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Uncoupling the effects of aspect ratio, Reynolds number and Rossby number on a rotating insect-wing planform

Published online by Cambridge University Press:  26 November 2018

Shantanu S. Bhat Open the ORCID record for Shantanu S. Bhat [Opens in a new window] ,
Jisheng Zhao ,
John Sheridan ,
Kerry Hourigan  and
Mark C. Thompson
Shantanu S. Bhat*
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
Jisheng Zhao
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
John Sheridan
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
Kerry Hourigan
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
Mark C. Thompson
Affiliation:
Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
*
†Email address for correspondence: [email protected]
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Abstract

The individual and combined influences of aspect ratio ($A$), Reynolds number ($Re$) and Rossby number ($Ro$) on the leading-edge vortex (LEV) of a rotating wing of insect-like planform are investigated numerically. A previous study from our group has determined the wingspan to be an appropriate length scale governing the large-scale LEV structure. In this study, the $A$ range considered is further extended, to show that this scaling works well as $A$ is varied by a factor of 4 ($1.8\leqslant A\leqslant 7.28$) and over a $Re$ range of two orders of magnitude. The present study also extends this scaling for wings with an offset from the rotation axis, which is typically the case for actual insects and often for experiments. Remarkably, the optimum range of $A$ based on the lift coefficients at different $Re$ coincides with that observed in nature. The scaling based on the wingspan is extended to the acceleration terms of the Navier–Stokes equations, suggesting a modified scaling of $Ro$, which decouples the effects of $A$. A detailed investigation of the flow structures, by increasing $Ro$ in a wide range, reveals the weakening of the LEV due to the reduced spanwise flow, resulting in a reduced lift. Overall, the use of span-based scaling of $Re$ and $Ro$, together with $A$, may help reconcile apparent conflicting trends between observed variations in aerodynamic performance in different sets of experiments and simulations.

JFM classification

Aerodynamics: Aerodynamics Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Swimming/flying
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 859 , 25 January 2019 , pp. 921 - 948
Copyright
© 2018 Cambridge University Press 

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Bhat et al. supplementary movie

A comparison of the temporal evolution of the flow structures over the wings of aspect ratios 7.28 and 2.91 rotating at the span based Reynolds number of 300 is shown. The top row shows the comparison at constant Rg/c, whereas the left column shows the comparison at constant Rg/b, in which the AR=7.28 wing is common. Phi represents the rotation phase of the wing. The vortices are identified by the isosurfaces of the constant Q criterion.

Download Bhat et al. supplementary movie(Video)
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