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Topology Optimization of the Caudal Fin of the Three-Dimensional Self-Propelled Swimming Fish

Published online by Cambridge University Press:  03 June 2015

Zhiqiang Xin  and
Chuijie Wu
Zhiqiang Xin
Affiliation:
College of Mechanics and Materials, Hohai University, Nanjing 210098, China
Chuijie Wu*
Affiliation:
College of Mechanics and Materials, Hohai University, Nanjing 210098, China State Key Laboratory of Structural Analysis for Industrial Equipment & School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China
*
*Corresponding author. Email: cjwudut@dlut.edu.cn
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Abstract

Based on the boundary vorticity-flux theory, topology optimization of the caudal fin of the three-dimensional self-propelled swimming fish is investigated by combining unsteady computational fluid dynamics with moving boundary and topology optimization algorithms in this study. The objective functional of topology optimization is the function of swimming efficiency, swimming speed and motion direction control. The optimal caudal fin, whose topology is different from that of the natural fish caudal fin, make the 3D bionic fish achieve higher swimming efficiency, faster swimming speed and better maneuverability. The boundary vorticity-flux on the body surface of the 3D fish before and after optimization reveals the mechanism of high performance swimming of the topology optimization bionic fish. The comparative analysis between the swimming performance of the 3D topology optimization bionic fish and the 3D lunate tail bionic fish is also carried out, and the wake structures of two types of bionic fish show the physical nature that the swimming performance of the 3D topology optimization bionic fish is significantly better than the 3D lunate tail bionic fish.

Keywords

76Z1074F103D bionic fishcaudal fintopology optimizationswimming performancevortex dynamics
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 6 , December 2014 , pp. 732 - 763
Copyright
Copyright © Global-Science Press 2014

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References

[1]Gray, J., Studies in animal locomotion: Roman 6. The propulsive powers of the dolphin, J. Exp. Biol., 13 (1936), pp. 192–199.CrossRefGoogle Scholar
[2]Wu, T. Y., Fish swimming and bird/insect flight, Annu. Rev. Fluid Mech., 43 (2011), pp. 25–58.CrossRefGoogle Scholar
[3]Cheng, J. Y., Zhuang, L. X., and Tong, B. G., Analysis of swimming 3-D waving plate, J. Fluid. Mech., 232 (1991), pp. 341–355.Google Scholar
[4]Candelier, F., Boyer, F., and Leroyer, A., Three-dimensional extension of Lighthill’s large- amplitude elongated-body theory of fish locomotion, J. Fluid. Mech., 674 (2011), pp. 196–226.Google Scholar
[5]Fish, F. E. and Lauder, G. V., Passive and active flow control by swimming fishes and mammals, Annu. Rev. Fluid Mech., 38 (2006), pp. 193–224.Google Scholar
[6]Tytell, E. D. and Lauder, G. V., The hydrodynamics of eel swimming, Roman 1. Wake structure, J. Exp. Biol., 207 (2004), pp. 1825–1841.Google Scholar
[7]Triantafyllou, M. S., Triantafyllou, G. S. and Yue, D. K. P., Hydrodynamics of fishlike of swimming, Annu. Rev. Fluid Mech., 32 (2000), pp. 33–53.Google Scholar
[8]Zhu, Q., Wolfgang, M. J., Yue, D. K. P. and Traintafyllou, M. S., Three-dimensional flow structures and vorticity control in fish-like swimming, J. Fluid. Mech., 468 (2002), pp. 1–28.Google Scholar
[9]Liu, H. and Kawachi, K., A numerical study ofundulatory swimming, J. Comput. Phys., 155 (1999), pp. 223–247.CrossRefGoogle Scholar
[10]Wu, C. J. and Wang, L., Numerical simulations of self-propelled swimming of 3D bionic fish school, Sci. China, 52(3) (2009), pp. 658–669.Google Scholar
[11]Sfakiotakis, M., Lane, D. M., and Davies, J. B. C., Review of fish swimming modes for aquatic locomotion, IEEE J. Oceanic. Eng., 24(2) (1999), pp. 237–252.Google Scholar
[12]Lauder, G. V., Function of the caudal fin during locomotion in fishes: kinematics, flow visualization, and evolutionary patterns, Amer. Zool., 40(1) (2000), pp. 101–122.Google Scholar
[13]Lauder, G. V. and Nauen, J. C., Hydrodynamics of caudal fin locomotion by chub mackerel, Scomber japonicus, J. Exp. Biol., 205 (2002), pp. 1709–1724.Google Scholar
[14]Heo, S., Wiguna, T., Park, H. C. and Goo, N. S., Effect of an artificial caudal fin on the performance of a biomimetic fish robot propelled by piezoelectric actuators, J. Bionic. Eng., 4 (2007), pp.151-158.CrossRefGoogle Scholar
[15]Zhang, X., Su, Y. M., and Wang, Z. L., Numerical and experimental studies of influence of the caudal fin shape on the propulsion performance of a flapping caudal fin, J. Hydrodyn., 23(3) (2011), pp. 325–332.Google Scholar
[16]BendsoE, M. P. AND Sigmund, O., Topology Optimization: Theory, Methods and Applications, Springer-Verlag., Berlin, Germany, 2003.Google Scholar
[17]Borrvall, T. and Petersson, J., Topology optimization of fluids in Stokes flow, J. Numer. Methods Fluids., 41(1) (2003), pp. 77–107.Google Scholar
[18]Guest, J. K. and Prevost, J. H., Topology optimization of creeping fluid flows using a Darcy- Stokes finite element, Int. J. Numer. Meth. Eng., 66, (2006), pp. 461–484.Google Scholar
[19]Olesen, L. H., Okkels, F. and Bruus, H., A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow, int. J. Numer. Meth. Eng., 69 (2006), pp. 975–1001.Google Scholar
[20]Zhou, S. W. and Li, Q., A variational level set method for the topology optimization of steady-state Navier-Stokes flow, J. Comput. Phys., 227 (2008), pp. 10178–10195.CrossRefGoogle Scholar
[21]Duan, X. B., Ma, Y. C. and Zhang, R., Shape-topology optimization for Navier-Stokes problem using variational level set method, J. Comput. Appl. Math., 222 (2008), pp. 487–499.Google Scholar
[22]Wu, J. Z., Ma, H. Y. and Zhou, M. D., Vorticity and Vortex Dynamics, Springer-Verlag., Berlin, Germany, 2006.Google Scholar
[23]Wu, J. Z., Lu, X. Y. and Zhang, L. X., Integral force acting on a body due to local flow structures, J. Fluid. Mech., 576 (2007), pp. 265–286.Google Scholar
[24]Johnson, A. T., and Patel, V. C., Flow past a sphere up to a Reynolds number of 300, J. Fluid. Mech., 378 (1999), pp. 19–70.Google Scholar
[25]Anderson, J. M., Streitlien, K., Barrett, D. S., and Triantafyllou, M. S., Oscillating foils of high propulsive efficiency, J. Fluid Mech., 360 (1998), pp. 41–72.Google Scholar
[26]Kaufman, E. K.Leeming, D. J. and Taylor, G. D., An ODE-based approach to nonlinearly constrained minimax problems, Numer. Algorithms, 9 (1995), pp. 25–37.CrossRefGoogle Scholar
[27]Wang, L. and Wu, C. J., Adaptive optimal control of unsteady seperated flow with a smart body surface, China J. Theory. Appl. Mech., 37(6) (2005), pp. 764–768.Google Scholar
[28]Wu, C. J. and Wang, L., Adaptive optimal control of the flapping rule of a fixed flapping plate, Adv. Appl. Math. Mech., 1(3) (2009), pp. 402–414.Google Scholar
[29]Wu, C. J. and Wang, L., Where is the rudder of a fish?: the mechanism of swimming and control of self-propelled fish school, Acta Mech. Sin., 26(1) (2009), pp. 45–65.Google Scholar
[30]Wang, L., Numerical Simulation and Control of Self-Propelled Swimming of Bionics Fish School, PhD thesis, Hohai university, Nanjing, 2009.Google Scholar
[31]Kern, S. and Koumoutsakos, P., Simulations of optimized anguilliform swimming, J. Exp. Biol., 209 (2006), pp. 4841–4857.CrossRefGoogle ScholarPubMed
[32]Guglielmini, L. and Blondeaux, P., Propulsive efficiency of oscillating foils, Euro. J. Mech. B/Fluids, 23 (2004), pp. 255–278.Google Scholar
[33]Xin, Z. Q. and Wu, C. J., Numerical simulations and vorticity dynamics of self-propelled swimming of 3D bionic fish, Sci. China-Phys. Mech. Astron., 55(2) (2012), pp. 272–283.CrossRefGoogle Scholar
[34]Xin, Z. Q. and Wu, C. J., Shape optimization of the caudal fin of the three-dimensional self-propelled swimming fish, Sci. China-Phys. Mech. Astron., 56(2) (2012), pp. 328–339.Google Scholar
[35]Jeong, J. and Hussain, F., On the identification of a vortex, J. Fluid Mech., 285 (1995), pp. 69–94.Google Scholar
[36]von Ellenrieder, K. D., Parker, K. and Soria, J., Flow structures behind a heaving and pitchingfinite-span wing, J. Fluid. Mech., 490 (2003), pp. 129–138.Google Scholar
[37]Dong, H., Mittal, R. and Najjar, F. M., Wake topology and hydrodynamic performance of low-aspect-ratio flapping foils, J. Fluid. Mech., 566 (2006), pp. 309–343.Google Scholar