Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-23T19:03:07.406Z Has data issue: false hasContentIssue false

Nonlinear fluid damping of elastically mounted pitching wings in quiescent water

Published online by Cambridge University Press:  22 July 2021

Yuanhang Zhu*
Center for Fluid Mechanics, School of Engineering, Brown University, Providence, RI 02912, USA
Varghese Mathai
Department of Physics, University of Massachusetts, Amherst, MA 01003, USA
Kenneth Breuer
Center for Fluid Mechanics, School of Engineering, Brown University, Providence, RI 02912, USA
Email address for correspondence:


We experimentally study the nonlinear fluid damping of a rigid but elastically mounted pitching wing in the absence of a free-stream flow. The dynamics of the elastic mount are simulated using a cyber-physical system. We perturb the wing and measure the fluid damping coefficient from damped oscillations over a large range of pitching frequencies, pitching amplitudes, pivot locations and sweep angles. A universal fluid damping scaling is proposed to incorporate all these parameters. Flow fields obtained using particle image velocimetry are analysed to explain the nonlinear behaviours of the fluid damping.

JFM Rapids
© 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.)



Alben, S. 2008 Optimal flexibility of a flapping appendage in an inviscid fluid. J. Fluid Mech. 614, 355380.CrossRefGoogle Scholar
Beatus, T. & Cohen, I. 2015 Wing-pitch modulation in maneuvering fruit flies is explained by an interplay between aerodynamics and a torsional spring. Phys. Rev. E 92 (2), 022712.CrossRefGoogle Scholar
Bergou, A.J., Xu, S. & Wang, Z.J. 2007 Passive wing pitch reversal in insect flight. J. Fluid Mech. 591, 321337.CrossRefGoogle Scholar
Brennen, C.E. 1982 A review of added mass and fluid inertial forces. Tech. Rep. CR82.010. Naval Civil Engineering Laboratory.Google Scholar
Corke, T.C. & Thomas, F.O. 2015 Dynamic stall in pitching airfoils: aerodynamic damping and compressibility effects. Annu. Rev. Fluid Mech. 47, 479505.CrossRefGoogle Scholar
Corkery, S.J., Babinsky, H. & Graham, W.R. 2019 Quantification of added-mass effects using particle image velocimetry data for a translating and rotating flat plate. J. Fluid Mech. 870, 492518.CrossRefGoogle Scholar
Dowell, E.H., Curtiss, H.C., Scanlan, R.H. & Sisto, F. 1989 A Modern Course in Aeroelasticity. Springer.CrossRefGoogle Scholar
Dugundji, J. 2008 Some aeroelastic and nonlinear vibration problems encountered on the journey to Ithaca. AIAA J. 46 (1), 2135.CrossRefGoogle Scholar
Glauert, H. 1983 The Elements of Aerofoil and Airscrew Theory. Cambridge University Press.CrossRefGoogle Scholar
Kang, C.-K. & Shyy, W. 2014 Analytical model for instantaneous lift and shape deformation of an insect-scale flapping wing in hover. J. R. Soc. Interface 11 (101), 20140933.CrossRefGoogle ScholarPubMed
Keulegan, G.H. & Carpenter, L.H. 1958 Forces on cylinders and plates in an oscillating fluid. J. Res. Natl Bur. Stand. 60 (5), 423440.CrossRefGoogle Scholar
Mathai, V., Loeffen, L.A.W.M., Chan, T.T.K. & Wildeman, S. 2019 Dynamics of heavy and buoyant underwater pendulums. J. Fluid Mech. 862, 348363.CrossRefGoogle Scholar
McCroskey, W.J. 1982 Unsteady airfoils. Annu. Rev. Fluid Mech. 14 (1), 285311.CrossRefGoogle Scholar
Menon, K. & Mittal, R. 2019 Flow physics and dynamics of flow-induced pitch oscillations of an airfoil. J. Fluid Mech. 877, 582613.CrossRefGoogle Scholar
Morison, J.R., Johnson, J.W. & Schaaf, S.A. 1950 The force exerted by surface waves on piles. J. Petrol. Tech. 2 (05), 149154.CrossRefGoogle Scholar
Onoue, K. & Breuer, K.S. 2016 Vortex formation and shedding from a cyber-physical pitching plate. J. Fluid Mech. 793, 229247.CrossRefGoogle Scholar
Onoue, K. & Breuer, K.S. 2017 A scaling for vortex formation on swept and unswept pitching wings. J. Fluid Mech. 832, 697720.CrossRefGoogle Scholar
Rao, S.S. 1995 Mechanical Vibrations. Addison-Wesley.Google Scholar
Ringuette, M.J., Milano, M. & Gharib, M. 2007 Role of the tip vortex in the force generation of low-aspect-ratio normal flat plates. J. Fluid Mech. 581, 453468.CrossRefGoogle Scholar
Shih, C.C. & Buchanan, H.J. 1971 The drag on oscillating flat plates in liquids at low Reynolds numbers. J. Fluid Mech. 48 (2), 229239.CrossRefGoogle Scholar
Shinde, S.Y. & Arakeri, J.H. 2013 Jet meandering by a foil pitching in quiescent fluid. Phys. Fluids 25 (4), 041701.CrossRefGoogle Scholar
Su, Y. & Breuer, K.S. 2019 Resonant response and optimal energy harvesting of an elastically mounted pitching and heaving hydrofoil. Phys. Rev. Fluids 4 (6), 064701.CrossRefGoogle Scholar
Tzezana, G.A. & Breuer, K.S. 2019 Thrust, drag and wake structure in flapping compliant membrane wings. J. Fluid Mech. 862, 871888.CrossRefGoogle Scholar
Wang, Z.J. 2005 Dissecting insect flight. Annu. Rev. Fluid Mech. 37, 183210.CrossRefGoogle Scholar
Xiao, Q. & Zhu, Q. 2014 A review on flow energy harvesters based on flapping foils. J. Fluids Struct. 46, 174191.CrossRefGoogle Scholar
Young, J., Lai, J.C.S. & Platzer, M.F. 2014 A review of progress and challenges in flapping foil power generation. Prog. Aerosp. Sci. 67, 228.CrossRefGoogle Scholar
Zhu, Y., Su, Y. & Breuer, K.S. 2020 Nonlinear flow-induced instability of an elastically mounted pitching wing. J. Fluid Mech. 899, A35.CrossRefGoogle Scholar

Zhu et al. supplementary movie

PIV flow field measurements for an unswept wing undergoing prescribed sinusoidal pitching motions in quiescent water

Download Zhu et al. supplementary movie(Video)
Video 8.8 MB