Locomotion of a flapping flexible plate

Physics of Fluids

Volumn 25, Issue 12, 2013, Pages

  Hua, Ru Nan ^a   Zhu, Luoding ^b   Lu, Xi Yun ^a  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMALS; COMPUTATIONAL FLUID DYNAMICS; FINITE ELEMENT METHOD; FLUID STRUCTURE INTERACTION;

BENDING RIGIDITY; DEGREE OF FLEXIBILITY; DYNAMIC BEHAVIORS; IMMERSED BOUNDARY; LATTICE BOLTZMANN METHOD; OBSERVATIONS AND MEASUREMENTS; PROPULSIVE PERFORMANCE; STATIONARY FLUIDS;

PLATES (STRUCTURAL COMPONENTS);

EID: 84891620166     PISSN: 10706631     EISSN: 10897666     Source Type: Journal    
DOI: 10.1063/1.4832857     Document Type: Article

References (81)

1. Blake R.W. Fish Locomotion 1983, (Cambridge University Press, Cambridge).
2. Videler J.J. Fish Swimming 1993, (Chapman and Hall, New York).
3. Brodsky A.K. The Evolution of Insect Flight 1994, (Oxford University Press, Oxford).
4. Combes S.A. Daniel T.L. Flexural stiffness in insect wings. I. Scaling and the influence of wing venation. J. Exp. Biol. 2003, 206:2979-2987. 10.1242/jeb.00523
5. Combes S.A. Daniel T.L. Flexural stiffness in insect wings. II. Spatial distribution and dynamic wing bending. J. Exp. Biol. 2003, 206:2989-2997. 10.1242/jeb.00524
6. Wootton R.J. Invertebrate paraxial locomotory appendages: Design, deformation and control. J. Exp. Biol. 1999, 202:3333-3345.
7. Fish F.E. Lauder G.V. Passive and active flow control by swimming fishes and mammals. Annu. Rev. Fluid Mech. 2006, 38:193-224. 10.1146/annurev.fluid.38.050304.092201
8. Shyy W. Lian Y. Tang J. Viieru D. Liu H. Aerodynamics of Low Reynolds Number Flyers 2008, and (Cambridge University Press, Cambridge).
9. Shyy W. Aono H. Chimakurthi S.K. Trizila P. Kang C.-K. Cesnik C.E. S. Liu H. Recent progress in flapping wing aerodynamics and aeroelasticity. Prog. Aerosp. Sci. 2010, 46:284-327. 10.1016/j.paerosci.2010.01.001
10. Wootton R.J. Herbert R.C. Young P.G. Evans K.E. Approaches to structural modeling of insect wings. Philos. Trans. R. Soc. London, Ser. B 2003, 358:1577-1587. 10.1098/rstb.2003.1351
11. Alben S. Madden P.G. Lauder G.V. The mechanics of active fin-shape control in ray-finned fishes. J. R. Soc., Interface 2007, 4:243-256. 10.1098/rsif.2006.0181
12. Triantafyllou M.S. Triantafyllou G.S. Gopalkrishnan R. Wake mechanics for thrust generation in oscillating foils. Phys. Fluids 1991, 3:2835-2837. 10.1063/1.858173
13. Anderson J.M. Streitlien K. Barrett D.S. Triantafyllou M.S. Oscillating foils of high propulsive efficiency. J. Fluid Mech. 1998, 360:41-72. 10.1017/S0022112097008392
14. Vandenberghe N. Zhang J. Childress S. Symmetry breaking leads to forward flapping flight. J. Fluid Mech. 2004, 506:147-155. 10.1017/S0022112004008468
15. Vandenberghe N. Childress S. Zhang J. On unidirectional flight of a free flapping wing. Phys. Fluids 2006, 18:014102. 10.1063/1.2148989
16. Godoy-Diana R. Aider J.-L. Wesfreid J.E. Transitions in the wake of a flapping foil. Phys. Rev. E 2008, 77:016308. 10.1103/PhysRevE.77.016308
17. Buchholz J.H. Smits A.J. The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel. J. Fluid Mech. 2008, 603:331-365. 10.1017/S0022112008000906
18. Lighthill M.J. Note on the swimming of slender fish. J. Fluid Mech. 1960, 9:305-317. 10.1017/S0022112060001110.
19. Wu T.Y.-T. Swimming of a waving plate. J. Fluid Mech. 1961, 10:321-344. 10.1017/S0022112061000949.
20. Cheng J.-Y. Zhuang L.-X. Tong B.-G. Analysis of swimming three-dimensional waving plates. J. Fluid Mech. 1991, 232:341-355. 10.1017/S0022112091003713
21. Wang Z.J. Vortex shedding and frequency selection in flapping fight. J. Fluid Mech. 2000, 410:323-341. 10.1017/S0022112099008071.
22. Wang Z.J. Two dimensional mechanism for insect hovering. Phys. Rev. Lett. 2000, 85:2216. 10.1103/PhysRevLett.85.2216.
23. Dong H. Mittal R. Najjar F.M. Wake topology and hydrodynamic performance of low-aspect-ratio flapping foils. J. Fluid Mech. 2006, 566:309-343. 10.1017/S002211200600190X
24. Carling J. Williams T.L. Bowtell G. Self-propelled anguilliform swimming: Simultaneous solution of the two-dimensional Navier-Stokes equations and Newton's laws of motion. J. Exp. Biol. 1998, 201.
25. Alben S. Shelley M. Coherent locomotion as an attracting state for a free flapping body. Proc. Natl Acad. Sci. U.S.A. 2005, 102:11163. 10.1073/pnas.0505064102
26. Kern S. Koumoutsakos P. Simulations of optimized anguilliform swimming. J. Exp. Biol. 2006, 209:4841-4857. 10.1242/jeb.02526
27. Lu X.-Y. Liao Q. Dynamic responses of a two-dimensional flapping foil motion. Phys. Fluids 2006, 18:098104. 10.1063/1.2357733
28. Zhang X. Ni S.Z. Wang S.Z. He G.W. Effects of geometric shape on the hydrodynamics of a self-propelled flapping foil. Phys. Fluids 2009, 21:103302. 10.1063/1.3251045
29. Borazjani I. Sotiropoulos F. On the role of form and kinematics on the hydrodynamics of self-propelled body/caudal fin swimming. J. Exp. Biol. 2010, 213:89-107. 10.1242/jeb.030932
30. Zhu Q. Optimal frequency for flow energy harvesting of a flapping foil. J. Fluid Mech. 2011, 675:495-517. 10.1017/S0022112011000334.
31. Heathcote S. Gursul I. Flexible flapping airfoil propulsion at low Reynolds numbers. AIAA J. 2007, 45:1066-1079. 10.2514/1.25431
32. Heathcote S. Wang Z. Gursul I. Effect of spanwise flexibility on flapping wing propulsion. J. Fluids Struct. 2008, 24:183-199. 10.1016/j.jfluidstructs.2007.08.003
33. Michelin S. Smith S.G. L. Resonance and propulsion performance of a heaving flexible wing. Phys. Fluids 2009, 21:071902. 10.1063/1.3177356
34. Eldredge J.D. Toomey J. Medina A. On the roles of chord-wise flexibility in a flapping wing with hovering kinematics. J. Fluid Mech. 2010, 659:94-115. 10.1017/S0022112010002363
35. Ferreira de Sousa P.J. S. A. Allen J.J. Thrust efficiency of harmonically oscillating flexible flat plates. J. Fluid Mech. 2011, 674:43-66. 10.1017/S0022112010006373
36. Kang C.-K. Aono H. Cesnik C.E. S. Shyy W. Effects of flexibility on the aerodynamic performance of flapping wings. J. Fluid Mech. 2011, 689:32-74. 10.1017/jfm.2011.428
37. Wu T.Y.-T. On theoretical modeling of aquatic and aerial animal locomotion. Adv. Appl. Mech. 2002, 38:291-353. 10.1016/S0065-2156(02)80105-3.
38. Tytell E.D. Hsu C.Y. Williams T.L. Cohen A.H. Fauci L.J. Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming. Proc. Natl Acad. Sci. U.S.A. 2010, 107:19832. 10.1073/pnas.1011564107
39. Spagnolie S.E. Moret L. Shelley M.J. Zhang J. Surprising behaviors in flapping locomotion with passive pitching. Phys. Fluids 2010, 22:041903. 10.1063/1.3383215
40. Zhang J. Liu N.-S. Lu X.-Y. Locomotion of a passively flapping flat plate. J. Fluid Mech. 2010, 659:43-68. 10.1017/S0022112010002387
41. Zhu L. Peskin C.S. Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method. J. Comput. Phys. 2002, 179:452-468. 10.1006/jcph.2002.7066
42. Connell B.S. H. Yue D.K. P. Flapping dynamics of a flag in a uniform stream. J. Fluid Mech. 2007, 581:33-67. 10.1017/S0022112007005307
43. Peskin C.S. The immersed boundary method. Acta Numer. 2002, 11:479-517. 10.1017/S0962492902000077.
44. Mittal R. Iaccarino G. Immersed boundary methods. Annu. Rev. Fluid Mech. 2005, 37:239-261. 10.1146/annurev.fluid.37.061903.175743
45. Goldstein D. Handler R. Sirovich L. Modeling a no slip flow boundary with an external force field. J. Comput. Phys. 1993, 105:354-366. 10.1006/jcph.1993.1081
46. Huang W.-X. Shin S.J. Sung H.J. Simulation of flexible filaments in a uniform flow by the immersed boundary method. J. Comput. Phys. 2007, 226:2206-2228. 10.1016/j.jcp.2007.07.002
47. Huang W.-X. Sung H.J. Three-dimensional simulation of a flapping flag in a uniform flow. J. Fluid Mech. 2010, 653:301-336. 10.1017/S0022112010000248
48. Gao T. Lu X.-Y. Insect normal hovering flight in ground effect. Phys. Fluids 2008, 20:087101. 10.1063/1.2958318
49. Tian F.-B. Luo H. Zhu L. Lu X.-Y. Coupling modes of three filaments in side-by-side arrangement. Phys. Fluids 2011, 23:111903. 10.1063/1.3659892
50. Chen S. Doolen G.D. Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 1998, 30:329-364. 10.1146/annurev.fluid.30.1.329
51. Aidun C.K. Lu Y. Ding E.-J. Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation. J. Fluid Mech. 1998, 373:287-311. 10.1017/S0022112098002493
52. Xia Z. Connington K.W. Rapaka S. Yue P. Feng J.J. Chen S. Flow patterns in the sedimentation of an elliptical particle. J. Fluid Mech. 2009, 625:249-272. 10.1017/S0022112008005521
53. Guo Z. Zheng C. Shi B. Discrete lattice effects on the forcing term in the lattice boltzmann method. Phys. Rev. E 2002, 65:046308. 10.1103/PhysRevE.65.046308
54. Cheng Y. Li J. Introducing unsteady non-uniform source terms into the lattice Boltzmann model. Int. J. Numer. Methods Fluids 2008, 56:629-641. 10.1002/fld.1543
55. Yu D. Mei R. Shyy W. A multi-block lattice Boltzmann method for viscous fluid flows. Int. J. Numer. Methods Fluids 2002, 39:99-120. 10.1002/fld.280
56. Peng Y. Shu C. Chew Y.T. Niu X.D. Lu X.-Y. Application of multi-block approach in the immersed boundaryr̈clattice Boltzmann method for viscous fluid flows. J. Comput. Phys. 2006, 218:460-478. 10.1016/j.jcp.2006.02.017
57. Pacoste C. Co-rotational flat facet triangular elements for shell instability analyses. Comput. Methods Appl. Mech. Eng. 1998, 156:75-110. 10.1016/S0045-7825(98)80004-2.
58. Doyle J.F. Nonlinear Analysis of Thin-Walled Structures: Statics, Dynamics, and Stability 2001, (Springer-Verlag, New York).
59. Yin B. Luo H. Effect of wing inertia on hovering performance of flexible flapping wings. Phys. Fluids 2010, 22:111902. 10.1063/1.3499739
60. Tian F.-B. Luo H. Zhu L. Liao J.C. Lu X.-Y. An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments. J. Comput. Phys. 2011, 230:7266-7283. 10.1016/j.jcp.2011.05.028
61. Richard B. The speed of swimming of fish as related to size and to the frequency and amplitude of the tail beat. J. Exp. Biol. 1958, 35:109-133.
62. Ellington C.P. The aerodynamics of hovering insect flight. II. Morphological parameters. Philos. Trans. R. Soc. London, Ser. B 1984, 305:17-40. 10.1098/rstb.1984.0050.
63. Ellington C.P. The aerodynamics of hovering insect flight. III. Kinematics. Philos. Trans. R. Soc. London, Ser. B 1984, 305:41-78. 10.1098/rstb.1984.0051.
64. Fish F.E. Power output and propulsive efficiency of swimming bottlenose dolphins (Tursiops truncatus). J. Exp. Biol. 1993, 185:179-193.
65. Taylor G.K. Nudds R.L. Thomas A.L. R. Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency. Nature (London) 2003, 425:707-711. 10.1038/nature02000
66. Combes S.A. Daniel T.L. Into thin air: Contributions of aerodynamic and inertial-elastic forces to wing bending in the hawkmoth Manduca sexta. J. Exp. Biol. 2003, 206:2999-3006. 10.1242/jeb.00502
67. Chen J.-S. Chen J.-Y. Chou Y.-F. On the natural frequencies and mode shapes of dragonfly wings. J. Sound Vib. 2008, 313:643-654. 10.1016/j.jsv.2007.11.056
68. Jongerius S.R. Lentink D. Structural analysis of a dragonfly wing. Exp. Mech. 2010, 50:1323-1334. 10.1007/s11340-010-9411-x
69. Triantafyllou M.S. Triantafyllou G.S. Yue D.K. P. Hydrodynamics of fishlike swimming. Annu. Rev. Fluid Mech. 2000, 32:33-53. 10.1146/annurev.fluid.32.1.33
70. Ishihara D. Horie T. Denda M. A two-dimensional computational study on the fluid-structure interaction cause of wing pitch changes in dipteran flapping flight. J. Exp. Biol. 2009, 212:1-10. 10.1242/jeb.020404
71. Thomson W.T. Theory of Vibration with Applications 1981, (Prentice-Hall, Englewood Cliffs, NJ).
72. Schultz W.W. Webb P.W. Power requirements of swimming: Do new methods resolve old questions?. Integr. Comp. Biol. 2002, 42:1018-1025. 10.1093/icb/42.5.1018.
73. Zhu L. Interaction of two tandem deformable bodies in a viscous incompressible flow. J. Fluid Mech. 2009, 635:455-475. 10.1017/S0022112009007903
74. Bagheri S. Mazzino A. Bottaro A. Spontaneous symmetry breaking of a hinged flapping filament generates lift. Phys. Rev. Lett. 2012, 109:154502. 10.1103/PhysRevLett.109.154502
75. Young W.C. Budynas R. Roark's Formulas for Stress and Strain 2001, and (McGraw-Hill, New York).
76. Wu J.-Z. Lu X.-Y. Zhuang L.-X. Integral force acting on a body due to local flow structures. J. Fluid Mech. 2007, 576:265-286. 10.1017/S0022112006004551
77. Li G.-J. Lu X.-Y. Force and power of flapping plates in a fluid. J. Fluid Mech. 2012, 712:598-613. 10.1017/jfm.2012.443
78. Jones K.D. Dohring C.M. Platzer M.F. Experimental and computational investigation of the Knoller-Betz effect. AIAA J. 1998, 36:1240-1246. 10.2514/2.505
79. Lewin G.C. Haj-Hariri H. Modelling thrust generation of a two-dimensional heaving airfoil in a viscous flow. J. Fluid Mech. 2003, 492:339-362. 10.1017/S0022112003005743
80. Vogel S. Life in Moving Fluids 1994, (Princeton University Press, Princeton).
81. Wainwright S.A. Biggs W.D. Currey J.D. Gosline J.M. Mechanical Design in Organisms 1982, and (Princeton University Press, Princeton).