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Swimming freely near the ground leads to flow-mediated equilibrium altitudes

  • Melike Kurt (a1), Jackson Cochran-Carney (a1), Qiang Zhong (a2), Amin Mivehchi (a1), Daniel B. Quinn (a2) and Keith W. Moored (a1)...

Abstract

Experiments and computations are presented for a foil pitching about its leading edge near a planar, solid boundary. The foil is examined when it is constrained in space and when it is unconstrained or freely swimming in the cross-stream direction. It was found that the foil has stable equilibrium altitudes: the time-averaged lift is zero at certain altitudes and acts to return the foil to these equilibria. These stable equilibrium altitudes exist for both constrained and freely swimming foils and are independent of the initial conditions of the foil. In all cases, the equilibrium altitudes move farther from the ground when the Strouhal number is increased or the reduced frequency is decreased. Potential flow simulations predict the equilibrium altitudes to within 3 %–11 %, indicating that the equilibrium altitudes are primarily due to inviscid mechanisms. In fact, it is determined that stable equilibrium altitudes arise from an interplay among three time-averaged forces: a negative jet deflection circulatory force, a positive quasistatic circulatory force and a negative added mass force. At equilibrium, the foil exhibits a deflected wake and experiences a thrust enhancement of 4 %–17 % with no penalty in efficiency as compared to a pitching foil far from the ground. These newfound lateral stability characteristics suggest that unsteady ground effect may play a role in the control strategies of near-boundary fish and fish-inspired robots.

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Corresponding author

Email address for correspondence: mek514@lehigh.edu

References

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Blake, R. W. 1983 Mechanics of gliding in birds with special reference to the influence of the ground effect. J. Biomech. 16 (8), 649654.10.1016/0021-9290(83)90115-X
Blevins, E. & Lauder, G. V. 2013 Swimming near the substrate: a simple robotic model of stingray locomotion. Bioinspir. Biomim. 8 (1), 016005.10.1088/1748-3182/8/1/016005
Brennen, C. E.1982 A review of added mass and fluid inertial forces. Tech. Rep. CR 82.010. Naval Civil Engineering Laboratory.
Cui, E. & Zhang, X. 2010 Ground effect aerodynamics. In Encyclopedia of Aerospace Engineering. American Cancer Society.
Dai, L., He, G. & Zhang, X. 2016 Self-propelled swimming of a flexible plunging foil near a solid wall. Bioinspir. Biomim. 11 (4), 046005.10.1088/1748-3190/11/4/046005
Fernández-Prats, R., Raspa, V., Thiria, B., Huera-Huarte, F. & Godoy-Diana, R. 2015 Large-amplitude undulatory swimming near a wall. Bioinspir. Biomim. 10 (1), 016003.10.1088/1748-3190/10/1/016003
Godoy-Diana, R., Aider, J.-L. & Wesfreid, J. E. 2008 Transitions in the wake of a flapping foil. Phys. Rev. E 77 (1), 016308.
Hainsworth, F. R. 1988 Induced drag savings from ground effect and formation flight in brown pelicans. J. Expl Biol. 135 (1), 431444.
Iosilevskii, G. 2008 Asymptotic theory of an oscillating wing section in weak ground effect. Eur. J. Mech. (B/Fluids) 27 (4), 477490.10.1016/j.euromechflu.2007.08.005
Katz, J. & Plotkin, A. 2001 Low-speed Aerodynamics, vol. 13. Cambridge University Press.10.1017/CBO9780511810329
Keulegan, G. H. 1958 Forces on cylinders and plates in an oscillating fluid. J. Res. Natl Bur. Stand. 2857, 423440.10.6028/jres.060.043
Kim, B., Park, S. G., Huang, W.-X. & Sung, H. J. 2017 An autonomous flexible propulsor in a quiescent flow. Intl J. Heat Fluid Flow 68, 151157.10.1016/j.ijheatfluidflow.2017.10.006
Krasny, R. 1986 Desingularization of periodic vortex sheet roll-up. J. Comput. Phys. 65, 292313.10.1016/0021-9991(86)90210-X
Mivehchi, A., Dahl, J. & Licht, S. 2016 Heaving and pitching oscillating foil propulsion in ground effect. J. Fluids Struct. 63, 174187.10.1016/j.jfluidstructs.2016.03.007
Moored, K. W. 2018 Unsteady three-dimensional boundary element method for self-propelled bio-inspired locomotion. Comput. Fluids 167, 324340.10.1016/j.compfluid.2018.03.045
Moored, K. W. & Quinn, D. B. 2018 Inviscid scaling laws of a self-propelled pitching airfoil. AIAA J. 0 (0), 115.10.2514/1.J056634
Nowroozi, B. N., Strother, J. A., Horton, J. M., Summers, A. P. & Brainerd, E. L. 2009 Whole-body lift and ground effect during pectoral fin locomotion in the northern spearnose poacher (Agonopsis vulsa). Zoology 112 (5), 393402.10.1016/j.zool.2008.10.005
Pan, Y., Dong, X., Zhu, Q. & Yue, D. K. P. 2012 Boundary-element method for the prediction of performance of flapping foils with leading-edge separation. J. Fluid Mech. 698, 446467.10.1017/jfm.2012.119
Park, H. & Choi, H. 2010 Aerodynamic characteristics of flying fish in gliding flight. J. Expl Biol. 213 (19), 32693279.10.1242/jeb.046052
Park, S. G., Kim, B. & Sung, H. J. 2017 Hydrodynamics of a self-propelled flexible fin near the ground. Phys. Fluids 29 (5), 051902.10.1063/1.4983723
Perkins, M., Elles, D., Badlissi, G., Mivehchi, A., Dahl, J. & Licht, S. 2018 Rolling and pitching oscillating foil propulsion in ground effect. Bioinspir. Biomim. 13, 016003.
Quinn, D. B., Lauder, G. V. & Smits, A. J. 2014a Flexible propulsors in ground effect. Bioinspir. Biomim. 9 (3), 036008.10.1088/1748-3182/9/3/036008
Quinn, D. B., Moored, K. W., Dewey, P. A. & Smits, A. J. 2014b Unsteady propulsion near a solid boundary. J. Fluid Mech. 742, 152170.10.1017/jfm.2013.659
Rayner, J. M. V. 1991 On the aerodynamics of animal flight in ground effect. Phil. Trans. R. Soc. Lond. B 334 (1269), 119128.
Rozhdestvensky, K. V. 2006 Wing-in-ground effect vehicles. Prog. Aerosp. Sci. 42 (3), 211283.10.1016/j.paerosci.2006.10.001
Tanida, Y. 2001 Ground effect in flight. JSME Intl J. Ser. B Fluids Therm. Engng 44 (4), 481486.10.1299/jsmeb.44.481
Van Truong, T., Byun, D., Kim, M. J., Yoon, K. J. & Park, H. C. 2013a Aerodynamic forces and flow structures of the leading edge vortex on a flapping wing considering ground effect. Bioinspir. Biomim. 8 (3), 036007.10.1088/1748-3182/8/3/036007
Van Truong, T., Kim, J., Kim, M. J., Park, H. C., Yoon, K. J. & Byun, D. 2013b Flow structures around a flapping wing considering ground effect. Exp. Fluids 54 (7), 1575.10.1007/s00348-013-1575-6
Webb, P. W. 1993 The effect of solid and porous channel walls on steady swimming of steelhead trout Oncorhynchus mykiss . J. Expl Biol. 178 (1), 97108.
Webb, P. W. 2002 Kinematics of plaice, Pleuronectes platessa, and cod, Gadus morhua, swimming near the bottom. J. Expl Biol. 205 (14), 21252134.
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), 10301041.10.2514/1.40001
Willis, D. J.2006 An unsteady, accelerated, high order panel method with vortex particle wakes. PhD thesis, Massachusetts Institute of Technology.
Zhang, C., Huang, H. & Lu, X.-Y. 2017 Free locomotion of a flexible plate near the ground. Phys. Fluids 29 (4), 041903.10.1063/1.4981778
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