Hostname: page-component-7dd5485656-g8tfn Total loading time: 0 Render date: 2025-10-31T05:57:16.799Z Has data issue: false hasContentIssue false
  • English
  • Français

Scaling laws for the propulsive performance of a purely pitching foil in ground effect

Published online by Cambridge University Press:  20 May 2021

Amin Mivehchi Open the ORCID record for Amin Mivehchi [Opens in a new window] ,
Qiang Zhong Open the ORCID record for Qiang Zhong [Opens in a new window] ,
Melike Kurt Open the ORCID record for Melike Kurt [Opens in a new window] ,
Daniel B. Quinn Open the ORCID record for Daniel B. Quinn [Opens in a new window]  and
Keith W. Moored Open the ORCID record for Keith W. Moored [Opens in a new window]
Amin Mivehchi*
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
Qiang Zhong
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22094, USA
Melike Kurt
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
Daniel B. Quinn
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22094, USA Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22904, USA
Keith W. Moored
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
*
†Email address for correspondence: mivehchi@lehigh.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Scaling laws for the thrust production and power consumption of a purely pitching hydrofoil in ground effect are presented. For the first time, ground-effect scaling laws based on physical insights capture the propulsive performance over a wide range of biologically relevant Strouhal numbers, dimensionless amplitudes and dimensionless ground distances. This is achieved by advancing previous scaling laws (Moored & Quinn (AIAA J., 2018, pp. 1–15)) with physics-driven modifications to the added mass and circulatory forces to account for ground distance variations. The key physics introduced are the increase in the added mass of a foil near the ground and the reduction in the influence of a wake-vortex system due to the influence of its image system. The scaling laws are found to be in good agreement with new inviscid simulations and viscous experiments, and can be used to accelerate the design of bio-inspired hydrofoils that oscillate near a ground plane or two out-of-phase foils in a side-by-side arrangement.

JFM classification

Biological Fluid Dynamics: Swimming/flying Biological Fluid Dynamics: Propulsion

Information

Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 919 , 25 July 2021 , R1
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

‡

Present address: Aerodynamics and Flight Mechanics Group, Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, UK.

References

REFERENCES

Ayancik, F., Zhong, Q., Quinn, D.B., Brandes, A., Bart-Smith, H. & Moored, K.W. 2019 Scaling laws for the propulsive performance of three-dimensional pitching propulsors. J. Fluid Mech. 871, 1117–1138.CrossRefGoogle Scholar
Blake, R.W. 1983 Mechanics of gliding in birds with special reference to the influence of the ground effect. J. Biomech. 16 (8), 649–654.CrossRefGoogle ScholarPubMed
Blevins, E. & Lauder, G.V. 2013 Swimming near the substrate: a simple robotic model of stingray locomotion. Bioinspir. Biomim. 8 (1), 016005.CrossRefGoogle ScholarPubMed
Brennen, C.E. 1982 A review of added mass and fluid inertial forces. Tech. Rep. CR 82.010. Naval Civil Engineering Laboratory.Google Scholar
Dai, L., He, G. & Zhang, X. 2016 Self-propelled swimming of a flexible plunging foil near a solid wall. Bioinspir. Biomim. 11 (4), 046005.CrossRefGoogle Scholar
Dewey, P.A., Boschitsch, 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, 29–46.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Floryan, D., Van Buren, T., Rowley, C.W. & Smits, A.J. 2017 Scaling the propulsive performance of heaving and pitching foils. J. Fluid Mech. 822, 386–397.CrossRefGoogle Scholar
Garrick, I.E. 1936 Propulsion of a flapping and oscillating airfoil. NACA Tech. Rep. 567.Google Scholar
Iosilevskii, G. 2008 Asymptotic theory of an oscillating wing section in weak ground effect. Eur. J. Mech. B/Fluids 27 (4), 477–490.CrossRefGoogle Scholar
von Kármán, T.H. & Sears, W.R. 1938 Airfoil theory for non-uniform motion. J. Aeronaut. Sci. 5 (10), 379–390.CrossRefGoogle Scholar
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, 151–157.CrossRefGoogle Scholar
Krasny, R. 1986 Desingularization of periodic vortex sheet roll-up. J. Comput. Phys. 65, 292–313.CrossRefGoogle Scholar
Kurt, M., Cochran-Carney, J., Zhong, Q., Mivehchi, A., Quinn, D.B. & Moored, K.W. 2019 Swimming freely near the ground leads to flow-mediated equilibrium altitudes. J. Fluid Mech. 875, R1.CrossRefGoogle Scholar
Mivehchi, A., Dahl, J. & Licht, S. 2016 Heaving and pitching oscillating foil propulsion in ground effect. J. Fluids Struct. 63, 174–187.CrossRefGoogle Scholar
Moored, K.W. 2018 Unsteady three-dimensional boundary element method for self-propelled bio-inspired locomotion. Comput. Fluids 167, 324–340.CrossRefGoogle Scholar
Moored, K.W. & Quinn, D.B. 2018 Inviscid scaling laws of a self-propelled pitching airfoil. AIAA J. 57 (9), 1–15.Google Scholar
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), 393–402.CrossRefGoogle Scholar
Park, S.G., Kim, B. & Sung, H.J. 2017 Hydrodynamics of a self-propelled flexible fin near the ground. Phys. Fluids 29 (5), 051902.CrossRefGoogle Scholar
Perkins, M., Elles, D., Badlissi, G., Mivehchi, A., Dahl, J. & Licht, S. 2017 Rolling and pitching oscillating foil propulsion in ground effect. Bioinspir. Biomim. 13 (1), 016003.CrossRefGoogle ScholarPubMed
Quinn, D.B., Lauder, G.V. & Smits, A.J. 2014 a Flexible propulsors in ground effect. Bioinspir. Biomim. 9 (3), 036008.CrossRefGoogle ScholarPubMed
Quinn, D.B., Lauder, G.V. & Smits, A.J. 2014 b Scaling the propulsive performance of heaving flexible panels. J. Fluid Mech. 738, 250–267.CrossRefGoogle Scholar
Quinn, D.B., Moored, K.W., Dewey, P.A. & Smits, A.J. 2014 c Unsteady propulsion near a solid boundary. J. Fluid Mech. 742, 152–170.CrossRefGoogle Scholar
Senturk, U. & Smits, A.J. 2019 Reynolds number scaling of the propulsive performance of a pitching airfoil. AIAA J. 57 (7), 2663–2669.CrossRefGoogle Scholar
Tanida, Y. 2001 Ground effect in flight. JSME Intl J. Ser. B Fluids Thermal Engng 44 (4), 481–486.CrossRefGoogle Scholar
Theodorsen, T. 1935 General theory of aerodynamic instability and the mechanism of flutter. NACA Tech. Rep. 496.Google Scholar
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), 97–108.CrossRefGoogle Scholar
Webb, P.W. 2002 Kinematics of plaice, Pleuronectes platessa, and cod, Gadus morhua, swimming near the bottom. J. Expl Biol. 205 (14), 2125–2134.CrossRefGoogle Scholar
Zhang, C., Huang, H. & Lu, X.-Y. 2017 Free locomotion of a flexible plate near the ground. Phys. Fluids 29 (4), 041903.CrossRefGoogle Scholar