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Leading edge strengthening and the propulsion performance of flexible ray fins

Published online by Cambridge University Press:  12 January 2012

Kourosh Shoele  and
Qiang Zhu
Kourosh Shoele
Affiliation:
Department of Structural Engineering, University of California San Diego, La Jolla, CA 92093, USA
Qiang Zhu*
Affiliation:
Department of Structural Engineering, University of California San Diego, La Jolla, CA 92093, USA
*
†Email address for correspondence: [email protected]
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Abstract

A numerical model of a ray-reinforced fin is developed to investigate the relation between its structural characteristics and its force generation capacity during flapping motion. In this two-dimensional rendition, the underlying rays are modelled as springs, and the membrane is modelled as a flexible but inextensible plate. The fin kinematics is characterized by its oscillation frequency and the phase difference between different rays (which generates a pitching motion). An immersed boundary method (IBM) is applied to solve the fluid–structure interaction problem. The focus of the current paper is on the effects of ray flexibility, especially the detailed distribution of ray stiffness, upon the capacity of thrust generation. The correlation between thrust generation and features of the surrounding flow (especially the leading edge separation) is also examined. Comparisons are made between a fin with rigid rays, a fin with identical flexible rays, and a fin with flexible rays and strengthened leading edge. It is shown that with flexible rays, the thrust production can be significantly increased, especially in cases when the phase difference between different rays is not optimized. By strengthening the leading edge, a higher propulsion efficiency is observed. This is mostly attributed to the reduction of the effective angle of attack at the leading edge, accompanied by mitigation of leading edge separation and dramatic changes in characteristics of the wake. In addition, the flexibility of the rays causes reorientation of the fluid force so that it tilts more towards the swimming direction and the thrust is thus increased.

JFM classification

Biological Fluid Dynamics: Propulsion Biological Fluid Dynamics: Swimming/flying
Type
Papers
Information
Journal of Fluid Mechanics , Volume 693 , 25 February 2012 , pp. 402 - 432
Copyright
Copyright © Cambridge University Press 2012

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Footnotes

‡

Present address: RE Vision Consulting, LLC, Sacramento, CA 95831, USA

References

1. Ahn, H. & Kallinderis, Y. 2006 Strongly coupled flow/structure interactions with a geometrically conservative ALE scheme on general hybrid meshes. J. Comput. Phys. 219, 671–696.CrossRefGoogle Scholar
2. Alben, S., Madden, P. G. A. & Lauder, G. V. 2007 The mechanics of active fin-shape control in ray-finned fishes. J. Royal Soc. Interface 4, 243–256.CrossRefGoogle ScholarPubMed
3. Anagnostopoulos, P. & Bearman, P. W. 1992 Response characteristics of a vortex-excited cylinder at low Reynolds numbers. J. Fluids Struct. 6, 39–50.CrossRefGoogle Scholar
4. Anderson, J. M., Streitlien, K., Barret, D. S. & Triantafyllou, M. S. 1998 Oscillating foils for high propulsive efficiency. J. Fluid Mech. 360, 41–72.CrossRefGoogle Scholar
5. Birch, J. M. & Dickinson, M. H. 2001 Spanwise flow and the attachment of the leading-edge vortex on insect wings. Nature 412, 729–733.CrossRefGoogle Scholar
6. Blake, R. W. 1977 On ostraciiform locomotion. J. Mar. Biol. Assoc. UK 57, 1047–1055.CrossRefGoogle Scholar
7. Blake, R. W. 1979 The mechanics of labriform locomotion. Part I. Labriform locomotion in the angelfish (Pterophyllum eimekei): an analysis of the power stroke. J. Expl Biol. 82, 255–271.CrossRefGoogle Scholar
8. Blake, R. W. 1983 Fish Locomotion. Cambridge University Press.Google Scholar
9. Blake, R. W., Li, J. & Chan, K. H. S. 2009 Swimming in four goldfish Carassius auratus morphotypes: understanding functional design and performance employing artificially selected forms. J. Fish Biol. 75 (3), 591–617.CrossRefGoogle ScholarPubMed
10. Borazjani, I., Ge, L. & Sotiropoulos, F. 2008 Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies. J. Comput. Phys. 227, 7587–7620.CrossRefGoogle ScholarPubMed
11. Combes, S. A. & Daniel, T. L. 2003a Flexible stiffness in insect wings. Part 1. Scaling and the influence of wing venation. J. Expl Biol. 206, 2979–2987.CrossRefGoogle Scholar
12. Combes, S. A. & Daniel, T. L. 2003b Flexible stiffness in insect wings. Part 2. Spatial distribution and dynamic wing bending. J. Expl Biol. 206, 2989–2997.CrossRefGoogle Scholar
13. Conte, S. D. & de Boor, C. 1980 Elementary Numerical Analysis: An Algorithmic Approach. McGraw-Hill.Google Scholar
14. Dickinson, M. H. 2005 The initiation and control of rapid flight maneuvers in fruit flies. Integr. Compar. Biol. 45 (2), 274–281.CrossRefGoogle ScholarPubMed
15. Dickinson, M. H. & Götz, K. G. 1993 Unsteady aerodynamic performance on model wings at low Reynolds numbers. J. Expl Biol. 174, 45–64.CrossRefGoogle Scholar
16. Dong, H., Bozkurttas, M., Mittal, R., Madden, P. G. A. & Lauder, G. V. 2010 Computational modelling and analysis of the hydrodynamics of a highly deformable fish pectoral fin. J. Fluid Mech. 645, 345–373.CrossRefGoogle Scholar
17. Dong, H., Mittal, R. & Najjar, F. M. 2006 Wake topology and hydrodynamic performance of low-aspect-ratio flapping foils. J. Fluid Mech. 566, 309–343.CrossRefGoogle Scholar
18. Drucker, E. G. & Lauder, G. V. 2003 Function of pectoral fins in rainbow trout: behavioral repertoire and hydrodynamic forces. J. Expl Biol. 206 (5), 813–826.CrossRefGoogle ScholarPubMed
19. Drucker, E. G., Walker, J. A. & Westneat, M. W. 2006 Mechanics of pectoral fin swimming in fishes. In Fish Biomechanics (ed. Shadwick, R.E. & Lauder, G.V. ), vol. 23. pp. 369–423. Elsevier Academic.CrossRefGoogle Scholar
20. Ellington, C. P. 1984 The aerodynamics of hovering insect flight. Part IV. Aerodynamic mechanisms. Phil. Trans. R. Soc. Lond. B 305, 79–113.Google Scholar
21. Goldstein, D., Handler, R. & Sirovich, L. 1993 Modelling a no-slip flow boundary with an external force field. J. Comput. Phys. 105, 354–366.CrossRefGoogle Scholar
22. Guilmineau, E. & Queutey, P. 2002 A numerical simulation of vortex shedding from an oscillating circular cylinder. J. Fluids Struct. 16 (6), 773–794.CrossRefGoogle Scholar
23. Heathcote, S. & Gursul, I. 2007 Flexible flapping airfoil propulsion at low Reynolds numbers. AIAA J. 45 (5), 1066–1079.CrossRefGoogle Scholar
24. Huang, W. X., Shin, S. J. & Sung, H. J. 2007 Simulation of flexible filaments in a uniform flow by the immersed boundary method. J. Comput. Phys. 226, 2206–2228.CrossRefGoogle Scholar
25. Isogai, K., Shinmoto, Y. & Watanabe, Y. 1999 Effects of dynamic stall on propulsive efficiency and thrust of flapping airfoil. AIAA J. 37 (10), 1145–1151.CrossRefGoogle Scholar
26. Katz, J. & Weihs, D. 1978 Hydrodynamic propulsion by large amplitude oscillation of an airfoil with chordwise flexibility. J. Fluid Mech. 88 (3), 485–497.CrossRefGoogle Scholar
27. Kim, K., Baek, S. J. & Sung, H. J. 2002 An implicit velocity decoupling procedure for incompressible Navier–Stokes equations. Intl J. Numer. Meth. Fluids 38, 125–138.CrossRefGoogle Scholar
28. Kim, D. & Choi, H. 2006 Immersed boundary method for flow around an arbitrarily moving body. J. Comput. Phys. 212, 662–680.CrossRefGoogle Scholar
29. Kim, J., Kim, D. & Choi, H. 2001 An immersed boundary finite-volume method for simulations of flow in complex geometries. J. Comput. Phys. 171, 132–150.CrossRefGoogle Scholar
30. Kim, J. & Moin, J. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308–323.CrossRefGoogle Scholar
31. Lai, M. C. & Peskin, C. S. 2000 An immersed boundary method with formal second-order accuracy and reduced numerical viscosity. J. Comput. Phys. 160, 705–719.CrossRefGoogle Scholar
32. Lee, C. 2003 Stability characteristics of the virtual boundary method in three-dimensional applications. J. Comput. Phys. 184, 559–591.CrossRefGoogle Scholar
33. Lighthill, M. J. 1970 Aquatic animal propulsion of high hydromechanical efficiency. J. Fluid Mech. 44 (02), 265–301.CrossRefGoogle Scholar
34. Linnick, M. N. & Fasel, H. F. 2005 A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains. J. Comput. Phys. 204, 157–192.CrossRefGoogle Scholar
35. Liu, P. & Bose, N. 1997 Propulsive performance from oscillating propulsors with spanwise flexibility. Proc. Math. Phys. Eng. Sci. 453, 1763–1770.CrossRefGoogle Scholar
36. Peskin, C. S. 2002 The immersed boundary method. Acta Numerica 11, 1–39.CrossRefGoogle Scholar
37. Ramamurti, R., Sandberg, W. C., Lohner, R., Walker, J. A. & Westneat, M. W. 2002 Fluid dynamics of flapping aquatic flight in the bird wrasse: three-dimensional unsteady computations with fin deformation. J. Expl Biol. 205 (19), 2997–3008.CrossRefGoogle ScholarPubMed
38. Roshko, A. 1954 On the development of turbulent wakes from vortex streets. NACA Tech. Rep. 1191.Google Scholar
39. Rozhdestvensky, K. V. & Ryzhov, V. A. 2003 Aerohydrodynamics of flapping-wing propulsors. Prog. Aerosp. Sci. 39 (8), 585–633.CrossRefGoogle Scholar
40. Saad, Y. 1994 SPARSKIT: a basic tool kit for sparse matrix computations, ver. 2. Tech. Rep. Research Institute for Advanced Computer Science, NASA Ames Research Center, Moffet Field, California, USA.Google Scholar
41. Schultz, W. W. & Webb, P. W. 2002 Power requirements of swimming: Do new methods resolve old questions? Integr. Compar. Biol. 42 (5), 1018–1025.CrossRefGoogle ScholarPubMed
42. Shin, S. J., Huang, W. X. & Sung, H. J. 2008 Assessment of regularized delta functions and feedback forcing schemes for an immersed boundary method. Intl J. Numer. Meth. Fluids 58, 263–286.CrossRefGoogle Scholar
43. Shoele, K. 2011 Flow interaction with highly flexible structures. PhD thesis, University of California, San Diego, USA.Google Scholar
44. Shoele, K. & Zhu, Q. 2009 Fluid–structure interactions of skeleton-reinforced fins: performance analysis of a paired fin in lift-based propulsion. J. Expl Biol. 212, 2679–2690.CrossRefGoogle ScholarPubMed
45. Shoele, K. & Zhu, Q. 2010a Flow-induced vibrations of a deformable ring. J. Fluid Mech. 650, 343–362.CrossRefGoogle Scholar
46. Shoele, K. & Zhu, Q. 2010b Numerical simulation of a pectoral fin during labriform swimming. J. Expl Biol. 213, 2038–2047.CrossRefGoogle ScholarPubMed
47. Shyy, W., Aono, H., Chimakurthi, S. K., Trizila, P., Kang, C. K., Cesnik, C. E. S. & Liu, H. 2010 Recent progress in flapping wing aerodynamics and aeroelasticity. Prog. Aerosp. Sci. 46 (7), 284–327.Google Scholar
48. Standen, E. M. 2008 Pelvic fin locomotor function in fishes: three-dimensional kinematics in rainbow trout (Oncorhynchus mykiss). J. Expl Biol. 211, 2931–2942.CrossRefGoogle ScholarPubMed
49. Tangorra, J. L., Davidson, S. N., Hunter, I. W., Madden, P. G. A., Lauder, G. V., Dong, H., Bozkurttas, M. & Mittal, R. 2007 The development of a biologically inspired propulsor for unmanned underwater vehicles. IEEE J. Ocean. Engng 32, 533–550.Google Scholar
50. Tangorra, J. L., Lauder, G. V., Hunter, I. W., Mittal, R., Madden, P. G. A. & Bozkurttas, M. 2010 The effect of fin ray flexural rigidity on the propulsive forces generated by a biorobotic fish pectoral fin. J. Expl Biol. 213, 4043–4054.CrossRefGoogle ScholarPubMed
51. Tornberg, A. K. & Shelley, M. J. 2004 Simulating the dynamics and interactions of flexible fibers in Stokes flows. J. Comput. Phys. 196, 8–40.CrossRefGoogle Scholar
52. Triantafyllou, M. S., Techet, A. H. & Hover, F. S. 2004 Review of experimental work in biomimetic foils. IEEE J. Ocean. Engng 29 (3), 585–594.CrossRefGoogle Scholar
53. Tsang, K. K. Y., So, R. M. C., Leung, R. C. K. & Wang, X. Q. 2008 Dynamic stall behavior from unsteady force measurements. J. Fluids Struct. 24 (1), 129–150.CrossRefGoogle Scholar
54. Uhlmann, M. 2005 An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209, 448–476.Google Scholar
55. Videler, J. J. 1993 Fish Swimming. Chapman & Hall.CrossRefGoogle Scholar
56. Vogel, S. 1996 Life in Moving Fluids: The Physical Biology of Flow. Princeton University Press.Google Scholar
57. Walker, J. A. 2004 Dynamics of pectoral fin rowing in a fish with an extreme rowing stroke: the threespine stickleback (Gasterosteus aculeatus). J. Expl Biol. 207, 1925–1939.CrossRefGoogle Scholar
58. Walker, J. A. & Westneat, M. 1997 Labriform propulsion in fishes, kinematics of flapping aquatic flight in the bird wrasse Gomphosus varius (Labridae). J. Expl Biol. 200, 1549–1569.CrossRefGoogle ScholarPubMed
59. Webb, P. W. 1973 Kinematics of pectoral fin propulsion in Cymatogaster aggregata. J. Expl Biol. 59, 697–710.CrossRefGoogle Scholar
60. Webb, P. W., Kostecki, P. T. & Stevens, E. D. 1984 The effect of size and swimming speed on locomotor kinematics of rainbow trout. J. Expl Biol. 109 (1), 77–95.CrossRefGoogle Scholar
61. Westneat, M. 1996 Functional morphology of aquatic flight in fishes: mechanical modeling, kinematics, and electromyography of labriform locomotion. Am. Zool. 36, 582–598.CrossRefGoogle Scholar
62. Westneat, M., Thorsen, D. H., Walker, J. A. & Hale, M. 2004 Structure, function, and neural control of pectoral fins in fishes. IEEE J. Ocean. Engng 29, 674–683.CrossRefGoogle Scholar
63. Williamson, C. H. K. & Govardhan, R. 2004 Vortex-induced vibrations. Annu. Rev. Fluid Mech. 36, 413–455.CrossRefGoogle Scholar
64. Williamson, C. H. K. & Roshko, A. 1988 Vortex formation in the wake of an oscillating cylinder. J. Fluids Struct. 2 (4), 355–381.CrossRefGoogle Scholar
65. Xu, S. & Wang, Z. J. 2006 An immersed interface method for simulating the interaction of a fluid with moving boundaries. J. Comput. Phys. 216 (2), 454–493.Google Scholar
66. Zhu, Q. 2007 Numerical simulation of a flapping foil with chordwise or spanwise flexibility. AIAA J. 45 (10), 2448–2457.CrossRefGoogle Scholar
67. Zhu, Q. & Shoele, K. 2008 Propulsion performance of a skeleton-strengthened fin. J. Expl Biol. 211, 2087–2100.CrossRefGoogle ScholarPubMed