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.
Issue Section:
CFD and VIV
References
1.
Bandyopadhyay
, P. R.
, 2005
, “Trends in Biorobotic Autonomous Undersea Vehicles
,” IEEE J. Oceanic Eng.
, 30
(1
), pp. 109
–139
. 10.1109/JOE.2005.8437482.
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/s12204-019-2076-43.
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.2017.11.0124.
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.1993.10125.
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/S002211200600190X6.
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.025268.
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/S00221120090070469.
Heathcote
, S.
, and Gursul
, I.
, 2007
, “Flexible Flapping Airfoil Propulsion at Low Reynolds Numbers
,” AIAA J.
, 45
(5
), pp. 1066
–1079
. 10.2514/1.2543110.
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
. 10.1088/1748-3190/11/4/04600511.
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.1982.197.4.48312.
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
. 10.1088/1748-3182/9/3/03600213.
Kancharala
, A. K.
, and Philen
, M. K.
, 2016
, “Optimal Chordwise Stiffness Profiles of Self-Propelled Flapping Fins
,” Bioinspiration Biomimetics
, 11
(5
), p. 056016
. 10.1088/1748-3190/11/5/05601614.
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/aa5d3f15.
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.06271117.
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
. 10.1088/1748-3190/11/1/01600818.
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.2010.04.00621.
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.2011.05.02922.
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
. 10.1088/1748-3182/8/3/03601123.
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/ab0fbe24.
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.J05420526.
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.2016.04.00327.
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.2008.11.01328.
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.2016.04.00129.
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
. 10.2514/2.144230.
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.2019.10277832.
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.01209633.
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
. 10.5772/6357134.
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.2008.08.00537.
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.2011.11.00538.
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.2012.11.00439.
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.2005.10.01940.
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)00409-141.
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.2011.56.6.200342.
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.2013.10.04743.
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
. 10.1063/1.493949944.
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.2014.06.00445.
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
. 10.1063/1.476404746.
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.2016.03.01047.
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.2017.07.00348.
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.2017.06.00150.
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
.Copyright © 2020 by ASME
You do not currently have access to this content.
