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Unsteady propulsion near a solid boundary

  • Daniel B. Quinn (a1), Keith W. Moored (a2), Peter A. Dewey (a1) and Alexander J. Smits (a1) (a3)


Experimental and computational results are presented on an aerofoil undergoing pitch oscillations in ground effect, that is, close to a solid boundary. The time-averaged thrust is found to increase monotonically as the mean position of the aerofoil approaches the boundary while the propulsive efficiency stays relatively constant, showing that ground effect can enhance thrust at little extra cost for a pitching aerofoil. Vortices shed into the wake form pairs rather than vortex streets, so that in the mean a momentum jet is formed that angles away from the boundary. The time-averaged lift production is found to have two distinct regimes. When the pitching aerofoil is between 0.4 and 1 chord lengths from the ground, the lift force pulls the aerofoil towards the ground. In contrast, for wall proximities between 0.25 and 0.4 chord lengths, the lift force pushes the aerofoil away from the ground. Between these two regimes there is a stable equilibrium point where the time-averaged lift is zero and thrust is enhanced by approximately 40 %.


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Baudinette, R. V. & Schmidt-Nielsen, K. 1974 Energy cost of gliding flight in herring gulls. Nature 248, 8384.
Betz, A. 1912 Ein beitrag zur erklaerung des segelfluges. Z. Flugtech. Motorluftschiff. 3, 269270.
Blake, R. W. 1979 The energetics of hovering in the mandarin fish (Synchropus picturatus). J. Expl Biol. 82, 2533.
Blevins, E. & Lauder, G. V. 2012 Rajiform locomotion: three-dimensional kinematics of the pectoral fin surface during swimming by freshwater stingrey Potamotrygon orbignyi. J. Expl Biol. 215, 32313241.
Blevins, E. & Lauder, G. V. 2013 Swimming near the substrate: a simple robotic model of stingrey locomotion. Bioinspir. Biomim. 8, 016005.
Buchholz, J. H. J. & Smits, A. J. 2008 The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel. J. Fluid Mech. 603, 331365.
Coulliette, C. & Plotkin, A. 1996 Airfoil ground effect revisited. Aeronautical Journal 100 (992), 6574.
Dewey, P. A., Boschitch, B. M., Moored, K. W., Stone, H. A. & Smits, A. J. 2013 Scaling laws for the thrust production of flexible pitching panels. J. Fluid Mech. 732, 2946.
Drucker, E. G. & Lauder, G. V. 2001 Locomotor function of the dorsal fin in teleost fishes: experimental analysis of wake forces in sunfish. J. Expl Biol. 204, 29432958.
Godoy-Diana, R., Marais, C., Aider, J. & Wesfreid, J. E. 2009 A model for the symmetry breaking of the reverse Bénard–von Kármán vortex street produced by a flapping foil. J. Fluid Mech. 622, 2332.
Hainsworth, F. R. 1988 Induced drag savings from ground effect and formation flight in brown pelicans. J. Expl Biol. 135, 431434.
Iosilevskii, G. 2008 Asymptotic theory of an oscillating wing section in weak ground effect. Eur. J. Mech. 27, 477490.
Kang, C. K., Aono, H., Baik, Y. S., Bernal, L. P. & Shyy, W. 2013 Fluid dynamics of pitching and plunging flat plate at intermediate Reynolds numbers. AIAA J. 51 (2), 315329.
Katz, J. & Plotkin, A. 2001 Low-Speed Aerodynamics. 13th edn. Cambridge University Press.
Knoller, R. 1909 Die gesetze des luftwiderstandes. Flug- Motortech. 3 (21), 17.
Krasny, R. 1986 Desingularization of periodic vortex sheet roll-up. J. Comput. Phys. 65 (2), 292313.
Liu, P., Wang, T., Huang, G., Veitch, B. & Millan, J. 2010 Propulsion characteristics of wing-in-ground effect dual-foil propulsors. Appl. Ocean Res. 32, 103112.
Molina, J. & Zheng, X. 2011 Aerodynamics of a heaving aerofoil in ground effect. AIAA J. 49, 11681179.
Moryossef, Y. & Levy, Y. 2004 Effect of oscillations on aerofoils in close proximity to the ground. AIAA J. 42, 17551764.
Pan, Y., Dong, X., Zhu, Q. & Yue, D. K. 2012 Boundary-element method for the prediction of performance of flapping foils with leading-edge separation. J. Fluid Mech. 698, 446467.
Park, H. & Choi, H. 2010 Aerodynamic characteristics of flying fish in gliding flight. J. Expl Biol. 213, 32693279.
Rozhdestvensky, K. V. 2006 Wing-in-ground effect vehicles. Prog. Aerosp. Sci. 42, 211283.
Schnipper, T., Andersen, A. & Bohr, T. 2009 Vortex wakes of a flapping foil. J. Fluid Mech. 633, 411423.
Sciacchitano, A., Wieneke, B. & Scarano, F. 2013 PIV uncertainty quantification by image matching. Meas. Sci. Technol. 24 (045302).
Stanislas, M., Okamoto, K., Kahler, C. J. & Westerweel, J. 2005 Main results of the second international PIV challenge. Exp. Fluids 39, 170191.
Tanida, Y. 2001 Ground effect in flight. JSME 44, 481486.
Theodorsen, T. 1935 General theory of aerodynamic instability and the mechanism of flutter. Tech. Rep. National Advisory Committee for Aeronautics.
van de Vooren, A. I. & de Jong, L. S. 1970 Calculation of incompressible flow about aerofoils using source, vortex or doublet distributions. Tech. Rep. Math. Inst. of the University of Groningen, The Netherlands.
Webb, P. W. 1993 The effect of solid and porous channel walls on steady swimming of stealhead trout, Oncorhynchus mykiss. J. Expl Biol. 178, 97108.
Wie, S. Y., Lee, S. & Lee, D. J. 2009 Potential panel and time-marching free-wake coupling analysis for helicopter rotor. J. Aircraft 46 (3), 10301041.
Willis, D. J., Peraire, J. & White, J. K. 2007 A combined PFFT-multipole tree code, unsteady panel method with vortex particle wakes. Intl J. Numer. Meth. Fluids 53 (8), 13991422.
Withers, P. C. & Timko, P. L. 1977 The significance of ground effect to the aerodynamic cost of flight and energetics of the black skimmer (Rhyncops nigra). J. Expl Biol. 70, 1326.
Zhu, Q. 2007 Numerical simulation of a flapping foil with chordwise or spanwise flexibility. AIAA J. 45 (10), 24482457.
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