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Boundary-element method for the prediction of performance of flapping foils with leading-edge separation

Published online by Cambridge University Press:  12 April 2012

Yulin Pan ,
Xiaoxia Dong ,
Qiang Zhu  and
Dick K. P. Yue
Yulin Pan
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Xiaoxia Dong
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Qiang Zhu
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Dick K. P. Yue*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: yue@mit.edu
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Abstract

A numerical model based on a boundary-element method is developed to predict the performance of flapping foils for the general cases where vorticities are shed near the leading edge as well as from the trailing edge. The shed vorticities are modelled as desingularized thin shear layers which propagate with the local flow velocity. Special treatments are developed to model the unsteady and alternating leading-edge separation (LES), which is a main element of difficulty for theoretical and numerical analyses of general flapping foils. The present method is compared with existing experiments where it is shown that the inclusion of LES significantly improves the prediction of thrust and efficiency, obtaining excellent agreement with measurements over a broad range of flapping frequencies (Strouhal number) and motion amplitudes (maximum angle of attack). It is found that the neglect of LES leads to substantial over-prediction of the thrust (and efficiency). The effects of LES on thrust generation in terms of the circulation around the foil, the steady and unsteady thrust components, and the vortex-induced pressure on the foil are elucidated. The efficiency and robustness of the method render it suitable for design optimization which generally requires large numbers of performance evaluations. To illustrate this, we present a sample problem of designing the flapping motion, with the inclusion of higher harmonic components, to maximize the efficiency under specified thrust. When optimal higher harmonic motions are included, the performance of the flapping foil is appreciably improved, mitigating the adverse effects of LES vortex on the performance.

JFM classification

Biological Fluid Dynamics: Propulsion
Type
Papers
Information
Journal of Fluid Mechanics , Volume 698 , 10 May 2012 , pp. 446 - 467
Copyright
Copyright © Cambridge University Press 2012

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Footnotes

‡

Present address: Department of Structural Engineering, University of California, San Diego, La Jolla, CA 92093, USA.

References

1. Acharya, M. & Metwally, H. M. 1992 Unsteady pressure field and vorticity production over a pitching airfoil. AIAA J. 30 (2), 403–411.Google Scholar
2. Anderson, J. M., Streitlien, K., Barrett, D. S. & Triantafyllou, M. S. 1998 Oscillating foils of high propulsive efficiency. J. Fluid Mech. 360, 41–72.CrossRefGoogle Scholar
3. Bellamy-Knights, P. G., Benson, M. G., Gerrard, J. H. & Gladwell, I. 1989 Convergence properties of panel methods. Comput. Meth. Appl. Mech. Engng 76 (2), 171–178.CrossRefGoogle Scholar
4. Burns, J. H. 1988 A 3-D tunnel correction panel method for swept tapered airfoils with separation. Master’s thesis, Department of Aeronautics and Astronautics Engineering, Massachusetts Institute of Technology.Google Scholar
5. Degani, A. T., Li, Q. & Walker, J. D. A. 1996 Unsteady separation from the leading edge of a thin airfoil. Phys. Fluids 8, 704.Google Scholar
6. Haller, G. 2004 Exact theory of unsteady separation for two-dimensional flows. J. Fluid Mech. 512, 257–311.Google Scholar
7. He, L. 2010 Numerical simulation of unsteady rotor/stator interaction and application to propeller/rudder combination. PhD thesis, Ocean Engineering Group, Department of Civil Engineering, The University of Texas at Austin.Google Scholar
8. Hess, J. L. 1990 Panel methods in computational fluid dynamics. Annu. Rev. Fluid Mech. 22 (1), 255–274.Google Scholar
9. 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.Google Scholar
10. Jones, M. A. 2003 The separated flow of an inviscid fluid around a moving flat plate. J. Fluid Mech. 496, 405–441.Google Scholar
11. Jones, M. A. & Shelley, M. J. 2005 Falling cards. J. Fluid Mech. 540, 393–426.Google Scholar
12. Kármán, T. & Sears, W. R. 1938 Airfoil theory for non-uniform motion. J. Aeronaut. Sci. 5 (10), 379–390.Google Scholar
13. Katz, J. 1981 A discrete vortex method for the non-steady separated flow over an airfoil. J. Fluid Mech. 102, 315–328.Google Scholar
14. Katz, J. & Plotkin, A. 1991 Low-Speed Aerodynamics: From Wing Theory to Panel Methods. McGraw-Hill.Google Scholar
15. Kinnas, S. A. & Hsin, C.-Y. 1992 Boundary element method for the analysis of the unsteady flow around extreme propeller geometries. AIAA J. 30 (3), 688–696.Google Scholar
16. Kiya, M. & Arie, M. 1977 A contribution to an inviscid vortex-shedding model for an inclined flat plate in uniform flow. J. Fluid Mech. 82 (02), 223–240.CrossRefGoogle Scholar
17. Koochesfahani, M. 1989 Vortical patterns in the wake of an oscillating airfoil. AIAA J. 27 (9), 1200–1205.CrossRefGoogle Scholar
18. Krasny, R. 1987 Computation of vortex sheet roll-up in the Trefftz plane. J. Fluid Mech. 184, 123–155.Google Scholar
19. Lewin, G. C. & Haj-Hariri, H. 2003 Modelling thrust generation of a two-dimensional heaving airfoil in a viscous flow. J. Fluid Mech. 492, 339–362.CrossRefGoogle Scholar
20. Licht, S., Hover, F. & Triantafyllou, M. S. 2004 Design of a flapping foil underwater vehicle. In International Symposium on Underwater Technology, 2004, pp. 311–316. IEEE.Google Scholar
21. Luenberger, D. G. & Ye, Y. 2008 Linear and Nonlinear Programming. Springer.Google Scholar
22. Maskew, B. 1993 USAERO User’s Manual. Analytical Methods, Inc.Google Scholar
23. McCroskey, WJ 1982 Unsteady airfoils. Annu. Rev. Fluid Mech. 14 (1), 285–311.Google Scholar
24. Mishima, S. 1996 Design of cavitating propeller blades in non-uniform flow by numerical optimization. PhD thesis, Department of Ocean Engineering, Massachusetts Institute of Technology.Google Scholar
25. Morino, L. & Kuo, C. C. 1974 Subsonic potential aerodynamics for complex configurations – a general theory. AIAA J. 12, 191–197.Google Scholar
26. Peace, A. J. & Riley, N. 1983 A viscous vortex pair in ground effect. J. Fluid Mech. 129 (1), 409–426.Google Scholar
27. Read, D. A., Hover, F. S. & Triantafyllou, M. S. 2003 Forces on oscillating foils for propulsion and maneuvering. J. Fluids Struct. 17 (1), 163–183.Google Scholar
28. Reynolds, W. C. & Carr, L. W. 1985 Review of unsteady, driven, separated flows. AIAA paper.Google Scholar
29. Robinson, D. E. 1988 Implementation of a separated flow panel method for wall effects on finite swept wings. Master’s thesis, Department of Aeronautics and Astronautics Engineering, Massachusetts Institute of Technology.Google Scholar
30. Sarpkaya, T. 1975 An inviscid model of two-dimensional vortex shedding for transient and asymptotically steady separated flow over an inclined plate. J. Fluid Mech. 68 (01), 109–128.Google Scholar
31. Sarpkaya, T. & Shoaff, R. L. 1979 An inviscid model of two dimensional vortex shedding for transient and asymptotically steady separated flow over a cylinder. In 17th American Institute of Aeronautics and Astronautics, Aerospace Sciences Meeting, New Orleans, LA.Google Scholar
32. Satyanarayana, B. & Davis, S. 1978 Experimental studies of unsteady trailing-edge conditions. AIAA J. 16, 125–129.Google Scholar
33. Shukla, R. K. & Eldredge, J. D. 2007 An inviscid model for vortex shedding from a deforming body. Theor. Comput. Fluid Dyn. 21 (5), 343–368.Google Scholar
34. Stratford, B. S. 1959 The prediction of separation of the turbulent boundary layer. J. Fluid Mech. 5 (01), 1–16.CrossRefGoogle Scholar
35. Streitlien, K. & Triantafyllou, M. S. 1995 Force and moment on a joukowski profile in the presence of point vortices. AIAA J. 33 (4), 603–610.Google Scholar
36. Taneda, S. 1977 Visual study of unsteady separated flows around bodies. Prog. Aeronaut. Sci. 17, 287–348.Google Scholar
37. Theodorsen, T. 1935 General Theory of Aerodynamic Instability and the Mechanism of Flutter. National Advisory Committee for Aeronautics.Google Scholar
38. Triantafyllou, M. S. & Triantafyllou, G. S. 1995 An efficient swimming machine. Sci. Am. 272 (3), 64–71.Google Scholar
39. Visbal, M. R. 1991 On the formation and control of the dynamic stall vortex on a pitching airfoil. AIAA Paper 91-0006.Google Scholar
40. Wang, Z. J. 2000 Vortex shedding and frequency selection in flapping flight. J. Fluid Mech. 410, 323–341.Google Scholar
41. Yao, Z. X. & Liu, D. D. 1998 Vortex dynamics of blade–blade interaction. AIAA J. 36 (4).CrossRefGoogle Scholar
42. Zhu, Q. & Peng, Z. 2009 Mode coupling and flow energy harvesting by a flapping foil. Phys. Fluids 21, 033601.Google Scholar
43. Zhu, Q., Wolfgang, M. J., Yue, D. K. P. & Triantafyllou, M. S. 2002 Three-dimensional flow structures and vorticity control in fish-like swimming. J. Fluid Mech. 468, 1–28.Google Scholar