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Maximizing the efficiency of a flexible propulsor using experimental optimization

Published online by Cambridge University Press:  16 February 2015

Daniel B. Quinn*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
George V. Lauder
Affiliation:
Department of Organismal and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
Alexander J. Smits
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA Department of Mechanical and Aerospace Engineering, Monash University, Victoria, Australia
*
Email address for correspondence: danielq@princeton.edu

Abstract

Experimental gradient-based optimization is used to maximize the propulsive efficiency of a heaving and pitching flexible panel. Optimum and near-optimum conditions are studied via direct force measurements and particle image velocimetry (PIV). The net thrust and power scale predictably with the frequency and amplitude of the leading edge, but the efficiency shows a complex multimodal response. Optimum pitch and heave motions are found to produce nearly twice the efficiencies of optimum heave-only motions. Efficiency is globally optimized when (i) the Strouhal number is within an optimal range that varies weakly with amplitude and boundary conditions; (ii) the panel is actuated at a resonant frequency of the fluid–panel system; (iii) heave amplitude is tuned such that trailing-edge amplitude is maximized while the flow along the body remains attached; and (iv) the maximum pitch angle and phase lag are chosen so that the effective angle of attack is minimized. The multi-dimensionality and multi-modality of the efficiency response demonstrate that experimental optimization is well-suited for the design of flexible underwater propulsors.

Type
Papers
Copyright
© 2015 Cambridge University Press 

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References

Alben, S., Witt, C., Baker, T. V., Anderson, E. & Lauder, G. V. 2012 Dynamics of freely swimming flexible foils. Phys. Fluids 24, 051901.Google Scholar
Anderson, J. M., Streitlien, K., Barrett, D. S. & Triantafyllou, M. S. 1998 Oscillating foils of high propulsive efficiency. J. Fluid Mech. 360, 4172.Google Scholar
Borg, I. & Groenen, P. 2005 Modern Multidimensional Scaling. Springer.Google Scholar
Dai, H., Luo, H., Paulo, J. S., Ferreira de Sousa, A. & Doyle, J. F. 2012 Thrust performance of a flexible low-aspect ratio pitching plate. Phys. Fluids 24, 101903.Google Scholar
Daniel, T. L. & Combes, S. A. 2002 Flexible wings and fins: bending by inertial or fluid-dynamic force? Integr. Compar. Biol. 42, 10441049.CrossRefGoogle ScholarPubMed
Dewey, P. A., Boschitch, B. M., Moored, K. W., Stone, H. A. & Smits, A. J. 2013 Scaling laws for the thrust production of flexible pitching panels. J. Fluid Mech. 732, 2946.Google Scholar
Eloy, C. 2012 Optimal strouhal number for swimming animals. J. Fluids Struct. 30, 205218.Google Scholar
Eloy, C. & Schouveiler, L. 2011 Optimisation of two-dimensional undulatory swimming at high reynolds number. Intl J. Non-Linear Mech. 46, 568576.Google Scholar
Gill, P. E., Murray, W. & Saunders, M. A. 2005 Snopt: an sqp algorithm for large-scale constrained optimization. SIAM Rev. 47 (1), 99131.Google Scholar
Heathcote, S. & Gursul, I. 2007 Flexible flapping airfoil propulsion at low Reynolds numbers. AIAA J. 45 (5), 10661079.CrossRefGoogle Scholar
Isogai, K. & Shinmoto, Y. 1999 Effects of dynamic stall on propulsive efficiency and thrust of flapping airfoil. AIAA J. 37 (10), 11451151.Google Scholar
Izraelevitz, J. S. & Triantafyllou, M. S. 2014 Adding in-line motion and model-based optimization offers exceptional force control authority in flapping foils. J. Fluid Mech. 742, 534.Google Scholar
Kang, C. K., Aono, H., Baik, Y. S., Bernal, L. P. & Shyy, W. 2013 Fluid dynamics of pitching of plunging flat plate at intermediate reynolds numbers. AIAA J. 51 (2), 315329.Google Scholar
Kang, C. K., Aono, H., Cesnik, C. E. S. & Shyy, W. 2011 Effects of flexibility on the aerodynamic performance of flapping wings. J. Fluid Mech. 689, 3274.Google Scholar
Katz, J. & Weihs, D. 1978 Hydrodynamic propulsion by large amplitude oscillation of an airfoil with chordwise flexibility. J. Fluid Mech. 88 (3), 485497.Google Scholar
Kern, S., Koumoutsakos, P. & Eschler, K. 2007 Optimization of anguilliform swimming. Phys. Fluids 19 (9), 91102.CrossRefGoogle Scholar
Lauder, G. V., Flammang, B. E. & Alben, S. 2012 Passive robotic models of propulsion by the bodies and caudal fins of fish. Integr. Compar. Biol. 52, 576587.CrossRefGoogle ScholarPubMed
Lauder, G. V., Lim, J., Shelton, R., Witt, C., Anderson, E. & Tangorra, J. L. 2011 Robotic models for studying undulatory locomotion in fishes. Mar. Technol. Soc. J. 45 (4), 4155.Google Scholar
Lewin, G. C. & Haj-Hariri, H. 2003 Modelling thrust generation of a two-dimensional heaving airfoil in a viscous fluid. J. Fluid Mech. 492, 339362.Google Scholar
Lighthill, J. 1975 Mathematical Biofluiddynamics. SIAM.Google Scholar
Lighthill, M. J. 1970 Aquatic animal propulsion of high hydromechanical efficiency. J. Fluid Mech. 44, 265301.Google Scholar
Liu, W., Xiao, Q. & Cheng, F. 2013 A bio-inspired study on tidal energy extraction with flexible flapping wings. Bioinspir. Biomim. 8 (3).Google Scholar
Low, K. H.2011 Current and future trends of biologically inspired underwater vehicles. Tech. Rep. Nanyang Technical University.CrossRefGoogle Scholar
Masoud, H. & Alexeev, A. 2010 Resonance of flexible flapping wings at low Reynolds number. Phys. Rev. 81, 056304.Google Scholar
Michelin, S. & Llewellyn, S. S. G. 2009 Resonance and propulsion performance of a heaving flexible wing. Phys. Fluids 21, 071902.Google Scholar
Milano, M. & Gharib, M. 2005 Uncovering the physics of flapping flat plates with artificial evolution. J. Fluid Mech. 534, 403409.Google Scholar
Park, Y. J., Huh, T., Park, D. & Cho, K. J. 2014 Design of a variable-stiffness flapping mechanism for maximizing the thrust of a bio-inspired underwater robot. Bioinspir. Biomim. 9, 036002.Google Scholar
Paulo, J. S., Ferreira de Sousa, A. & Allen, J. J. 2011 Thrust efficiency of harmonically oscillating flexible flat plates. J. Fluid Mech. 674, 4366.Google Scholar
Pederzani, J. & Haj-Hariri, H. 2006 Analysis of heaving flexible airfoils in viscous flow. AIAA J. 44 (11), 27732779.Google Scholar
Prempraneerach, P., Hover, F. S. & Triantafyllou, M. S. 2003 The effect of chordwise flexibility on the thrust and efficiency of a flapping foil. In Proceedings of the Thirteenth International Symposium on Unmanned Untethered Submersible Technology, Autonomous Undersea Systems Institute, New Hampshire.Google Scholar
Quinn, D. B., Lauder, G. V. & Smits, A. J. 2014 a Scaling the propulsive performance of heaving flexible panels. J. Fluid Mech. 738, 250267.Google Scholar
Quinn, D. B., Moored, K. W., Dewey, P. A. & Smits, A. J. 2014 b Unsteady propulsion near a solid boundary. J. Fluid Mech. 742, 152170.Google Scholar
Ramananarivo, S., Godoy-Diana, R. & Thiria, B. 2013 Passive elastic mechanism to mimic fish-muscle action in anguilliform swimming. J. R. Soc. Interface 10, 20130667.Google Scholar
Raspa, V., Ramananarivo, S., Thiria, B. & Godoy-Diana, R. 2014 Vortex-induced drag and the role of aspect ratio in undulatory swimmers. Phys. Fluids 26, 041701.CrossRefGoogle Scholar
van Rees, W. M., Gazzola, M. & Koumoutsakos, P. 2013 Optimal shapes for anguilliform swimmers at intermediate reynolds numbers. J. Fluid Mech. 722, R3.Google Scholar
Shelton, R., Thornycroft, P. & Lauder, G. V. 2014 Undulatory locomotion by flexible foils as biomimetic models for understanding fish propulsion. J. Expl Biol. 217, 21102120.Google Scholar
Snyman, J. A. 2005 Practical Mathematical Optimization: An Introduction to Basic Optimization Theory and Classical and New Gradient-Based Algorithms. Springer.Google Scholar
Stanislas, M., Okamoto, K., Kahler, C. J. & Westerweel, J. 2005 Main results of the second international PIV challenge. Exp. Fluids 39, 170191.CrossRefGoogle Scholar
Taylor, G. K., Nudds, R. L. & Thomas, A. L. R. 2003 Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency. Nature 425, 707711.Google Scholar
Tokic, G. & Yue, D. K. P. 2012 Optimal shape and motion of undulatory swimming organisms. Proc. R. Soc. Lond. B 282; doi:10.1098/rspb.2012.0057.Google Scholar
Triantafyllou, G. S., Triantafyllou, M. S. & Grosenbaugh, M. A. 1993 Optimal thrust development in oscillating foils with application to fish propulsion. J. Fluids Struct. 7, 205224.Google Scholar
Triantafyllou, M. S., Triantafyllou, G. S. & Yue, D. K. P. 2000 Hydrodynamics of fishlike swimming. Annu. Rev. Fluid Mech. 32 (1), 3353.Google Scholar
Tuncer, I. H. & Kaya, M. 2005 Optimization of flapping airfoils for maximum thrust and propulsive efficiency. AIAA J. 43 (11), 23292336.Google Scholar
Wang, Z. J. 2000 Vortex shedding and frequency selection in flapping flight. J. Fluid Mech. 410, 323341.Google Scholar
Weaver, W., Timoshenko, S. P. & Young, D. H. 1990 Vibration Problems in Engineering, 5th edn. John Wiley and Sons.Google Scholar
Wu, T. Y. 1971 a Hydrodynamics of swimming propulsion. Part 1. Swimming of a two-dimensional flexible plate at variable forward speeds in an inviscid fluid. J. Fluid Mech. 46 (2), 337355.Google Scholar
Wu, T. Y. 1971 b Hydrodynamics of swimming propulsion. Part 2. Some optimum shape problems. J. Fluid Mech. 46 (3), 521524.Google Scholar
Zhu, Q. 2007 Numerical simulation of a flapping foil with chordwise or spanwise flexibility. AIAA J. 45 (10), 24482457.Google Scholar