Abstract
Flying and marine animals often use flapping wings or tails to generate thrust. In this paper, we will use the simplest flapping model with a sinusoidal pitching motion over a range of frequency and amplitude to investigate the mechanism of thrust generation. Previous work focuses on the Karman vortex street and the reversed Karman vortex street but the transition between two states remains unknown. The present numerical simulation provides a complete scenario of flow patterns from the Karman vortex street to reversed Karman vortex street via aligned vortices and the ultimate state is the deflected Karman vortex street, as the parameters of flapping motions change. The results are in agreement with the previous experiment. We make further discussion on the relationship of the observed states with drag and thrust coefficients and explore the mechanism of enhanced thrust generation using flapping motions.
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Anderson, J.M., Streitlien, K., Barrett, D.S., et al.: Oscillating foils of high propulsive efficiency. J. Fluid Mech. 360, 4–72 (1998)
Buchholz, J.H.J., Smits, A.J.: On the evolution of the wake structure produced by a low-aspect-ratio pitching panel. J. Fluid Mech. 546, 43–443 (2006)
Buchholz, J.H.J., Smits, A.J.: The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel. J. Fluid Mech. 603, 331–365 (2008)
Couder, Y., Basdevant, C.: Experimental and numerical study of vortex couples in two dimensional flows. J. Fluid Mech. 173, 225–251 (1986)
von Ellenrieder, K.D., Parker, K., Soria, J.: Flow structures behind a heaving and pitching finite-span wing. J. Fluid Mech. 490, 129–138 (2003)
von Ellenrieder, K.D., Pothos, S.: PIV measurements of the asymmetric wake of a two dimensional heaving hydrofoil. Exp. Fluids 44, 733–745 (2008)
Knoller, R.: Die Gesetze des Luftwiderstandes. Flug- und Motor-technik (Wien). 3, 1–7 (1909)
Betz, A.: Ein Beitrag zur Erklärung des Segelfluges. Zeitschrift fur Flugtechnik und Motorluftschiffahrt 3, 269–272 (1912)
von Karman, T., Burgers, J.M.: General Aerodynamic Theory Perfect Fluids, Aerodynamic Theory. Durand, W. F. edn. Division E 2, Julius-Springer, Berlin (1943)
Bohl, D.G., Koochesfahani, M.M.: MTV measurements of the vertical field in the wake of an airfoil oscillating at high reduced frequency. J. Fluid Mech. 620, 63–88 (2009)
von Ellenrieder, K.D., Parker, K., Soria, J.: Fluid mechanics of flapping wings. Experimental Thermal and Fluid Science 32, 1578–1589 (2008)
Wolfgang, M.J., Anderson, J.M., Grosenbaugh, M.A., et al.: Near-body flow dynamics in swimming fish. J. Exp. Biol. J. Exp. Biol. 202, 2303–2307 (1999)
Drucker, E.G., Lauder, G.V.: Locomotor function of the dorsal fin in teleost fishes: Experimental analysis of wake forces in sunfish. J. Exp. Biol. 204, 2943–2958 (2001)
Koochesfahani, M.M.: Vortical patterns in the wake of an oscillating airfoil. AIAA J. 27, 1200–1205 (1989)
Gopalkrishnan, R., Triantafyllou, M.S., Triantafyllou, G.S., et al.: Active vorticity control in a shear-flow using a flapping foil. J. Fluid Mech. 274, 1–21 (1994)
Jones, K.D., Dohring, C.M., Platzer, M.F.: An experimental and computational investigation of the Knoller-Betz effect. AIAA J. 36, 1240–1246 (1998)
Molina, J., Zhang, X., Angland, D.: On the unsteady motion and stability of a heaving airfoil in ground effect. Acta Mech. Sin. 27, 164–178 (2011)
Shyy, W., Liang, Y., Tang, J., et al.: Computational aerodynamics of low Reynolds number plunging, pitching and flexible wings. Acta Mech. Sin. 24, 351–373 (2008)
Dong, G.J., Lu, X.Y.: Numerical analysis on the propulsive performance and vortex shedding of fish-like traveling wavy plate. Int. J. Numer. Meth. Fluids 49, 1351–1373 (2005)
Sun, M., Wang, J.K., Xiong, Y.: Dynamic flight stability of hovering insects. Acta Mech. Sin. 23, 231–246 (2007)
Wu, J.H., Sun, M.: Unsteady aerodynamic forces of a flapping wing. J. Exp. Biol. 207, 1137–1150 (2004)
Godoy-Diana, R., Aider, J.L., Wesfreid, J.E.: Transitions in the wake of a flapping foil. Physical Review E 77 (2008)
Mittal, R., Iaccarino, G.: Immersed boundary methods. Annual Review of Fluid Mechanics 37, 239–261 (2005)
Kim, J., Kim, D., Choi, H.: An immersed-boundary finitevolume method for simulations of flow in complex geometries. J. Comp. Phys. 171, 132–150 (2001)
Su, S.W., Lai, M.C., Lin, C.A.: An immersed boundary technique for simulating complex flows with rigid boundary. Computers and Fluids 36, 313–324 (2007)
Yang, X.L., He, G.W., Zhang, X.: Large-eddy simulation of flows past a flapping airfoil using immersed boundary method. Science China Physics, Mechanics and Astronomy 53, 1101–1108 (2010)
Yang, X.L., Zhang, X., Li, Z.L., et al.: A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations. Journal of Computational Physics 228, 7821–7836 (2009)
Ravoux, J.F., Nadim, A., Haj-Hariri H.: An embedding method for bluff body flows: Interactions of two side-by-side cylinder wakes. Theoret. Comput. Fluid Dynamics 16, 433–466 (2003)
Dutsch, H., Durst, F., Becker, S., et al.: Low-Reynolds-number flow around an oscillating circular cylinder at low Keulegan-Carpenter numbers. J. Fluid Mech. 360, 249–271 (1998)
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The project was supported by the Natural Science Foundation of Jiangxi Province (2010GZC0162).
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He, GY., Wang, Q., Zhang, X. et al. Numerical analysis on transitions and symmetry-breaking in the wake of a flapping foil. Acta Mech Sin 28, 1551–1556 (2012). https://doi.org/10.1007/s10409-012-0158-8
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DOI: https://doi.org/10.1007/s10409-012-0158-8