Abstract
An immersed-boundary method is used to investigate the flapping wings with different aspect ratios ranging from 1 to 5. The numerical results on wake structures and the performance of the propulsion are given. Unlike the case of the two-dimensional flapping foil, the wing-tip vortices appear for the flow past a three-dimensional flapping wing, which makes the wake vortex structures much different. The results show that the leading edge vortex merges into the trailing edge vortex, connects with the wing tip vortices and then sheds from the wing. A vortex ring forms in the wake, and exhibits different patterns for different foil aspect ratios. Analysis of hydrodynamic performances shows that both thrust coefficient and efficiency of the flapping wing increase with increasing aspect ratio.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
SFAKIOTAKIS M., LANE D. M. and BRUCE J. Review of foil swimming modes for aquatic locomotion[J]. IEEE Journal of Oceanic Engineering, 1999, 24(2): 237–352.
ANDERSON J. M., STREITLIEN K. and BARRETT D. S. et al. Oscillating foils of high propulsive efficiency[J]. Journal of Fluid Mechanics, 1998, 360: 41–72.
VON ELLENRIEDER K. D., PARKER K. and SORIA J. Flow structures behind a heaving and pitching finite-span wing[J]. Journal of Fluid Mechanics, 2003, 490: 129–138.
LIU Zhen, HYUN Beom-soo and KIM M. et al. Experimental and numerical study for hydrodynamic characteristics of an oscillating hydrofoil[J]. Journal of Hydrodynamics, 2008, 20(3): 280–287.
POLIDORO V. Flapping foil propulsion for cruising and hovering autonomous underwater vehicles[D]. Master Thesis, Cambridge, MA, USA: Massachusetts Institute of Technology, 2003.
MCLETCHIE K. W. Force and hydrodynamic efficiency measurements of a three-dimensional flapping foil[D]. Master Thesis, Cambridge, MA, USA: Massachusetts Institute of Technology, 2004.
LIM K. Hydrodynamic performance and vortex shedding of a biologically inspired three-dimensional flapping foil[D]. Master Thesis, Cambridge, MA, USA: Massachusetts Institute of Technology, 2005.
READ M. Performance of biologically inspired flapping foils[D]. Master Thesis, Cambridge, MA, USA: Massachusetts Institute of Technology, 2006.
LICHT S., POLODORO V. and FLORES M. et al. Design and projected performance of a flapping foil AUV[J]. IEEE Journal of Oceanic Engineering, 2004, 29(3): 786–794.
PEDRO G., SULEMAN A. and DJILALI N. A numerical study of the propulsive efficiency of a flapping hydrofoil[J]. International Journal for Numerical Methods in Fluids, 2003, 42(5): 493–526.
LU X.-Y., YANG J.-M. and YIN X.-Z. Propulsive performance and vortex shedding of a foil in flapping flight[J]. Acta Mechanics, 2003, 165(3–4): 189–206
GUGLIELMINI L., BLONDEAUX P. Propulsive efficiency of oscillating foils[J]. European Journal of Mechanics B/Fluids, 2004, 23(2): 255–278.
AKHTAR I., MITTAL R. A biologically inspired computational study of flow past tandem flapping foils[C]. 35th AIAA Fluid Dynamics Conference and Exhibit. Toronto, Ontario, Canada, 2005, AIAA-2005-4760.
BLONDEAUX P., FORNARELLI F. and GUGLIELMINI L. et al. Numerical experiments on flapping foils mimicking fish-like locomotion[J]. Physics of Fluids, 2005, 17(11): 113601.
DONG H., MITTAL R. and NAJJAR F. M. Wake topology and hydrodynamic performance of low-aspect-ratio flapping foils[J]. Journal of Fluid Mechanics, 2006, 566: 309–343.
HU Wen-rong. Hydrodynamic study on a pectoral fin rowing model of a fish[J]. Journal of Hydrodynamics, 2009, 21(4): 463–472.
GUGLIELMINI L., BLONDEAUX P. Numerical experiments on the transient motions of a flapping foil[J]. European Journal of Mechanics B/Fluids, 2009, 28(1): 136–145.
GAO Tong, LIU Nan-sheng and LU Xi-yun. Numerical analysis of the ground effect on insect hovering[J]. Journal of Hydrodynamics, 2008, 20(1): 17–22.
FADLUN E. A., VERZICCO R. and ORLANDI P. et al. Combined immersed-boundary finite difference methods for three-dimensional complex flow simulations[J]. Journal of Computational Physics, 2000, 161(1): 35–60.
DENG J., SHAO X. M. and REN A. L. A new modification of the immersed-boundary method for simulating flows with complex moving boundaries[J]. International Journal for Numerical Methods in Fluids, 2006, 52(11): 1195–1213.
LIMA E SILVA A. L. F., SILVERIRA-NETO A. and DAMASCENO J. J. R. Numerical simulation of two-dimensional flows over a circular cylinder using the immersed boundary method[J]. Journal of Computational Physics, 2003, 189(2): 351–370.
SHEEN S. C., WU J. L. Solution of the pressure correction equation by the preconditioned conjugate gradient method[J]. Numerical Heart Transfer, Part B, 1997, 32(2): 215–230.
DENG J., REN A. L. and ZOU J. F. et al. Three-dimensional flow around two circular cylinders in tandem arrangement[J]. Fluid Dynamics Research, 2006, 38(6): 386–404.
DENG J., REN A. L. and SHAO X. M. The flow between a stationary cylinder and a downstream elastic cylinder in cruciform arrangement[J]. Journal of Fluids and Structures, 2007, 23(5): 715–731.
JEONG J., HUSSAIN F. On the identification of a vortex[J]. Journal of Fluid Mechanics, 1995, 285: 69–94.
BUCHHOLZ J. H. J., SMITS A. J. On the evolution of the wake structure produced by a low-aspect-ratio pitching panel[J]. Journal of Fluid Mechanics, 2006, 546: 433–443.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the Doctoral Research Foundation of Chinese Universities (Grant No. 20070335066), the National Natural Science Foundation of China (Grant Nos. 50735004, 10802075).
Biography: SHAO Xue-ming (1972-), Male, Ph. D., Professor
Rights and permissions
About this article
Cite this article
Shao, Xm., Pan, Dy., Deng, J. et al. Numerical Studies on the Propulsion and Wake Structures of Finite-Span Flapping Wings with Different Aspect Ratios. J Hydrodyn 22, 147–154 (2010). https://doi.org/10.1016/S1001-6058(09)60040-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1016/S1001-6058(09)60040-8