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

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.

Effects of flapping-motion profiles on insect-wing aerodynamics

“…This range is scaled to, approximately, , based on the wingspan (b) and the mean velocity at the radius of gyration (R g ). This span-based scaling of the Reynolds number (Re b ) has been shown to appropriately govern the large-scale flow structures over a wing in our recent studies (Harbig, Sheridan & Thompson 2013;Bhat et al 2019). In the case of flapping wings, Re b is defined as…”

Inter-species variation in number of bristles on forewings of tiny insects does not impact clap-and-fling aerodynamics

“…Several studies examining the aerodynamic effects of varying S have reported contradictory findings. While some studies found little variation in force coefficients (Usherwood & Ellington, 2002; Luo & Sun, 2005; Garmann & Visbal, 2014), others have postulated that larger wing spans are detrimental for force generation (Harbig et al, 2012; Han, Chang & Cho, 2015; Bhat et al, 2019). All these studies considered solid wings at Re c >100.…”

A simple vortex-loop-based model for unsteady rotating wings

“…The LEV evolution depends on , and (see Bhat et al. (2019), who determined that these effects are best isolated using span-based definitions of and ), but often exhibits arch-like liftoff outboard and further LEVs forming ahead of the main one (e.g. Jardin, Farcy & David 2012; Harbig, Sheridan & Thompson 2013; Garmann & Visbal 2014; Carr et al.…”

“…2016 a ; Bhat et al. 2019). However, the LEV remains close to the wing over much of the span and the overall flow exhibits a growing vortex loop for up to , albeit with complex outboard structures (Garmann & Visbal 2014; Carr et al.…”