The stability of leading-edge vortices to perturbations on samara-inspired rotors: a novel solution for gust resistance

Abstract

The stability of leading-edge vortices (LEVs) on a samara-inspired rotor during steady and unsteady gusty incoming flow was investigated experimentally using direct rotational speed measurements, as well as time-resolved particle image velocimetry (PIV). The blades of the samara-inspired rotor were designed to match the tip-speed ratio, the aspect ratio, and the distribution of the effective angle of attack of samara seeds to utilize LEVs similar to samara seeds. The flow around the blades of the samara-inspired rotor was compared to a reference rotor, which possesses a constant spanwise effective angle of attack, to investigate the influence of the samara-like spanwise effective angle-ofattack distribution on LEV stability. Furthermore, the unsteady performance of the samara-inspired rotor was compared to a generic low-inertia rotor that possesses blades with a constant effective angle of attack less than the stall angle. During steady rotation, the samara-inspired rotor exhibited a stably-attached LEV, while the reference rotor demonstrated unstable LEV shedding. Compared to a generic low-inertia rotor, the samara-inspired rotor demonstrated a relatively stable tip-speed ratio (λ) during the gust. Furthermore, the LEV remained stably-attached on the rotor's blades with a constant normalized circulation during the gust. Finally, the analysis of the LEV stability during the gust using the vorticity transport equation suggests that LEV stability is coupled with constant tipspeed ratio during gusts.

On the robust autorotation of a samara-inspired rotor in gusty environments

“…Inspired by samaras, we designed a three-bladed rotor that captured the key aerodynamic properties of samaras by matching tip-speed ratio (λ), aspect ratio (AR), and the effective angle-of-attack (α eff ) distribution of samaras. Consequently, the rotor exhibited stably-attached LEVs when towed in the towing tank as shown in a previous study [6]. The rotor was designed to operate at a tip-speed ratio (λ) of 4 at an incoming flow speed of 0.8 m s −1 , which is within the typical tip-speed ratio range (1.5 λ 5.5) reported for samaras [10].…”

“…It should be noted that an aspect ratio less than 4 is required for LEV stability on rotating blades [19]. More details on the construction of the samara-inspired rotor can be found in a previous study [6].…”

“…The resulting aerodynamic force (lift) is the result of the formation of stable leading-edge vortices (LEVs) on the suction side of the rotating seed wing [2,4,5]. Consequently, such seeds fall rapidly once autorotation is stopped [6]. Since samara seeds propagate effectively in gusty environments, it is speculated that such seeds possess unique characteristics allowing for robust autorotation that is resistant to perturbations.…”

“…Thus by incorporating aspects of samaras into low-inertia rotor systems, there is potential to drastically improve performance in unsteady environments. For instance, in a previous study, a samarainspired rotor was designed by incorporating stable LEVs by matching tip-speed ratio (λ), aspect ratio (AR), and the effective angle-of-attack (α eff ) distribution of natural samaras [6]. The samara-inspired rotor exhibited a constant tip-speed ratio when subjected to axial gusts, suggesting that its performance was not negatively affected by gusts.…”

Reynolds-number scaling of a vorticity-annihilating boundary layer

“…While already adapted in engineering solutions (such as helicopter flight (Ham & Garelick 1968), low-inertia rotor design (El Makdah et al. 2019), and micro-aerial vehicles (Pitt Ford & Babinsky 2013)), the aerodynamic principle is often associated with biological propulsion. An example of an LEV is shown in figure 1( a ), where the acceleration of propulsors (such as wings or flippers) initiate the separation of a shear layer that in turn rolls up into a vortex.…”