Helical vortices generated by flapping wings of bumblebees

High resolution direct numerical simulations of rotating and flapping bumblebee wings are presented and their aerodynamics is studied focusing on the role of leading edge vortices and the associated helicity production. We first study the flow generated by only one rotating bumblebee wing in circular motion with $45^{\circ}$ angle of attack. We then consider a model bumblebee flying in a numerical wind tunnel, which is tethered and has rigid wings flapping with a prescribed generic motion. The inflow condition of the wind varies from laminar to strongly turbulent regimes. Massively parallel simulations show that inflow turbulence does not significantly alter the wings' leading edge vortex (LEV), which enhances lift production. Finally, we focus on studying the helicity of the generated vortices and analyze their contribution at different scales using orthogonal wavelets.

[1]  J. Kingsbury.  The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance , 2004 .

[2]  C. Ellington.  The novel aerodynamics of insect flight: applications to micro-air vehicles. , 1999, The Journal of experimental biology.

[3]  Philippe Angot,et al.  A penalization method to take into account obstacles in incompressible viscous flows , 1999, Numerische Mathematik.

[4]  R. Betchov.  Semi‐Isotropic Turbulence and Helicoidal Flows , 1961 .

[5]  C. Ellington.  The Aerodynamics of Hovering Insect Flight. I. The Quasi-Steady Analysis , 1984 .

[6]  Adrian L. R. Thomas,et al.  Leading-edge vortices in insect flight , 1996, Nature.

[7]  M. Thompson,et al.  Reynolds number and aspect ratio effects on the leading-edge vortex for rotating insect wing planforms , 2013, Journal of Fluid Mechanics.

[8]  M. Dickinson,et al.  Rotational accelerations stabilize leading edge vortices on revolving fly wings , 2009, Journal of Experimental Biology.

[9]  M. Farge.  Wavelet Transforms and their Applications to Turbulence , 1992 .

[10]  T. Weis-Fogh.  Quick estimates of flight fitness in hovering animals , 1973 .

[11]  Dmitry Kolomenskiy,et al.  Closed-form solution for the edge vortex of a revolving plate , 2016, Journal of Fluid Mechanics.

[12]  K. S. Yeo,et al.  Scaling of Aerodynamic Forces of Three-Dimensional Flapping Wings , 2014 .

[13]  S. Combes,et al.  Rolling with the flow: bumblebees flying in unsteady wakes , 2013, Journal of Experimental Biology.

[14]  Kai Schneider,et al.  FluSI: A Novel Parallel Simulation Tool for Flapping Insect Flight Using a Fourier Method with Volume Penalization , 2015, SIAM J. Sci. Comput..

[15]  P. Lissaman,et al.  Low-Reynolds-Number Airfoils , 1983 .

[16]  Kai Schneider,et al.  Numerical simulation of the transient flow behaviour in chemical reactors using a penalisation method , 2005 .

[17]  F. Lehmann,et al.  Bumblebee Flight in Heavy Turbulence. , 2015, Physical review letters.

[18]  W. Shyy,et al.  Reynolds number and aspect ratio effects on a revolving wing with a sinusoidal motion , 2016 .

[19]  Karen Mulleners,et al.  Characterizing a burst leading-edge vortex on a rotating flat plate wing , 2016 .

[20]  T. Maxworthy.  Experiments on the Weis-Fogh mechanism of lift generation by insects in hovering flight. Part 1. Dynamics of the ‘fling’ , 1979, Journal of Fluid Mechanics.

[21]  Paul S. Addison,et al.  The Illustrated Wavelet Transform Handbook Introductory Theory And Applications In Science , 2002 .

[22]  Kai Schneider,et al.  Leading-edge vortex shedding from rotating wings , 2014, 1405.4838.

[23]  M. Farge,et al.  Wavelet transforms and their applications to MHD and plasma turbulence: a review , 2015, 1508.05650.

[24]  D. Adam.  The illustrated wavelet transform handbook: introductory theory and applications in science, engineering, medicine and finance , 2004 .

[25]  Kai Schneider,et al.  The Lighthill–Weis-Fogh clap–fling–sweep mechanism revisited , 2011, Journal of Fluid Mechanics.

[26]  H. K. Moffatt,et al.  Helicity in Laminar and Turbulent Flow , 1992 .

[27]  T. Inamuro,et al.  Free flight simulations of a dragonfly-like flapping wing-body model using the immersed boundary-lattice Boltzmann method , 2014 .

[28]  K. Kawachi,et al.  A Numerical Study of Insect Flight , 1998 .

[29]  Dmitry Kolomenskiy,et al.  A Fourier spectral method for the Navier-Stokes equations with volume penalization for moving solid obstacles , 2009, J. Comput. Phys..

[30]  C. Meneveau.  Analysis of turbulence in the orthonormal wavelet representation , 1991, Journal of Fluid Mechanics.

[31]  Fritz-Olaf Lehmann,et al.  Phasing of dragonfly wings can improve aerodynamic efficiency by removing swirl , 2008, Journal of The Royal Society Interface.

[32]  Y. J. Lee,et al.  Aspect ratio effects on revolving wings with Rossby number consideration , 2016, Bioinspiration & biomimetics.

[33]  T. Maxworthy,et al.  The formation and maintenance of a leading-edge vortex during the forward motion of an animal wing , 2007, Journal of Fluid Mechanics.

[34]  H. K. Moffatt,et al.  The degree of knottedness of tangled vortex lines , 1969, Journal of Fluid Mechanics.

[35]  M H Dickinson,et al.  Leading-Edge Vortices Elevate Lift of Autorotating Plant Seeds , 2009, Science.

[36]  M. Farge,et al.  Coherent vortex extraction in 3D turbulent flows using orthogonal wavelets. , 2001, Physical review letters.

[37]  C. Ellington,et al.  Foraging costs in bumblebees: field conditions cause large individual differences , 1999, Insectes Sociaux.

[38]  H. K. Moffatt,et al.  Helicity and singular structures in fluid dynamics , 2014, Proceedings of the National Academy of Sciences.

[39]  Kai Schneider,et al.  Two- and three-dimensional numerical simulations of the clap–fling–sweep of hovering insects , 2010 .

[40]  S A Combes,et al.  Foraging in an unsteady world: bumblebee flight performance in field-realistic turbulence , 2017, Interface Focus.

[41]  M. Farge,et al.  Intermittency and scale-dependent statistics in fully developed turbulence. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  Kai Schneider,et al.  Numerical Modelling of Flexible Heaving Foils , 2013 .

[43]  Ellington,et al.  A computational fluid dynamic study of hawkmoth hovering , 1998, The Journal of experimental biology.

[44]  Paul S. Addison,et al.  The Illustrated Wavelet Transform Handbook , 2002 .

[45]  F. Lehmann,et al.  The aerodynamic benefit of wing–wing interaction depends on stroke trajectory in flapping insect wings , 2007, Journal of Experimental Biology.

[46]  Charles P. Ellington,et al.  THE AERODYNAMICS OF HOVERING INSECT FLIGHT. , 2016 .

[47]  M. R. Visbal,et al.  Dynamics of revolving wings for various aspect ratios , 2014, Journal of Fluid Mechanics.

[48]  K. Schneider,et al.  Aerodynamic Ground Effect in Fruitfly Sized Insect Takeoff , 2015, PloS one.

[49]  S. Kurien,et al.  Cascade time scales for energy and helicity in homogeneous isotropic turbulence. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[50]  Simon Pick,et al.  Stereoscopic PIV on multiple color-coded light sheets and its application to axial flow in flapping robotic insect wings , 2009 .