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Low-dimensional models and performance scaling of a highly deformable fish pectoral fin

Published online by Cambridge University Press:  17 July 2009

M. BOZKURTTAS ,
R. MITTAL ,
H. DONG ,
G. V. LAUDER  and
P. MADDEN
M. BOZKURTTAS
Affiliation:
Department of Mechanical and Aerospace Engineering, The George Washington University, 801 22nd St NW, Washington DC 20052, USA
R. MITTAL*
Affiliation:
Department of Mechanical and Aerospace Engineering, The George Washington University, 801 22nd St NW, Washington DC 20052, USA
H. DONG
Affiliation:
Department of Mechanical and Aerospace Engineering, The George Washington University, 801 22nd St NW, Washington DC 20052, USA
G. V. LAUDER
Affiliation:
Organismic and Evolutionary Biology, 26 Oxford St, Harvard University, Cambridge, MA 02138, USA
P. MADDEN
Affiliation:
Organismic and Evolutionary Biology, 26 Oxford St, Harvard University, Cambridge, MA 02138, USA
*
‡Email address for correspondence: [email protected]
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Abstract

The hydrodynamics of a highly deformable fish pectoral fin used by a bluegill sunfish (Lepomis macrochirus) during steady forward swimming are examined in detail. Low-dimensional models of the fin gait based on proper orthogonal decomposition (POD) are developed, and these are subjected to analysis using an incompressible Navier–Stokes flow solver. The approach adopted here is primarily motivated by the quest to develop insights into the fin function and associated hydrodynamics, which are specifically useful for the design of a biomimetic, pectoral fin propulsor. The POD analysis shows that the complex kinematics of the pectoral fin can be described by a few (<5) POD modes and that the first three POD modes are highly distinct. The significance of these modes for thrust production is examined by synthesizing a sequence of fin gaits from these modes and simulating the flow associated with these gaits. We also conduct a scale study of the pectoral fin in order to understand the effect of the two key non-dimensional parameters, Reynolds number and Strouhal number, on the propulsive performance. The implications of the POD analysis and performance scaling on the design of a robotic pectoral fin are discussed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 631 , 25 July 2009 , pp. 311 - 342
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

†

Present address: Exa Corporation, 55 Network Drive, Burlington, MA 01803, USA

Present address: Mechanical and Materials Engineering, Wright State University, Dayton, OH 45435, USA

References

REFERENCES

Alexa, M. & Mueller, W. 2000 Representing animations by principal components. Eurographics 19, 411–418.Google Scholar
Anderson, J. M., Streitlien, K., Barrett, D. S. & Triantafyllou, M. S. 1998 Oscillating foils of high propulsive efficiency. J. Fluid Mech. 360, 41–72.Google Scholar
Barber, T. J., Ahmed, M. H. & Shafi, N. A. 2005 POD snapshot data reduction for periodic flows. In Proceedings of 43th Aerospace Sciences and Meeting Exhibit. Reno, NV.Google Scholar
Berkooz, G, Holmes, P. & Lumley, J. L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25, 539–75.CrossRefGoogle Scholar
Bozkurttas, M. 2007 Hydrodynamic performance of fish pectoral fins with application to autonomous underwater vehicles. PhD thesis, The George Washington University, Washington, DC.Google Scholar
Bozkurttas, M., Dong, H., Mittal, R., Lauder, G. V. & Madden, P. 2006 Hydrodynamic performance of deformable fish fins and flapping foils. Paper 2005–1392. AIAA.CrossRefGoogle Scholar
Dong, H., Bozkurttas, M., Mittal, R., Madden, P. & Lauder, G. V. 2009 Computational modelling and analysis of the hydrodynamics of a highly deformable fish pectoral fin. J. Fluid Mech. submitted February 2009.CrossRefGoogle Scholar
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.Google Scholar
Drucker, E. G. 1996 The use of gait transition speed in comparative studies of fish locomotion. Amer. Zool. 36, 555–566.CrossRefGoogle Scholar
Drucker, E. G. & Jensen, J. 1996 Pectoral fin locomotion in the striped surfperch. Part 1. Kinematic effects of swimming speed and body size. J. Exp. Biol. 199, 2235–2242.CrossRefGoogle Scholar
Drucker, E. G. & Lauder, G. V. 2000 A hydrodynamic analysis of fish swimming speed: Wake structures and locomotor force in slow and fast labriform swimmer. J. Exp. Biol. 203, 2379–2393.Google Scholar
Freymuth, P. 1990 Thrust generation by an airfoil in hover modes. Exp. Fluids. 9, 17–24.Google Scholar
Gibb, A., Jayne, B. C. & Lauder, G. V. 1994 Kinematics of pectoral fin locomotion in the bluegill sunfish lepomis macrochirus. J. Exp. Biol. 189, 133–161.Google Scholar
Hartley, R. & Zisserman, A. 2004 Multiole View Geometry in Computer Vision, 2nd edn. Cambridge University Press.CrossRefGoogle Scholar
Jayne, B. C., Lozada, A. & Lauder, G. V. 1996 Function of the dorsal fin in bluegill sunfish: motor patterns during four distinct locomotor behaviours. J. Morphol. 228, 307–326.3.0.CO;2-Z>CrossRefGoogle Scholar
Kato, N. & Furushima, M. 1996 Pectoral fin model for maneuver of underwater vehicles. In Proceedings of 14th International Symposium on Unmanned Untethered Submersible Technology, Durham, NH.Google Scholar
Lauder, G. V. & Madden, P. 2006 Learning from fish: Kinematics and experimental hydrodynamics for roboticists. Intl J. Automat. Comput. 3 (4), 325–335.Google Scholar
Lauder, G. V., Madden, P., Hunter, I., Tangorra, J., Davidson, N., Proctor, L., Mittal, R., Dong, H. & Bozkurttas, M. 2005 Design and performance of a fish fin-like propulsor for AUVs. In Proceedings of 14th International Symposium on Unmanned Untethered Submersible Technology, Durham, NH.Google Scholar
Lauder, G. V., Madden, P., Mittal, R., Dong, H. & Bozkurttas, M. 2006 Locomotion with flexible propulsors. Part 1. Experimental analysis of pectoral fin swimming in sunfish. Bioinsp. Biomimet. 1, S25–S34.Google Scholar
Liang, Y. C., Lee, H. P., Lim, S. P., Lin, W. Z., Lee, K. H. & Wu, C. G. 2002 Proper orthogonal decomposition and its applications. Part 1. Theory. J. Sound Vib. 252 (3), 527–544.CrossRefGoogle Scholar
Lighthill, J. 1975 Mathematical Biofluiddynamics. SIAM.CrossRefGoogle Scholar
Mittal, R., Dong, H., Bozkurttas, M., Lauder, G. V. & Madden, P. 2006 Locomotion with flexible propulsors. Part 2. Computational modelling of pectoral fin swimming in a sunfish. Bioinsp. Biomim. 1, S35–S41.Google Scholar
Mittal, R., Dong, H., Bozkurttas, M., Najjar, F., Vargas, A. & von Loebbecke, A. 2008 A versatile immersed boundary method for incompressible flows with complex boundaries. J. Comp. Phys. 227, 4825–4852.Google Scholar
Mittal, R. & Iaccarino, G. 2005 Immersed boundary methods. Annu. Rev. Fluid Mech. 37, 239–261.CrossRefGoogle Scholar
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. Exp. Biol. 205 (10), 2997–3008.CrossRefGoogle ScholarPubMed
Ramamurti, R., Sandberg, W., Ratna, B., Naciri, J. & Spilman, C. 2005 3-d unsteady computational investigations of the effect of fin deformation on force production in fishes. In Proceedings of 14th International Symposium on Unmanned Untethered Submersible Technology, Durham, NH.Google Scholar
Rohr, J. J. & Fish, F. E 2004 Strouhal numbers and optimization of swimming by odontocete cetaceans. J. Exp. Biol. 207, 1633–1642.CrossRefGoogle ScholarPubMed
Soria, J. & Cantwell, B. J. 1993 Identification and classification of topological structures in free shear flows. In Eddy Structure Identification in Free Turbulent Shear Flows (ed. J. P. Bonnet & M. N. Glauser), pp. 379–390. Academic.CrossRefGoogle Scholar
Standen, E. M. & Lauder, G. V. 2005 Dorsal and anal fin function in bluegill sunfish (Lepomis macrochirus): three-dimensional kinematics during propulsion and maneuvering. J. Exp. Biol. 3 205, 2753–2763.Google Scholar
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 (3), 533–550.CrossRefGoogle Scholar
Techet, A. H., Lim, K. L., Hover, F. S. & Triantafylou, M. S. 2005 Hydrodynamic performance of a biologically inspired 3D flapping foil. In Proceedings of 14th International Symposium on Unmanned Untethered Submersible Technology, Durham, NH.Google Scholar
Triantafyllou, M. S., Hover, F. S. & Licht, S. 2003 The mechanics of force production in flapping foils under steady-state and transient motion conditions. Tech Rep. Testing Tank Facility Report 031903. MIT Department of Ocean Engineering.Google Scholar
Triantafyllou, M. S., Techet, A. H. & Hover, F. S. 2004 Review of experimental work in biomimetic foils. IEEE J. Ocean. Engng 29, 585–595.Google Scholar
Triantafyllou, M. S., Triantafyllou, G. S. & Gopalkrishnan, R. 1991 Wake mechanics for thrust generation in oscillating foils. Phys. Fluids 3 (12), 2835–2837.Google Scholar
Triantafyllou, G. S., Triantafyllou, M. S. & Grosenbaugh, M. A. 1992 Optimal thrust development in oscillating foils with applications to fish propulsion. J. Fluids Struct. 7, 204–224.Google Scholar
Triantafyllou, M. S., Triantafyllou, G. S. & Grosenbaugh, M. A. 1993 Optimal thrust development in oscillating foils with applications to fish propulsion. J. Fluids Struct. 7, 205–224.Google Scholar
Troje, N. 2000 Decomposing biological locomotion: a framework for analysis and synthesis of human gait patterns. J. Vision 2 (5).Google Scholar
Udaykumar, H. S., Mittal, R., Rampunggoon, P. & Khanna, A. 2001 A sharp interface Cartesian grid method for simulating flows with complex moving boundaries. J. Comput. Phys. 174, 345–380.CrossRefGoogle Scholar
Urtasun, R., Fua, P., Glardon, P. & Thalmann, D. 2004 Mahalanobis motion generation. Tech Rep. IC/2004/13. Swiss Federal Office for Education and Science.Google Scholar
Van-Kan, J. 1986 A second order accurate pressure correction scheme for viscous incompressible flow. SIAM J. Sci. Stat. Comput. 7, 870–891.CrossRefGoogle Scholar
Walker, J. A. & Westneat, M. W. 1997 Labriform propulsion in fishes: kinematics of flapping aquatic flight in the bird wrasse, gomphosus varius (Labridae). J. Exp. Biol. 200, 1549–1569.Google Scholar
Walker, J. A. & Westneat, M. W. 2000 Mechanical performance of aquatic rowing and flying. Proc. R. Soc Lond. B 267, 1875–1881.Google Scholar
Walker, J. A. & Westneat, M. W. 2002 a Kinematics, dynamics, and energetics of rowing and flapping propulsion in fishes. Integr. Compar. Biol. 42.Google Scholar
Walker, J. A. & Westneat, M. W. 2002 b Performance limits of labriform propulsion and correlates with fin shape and motion. J. Exp. Biol. 205, 177–187.CrossRefGoogle ScholarPubMed
Ye, T., Mittal, R., Udaykumar, H. S. & Shyy, W. 1999 An accurate Cartesian grid method for simulation of viscous incompressible flows with complex immersed boundaries. J. Comput. Phys. 156, 209–240.CrossRefGoogle Scholar