Computational Fluid-Structure Interaction of a Deformable Flapping Wing for Micro Air Vehicle Applications

Abstract Flapping, flexible wings deform under both aerodynamic and inertial loads. However, the fluid-structure interaction (FSI) governing flapping wing dynamics is not well understood. Conventional FSI models require excessive computational resources and are not conducive to parameter studies that consider variable wing kinematics or geometry. Here, we present a simple two-way coupled FSI model for a wing subjected to single-degree-of-freedom (SDOF) rotation. The model is reduced-order and can be solved several orders of magnitude faster than direct computational methods. We construct a SDOF rotation stage and measure basal strain of a flapping wing in-air and in-vacuum to study our model experimentally. Overall, agreement between theory and experiment is excellent. In-vacuum, the wing has a large 3ω response when flapping at approximately 1/3 its natural frequency. This response is attenuated substantially when flapping in-air as a result of aerodynamic damping. These results highlight the importance of two-way coupling between the fluid and structure, since one-way coupled approaches cannot describe such phenomena. Moving forward, our model enables advanced studies of biological flight and facilitates bio-inspired design of flapping wing technologies.

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Deformable Blade Element and Unsteady Vortex Lattice Fluid-Structure Interaction Modeling of a 2D Flapping Wing

Volume 7: 32nd Conference on Mechanical Vibration and Noise (VIB) ◽

10.1115/detc2020-22638 ◽

2020 ◽

Author(s):

Joseph Reade ◽

Mark A. Jankauski

Keyword(s):

Vortex Lattice ◽

Normal Force ◽

Aerodynamic Force ◽

Fluid Structure Interaction ◽

Force Production ◽

Flapping Wing ◽

Energetic Efficiency ◽

Fluid Structure ◽

Structure Interaction ◽

Blade Element

Abstract Flapping insect wings experience appreciable deformation due to aerodynamic and inertial forces. This deformation is believed to benefit the insect’s aerodynamic force production as well as energetic efficiency. However, the fluid-structure interaction (FSI) models used to estimate wing deformations are often computationally demanding and are therefore challenged by parametric studies. Here, we develop a simple FSI model of a flapping wing idealized as a two-dimensional pitching-plunging airfoil. Using the Lagrangian formulation, we derive the reduced-order structural framework governing wing’s elastic deformation. We consider two fluid models: quasi-steady Deformable Blade Element Theory (DBET) and Unsteady Vortex Lattice Method (UVLM). DBET is computationally economical but does not provide insight into the flow structure surrounding the wing, whereas UVLM approximates flows but requires more time to solve. For simple flapping kinematics, DBET and UVLM produce similar estimates of the aerodynamic force normal to the surface of a rigid wing. More importantly, when the wing is permitted to deform, DBET and UVLM agree well in predicting wingtip deflection and aerodynamic normal force. The most notable difference between the model predictions is a roughly 20° phase difference in normal force. DBET estimates wing deformation and force production approximately 15 times faster than UVLM for the parameters considered, and both models solve in under a minute when considering 15 flapping periods. Moving forward, we will benchmark both low-order models with respect to high fidelity computational fluid dynamics coupled to finite element analysis, and assess the agreement between DBET and UVLM over a broader range of flapping kinematics.

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Fluid Structure Interaction of Unsteady Aerodynamics of Flapping Wing at Low Reynolds Number

Engineering Applications of Computational Fluid Mechanics ◽

10.1080/19942060.2013.11015460 ◽

2013 ◽

Vol 7 (1) ◽

pp. 144-158 ◽

Cited By ~ 8

Author(s):

Z.M. Fairuz ◽

M.Z. Abdullah ◽

H. Yusoff ◽

M.K. Abdullah

Keyword(s):

Reynolds Number ◽

Low Reynolds Number ◽

Fluid Structure Interaction ◽

Unsteady Aerodynamics ◽

Flapping Wing ◽

Fluid Structure ◽

Structure Interaction ◽

Low Reynolds

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