Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T10:04:23.115Z Has data issue: false hasContentIssue false
  • English
  • Français

Aerodynamic response of a bristled wing in gusty flow

Published online by Cambridge University Press:  19 February 2021

Seung Hun Lee  and
Daegyoum Kim Open the ORCID record for Daegyoum Kim [Opens in a new window]
Seung Hun Lee
Affiliation:
Department of Mechanical Engineering, KAIST, Daejeon34141, Republic of Korea
Daegyoum Kim*
Affiliation:
Department of Mechanical Engineering, KAIST, Daejeon34141, Republic of Korea
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Some microscopic flying insects have evolved bristled wings. In the low-Reynolds-number regime they reside in, these porous wings perform like membranous wings because the virtual fluid barriers formed by strong viscous diffusion effectively block the gaps between bristles. In this study, the unsteady aerodynamic responses of a two-dimensional bristled wing to a single intermittent head-on gust are investigated numerically for a wide range of the Reynolds number, gust profile and gap width between the bristles. A comparison of a bristled wing with a corresponding flat wing shows that the gap flow alleviates the undesired aerodynamic loading induced by gusts. The Womersley number, which represents the ratio of the gap width to the length scale of unsteady viscous diffusion, is introduced to better characterize the unsteady drag and lift acting on the bristled wing. Under various model conditions, unsteady drag asymptotically converges beyond a specific value of the Womersley number, and unsteady lift exhibits peak values in a limited range of the Womersley number. Because of the linear property of the low-Reynolds-number flow, the unsteady force induced by the intermittent gusty flow is independent of the steady force produced by the basic steady and uniform free stream. For a large Womersley number, the aerodynamic interaction between the bristles is weak under a gusty flow, and thus the unsteady drag and lift forces can be analytically predicted, using the linear superposition approach of the velocity vector perturbed by a single isolated bristle.

JFM classification

Biological Fluid Dynamics: Swimming/flying
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 913 , 25 April 2021 , A4
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.)

References

REFERENCES

Barta, E. 2011 Motion of slender bodies in unsteady Stokes flow. J. Fluid Mech. 688, 66–87.CrossRefGoogle Scholar
Barta, E. & Weihs, D. 2006 Creeping flow arond a finite row of slender bodies in close proximity. J. Fluid Mech. 551, 1–17.CrossRefGoogle Scholar
Birch, J.M. & Dickinson, M.H. 2003 The influence of wing-wake interactions on the production of aerodynamic forces in flapping flight. J. Expl Biol. 206, 2257–2272.CrossRefGoogle ScholarPubMed
Bomphrey, R.J., Nakata, T., Phillips, N. & Walker, S.M. 2017 Smart wing rotation and trailing-edge vortices enable high frequency mosquito flight. Nature 544, 92–95.CrossRefGoogle ScholarPubMed
Cheer, A.Y.L. & Koehl, M.A.R. 1987 Paddles and rakes: fluid flow through bristles appendages of small organisms. J. Theor. Biol. 129, 17–39.CrossRefGoogle Scholar
Cheng, X. & Sun, M. 2018 Very small insects use novel wing flapping and drag principle to generate the weight-supporting vertical force. J. Fluid Mech. 855, 646–670.CrossRefGoogle Scholar
Combes, S.A. & Dudley, R. 2009 Turbulence-driven instabilities limit insect flight peformance. Proc. Natl Acad. Sci. USA 106, 9105–9108.CrossRefGoogle Scholar
Cummins, C., Seale, M., Macente, A., Certini, D., Mastropaolo, E., Viola, I.M. & Nakayama, N. 2018 A separated vortex ring underlies the flight of the dandelion. Nature 562 (7727), 414–418.CrossRefGoogle ScholarPubMed
Davidi, G. & Weihs, D. 2012 Flow around a comb wing in low-Reynolds-number flow. AIAA J. 50, 249–253.CrossRefGoogle Scholar
Dickinson, M.H., Farley, C.T., Full, R.J., Koehl, M.A.R., Kram, R. & Lehman, S. 2000 How animals move: an integrateive view. Science 288, 100–106.CrossRefGoogle ScholarPubMed
Dickinson, M.H., Lehmann, F.-O. & Sane, S.P. 1999 Wing rotation and the aerodynamic basis of insect flight. Science 284, 1954–1960.CrossRefGoogle ScholarPubMed
Ellington, C.P., vanden Berg, C., Willmott, A.P. & Thomas, A.L.R. 1996 Leading-edge vortices in insect flight. Nature 384, 626–630.CrossRefGoogle Scholar
George, P. Jr. & Huber, J.T. 2011 A new genus of fossil Mymaridae (Hymenoptera) from Cretaceous amber and key to Cretaceous mymarid genera. Zookeys 130, 461–472.Google Scholar
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics. Martin Nijhoff.Google Scholar
Huber, J.T. & Noyes, J.S. 2013 A new genus and species of fairyfly, Tinkerbella nana (Hymenoptera, Mymaridae), with comments on its sister genus Kikiki, and discussion on small size limits in arthropods. J. Hymenopt. Res. 32, 17–44.CrossRefGoogle Scholar
Humphrey, J.A.C., Devarakonda, R., Iglesias, I. & Barth, F.G. 1993 Dynamics of arthropod filiform hairs. I. Mathmetical modelling of the hair and air motions. Phil. Trans. R. Soc. Lond. B 340, 423–444.Google Scholar
Jones, S.K., Yun, Y.J.J., Hedrick, T.L., Griffith, B.E. & Miller, L.A. 2016 Bristles reduce the force required to ‘fling’ wings apart in the smallest insects. J. Expl Biol. 219, 3759–3772.CrossRefGoogle ScholarPubMed
Kasoju, V.T., Terrill, C.L., Ford, M.P. & Santhanakrishnan, A. 2018 Leaky flow through simplified physical models of bristled wings of tiny insects during clap and fling. Fluids 3, 44.CrossRefGoogle Scholar
Kim, D. & Gharib, M. 2011 Characteristics of vortex formation and thrust performance in drag-based paddling propulsion. J. Expl Biol. 214, 2283–2291.CrossRefGoogle ScholarPubMed
Lange, C.F., Durst, F. & Breuer, M. 1998 Momentum and heat transfer from cylinders in laminar crossflow at $10^{-4} \leqslant Re \leqslant 200$. Intl J. Heat Mass Transfer 41, 3409–3430.CrossRefGoogle Scholar
Lee, S.H. & Kim, D. 2017 Aerodynamics of a translating comb-like plate inspired by a fairyfly wing. Phys. Fluids 29, 081902.CrossRefGoogle Scholar
Lee, S.H., Lahooti, M. & Kim, D. 2018 Aerodynamic characteristics of unsteady gap flow in a bristled wing. Phys. Fluids 30, 071901.CrossRefGoogle Scholar
Lee, S.H., Lee, M. & Kim, D. 2020 Optimal configuration of a two-dimensional bristled wing. J. Fluid Mech. 888, A23.CrossRefGoogle Scholar
Lin, X.W., Bearman, P.W. & Graham, J.M.R. 1996 A numerical study of oscillatory flow about a circular cylinder for low values of beta parameter. J. Fluids Struct. 10, 501–526.CrossRefGoogle Scholar
Loudon, C. & Tordesillas, A. 1998 The use of the dimensionless Womersley number to characterize the unsteady nature of internal flow. J. Theor. Biol. 191, 63–78.CrossRefGoogle ScholarPubMed
Lovalenti, P.M. & Brady, J.F. 1993 The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number. J. Fluid Mech. 256, 561–605.CrossRefGoogle Scholar
Lyu, Y.Z., Zhu, H.J. & Sun, M. 2019 Flapping-mode changes and aerodynamic mechanisms in miniature insects. Phys. Rev. E 99, 012419.CrossRefGoogle ScholarPubMed
Maxey, M.R. & Riley, J.J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883.CrossRefGoogle Scholar
Nawroth, J.C., Feitl, K.E., Colin, S.P., Costello, J.H. & Dabiri, J.O. 2010 Phenotypic plasticity in juvenile jellyfish medusae facilitates effective animal-fluid interaction. Biol. Lett. 6, 389–393.CrossRefGoogle ScholarPubMed
Ortega-Jimenez, V.M., Sapir, N., Wold, M., Variano, E.A. & Dudley, R. 2014 Into turbulent air: size-dependent effects of von Karman vortex streets on hummingbird flight kinematics and energetics. Proc. R. Soc. Lond. B 281, 20140180.Google Scholar
Ristroph, L., Bergou, A.J., Ristroph, G., Coumes, K., Berman, G.J., Guckenheimer, J., Wang, Z.J. & Cohen, I. 2010 Discovering the flight autostabilizer of fruit flies by inducing aerial stumbles. Proc. Natl Acad. Sci. USA 107, 4820–4824.CrossRefGoogle ScholarPubMed
Santhanakrishnan, A., Robinson, A.K., Jones, S., Lowe, A., Gadi, S., Hedrick, T.L. & Miller, L.A. 2014 Clap and fling mechanism with interacting porous wings in tiny insect flight. J. Expl Biol. 217, 3898–3909.CrossRefGoogle ScholarPubMed
Stokes, G.G. 1851 On the effect of the internal friction of fluids on the motion of pendulums. Trans. Camb. Phil. Soc. 9, 8.Google Scholar
Sun, M. & Xiong, Y. 2005 Dynamic flight stability of a hovering bumblebee. J. Expl Biol. 208, 447–459.CrossRefGoogle ScholarPubMed
Sunada, S., Takashima, H., Hattori, T., Yasuda, K. & Kawachi, K. 2002 Fluid-dynamic characteristics of a bristled wing. J. Expl Biol. 205, 2737–2744.Google ScholarPubMed
Taylor, G.K. & Krapp, H.G. 2007 Sensory systems and flight stability: what do insects measure and why? Adv. Insect Physiol. 34, 231–316.CrossRefGoogle Scholar
Tomotika, S. & Aoi, T. 1951 An expansion formula for the drag on a circular cylinder moving through a viscous fluid at small Reynolds numbers. Q. J. Mech. Appl. Maths 4, 401–406.CrossRefGoogle Scholar
Weihs, D. & Barta, E. 2008 Comb wings for flapping flight at extremely low Reynolds numbers. AIAA J. 46, 285–288.CrossRefGoogle Scholar
Womersley, J.R. 1955 Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J. Physiol. 127, 553–563.CrossRefGoogle ScholarPubMed
Zussman, E., Yarin, A.L. & Weihs, D. 2002 A micro-aerodynamic decelerator based on permeable surfaces of nanofiber mats. Exp. Fluids 33, 315–320.CrossRefGoogle Scholar

Lee and Kim supplementary movie 1

Movie 1 for figures 5(a,b)

Download Lee and Kim supplementary movie 1(Video)
Video 352.2 KB

Lee and Kim supplementary movie 2

Movie 2 for figures 8(a,b)

Download Lee and Kim supplementary movie 2(Video)
Video 255.2 KB