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Unsteady aerodynamic theory for membrane wings

Published online by Cambridge University Press:  12 September 2022

Sonya Tiomkin Open the ORCID record for Sonya Tiomkin [Opens in a new window]  and
Justin W. Jaworski Open the ORCID record for Justin W. Jaworski [Opens in a new window]
Sonya Tiomkin*
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
Justin W. Jaworski
Affiliation:
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
*
†Email address for correspondence: [email protected]
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Abstract

We study analytically the dynamic response of membrane aerofoils subject to arbitrary, small-amplitude chord motions and transverse gusts in a two-dimensional inviscid incompressible flow. The theoretical model assumes linear deformations of an extensible membrane under constant tension, which are coupled aeroelastically to external aerodynamic loads using unsteady thin aerofoil theory. The structural and aerodynamic membrane responses are investigated for harmonic heave oscillations, an instantaneous change in angle of attack, sinusoidal transverse gusts and a sharp-edged gust. The unsteady lift responses for these scenarios produce aeroelastic extensions to the Theodorsen, Wagner, Sears and Küssner functions, respectively, for a membrane aerofoil. These extensions incorporate for the first time membrane fluid–structure interaction into the expressions for the unsteady lift response of a flexible aerofoil. The indicial responses to step changes in the angle of attack or gust profile are characterised by a slower lift response in short times relative to the classical rigid-plate response, while achieving a significantly higher asymptotic lift at long times due to aeroelastic camber. The unsteady lift for harmonic gusts or heaving motions follows closely the rigid plate lift responses at low reduced frequencies but with a reduced lift amplitude and greater phase lag. However, as the reduced frequency approaches the resonance of the fluid-loaded membrane, the lift response amplitude increases abruptly and is followed by a sharp decrease. This behaviour reveals a frequency region, controlled by the membrane tension coefficient, for which membrane aerofoils could possess substantial aerodynamic benefits over rigid aerofoils in unsteady flow conditions.

JFM classification

Biological Fluid Dynamics: Swimming/flying
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 948 , 10 October 2022 , A33
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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