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A scaling law for the lift of a bio-inspired wing hovering in low-density compressible flows

Published online by Cambridge University Press:  13 January 2025

Nathan Widdup ,
Li Wang ,
John Young Open the ORCID record for John Young [Opens in a new window] ,
Vincent Daria ,
Hao Liu Open the ORCID record for Hao Liu [Opens in a new window]  and
Fang-Bao Tian Open the ORCID record for Fang-Bao Tian [Opens in a new window]
Nathan Widdup
Affiliation:
School of Engineering and Technology, University of New South Wales, Canberra, ACT 2600, Australia Air and Space Power Centre, Royal Australian Air Force, Canberra, ACT 2609, Australia
Li Wang
Affiliation:
School of Engineering and Technology, University of New South Wales, Canberra, ACT 2600, Australia
John Young
Affiliation:
School of Engineering and Technology, University of New South Wales, Canberra, ACT 2600, Australia
Vincent Daria
Affiliation:
Air and Space Power Centre, Royal Australian Air Force, Canberra, ACT 2609, Australia
Hao Liu
Affiliation:
Graduate School of Engineering, Chiba University, Chiba 263-8522, Japan
Fang-Bao Tian*
Affiliation:
School of Engineering and Technology, University of New South Wales, Canberra, ACT 2600, Australia
*
†Email address for correspondence: fangbao.tian@unsw.edu.au
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Abstract

Aircraft with bio-inspired flapping wings that are operated in low-density atmospheric environments encounter unique challenges associated with the low density. The low density results in the requirement of high operating velocities of aircraft to generate sufficient lift resulting in significant compressibility effects. Here, we perform numerical simulations to investigate the compressibility effects on the lift generation of a bio-inspired wing during hovering flight using an immersed boundary method. The aim of this study is to develop a scaling law to understand how the lift is influenced by the Reynolds and Mach numbers, and the associated flow physics. Our simulations have identified a critical Mach number of approximately $0.6$ defined by the average wing-tip velocity. When the Mach number is lower than 0.6, compressibility does not have significant effects on the lift or flow fields, while when the Mach number is greater than $0.6$, the lift coefficient decreases linearly with increasing Mach number, due to the drastic change in the pressure on the wing surface caused by unsteady shock waves. Moreover, the decay rate is dependent on the Reynolds number and the angle of attack. Based on these observations, we propose a scaling law for the lift of a hovering flapping wing by considering compressible and viscous effects, with the scaled lift showing excellent collapse.

JFM classification

Biological Fluid Dynamics: Swimming/flying Compressible Flows: Supersonic flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1003 , 25 January 2025 , A10
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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