, smart material actuators have been explored for
small size autonomous underwater vehicles (AUV’s) and they
include shape memory alloy actuators (SMA), piezoelectric
actuators and giant magnetostrictive actuators (GMA).
However, there are some problems for real applications, such as
less simple structure, low response, leaking electric current,
safety in water and so on [10]. Ionic polymer metal composite
(IPMC) is a promising class of smart material that belongs to
the family of electroactive polymers (EAP), first reported by
Adolf et al [11] and Oguro et al [12], Shahinpoor et al [13]
coined the phrase IPMC. IPMC is produced by chemically
plating noble metals such as gold or platinum on a
perfluorosulfonic acid membrane which is known as an ionexchange membrane. The ion exchange membrane selectively
allow diffusion of mobile cations as well as a solvent (typically
polar solvents such as water) through nanosize pores and
1
Copyright © 2011 by ASME
channels of the polymer matrix, while the anions are covalently
bonded to the fixed polymer matrix. When input voltage is
applied across metal layers of the both surface, a solvent flux of
hydrated cations as well as free water is created with direction
towards the cathode. It is this solvent flux that creates an
electro-osmotic pressure differential resulting in a bending
motion towards the anode side of the IPMC. IPMC generates
large bending motions under low driving voltages, operates well
in wet environments and is flexible and biocompatible. IPMC
behaves like soft artificial muscle and has good response under
electric field. Additionally, it has more energy transforming
efficiency than traditional propellers. Fish like propulsion
systems actuated by IPMC can swim far distance more than
motor actuated propulsion at the same battery [14]. When in
operation, IPMC materials are quiet since they have no
vibration causing components, i.e. gears, motors, shafts, and
etc. For small AUV’s, these features are truly attractive.
Recently, enormous research effort has been devoted to
design and develop IPMC based propulsion systems for
underwater vehicles. Prototypes of fish like underwater vehicles
propelled using IPMC have been proposed [15, 16]. Yim et al
[17] developed the analytical model framework for the dynamic
characteristics of the segmented IPMC actuator under fluid
environment and they validated the model for small larval zebra
fish. Kim et al [18] designed an aquatic propulsor which
utilized an IPMC as a tail fin propulsor that generates thrust
force by oscillating at a predetermined frequency. Chen et al
[19] developed a physics based model to capture the actuation
physics of an IPMC caudal fin. Abdelnour et al [20]
numerically analyzed the hydrodynamics of IPMC propulsor
using the Navier Stokes equation. Time resolved particle image
velocimetry has been conducted to study the flow physics
generated around a vibrating IPMC in quiescent aqueous
environments [21] and a control volume analysis is utilized to
estimate the thrust production per unit IPMC width [22]. In a
recent study, Aureli et al. [9] developed a modeling framework
for studying the free-locomotion of biomimetic underwater
vehicles propelled by IPMC attached with a passive tail like fin.
The focus of all these pioneering efforts is to show the
feasibility of IPMCs as thrust-generating devices for
miniaturized biomimetic swimming systems and also the
performance of fish like Tail/Caudal fin propulsion of AUV’s
using IPMC. However, fish propulsion can be broadly classified
into body/or caudal fin (BCF) propulsion and median /or paired
fin (MPF) propulsion. BCF type propulsion offers high
acceleration and thrust forces whereas MPF type propulsion
offers good maneuverability. For miniature size underwater
vehicles maneuverability is an important factor in addition to
propulsion and roughly 15 – 20% of living fishes use their
pectoral fins (MPF type propulsion) as their primary mode of
locomotion. Thus research on mimicking the pectoral fin
locomotion of fishes can do justice to both propulsion and
maneuverability needs of miniature size AUV’s. Pectoral fin
locomotion can be classified on basis of the movements for
thrust generation such as undulatory or oscillatory. The
Rajiform and Diodontiform class of fishes follow undulatory
type fin motions whereas labriform class of fishes follow
oscillatory type fin motions as shown in Figure 1 [23]. In
literature, Takagi et al [24] developed an IPMC propulsor
mimicking the propulsion mode of a ray fish which uses
rajiform swimming. The propulsion mode creates a wave like
motion using several IPMC strips. As IPMC operates in self
oscillatory manner it is comparatively easy to mimic the
oscillatory fin motion of labriform fishes using IPMC than the
undulatory fin mode which is very challenging in terms of
controllability and power requirement and may lead to
unnecessary complexity.
Figure 1. Classification of fish propulsion, particularly
pectoral fin propulsion.
In this paper, we would employ IPMC to mimic the fish
species that follow dorso-ventral flapping stroke as the primary
mode of swimming. Dynamic characteristics of IPMC actuated
flapping fins, having the same size as to the actual fins of three
different Labridae fish species, are analyzed using numerical
simulations. Gomphosus varius, Scarus frenatus and
Sthethojulis trilineata are three different Labridae fish species
which perform high efficient flapping pectoral fin locomotion
[25]. The different classes of same species provide different
biomimetic designs for a flapping pectoral fin which can lead to
the discovery of better configurations for engineering use.
Therefore, flapping characteristics of different fishes can
provide design guidelines for the development of flapping fin
for the use in AUVs. Structural modeling of an underwater
IPMC flapping fin is done by modifying the Euler-Bernoulli
beam equation to take into account the electromechanical
dynamics of IPMC active beams in water. In addition,
hydrodynamic performance of the oscillating fin is analyzed
using a quasi-steady blade element model that accounted for
unsteady phenomena such as added mass effects, dynamic stall
2
Copyright © 2011 by ASME
and the cumulative Wagner effect. Thus, this model can be used
to extend our analysis on design and performance of oscillating
IPMC based pectoral flapping propulsor. Parametric study is
done on fin thickness to show the effect of fin thickness on
performance of the fin. Finally, a comparative study is
performed to analyze the performance of three different
biomimetic IPMC flapping pectoral fins.
NOMENCLATURE
A
Cross section area of beam
:
vn
:
Normal velocity component of chord relative
to the water
vx
:
Chord wise velocity of the section relative to
the fluid
V
:
Volume of the immersed body
V0
:
Applied voltage
w(x,t)
:
Beam deflection

:
Hydrodynamic angle of attack
b
:
Width of beam

:
Angle relative to the free stream
c
:
Chord length

:
Cm
:
Added mass coefficient
Thickness of thin viscous layer surrounding
IPMC actuator
Hydrodynamic function
:
Coefficient of skin friction drag


:
Cs f
:
Viscosity of fluid
CL
:
Lift coefficient
i f
:
Viscosity of water
Cm
:
Mass coefficient

:
Pitch angle relative to the flapping axis
d(  )
:
Electromechanical coupling coefficient
i
:
Normal mode
E
:
Young’s modulus

:
Density of IPMC
EI
:
Flexural stiffness
f
:
Density of water
Fa
:
Added mass force
m
:
Added mass coefficient
Fx
:
Chord wise force

:
Frequency of vibrating beam
gv
:
Fluid damping force
i
:
Natural frequency of vibrating free beam
h
:
Tangential velocity
:
Natural frequency of beam vibrating in water
H i  
i f
:
Frequency response function
La
:
Added mass lift
Lc
:
Circulatory lift
L*
:
Circulatory force component normal to the
local stream
ma
:
Added mass
md
:
Displaced mass
P
:
Input power
Pa
:
Input power due to added mass force
Pc
:
Input power due to circulatory force
qi  t 
:
Generalized coordinate
Re
:
Reynolds number
Ta
:
Added mass thrust
Tc
:
Circulatory thrust
T*
:
Circulatory force component parallel to the
local stream
STRUCTURAL MODEL
Figure 2 shows a schematic diagram of the IPMC actuator
geometry immersed in water. As shown in Figure 2 the IPMC
actuator is fixed at one end in cantilever configuration and has a
uniform rectangular cross-section across it. In the present study,
the Euler-Bernoulli beam theory is assumed for modeling the free
deflections. In order to describe the behavior of an IPMC actuator
in water, the dynamic model of the active beam needs to
explicitly take into account the interaction between the actuator
and water. This is because of the fact that the IPMC actuator
experiences a force which is exerted by the viscous fluid due to
its oscillations in the fluid. The effect of fluid is often negligible
in air, but becomes significant when the actuator is immersed in a
denser medium such as water [26]. Therefore, the IPMC actuator
drags an additional mass in the form of a skin of water during its
motion. This additional mass generates an additional inertial force
which can be expressed as
Fh = - ma
3
¶ 2w
¶ t2
(1)
Copyright © 2011 by ASME
The added mass (ma) is proportional to the displaced
mass of the fluid (md)
ma = Cm md = CmV r f
(2)
There are two main sources of damping forces: the fluid
damping force and damping force of IPMC actuator due to
internal friction effect [27]. In this case, internal damping force
of the IPMC actuator is neglected as it is negligible compared
to the fluid damping effect. Hence, the fluid damping force can
be expressed as
w
t
g  C
V
V
(3)
This modeling exploits the hydrodynamic function
concept which is prevalent in the study of passive beams
immersed in viscous fluids [26]. The hydrodynamic function
accounts for the interaction between actuator and the water.
Moreover, it includes geometry of the cross-section of the
IPMC actuator. Added mass co-efficient (Cm) and fluid
damping co-efficient (CV) can be expressed by the real and
imaginary part of the complex hydrodynamic function ()
Figure 2. Schematic diagram of the IPMC actuator geometry
used for structural modeling.
Finally, the deflection of the IPMC underwater
propulsor can be written as
w  x, t  
1
 A  md


H i  

2
i
i 1
i  L  i  x 
d   hbE
2
V0 e
j t
(9)
Cm  Re (  )
CV  md  Im(  )
md   f ( / 4)b
(4)
2
The real and imaginary parts of the hydrodynamic function are
Re     c1  c2


b
 
Im     c3  c4  
b
b
2
(5)
where  represents the thickness of the thin viscous layer
surrounding the IPMC actuator and can be written as

2
f
(6)
The equation of motion of the IPMC underwater
propulsor, taking into account its interaction with water, can be
written as [28]
EI
 4 w  x, t 
x
4
 CV
2
 w( x, t ) 
 2   w  x, t 
   A  Cm  f b 
 f  x, t 
t
4   t2

(7)
The general solution of the equation of motion can be
obtained using mode summation method which can be
expressed as

w  x, t    i  x  qi  t 
i 1
(8)
where
  f b

i  i 1 
Cm 
4

h


f
 if 

1
2
(10)
CV
2  Ai f
H i f   
(11)
1

1  / 
i
f

2

 j 2i f  / i f

(12)
Hydrodynamic Model
The hydrodynamic performance of flapping rectangular
shape (pectoral fin) appendage is captured using quasi-steady
blade element model that accounts for unsteady phenomena
such as added mass effects, dynamic stall, and the cumulative
Wagner effect [29]. The appendage oscillates around the
flapping axis, which has an angle , relative to the free stream.
Here,  is 0 for the flapping appendage as can be seen from
Figure 3. The appendages twist around the pitching axis giving
each element an instantaneous pitch , relative to the flapping
axis as shown in Figure 4. The flapping appendage twists about
its leading edge with simple harmonic motion. Blade element
models divide a propulsive structure along its span into a series
of blade elements and estimate force balance on an element
using force coefficients that are a function of the elements
instantaneous geometry. Empirically derived lift and drag
4
Copyright © 2011 by ASME
coefficients are measured from root oscillating plates at Re=192
and by modifying the coefficients by the Wagner function. Both
the circulatory forces resulting from velocity differences on
opposing sides of the appendage and added mass forces
resulting from the acceleration of a mass of fluid are modeled.
 n 

 x 
   tan1 
(19)
where vx is chordwise velocity of the section relative to the
fluid.
The thrust force per unit span, due to both circulatory and
added mass forces is shown by
dT  dTc  dTa
(20)
Thrust power is summed across all elements and time
increments, multiplied by two to reflect both appendages, and
divided by the number of time increments to give mean values.
Figure 3.  = 00 for the flapping appendage.
Validation of Model Implementation
In order to validate the model, numerical analysis is carried
out for IPMC actuator (30 mm  4 mm  0.18 mm) used by
Brunetto et al [28]. Figure 5 shows the variation of the bending
moment with different actuation frequencies. Tip deflection of
the IPMC actuator immersed in water is obtained for a first
mode of vibration at different actuation frequencies as shown in
Figure 6.
1.2
Present
Brunetto et al
1
M/Mmax
Figure 4. Hydrodynamic forces of a flapping appendage section
Circulatory thrust (dTc), circulatory lift (dLc), added mass thrust
(dTa), and added mass lift (dLa) per unit span of the flapping
appendage is given by
dTc   dFn sin  dFx cos 
(13)
dLc  dFn cos   dFx sin 
(14)
dTa  dFa sin
(15)
dLc   dFa cos 
(16)
0.2
0
20
40
60
80
Frequency (Hz)
100
Figure 5. Dependence of the bending moment on actuation
frequency.
2
x 10
-3
Present
Brunetto et al
Tip deflection (m)
1
 c 2 n
4
0.6
0.4
The added mass force per unit span is
dFa 
0.8
(17)
where, c is chord length and vn is the first derivative of the
1.5
1
0.5
normal velocity component of the chord relative to the water.
0
0
The normal force per unit span is given by
dFn   dT  sin  dL cos 
10
20
30
Frequency (Hz)
40
Figure 6. Tip deflection of an IPMC underwater propulsor.
(18)
where dT* and dL* are the components of the circulatory force
normal to and parallel with the local stream. The hydrodynamic
angle of attack is given by
5
Copyright © 2011 by ASME
0.02
0.5
0.45
0.4
Present
Brunetto et al
(N)
0.005
-2
0
0
0
2
10
10
Frequency (Hz)
10
Further, Figure 7 shows the variation of the thin
viscous layer of thickness  surrounding the IPMC actuator
with the input excitation frequencies. These results agree well
with the results presented by Brunetto et al. [28], thus
confirming the implementation of the structural dynamic model.
In order to verify the computer implementation of the
hydrodynamic model, numerical analysis is performed for the
oscillating rectangular appendage used by Walker and Westneat
[29]. The mean thrust over the full cycle of flapping appendage
is shown in Figure 8. Figure 9 shows the mean thrust force for
power stroke. The results of this numerical analysis are in
match well with the results presented in Walker and Westneat
[29]. Thus both the structural and hydrodynamic models are
validated and are subsequently used to analyze the performance
of pectoral fin based IPMC propulsor. At first, study on
baseline fin is carried out to understand the actuation behavior
of IPMC. Secondly, parametric study is performed to
understand the relationships between the IPMC fin thickness
and resonating frequency and its performance. Then, based on
the results, comparative study is carried out on the fish based
IPMC fin designs.
0.35
12
0.05
10
5
d (m/V)
0.1
4
(N)
6
a)
14
3
5
Baseline IPMC Flapping Fin
In order to understand the IPMC behavior, the underwater
propulsor is modeled as an active beam which shows frequency
dependent material properties. Figure 10 shows the dependence
of electromechanical coupling coefficient (d) on input
excitation frequencies. Subsequently, this material property is
used to study the behavior of IPMC as a hydrodynamic
propulsor with baseline configuration l=30 mm, b=4 mm,
h=0.18 mm as used by Brunetto et al [28]. Figure 11 shows the
tip deflection of the baseline fin at different input voltages with
maximum tip deflection of 2.1 mm obtained at 6 volt. It can be
noted that the peak tip deflection of flapping fin occurs at the
natural frequency for a given fin design. Deflected fin shapes of
baseline fin design for different applied voltages operating at
resonating frequency of 2.8 Hz is shown in Figure 12. These
voltages are typical of IPMC actuation. The variation in
flapping angles at the resonating frequency for one stroke
period for baseline design is shown in Figure 13 with maximum
flapping angle of 40 obtained at applied voltage of 6 volt.
Further, we see that the maximum dynamic performance is
obtained at higher applied voltages with maximum performance
at 6 volt.
0.15
2
4
RESULTS AND DISCUSSION
0.2
1
3
Figure 9. Effect of forward speed variation on mean thrust
generation during power stroke.
0.25
0
0
2
-1
Present
Walker and Westneat
0.3
1
Speed (BL s )
Figure 7. Variation of the thickness of the thin viscous layer
with the input excitation frequency.
avg
0.25
0.2
0.15
0.1
0.05
0
-4
10
T
0.35
0.3
avg
0.01
T
 (m)
0.015
Present
Walker and Westneat
6
-1
Speed (BL s )
x 10
-6
8
6
Figure 8. Mean thrust generation during full stroke versus
forward speed variation in terms of fish body length (BL).
4
2
0
6
20
40
60
Frequency (Hz)
80
100
Copyright © 2011 by ASME
5
Flapping angle (degree)
b)
0
Phase (deg)
-20
6 Volt
4 Volt
2 Volt
0
-40
-5
0
71
-60
-80
0
20
40
60
Frequency (Hz)
80
357
100
2.5
6 Volt
4 Volt
2 Volt
2
Next, parametric study is performed on baseline flapping
IPMC fin to investigate the effect of thickness on the
performance of the fin. Figure 14 shows that the natural
frequency of the IPMC propulsor increases with increase in fin
thickness for any given voltage. Design variable such as
thickness is varied along with the applied voltage and
corresponding actuation frequency (resonating frequency). The
maximum tip deflection is used as a measure of the
performance of the flapping fin.
1.5
15
1
Natural Frequency (Hz)
Tip deflections (mm)
286
Figure 13. Flapping angle variation of baseline flapping IPMC
fin design at different input voltages
Figure 10. Dependence of the electromechanical coupling
coefficient on input excitation frequency.
0.5
0
1
3
5
7
Frequency (Hz)
9
Figure 11. Variation of tip deflection of baseline IPMC fin
design at different applied voltages
2
10
5
0
1
6 Volt
4 Volt
2 Volt
5
x 10
-4
7
Maximum tip deflections (mm)
1.5
1
0.5
0
0
2
3
4
Fin Thickness (m)
Figure 14. Effect of fin thickness variation versus natural
frequencies.
2.5
Deflections (mm)
143
214
Time (ms)
0.01
0.02
Fin length (m)
0.03
Figure 12. Deflection shape of baseline flapping IPMC fin at
different applied voltages and operating at resonant
frequency
6
6 Volt
4 Volt
5
2 Volt
4
3
2
1
0
.1
.2
.3
.4
Fin thickness (mm)
.5
Figure 15. Fin thickness variation versus maximum tip
deflections.
7
Copyright © 2011 by ASME
the fin thickness of all the fish inspired flapping IPMC fins are
taken as 0.5 mm, as maximum performance of fins is obtained
at given thickness.
The variation in tip deflection for different actuation
frequencies with applied voltage of 6 volt is shown in Figure
19.
40
Natural frequency [Hz]
The effect of the variation of thickness of IPMC fin on the
flapping performance at three different input voltages is shown
in Figure 15. The peak value of tip deflection increases due to
increase in fin thickness as shown above due to the fact that fin
thickness does not influence the fluid damping and it further
improves ion mobility in the electrophoresis process that
increases the flapping fin actuation.
In summary, the effect of variation in thickness is
significant and it influences the performance of IPMC fin. The
maximum performance is obtained at higher applied voltage
such as 6 volt used in this study.
Biomimetic IPMC Flapping Fins:
The size of the fins varies substantially among different
fish species due to evolution from their habitat. In this study,
three different Labridae fish species which include Gomphosus
varius, Scarus frenatus and Sthethojulis trilineata are chosen
for IPMC flapping fin designs. Pectoral fin of each species
represents different biomimetic design and provides guidelines
for the development of the IPMC flapping fins. The leading
edge spans of fishes are taken as fin length and the tip chord of
the fishes are taken as chord length for the IPMC flapping fins.
The schematic diagram of three different flapping fin sizes of
fishes are shown in Figure 16.
Gomphosus varius
Scarus frenatus
Stethojulis trilineata
30
20
10
0
.1
.2
.3
.4
Fin thickness [mm]
.5
Figure 17. Effect of fin thickness variation versus natural
frequencies.
-3
Maximum tip deflections [m]
8
x 10
Gomphosus varius
Scarus frenatus
Stethojulis trilineata
7
6
5
4
3
2
1
.1
.2
.3
.4
.5
Fin thickness [mm]
Figure 18. Fin thickness variation versus maximum tip
deflections.
Figure 16. Schematic diagram of the planform of fish flapping
fin designs having the same size as (a) Gomphosus varius (b)
Scarus frenatus (c) Sthethojulis trilineata.
The effect of varying the fin thickness on natural
frequencies of IPMC fin at 6 volt is shown in Figure 17. The
natural frequency of the IPMC fin is found to increase with
increase in fin thickness. Maximum resonant frequencies of
IPMC fish fins inspired from Gomphosus varius, Scarus
frenatus, Stethojulis trilineata are 10.8 Hz, 2.2 Hz and 21.5 Hz
respectively. Moreover, the maximum value of tip deflection is
found to increase with increase of fin thickness as shown in
Figure 18. Maximum tip deflection of 4.66 mm is obtained for
IPMC fin inspired from Scarus frenatus and 4.52 mm for
Gomphosus varius and 3.3 mm for Stethojulis trilineata. Hence,
The mean thrust force over full stroke produced by three
different fish inspired IPMC flapping fins oscillating at their
respective resonating frequencies is shown in Figure 20. The
flapping angles for IPMC fin design inspired from Gomphosus
varius, Scarus frenatus, Stethojulis trilineata are 9.60, 5.50,
and 9.10, respectively, with pitch angle of 100 is used for thrust
evaluation of three IPMC flapping fin propulsors. It can be seen
from Figure 20 that the variation of thrust values for varied
forward speeds are 0.0068 N to 0.004 N for the IPMC
Gomphosus varius fin design and 0.0066 N to 0.0036 N for the
IPMC Scarus frenatus fin design and 0.0061 N to 0.0042 N for
the IPMC Stethojulis trilineata fin design. It can also be noted
that the thrust force generated for given fin designs decreases
along increase in forward speed. In addition, the thrust force
generated from fin design inspired from Scarus frenatus
decreases rapidly compared to other two fish fin designs. Fin
design inspired from Stethojulis trilineata generates thrust force
better than IPMC Scarus frenatus fin design beyond forward
8
Copyright © 2011 by ASME
speed of 0.33 m/sec and better than Gomphosus varius beyond
forward speed of 0.57 m/sec.The reason for this behavior can
be related to shape of flapping fins, which plays an important
role in generating thrust force. The aspect ratio of IPMC
Stethojulis trilineata fin design is found to be higher than other
two IPMC fin designs and hence better generation of thrust
force at higher forward speeds compared to other IPMC
flapping fish designs.
-3
Tip deflections [m]
8
x 10
Gomphosus varius
Scarus frenatus
Stethojulis trilineata
6
4
2
0
0
5
10
15
Frequency [Hz]
20
25
Figure 19. Variation of tip deflection for three different
IPMC fin designs at 6 volt.
T
avg
(mN)
8
Gomphosus varius
Scarus frenatus
Stethojulis trilineata
7
6
5
4
3
0
0.15 0.3 0.45 0.6 0.75 0.9
-1
Speed (m s )
Figure 20. Mean thrust of three different IPMC fin design
over full cycle versus speed.
CONCLUSION
In this paper, fish inspired biomimetic propulsion using
IPMC has been discussed. For this study we have followed the
lift based flapping stroke of Labriform fishes, which use
pectoral fins as the primary mode of locomotion. Gomphosus
varius, Scarus frenatus and Sthethojulis trilineata, perform
efficient flapping pectoral fin locomotion, are three chosen
fishes that generates thrust force by oscillatory flapping
locomotion. Dynamic characteristics of three different flapping
pectoral fin based IPMC underwater propulsors, having the
same size as to the actual fins of three different Labridae fish
species, are analyzed using numerical simulations. The effect of
variation in thickness of IPMC on resonant frequencies and tip
deflection is shown. The best performance of the IPMC fin is
obtained by operating at the resonant frequency and maximum
thickness of fin. From the thrust production for given designs,
the use of high aspect ratio IPMC flapping fish fins is found to
be better for high forward speeds and low aspect ratio IPMC
flapping fins is found to be good for low forward speeds.
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