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How flexibility affects the wake symmetry properties of a self-propelled plunging foil

Published online by Cambridge University Press:  18 June 2014

Xiaojue Zhu ,
Guowei He  and
Xing Zhang
Xiaojue Zhu
Affiliation:
The State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
Guowei He
Affiliation:
The State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
Xing Zhang*
Affiliation:
The State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
*
†Email address for correspondence: zhangx@lnm.imech.ac.cn
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Abstract

The wake symmetry properties of a flapping-foil system are closely associated with its propulsive performance. In the present work, the effect of the foil flexibility on the wake symmetry properties of a self-propelled plunging foil is studied numerically. We compare the wakes of a flexible foil and a rigid foil at a low flapping Reynolds number of 200. The two foils are of the same dimensions, flapping frequency, leading-edge amplitude and cruising velocity but different bending rigidities. The results indicate that flexibility can either inhibit or trigger the symmetry breaking of the wake. We find that there exists a threshold value of vortex circulation above which symmetry breaking occurs. The modification of vortex circulation is found to be the pivotal factor in the influence of the foil flexibility on the wake symmetry properties. An increase in flexibility can result in a reduction in the vorticity production at the leading edge because of the decrease in the effective angle of attack, but it also enhances vorticity production at the trailing edge because of the increase in the trailing-edge flapping velocity. The competition between these two opposing effects eventually determines the strength of vortex circulation, which, in turn, governs the wake symmetry properties. Further investigation indicates that the former effect is related to the streamlined shape of the deformed foil while the latter effect is associated with structural resonance. The results of this work provide new insights into the functional role of passive flexibility in flapping-based biolocomotion.

JFM classification

Biological Fluid Dynamics: Propulsion Wakes/Jets: Vortex streets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 751 , 25 July 2014 , pp. 164 - 183
Copyright
© 2014 Cambridge University Press 

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References

Alben, S., Witt, C., Baker, T. V., Anderson, E. & Lauder, G. V. 2012 Locomotion of a passively flapping flat plate. Phys. Fluids 24, 051901.Google Scholar
Anderson, J. M., Streitlien, K., Barret, D. S. & Triantafyllou, M. S. 1998 Oscillating foils for high propulsive efficiency. J. Fluid Mech. 360, 46–72.Google Scholar
Borazjani, I. & Sotiropoulos, F. 2008 Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes. J. Expl Biol. 211, 1541–1558.CrossRefGoogle ScholarPubMed
Cleaver, D. J., Wang, Z. & Gursul, I. 2012 Bifurcating flows of plunging aerofoils at high Strouhal numbers. J. Fluid Mech. 708, 349–376.Google Scholar
Combes, S. A. & Daniel, J. 2003 Flexural stiffness in insect wings II. Spatial distribution and dynamic wing bending. J. Expl Biol. 206, 2989–2997.Google Scholar
Eldredge, J. D., Toomey, J. & Medina, A. 2010 On the roles of chord-wise flexibility in a flapping wing with hovering kinematics. J. Fluid Mech. 659, 94–115.CrossRefGoogle Scholar
Godoy-Diana, R., Aider, J. L. & Wesfreid, J. E. 2008 Transition in the wake of a flapping foil. Phys. Rev. E 77, 016308.CrossRefGoogle ScholarPubMed
Godoy-Diana, R., Marais, C., Aider, J. L. & Wesfreid, J. E. 2009 A model for the symmetry breaking of the reverse Benard–von Karman vortex street produced by a flapping foil. J. Fluid Mech. 622, 23–32.Google Scholar
Heathcote, S. & Gursul, I. 2007a Flexible flapping airfoil propulsion at low Reynolds numbers. AIAA J. 45, 1066–1079.Google Scholar
Heathcote, S. & Gursul, I. 2007b Jet switching phenomenon for a periodically plunging airfoil. Phys. Fluids 19, 027104.Google Scholar
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.Google Scholar
Jones, K. D., Dohring, C. M. & Platzer, M. F. 1998 Experimental and computational investigation of the Knoller–Betz effect. AIAA J. 36, 1240–1246.Google Scholar
Kang, C. K., Aono, H., Cesnik, C. E. S. & Shyly, W. 2011 Effects of flexibility on the aerodynamic performance of flapping wings. J. Fluid Mech. 689, 32–74.Google Scholar
Katz, J. & Weihs, D. 1978 Hydrodynamic propulsion by large amplitude oscillation of an airfoil with chordwise flexibility. J. Fluid Mech. 88, 713–723.CrossRefGoogle Scholar
Kern, S. & Koumoutsakos, P. 2006 Simulations of optimized anguilliform swimming. J. Expl Biol. 209, 4841–4857.Google Scholar
Lauder, G. V., Anderson, E. J., Tangorra, J. & Madden, P. G. 2007 Fish biorobotics: kinematics and hydrodynamics of self-propulsion. J. Expl Biol. 210, 2767–2780.CrossRefGoogle ScholarPubMed
Lee, J. & Lee, S. 2013 Fluid–structure interaction for the propulsive velocity of a flapping flexible plate at low Reynolds number. Comput. Fluids 71, 348–374.CrossRefGoogle Scholar
Liang, C. L., Ou, K., Premasuthan, S., Jameson, A. & Wang, Z. J. 2011 High-order accurate simulations of unsteady flow past plunging and pitching airfoils. Comput. Fluids 40, 236–248.Google Scholar
Marais, C., Thiria, B., Wesfreid, J. E. & Godoy-Diana, R. 2012 Stabilizing effect of flexibility in the wake of a flapping foil. J. Fluid Mech. 710, 659–669.CrossRefGoogle Scholar
Masoud, H. & Alexeev, A. 2010 Resonance of flexible flapping wings at low Reynolds number. Phys. Rev. E 81, 056304.Google Scholar
Michelin, S. & Smith, S. G. L. 2009 Resonance and propulsion performance of a heaving flexible wing. Phys. Fluids 21, 071902.Google Scholar
Prempraneech, 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 13th International Symposium on Unmanned Untethered Submersible Technology, UUST, Durham, NH, USA.Google Scholar
Ramananarivo, S., Godoy-Diana, R. & Thiria, B. 2011 Rather than resonance, flapping wing flyers may play on aerodynamics to improve performance. Proc. Natl Acad. Sci. USA 108, 5964–5969.Google Scholar
Schnipper, T., Andersen, A. & Bohr, T. 2009 Vortex wakes of a flapping foil. J. Fluid Mech. 633, 411–423.Google Scholar
Schultz, W. W. & Webb, P. W. 2002 Power requirements of swimming: do new methods resolve old questions? Integr. Compar. Biol. 42, 1018–1025.Google Scholar
Shoele, K. & Zhu, Q. 2012 Leading edge strengthening and the propulsion performance of flexible ray fins. J. Fluid Mech. 693, 402–432.Google Scholar
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, 284–327.Google Scholar
Spagnolie, S. E., Moret, L., Shelley, M. J. & Zhang, J. 2010 Surprising behaviours in flapping locomotion with passive pitching. Phys. Fluids 22, 041903.Google Scholar
Thiria, B. & Godoy-Diana, R. 2010 How wing compliance drives the efficiency of self-propelled flapping flyers. Phys. Rev. E 82, 015303(R).Google Scholar
Vanella, M., Fitzgerald, T., Preidikman, S., Balaras, E. & Balachandran, B. 2009 Influence of flexibility on the aerodynamic performance of a hovering wing. J. Expl Biol. 212, 95–105.Google Scholar
Wang, S. Z. & Zhang, X. 2011 An immersed boundary method based on discrete stream function formulation for two- and three-dimensional incompressible flows. J. Comput. Phys. 230, 3479–3499.Google Scholar
Zhang, J., Liu, N. S. & Lu, X. Y. 2010 Locomotion of a passively flapping flat plate. J. Fluid Mech. 659, 43–68.Google Scholar
Zheng, Z. C. & Wei, Z. 2012 Study of mechanisms and factors that influence the formation of vortical wake of a heaving airfoil. Phys. Fluids 24, 103601.Google Scholar
Zhu, X. J., He, G. W. & Zhang, X. 2014 An improved direct-forcing immersed boundary method for fluid–structure interaction simulations. Trans. ASME J. Fluids Engng 136, 040903.Google Scholar