Abstract

In this paper, the propulsive performance of a caudal peduncle-fin swimmer mimicking a bio-inspired robotic fish model is numerically studied using a fully coupled FSI solver. The model consists of a rigid peduncle and a flexible fin which pitches in a uniform flow. The flexible fin is modeled as a thin plate assigned with non-uniformly distributed stiffness. A finite volume method based in-house Navier–Stokes solver is used to solve the fluid equations, while the fin deformation is resolved using a finite element code. The effect of the fin flexibility on the propulsive performance is investigated. The numerical results indicate that compliance has a significant influence on performance. Under the parameters studied in this paper, the medium flexible fin exhibits remarkable efficiency improvement, as well as thrust augment, while the least flexible fin shows no obvious difference from the rigid one. However, for the most flexible fin, although the thrust production decreases sharply, the efficiency reaches the maximum value. It should be noted that by non-uniformly distributing the rigidity across the caudal fin, our model is able to replicate some fin deformation patterns observed in both the live fish and the experimental robotic fish.

References

1.
Bandyopadhyay
,
P. R.
,
2005
, “
Trends in Biorobotic Autonomous Undersea Vehicles
,”
IEEE J. Oceanic Eng.
,
30
(
1
), pp.
109
139
. 10.1109/JOE.2005.843748
2.
Luo
,
Y.
,
Pan
,
G.
,
Huang
,
Q.
,
Shi
,
Y.
, and
Lai
,
H.
,
2019
, “
Parametric Geometric Model and Shape Optimization of Airfoils of a Biomimetic Manta Ray Underwater Vehicle
,”
J. Shanghai Jiaotong University (Science)
,
24
(
3
), pp.
402
408
. 10.1007/s12204-019-2076-4
3.
Salazar
,
R.
,
Fuentes
,
V.
, and
Abdelkefi
,
A.
,
2018
, “
Classification of Biological and Bioinspired Aquatic Systems: A Review
,”
Ocean Eng.
,
148
, pp.
75
114
. 10.1016/j.oceaneng.2017.11.012
4.
Triantafyllou
,
G. S.
,
Triantafyllou
,
M.
, and
Grosenbaugh
,
M.
,
1993
, “
Optimal Thrust Development in Oscillating Foils With Application to Fish Propulsion
,”
J. Fluids Struct.
,
7
(
2
), pp.
205
224
. 10.1006/jfls.1993.1012
5.
Dong
,
H.
,
Mittal
,
R.
, and
Najjar
,
F.
,
2006
, “
Wake Topology and Hydrodynamic Performance of Low-Aspect-Ratio Flapping Foils
,”
J. Fluid Mech.
,
566
, pp.
309
343
. 10.1017/S002211200600190X
6.
Wolfgang
,
M. J.
,
Anderson
,
J. M.
,
Grosenbaugh
,
M. A.
,
Yue
,
D. K.
, and
Triantafyllou
,
M. S.
,
1999
, “
Near-Body Flow Dynamics in Swimming Fish
,”
J. Exp. Biol.
,
202
(17), pp.
2303
2327
.
7.
Kern
,
S.
, and
Koumoutsakos
,
P.
,
2006
, “
Simulations of Optimized Anguilliform Swimming
,”
J. Exp. Biol.
,
209
(
24
), pp.
4841
4857
. 10.1242/jeb.02526
8.
Bozkurttas
,
M.
,
Mittal
,
R.
,
Dong
,
H.
,
Lauder
,
G. V.
, and
Madden
,
P.
,
2009
, “
Low-Dimensional Models and Performance Scaling of a Highly Deformable Fish Pectoral Fin
,”
J. Fluid Mech.
,
631
, pp.
311
342
. 10.1017/S0022112009007046
9.
Heathcote
,
S.
, and
Gursul
,
I.
,
2007
, “
Flexible Flapping Airfoil Propulsion at Low Reynolds Numbers
,”
AIAA J.
,
45
(
5
), pp.
1066
1079
. 10.2514/1.25431
10.
Longzhen
,
D.
,
Guowei
,
H.
, and
Xing
,
Z.
,
2016
, “
Self-Propelled Swimming of a Flexible Plunging Foil Near a Solid Wall
,”
Bioinspiration Biomimetics
,
11
(
4
), p.
046005
. 10.1088/1748-3190/11/4/046005
11.
Lauder
,
G. V.
,
1982
, “
Structure and Function in the Tail of the Pumpkinseed Sunfish (Lepomis gibbosus)
,”
J. Zool.
,
197
(
4
), pp.
483
495
. 10.1111/jzo.1982.197.4.483
12.
Park
,
Y.-J.
,
Huh
,
T. M.
,
Park
,
D.
, and
Cho
,
K.-J.
,
2014
, “
Design of a Variable-Stiffness Flapping Mechanism for Maximizing the Thrust of a Bio-Inspired Underwater Robot
,”
Bioinspiration Biomimetics
,
9
(
3
), p.
036002
. 10.1088/1748-3182/9/3/036002
13.
Kancharala
,
A. K.
, and
Philen
,
M. K.
,
2016
, “
Optimal Chordwise Stiffness Profiles of Self-Propelled Flapping Fins
,”
Bioinspiration Biomimetics
,
11
(
5
), p.
056016
. 10.1088/1748-3190/11/5/056016
14.
Zhu
,
Q.
, and
Bi
,
X.
,
2017
, “
Effects of Stiffness Distribution and Spanwise Deformation on the Dynamics of a Ray-Supported Caudal Fin
,”
Bioinspiration Biomimetics
,
12
(
2
), p.
026011
. 10.1088/1748-3190/aa5d3f
15.
Jayne
,
B. C.
, and
Lauder
,
G. V.
,
1995
, “
Speed Effects on Midline Kinematics During Steady Undulatory Swimming of Largemouth Bass, Micropterus Salmoides
,”
J. Exp. Biol.
,
198
(2), pp.
585
602
.
16.
Esposito
,
C. J.
,
Tangorra
,
J. L.
,
Flammang
,
B. E.
, and
Lauder
,
G. V.
,
2012
, “
A Robotic Fish Caudal Fin: Effects of Stiffness and Motor Program on Locomotor Performance
,”
J. Exp. Biol.
,
215
(
1
), pp.
56
67
. 10.1242/jeb.062711
17.
Ren
,
Z.
,
Yang
,
X.
,
Wang
,
T.
, and
Wen
,
L.
,
2016
, “
Hydrodynamics of a Robotic Fish Tail: Effects of the Caudal Peduncle, Fin Ray Motions and the Flow Speed
,”
Bioinspiration Biomimetics
,
11
(
1
), p.
016008
. 10.1088/1748-3190/11/1/016008
18.
Jameson
,
A.
,
Schmidt
,
W.
, and
Turkel
,
E. L. I.
,
1981
, “
Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge Kutta Time Stepping Schemes
,”
14th Fluid and Plasma Dynamics Conference
,
June 23–25
,
American Institute of Aeronautics and Astronautics
.
19.
Alonso
,
J.
, and
Jameson
,
A.
,
1994
, “
Fully-Implicit Time-Marching Aeroelastic Solutions
,”
32nd Aerospace Sciences Meeting and Exhibit
,
Reno, NV
,
Jan. 10–13
, p.
56
.
20.
Xiao
,
Q.
, and
Liao
,
W.
,
2010
, “
Numerical Investigation of Angle of Attack Profile on Propulsion Performance of an Oscillating Foil
,”
Comput. Fluids
,
39
(
8
), pp.
1366
1380
. 10.1016/j.compfluid.2010.04.006
21.
Xiao
,
Q.
,
Liao
,
W.
,
Yang
,
S.
, and
Peng
,
Y.
,
2012
, “
How Motion Trajectory Affects Energy Extraction Performance of a Biomimic Energy Generator With an Oscillating Foil?
,”
Renewable Energy
,
37
(
1
), pp.
61
75
. 10.1016/j.renene.2011.05.029
22.
Liu
,
W.
,
Xiao
,
Q.
, and
Cheng
,
F.
,
2013
, “
A Bio-Inspired Study on Tidal Energy Extraction With Flexible Flapping Wings
,”
Bioinspiration Biomimetics
,
8
(
3
), p.
036011
. 10.1088/1748-3182/8/3/036011
23.
Shi
,
G.
,
Qing
,
X.
,
Qiang
,
Z.
, and
Wei
,
L.
,
2019
, “
Fluid-Structure Interaction Modeling on a 3D Ray-Strengthened Caudal Fin
,”
Bioinspiration Biomimetics
,
14
(
3
), p.
036012
. 10.1088/1748-3190/ab0fbe
24.
Dhondt
,
G.
,
2004
,
The Finite Element Method for Three-Dimensional Thermomechanical Applications
,
John Wiley & Sons
,
New York
.
25.
Liu
,
W.
,
Xiao
,
Q.
, and
Zhu
,
Q.
,
2016
, “
Passive Flexibility Effect on Oscillating Foil Energy Harvester
,”
AIAA J.
,
54
(
4
), pp.
1172
1187
. 10.2514/1.J054205
26.
Bungartz
,
H.-J.
,
Lindner
,
F.
,
Gatzhammer
,
B.
,
Mehl
,
M.
,
Scheufele
,
K.
,
Shukaev
,
A.
, and
Uekermann
,
B.
,
2016
, “
preCICE—A Fully Parallel Library for Multi-Physics Surface Coupling
,”
Comput. Fluids
,
141
, pp.
250
258
. 10.1016/j.compfluid.2016.04.003
27.
Degroote
,
J.
,
Bathe
,
K.-J.
, and
Vierendeels
,
J.
,
2009
, “
Performance of a New Partitioned Procedure Versus a Monolithic Procedure in Fluid–Structure Interaction
,”
Comput. Struct.
,
87
(
11–12
), pp.
793
801
. 10.1016/j.compstruc.2008.11.013
28.
Haelterman
,
R.
,
Bogaers
,
A. E. J.
,
Scheufele
,
K.
,
Uekermann
,
B.
, and
Mehl
,
M.
,
2016
, “
Improving the Performance of the Partitioned QN-ILS Procedure for Fluid–Structure Interaction Problems: Filtering
,”
Comput. Struct.
,
171
, pp.
9
17
. 10.1016/j.compstruc.2016.04.001
29.
Tsai
,
H. M.
,
Wong
,
A. S. F.
,
Cai
,
J.
,
Zhu
,
Y.
, and
Liu
,
F.
,
2001
, “
Unsteady Flow Calculations With a Parallel Multiblock Moving Mesh Algorithm
,”
AIAA J.
,
39
(
6
), pp.
1021
1029
. 10.2514/2.1442
30.
Lindner
,
F.
,
Mehl
,
M.
, and
Uekermann
,
B.
,
2017
, “
Radial Basis Function Interpolation for Black-Box Multi-Physics Simulations
,”
VII International Conference on Computational Methods for Coupled Problems in Science and Engineering
,
Rhodes, Greece
,
June 12–14
, pp.
1
12
.
31.
Luo
,
Y.
,
Xiao
,
Q.
,
Shi
,
G.
,
Wen
,
L.
,
Chen
,
D.
, and
Pan
,
G.
,
2020
, “
A Fluid–Structure Interaction Solver for the Study on a Passively Deformed Fish Fin With Non-Uniformly Distributed Stiffness
,”
J. Fluids Struct.
,
92
, p.
102778
. 10.1016/j.jfluidstructs.2019.102778
32.
Flammang
,
B. E.
, and
Lauder
,
G. V.
,
2008
, “
Speed-Dependent Intrinsic Caudal Fin Muscle Recruitment During Steady Swimming in Bluegill Sunfish, Lepomis Macrochirus
,”
J. Exp. Biol.
,
211
(
4
), pp.
587
598
. 10.1242/jeb.012096
33.
Ren
,
Z.
,
Hu
,
K.
,
Wang
,
T.
, and
Wen
,
L.
,
2016
, “
Investigation of Fish Caudal Fin Locomotion Using a Bio-Inspired Robotic Model
,”
Int. J. Adv. Rob. Syst.
,
13
(
3
), p.
87
. 10.5772/63571
34.
Liu
,
G.
,
Geng
,
B.
,
Zheng
,
X.
,
Xue
,
Q.
,
Wang
,
J.
, and
Dong
,
H.
,
2018
, “
An Integrated High-Fidelity Approach for Modeling Flow-Structure Interaction in Biological Propulsion and Its Strong Validation
,”
2018 AIAA Aerospace Sciences Meeting
,
Jan. 8–12
,
American Institute of Aeronautics and Astronautics
.
35.
Olivier
,
M.
,
Morissette
,
J.-F.
, and
Dumas
,
G.
,
2009
, “
A Fluid-Structure Interaction Solver for Nano-Air-Vehicle Flapping Wings
,”
19th AIAA Computational Fluid Dynamics
,
June 22–25
,
American Institute of Aeronautics and Astronautics
.
36.
Wood
,
C.
,
Gil
,
A. J.
,
Hassan
,
O.
, and
Bonet
,
J.
,
2010
, “
Partitioned Block-Gauss–Seidel Coupling for Dynamic Fluid–Structure Interaction
,”
Comput. Struct.
,
88
(
23–24
), pp.
1367
1382
. 10.1016/j.compstruc.2008.08.005
37.
Nakata
,
T.
, and
Liu
,
H.
,
2012
, “
A Fluid–Structure Interaction Model of Insect Flight With Flexible Wings
,”
J. Comput. Phys.
,
231
(
4
), pp.
1822
1847
. 10.1016/j.jcp.2011.11.005
38.
Habchi
,
C.
,
Russeil
,
S.
,
Bougeard
,
D.
,
Harion
,
J.-L.
,
Lemenand
,
T.
,
Ghanem
,
A.
,
Valle
,
D. D.
, and
Peerhossaini
,
H.
,
2013
, “
Partitioned Solver for Strongly Coupled Fluid–Structure Interaction
,”
Comput. Fluids
,
71
, pp.
306
319
. 10.1016/j.compfluid.2012.11.004
39.
Dettmer
,
W.
, and
Perić
,
D.
,
2006
, “
A Computational Framework for Fluid–Structure Interaction: Finite Element Formulation and Applications
,”
Comput. Methods Appl. Mech. Eng.
,
195
(
41–43
), pp.
5754
5779
. 10.1016/j.cma.2005.10.019
40.
Matthies
,
H. G.
, and
Steindorf
,
J.
,
2003
, “
Partitioned Strong Coupling Algorithms for Fluid–Structure Interaction
,”
Comput. Struct.
,
81
(
8–11
), pp.
805
812
. 10.1016/S0045-7949(02)00409-1
41.
Luhar
,
M.
, and
Nepf
,
H. M.
,
2011
, “
Flow-Induced Reconfiguration of Buoyant and Flexible Aquatic Vegetation
,”
Limnol. Oceanogr.
,
56
(
6
), pp.
2003
2017
. 10.4319/lo.2011.56.6.2003
42.
Tian
,
F.-B.
,
Dai
,
H.
,
Luo
,
H.
,
Doyle
,
J. F.
, and
Rousseau
,
B.
,
2014
, “
Fluid–Structure Interaction Involving Large Deformations: 3D Simulations and Applications to Biological Systems
,”
J. Comput. Phys.
,
258
, pp.
451
469
. 10.1016/j.jcp.2013.10.047
43.
Paraz
,
F.
,
Schouveiler
,
L.
, and
Eloy
,
C.
,
2016
, “
Thrust Generation by a Heaving Flexible Foil: Resonance, Nonlinearities, and Optimality
,”
Phys. Fluids
,
28
(
1
), p.
011903
. 10.1063/1.4939499
44.
Paraz
,
F.
,
Eloy
,
C.
, and
Schouveiler
,
L.
,
2014
, “
Experimental Study of the Response of a Flexible Plate to a Harmonic Forcing in a Flow
,”
Comptes Rendus Mécanique
,
342
(
9
), pp.
532
538
. 10.1016/j.crme.2014.06.004
45.
Dai
,
H.
,
Luo
,
H.
,
Sousa
,
P. J. S. A. F. D.
, and
Doyle
,
J. F.
,
2012
, “
Thrust Performance of a Flexible Low-Aspect-Ratio Pitching Plate
,”
Phys. Fluids
,
24
(
10
), p.
101903
. 10.1063/1.4764047
46.
Olivier
,
M.
, and
Dumas
,
G.
,
2016
, “
A Parametric Investigation of the Propulsion of 2D Chordwise-Flexible Flapping Wings at Low Reynolds Number Using Numerical Simulations
,”
J. Fluids Struct.
,
63
, pp.
210
237
. 10.1016/j.jfluidstructs.2016.03.010
47.
Zhang
,
Y.
,
Zhou
,
C.
, and
Luo
,
H.
,
2017
, “
Effect of Mass Ratio on Thrust Production of an Elastic Panel Pitching or Heaving Near Resonance
,”
J. Fluids Struct.
,
74
, pp.
385
400
. 10.1016/j.jfluidstructs.2017.07.003
48.
Shi
,
G.
,
Xiao
,
Q.
, and
Zhu
,
Q.
,
2017
, “
A Study of 3D Flexible Caudal Fin for Fish Propulsion
,”
ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering
,
American Society of Mechanical Engineers
, p.
V07AT06A052
.
49.
Wang
,
E.
,
Xiao
,
Q.
, and
Incecik
,
A.
,
2017
, “
Three-Dimensional Numerical Simulation of Two-Degree-of-Freedom VIV of a Circular Cylinder With Varying Natural Frequency Ratios at Re=500
,”
J. Fluids Struct.
,
73
, pp.
162
182
. 10.1016/j.jfluidstructs.2017.06.001
50.
Hu
,
K.
,
Ren
,
Z.
,
Wang
,
Y.
,
Wang
,
T.
, and
Wen
,
L.
,
2016
, “
Quantitative Hydrodynamic Investigation of Fish Caudal Fin Cupping Motion Using a Bio-Robotic Model
,”
2016 IEEE International Conference on Robotics and Biomimetics (ROBIO)
,
Qingdao, China
,
Dec. 3–7
, pp.
295
300
.
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