Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T23:33:02.792Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal configuration of a two-dimensional bristled wing

Published online by Cambridge University Press:  07 February 2020

Seung Hun Lee ,
Minhyeong 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
Minhyeong 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

In contrast to common continuous wings, microscopic flying insects such as fairyfly and thrips possess extraordinary wings that comprise several bristles. In the low-Reynolds-number environment inhabited by these insects, a bristled wing benefits from the formation of virtual fluid barriers that prevent flow leakage in the gaps of bristles. In this study, the optimal configuration regarding the aerodynamic performance of simple bristled-wing models is investigated numerically in terms of the Reynolds number and the distance between bristles, which are known to be important parameters for determining the effectiveness of a virtual fluid barrier. Inspired by the inherent characteristics of low-Reynolds-number flow, we provide new insights into the aerodynamics of a bristled wing by using a scaling parameter that combines these two independent parameters: effective gap width. In addition, the force ratio is scaled with the Reynolds number to better characterize the generation of drag and lift by a bristled wing. Despite the Reynolds number and the gap width varying by several orders of magnitude, the scaled drag force converges asymptotically beyond a specific effective gap width, and the lift force ratio has a peak within a very narrow range of the effective gap width. The trend of the lift with the effective gap width is correlated with changes in the asymmetric distributions of pressure and vorticity on the surface of the bristles. In addition, the drag and lift predicted theoretically, by invoking the linear superposition of creeping flows, agree well with numerical results, in particular for large effective gap width.

JFM classification

Biological Fluid Dynamics: Swimming/flying
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 888 , 10 April 2020 , A23
Copyright
© The Author(s), 2020. 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

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 around a finite row of slender bodies in close proximity. J. Fluid Mech. 551, 1–17.CrossRefGoogle Scholar
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
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., 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., van den 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
Imai, I. 1954 A new method of solving Oseen’s equations and its application to the flow past an inclined elliptic cylinder. Proc. R. Soc. Lond. A 224, 141–160.Google Scholar
In, K. M., Choi, D. H. & Kim, M. U. 1995 Two-dimensional viscous flow past a flat plate. Fluid Dyn. Res. 15, 13–24.CrossRefGoogle 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
Khalili, A. & Liu, B. 2017 Stokes’ paradox: creeping flow past a two-dimensional cylinder in an infinite domain. J. Fluid Mech. 817, 374–387.CrossRefGoogle Scholar
Kim, D., Lee, S. H. & Kim, D. 2019 Aerodynamic interaction of collective plates in side-by-side arrangement. Phys. Fluids 31, 071902.CrossRefGoogle Scholar
Koehl, M. A. R. 1996 Small scale fluid dynamics of olfactory antennae. Mar. Freshw. Behav. Physiol. 27, 127–141.CrossRefGoogle Scholar
Koehl, M. A. R., Koseff, J. R., Crimaldi, J. P., McCay, M. G., Cooper, T., Wiley, M. B. & Moore, P. A. 2001 Lobster sniffing: antennule design and hydrodynamic filtering of information in an odor plume. Science 294, 1948–1951.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. & Leal, L. G. 1986 Low-Reynolds-number flow past cylindrical bodies of arbitrary cross-sectional shape. J. Fluid Mech. 164, 401–427.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
Proudman, I. & Pearson, J. R. A. 1957 Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder. J. Fluid Mech. 2, 237–262.CrossRefGoogle Scholar
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
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
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
Umemura, A. 1982 Matched-asymptotic analysis of low-Reynolds-number flow past two equal circular cylinders. J. Fluid Mech. 328, 345–407.CrossRefGoogle Scholar
Van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Parabolic.Google Scholar
Weihs, D. & Barta, E. 2008 Comb wings for flapping flight at extremely low Reynolds numbers. AIAA J. 46, 285–288.CrossRefGoogle Scholar
Weis-Fogh, T. 1973 Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production. J. Expl Biol. 59, 169–230.Google Scholar
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