Abstract
Numerical simulations have been used to analyze the effect that vortices, shed from one flapping foil, have on the thrust of another flapping foil placed directly downstream. The simulations attempt to model the dorsal–tail fin interaction observed in a swimming bluegill sunfish. The simulations have been carried out using a Cartesian grid method that allows us to simulate flows with complex moving boundaries on stationary Cartesian grids. The simulations indicate that vortex shedding from the upstream (dorsal) fin is indeed capable of increasing the thrust of the downstream (tail) fin significantly. Vortex structures shed by the upstream dorsal fin increase the effective angle-of-attack of the flow seen by the tail fin and initiate the formation of a strong leading edge stall vortex on the downstream fin. This stall vortex convects down the surface of the tail and the low pressure associated with this vortex increases the thrust on the downstream tail fin. However, this thrust augmentation is found to be quite sensitive to the phase relationship between the two flapping fins. The numerical simulations allows us to examine in detail, the underlying physical mechanism for this thrust augmentation.
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Long J.H., Joseph S., Nicholas L. and Mathieu K. (2006). Four flippers or two? Tetrapodal swimming with an aquatic robot. Bioinspirat. Biomimet. 1: 20–29
Triantafyllou G.S., Triantafyllou M.S. and Grosenbaugh M.A. (2003). Optimal thrust development in oscillating foils with application to fish propulsion. J. Fluids Structures 7: 205–224
Anderson, J.M., Kerrebrock, P.A.: The vorticity control unmanned undersea vehicle (VCUUV)—An autonomous vehicle employing fish swimming propulsion and maneuvering. In: Proceedings of 10th International Symposium Unmanned Untethered Submersible Technology, NH, 189–195 (1997)
Knoller R. (1909). Die Gesetze des Luftwiderstandes. Flug -und Motortechnik(Wien) 3(21): 1–7
Betz A. (1912). Ein Beitrag zur Erklarung des Segelfluges. Zeitschrift fur Flugtechnik und Motorluftschiffart 3: 269–272
Jones K.D., Dohring C.M. and Platzer M.F. (1998). Experimental and computational investigation of the Knoller Betz effect. Am. Inst. Aeronaut. Astronaut. J. 36(7): 1240–1246
Lighthill, M.J.: Mathematical Biofluiddynamics. Philadelphia: Society for Industrial and Applied Mathematics (1975)
Wu T. (1971). Hydrodynamics of swimming fishes and cetaceans. Advanced Appl Math 11: 1–63
Yates, G.T.: Hydrodynamics of body and caudal fin propulsion. In: Webb, P.W., Weihs, D. (eds.) Fish Biomechanics, pp. 177–213. Praeger, New York (1983)
Weihs D. (1989). Design features and mechanics of axial locomotion in fish. Am. Zool. 29: 151–160
Gopalkrishnan R., Triantafyllou M.S., Triantafyllou G.S. and Barrett D.S. (1994). Active vorticity control in a shear flow using a flapping foil. J. Fluid Mech. 274: 1–21
Tuncer I.H. and Platzer M.F. (1996). Thrust generation due to airfoil flapping. Am. Insit. Aeronaut. Astronaut. J. 34(2): 324–331
Liao J.C., Beal D.N., Lauder G.V. and Triantafyllou M.S. (2003). The Karman gait: novel body kinematics of rainbow trout swimming in a vortex street. J. Exp. Biol. 206: 1059–1073
Drucker E.G. and Lauder G.V. (1999). Locomotor forces on a swimming fish: three-dimensional vortex wake dynamics quantified using digital particle image velocimetry. J. Exp. Biol. 202: 2393–2412
Drucker E.G. and Lauder G.V. (2000). A hydrodynamic analysis of fish swimming speed: wake structure and locomotor force in slow and fast labriform swimmers. J. Exp. Biol. 203: 2379–2393
Drucker E.G. and Lauder G.V. (2001). Locomotor function of the dorsal fin in teleost fishes: experimental analysis of wake forces in sunfish. J. Exp. Biol. 204: 2943–58
Udaykumar H.S., Mittal R. and Shyy W. (1999). Computation of solid liquid phase fronts in the sharp interface limit on fixed grids. J. Comput. Phys. 153: 535
Ye T., Mittal R., UdayKumar H.S. and Shyy W. (1999). An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries. J. Comput. Phys. 156: 209–240
Scardovelli R. and Zaleski S. (1999). Direct numerical simulation of free surface and internal flow. Ann. Rev. Fluid Mech. 31: 567
Mittal R. and Iaccarino G. (2005). Immersed boundary methods. Ann. Rev. Fluid Mech. 37: 239–61
Triantafyllou G.S., Triantafyllou M.S. and Streitlien K. (1996). Efficient foil propulsion through vortex control. Am. Insit. Aeronaut. Astronaut. J. 34(11): 2315–2319
Akhtar, I.: Thrust augmentation through active flow control-lesson from a bluegill sunfish. MS Thesis, The George Washington University, Washington, DC, USA (2003)
Jayne B.C., Lozada A. and Lauder G.V. (1996). Function of the dorsal fin in Bluegill Sunfish: motor patterns during four locomotor behaviors. J. Morphol. 228: 307–326
Lauder G.V. (1989). Caudal fin locomotion in ray-finned fishes: historical and functional analysis. Am. Zool. 29: 85–102
Tytell E.D. (2006). Median fin function in bluegill sunfish, Lepomis macrochirus: streamwise vortex structure during steady swimming. J. Exp. Biol. 209: 1516–1534
Lauder, G.V., Madden, P.G.A., Mittal, R., Dong, H., Bozkurttas, M.: Locomotion with flexible propulsors I: experimental analysis of pectoral fin swimming in sunfish. Bioinspirat. Biomimet. (in press)
Mittal, R., Dong, H., Bozkurttas, M., Lauder, G.V., Madden, P.G.A.: Locomotion with flexible propulsors II: computational modeling and analysis of pectoral fin swimming in a sunfish. Bioinspirat. Biomimet. (in press)
Isogai K., Shinmoto Y. and Watanabe Y. (1999). Effects of dynamic stall on propulsive efficiency and thrust of flapping airfoil. Am. Insit. Aeronaut. Astronaut. J. 37(10): 1145–1151
Ramamurti R., Sandberg W.C. and Löhner R. (2001). Simulation of flow about flapping airfoils using a finite element incompressible flowsolver. Am. Inst. Aeronaut. Astronaut. J. 39(2): 253–260
Mittal R. (2004). Computational modeling in biohydrodynamics: trends, challenges and recent advances. IEEE J. Oceanic Eng. 29: 595–604
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Communicated by M.Y. Hussaini.
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Akhtar, I., Mittal, R., Lauder, G.V. et al. Hydrodynamics of a biologically inspired tandem flapping foil configuration. Theor. Comput. Fluid Dyn. 21, 155–170 (2007). https://doi.org/10.1007/s00162-007-0045-2
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DOI: https://doi.org/10.1007/s00162-007-0045-2