Effects of flapping wing kinematics on the aeroacoustics of hovering flight

Abstract

Despite the recent interest in flapping wing aerodynamics, the aerodynamic sound generation mechanism of a flapping wing is inadequately understood. In this paper, the interplay between the wing motion, resulting unsteady aerodynamics, and aeroacoustics of a flapping wing flyer is investigated. The wing motion is varied in terms of the flapping amplitude, pitching amplitude, and the phase difference between flap and pitch. The unsteady flow around the flapping wing is numerically calculated using a well-validated Navier-Stokes equation solver. Acoustic pressures are computed using the Ffowcs-Williams-Hawkings equation in a three-dimensional space at varying distances from the wing. Two main sound generation mechanisms are found. The flapping motion induces the highest sound pressure level (SPL) in the stroke plane. Furthermore, the SPL peaks under the wing due to the wake induced by lift generation. Effective motions, generating the highest lift and lowest SPL, are found when the flap and pitch amplitudes are high and when the pitch rotation is delayed with respect to flap. These results suggest that the delayed rotations observed for small hovering insects may aim to minimize sound production rather than maximize lift generation.

Introduction

Micro air vehicles (MAVs) are small unmanned aerial vehicles (UAVs) that have many potential recreational and military applications. Their development aim is to provide desirable flight characteristics including hovering, forward flight, and performing nimble maneuvers in confined spaces [1]. Despite their unassailable advantages, they still face challenges in wing loading, power requirements, stability and control, and noise production. These challenges arise, in part, due to their operating aerodynamic conditions being much different than those of larger air vehicles. Unlike passenger aircraft which operate at a Reynolds number Re ∼ O(10⁶-10⁷), MAVs typically operate in the range Re ∼ O(10²-10⁴), where the aerodynamics is inherently unsteady and dominated by viscous effects. Furthermore, the loud noise produced by rotary and fixed wing UAVs can become a major obstacle to their civilian and military applications [2].

Biologically-inspired MAV aerodynamic designs have received a wide range of interest in recent decades [3]. Natural flyers like bees, bats, and flies use flapping wings as their main lift and thrust generation mechanism. Natural flyers exhibit more advanced and efficient flight characters as compared to fixed wing MAVs at these low Reynolds numbers. This is because flapping wing motion at this scale takes advantage of unsteady mechanisms such as rapid wing rotation, delayed stall of the leading-edge vortex (LEV), and wake capture or wing-wake interaction. Such effects are driven by the complex but sophisticated kinematics of the flapping wing motion [1,3,4]. These unsteady aerodynamic mechanisms are significant in the process of enhancing aerodynamic force generation [1,4].

Very little attention is given to aerodynamic sound generation mechanisms produced by flapping wing flyers. In particular, nocturnal birds like bats, owls, and nighthawks are remarkably silent during their flight [5,6]. The minimal sound produced by a nocturnal bird can be a desirable characteristic for an MAV as it can be used for stealth purposes. Furthermore, natural flyers like some burrowing seabirds and mosquitoes use their sound production capability to communicate with others [7]. Male parasitic wasps use the fanning motion of their wing to produce courtship songs to attract female wasps [8]. Thus, a proper understanding of the sound production mechanisms used by these natural flyers can aid in the development of a silent MAVs as well as bio-inspired communication and sensing.

The main objective of this paper is to investigate the interplay between the wing kinematics, the resulting aerodynamic forces and vortical structures, and the sound generation of a flapping wing. We consider a Zimmerman wing with a flapping frequency of 25 Hz [9]. We vary the flap amplitude, pitch amplitude, and the phase difference between the flap and the pitch of the wing to assess the effects of wing kinematics and aerodynamics on the sound production mechanisms. We analyze the acoustic pressure and sound pressure level (SPL) to quantify the sound generation in the three-dimensional (3D) space.

The sound produced by the flapping motion of the wing is the direct result of the small compressibility effect around the wing at very low Mach numbers. It is challenging to compute these very low compressibility effects as they have a non-linear dependency on the unsteady flow field, which makes the computational process more expensive [10,11]. Hence we implement a splitting method in this study, following the approached used by Moon [12] and Inada et al. [10]. In this splitting method the unsteady flow field and the acoustics are calculated separately [13]. Furthermore, based on the argument by Manela et al. [14], we consider only one wing instead of two in this study for both the flow field and acoustic calculations as the distance between the wings and the wing motion being in-phase may result in an acoustic signature equivalent to one [14,15]. Inada et al. [10] used the Ffowcs-Williams-Hawkings (FWH) equation to calculate the acoustic pressure produced by three different insect wings using Navier-Stokes analysis [10]. This study complements the previous work by Inada et al. [10] by keeping the wing size fixed and varying the wing kinematics.

We compute the three-dimensional unsteady and viscous flow field around a flapping wing by using a well-validated incompressible Navier-Stokes equation solver [3,[16], [17], [18], [19]]. Using the computed instantaneous pressure distribution of the wing surface and prescribed wing surface orientation, the acoustic pressures are calculated by using the FWH equation. The case setup is motivated by previous hummingbird inspired MAV aeroacoustic experiments [20].

Manela et al. [14,15] show that wing flexibility is important when calculating acoustics as it can be used either to damp some of the sound produced or amplify the sound produced based on the actuating frequency of the wing [5,14]. Nevertheless, we consider a rigid wing to focus on the effects of wing kinematics on the resulting acoustics without considering the fluid-structure interaction of a flexible wing. Investigation of the effects of wing flexibility on the acoustics of flapping wings is left as a future study.

The organization of this paper is as follows. Section 2 describes the methodology used to conduct this investigation, describing the case setup, relevant non-dimensional parameters, kinematics, aerodynamic model, computational grids and the acoustic pressure in the wake behind an oscillating cylinder as a validation study. We highlight the effects of the wing kinematics on the sound production along with the three-dimensional unsteady aerodynamics in Section 3. We also focus on the influence of the wing motion on the acoustic pressure production in the regions of wing-wake interactions and LEVs. Moreover, the sound generation of cases with optimum lift and sound production are also presented.

A preliminary report on this investigation was presented at the AIAA SciTech Conference, Kissimmee, Florida, 2018 [21], where the simulation setup, computational methodology, and preliminary results were described. The main developments in the present paper involve addition of in-depth analysis of the results including 3D SPL distribution, frequency spectral analysis of the optimal motion, unsteady wake structures for advanced, symmetric and delayed rotations in relation to the resulting sound generation, SPL distribution of the various rotational motions, order of magnitude analysis of the FWH equation for flapping wing, and relative importance of the FWH equation terms.