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Rotational accelerations stabilize leading edge vortices on revolving fly wings.
J Exp Biol. 2009 Aug; 212(Pt 16):2705-19.JE

Abstract

The aerodynamic performance of hovering insects is largely explained by the presence of a stably attached leading edge vortex (LEV) on top of their wings. Although LEVs have been visualized on real, physically modeled, and simulated insects, the physical mechanisms responsible for their stability are poorly understood. To gain fundamental insight into LEV stability on flapping fly wings we expressed the Navier-Stokes equations in a rotating frame of reference attached to the wing's surface. Using these equations we show that LEV dynamics on flapping wings are governed by three terms: angular, centripetal and Coriolis acceleration. Our analysis for hovering conditions shows that angular acceleration is proportional to the inverse of dimensionless stroke amplitude, whereas Coriolis and centripetal acceleration are proportional to the inverse of the Rossby number. Using a dynamically scaled robot model of a flapping fruit fly wing to systematically vary these dimensionless numbers, we determined which of the three accelerations mediate LEV stability. Our force measurements and flow visualizations indicate that the LEV is stabilized by the ;quasi-steady' centripetal and Coriolis accelerations that are present at low Rossby number and result from the propeller-like sweep of the wing. In contrast, the unsteady angular acceleration that results from the back and forth motion of a flapping wing does not appear to play a role in the stable attachment of the LEV. Angular acceleration is, however, critical for LEV integrity as we found it can mediate LEV spiral bursting, a high Reynolds number effect. Our analysis and experiments further suggest that the mechanism responsible for LEV stability is not dependent on Reynolds number, at least over the range most relevant for insect flight (100<Re<14,000). LEVs are stable and continue to augment force even when they burst. These and similar findings for propellers and wind turbines at much higher Reynolds numbers suggest that even large flying animals could potentially exploit LEV-based force augmentation during slow hovering flight, take-offs or landing. We calculated the Rossby number from single-wing aspect ratios of over 300 insects, birds, bats, autorotating seeds, and pectoral fins of fish. We found that, on average, wings and fins have a Rossby number close to that of flies (Ro=3). Theoretically, many of these animals should therefore be able to generate a stable LEV, a prediction that is supported by recent findings for several insects, one bat, one bird and one fish. This suggests that force augmentation through stably attached (leading edge) vortices could represent a convergent solution for the generation of high fluid forces over a quite large range in size.

Authors+Show Affiliations

Experimental Zoology Group, Wageningen University, 6709 PG Wageningen, The Netherlands. david.lentink@wur.nlNo affiliation info available

Pub Type(s)

Journal Article
Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.

Language

eng

PubMed ID

19648415

Citation

Lentink, David, and Michael H. Dickinson. "Rotational Accelerations Stabilize Leading Edge Vortices On Revolving Fly Wings." The Journal of Experimental Biology, vol. 212, no. Pt 16, 2009, pp. 2705-19.
Lentink D, Dickinson MH. Rotational accelerations stabilize leading edge vortices on revolving fly wings. J Exp Biol. 2009;212(Pt 16):2705-19.
Lentink, D., & Dickinson, M. H. (2009). Rotational accelerations stabilize leading edge vortices on revolving fly wings. The Journal of Experimental Biology, 212(Pt 16), 2705-19. https://doi.org/10.1242/jeb.022269
Lentink D, Dickinson MH. Rotational Accelerations Stabilize Leading Edge Vortices On Revolving Fly Wings. J Exp Biol. 2009;212(Pt 16):2705-19. PubMed PMID: 19648415.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Rotational accelerations stabilize leading edge vortices on revolving fly wings. AU - Lentink,David, AU - Dickinson,Michael H, PY - 2009/8/4/entrez PY - 2009/8/4/pubmed PY - 2009/11/6/medline SP - 2705 EP - 19 JF - The Journal of experimental biology JO - J. Exp. Biol. VL - 212 IS - Pt 16 N2 - The aerodynamic performance of hovering insects is largely explained by the presence of a stably attached leading edge vortex (LEV) on top of their wings. Although LEVs have been visualized on real, physically modeled, and simulated insects, the physical mechanisms responsible for their stability are poorly understood. To gain fundamental insight into LEV stability on flapping fly wings we expressed the Navier-Stokes equations in a rotating frame of reference attached to the wing's surface. Using these equations we show that LEV dynamics on flapping wings are governed by three terms: angular, centripetal and Coriolis acceleration. Our analysis for hovering conditions shows that angular acceleration is proportional to the inverse of dimensionless stroke amplitude, whereas Coriolis and centripetal acceleration are proportional to the inverse of the Rossby number. Using a dynamically scaled robot model of a flapping fruit fly wing to systematically vary these dimensionless numbers, we determined which of the three accelerations mediate LEV stability. Our force measurements and flow visualizations indicate that the LEV is stabilized by the ;quasi-steady' centripetal and Coriolis accelerations that are present at low Rossby number and result from the propeller-like sweep of the wing. In contrast, the unsteady angular acceleration that results from the back and forth motion of a flapping wing does not appear to play a role in the stable attachment of the LEV. Angular acceleration is, however, critical for LEV integrity as we found it can mediate LEV spiral bursting, a high Reynolds number effect. Our analysis and experiments further suggest that the mechanism responsible for LEV stability is not dependent on Reynolds number, at least over the range most relevant for insect flight (100<Re<14,000). LEVs are stable and continue to augment force even when they burst. These and similar findings for propellers and wind turbines at much higher Reynolds numbers suggest that even large flying animals could potentially exploit LEV-based force augmentation during slow hovering flight, take-offs or landing. We calculated the Rossby number from single-wing aspect ratios of over 300 insects, birds, bats, autorotating seeds, and pectoral fins of fish. We found that, on average, wings and fins have a Rossby number close to that of flies (Ro=3). Theoretically, many of these animals should therefore be able to generate a stable LEV, a prediction that is supported by recent findings for several insects, one bat, one bird and one fish. This suggests that force augmentation through stably attached (leading edge) vortices could represent a convergent solution for the generation of high fluid forces over a quite large range in size. SN - 0022-0949 UR - https://www.unboundmedicine.com/medline/citation/19648415/Rotational_accelerations_stabilize_leading_edge_vortices_on_revolving_fly_wings_ L2 - http://jeb.biologists.org/cgi/pmidlookup?view=long&amp;pmid=19648415 DB - PRIME DP - Unbound Medicine ER -