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1. Nonlinear Aeroelastic Analysis for Highly Flexible Flapping Wing in Hover

   https://doi.org/10.4050/JAHS.67.022002  

   Yang, Xuan ; Sudhir, Aswathi ; Halder, Atanu ; Benedict, Moble ( April 2022 , Journal of the American Helicopter Society)

   Aeromechanics of highly flexible flapping wings is a complex nonlinear fluid–structure interaction problem and, therefore, cannot be analyzed using conventional linear aeroelasticity methods. This paper presents a standalone coupled aeroelastic framework for highly flexible flapping wings in hover for micro air vehicle (MAV) applications. The MAV-scale flapping wing structure is modeled using fully nonlinear beam and shell finite elements. A potential-flow-based unsteady aerodynamic model is then coupled with the structural model to generate the coupled aeroelastic framework. Both the structural and aerodynamic models are validated independently before coupling. Instantaneous lift force and wing deflection predictions from the coupled aeroelastic simulations are compared with the force and deflection measurements (using digital image correlation) obtained from in-house flapping wing experiments at both moderate (13 Hz) and high (20 Hz) flapping frequencies. Coupled trim analysis is then performed by simultaneously solving wing response equations and vehicle trim equations until trim controls, wing elastic response, inflow and circulation converge all together. The dependence of control inputs on weight and center of gravity (cg) location of the vehicle is studied for the hovering flight case.
2. The hawkmoth wingbeat is not at resonance

   https://doi.org/10.1098/rsbl.2022.0063  

   Gau, Jeff ; Wold, Ethan S. ; Lynch, James ; Gravish, Nick ; Sponberg, Simon ( May 2022 , Biology Letters)

   Flying insects have elastic materials within their exoskeletons that could reduce the energetic cost of flight if their wingbeat frequency is matched to a mechanical resonance frequency. Flapping at resonance may be essential across flying insects because of the power demands of small-scale flapping flight. However, building up large-amplitude resonant wingbeats over many wingstrokes may be detrimental for control if the total mechanical energy in the spring-wing system exceeds the per-cycle work capacity of the flight musculature. While the mechanics of the insect flight apparatus can behave as a resonant system, the question of whether insects flap their wings at their resonant frequency remains unanswered. Using previous measurements of body stiffness in the hawkmoth, Manduca sexta , we develop a mechanical model of spring-wing resonance with aerodynamic damping and characterize the hawkmoth's resonant frequency. We find that the hawkmoth's wingbeat frequency is approximately 80% above resonance and remains so when accounting for uncertainty in model parameters. In this regime, hawkmoths may still benefit from elastic energy exchange while enabling control of aerodynamic forces via frequency modulation. We conclude that, while insects use resonant mechanics, tuning wingbeats to a simple resonance peak is not a necessary feature for all centimetre-scale flappingmore »flyers.« less
3. Effects of Wing Kinematics on Modulating Odor Plume Structures in the Odor Tracking Flight of Fruit Flies

   https://doi.org/10.1115/FEDSM2021-61832  

   Lei, Menglong ; Li, Chengyu ( August 2021 , ASME 2021 Fluids Engineering Division Summer Meeting)

   Insects rely on their olfactory system to forage, prey, and mate. They can sense odorant plumes emitted from sources of their interests with their bilateral odorant antennae, and track down odor sources using their highly efficient flapping-wing mechanism. The odor-tracking process typically consists of two distinct behaviors: surging upwind and zigzagging crosswind. Despite the extensive numerical and experimental studies on the flying trajectories and wing flapping kinematics during odor tracking flight, we have limited understanding of how the flying trajectories and flapping wings modulate odor plume structures. In this study, a fully coupled three-way numerical solver is developed, which solves the 3D Navier-Stokes equations coupled with equations of motion for the passive flapping wings, and the odorant convection-diffusion equation. This numerical solver is applied to investigate the unsteady flow field and the odorant transport phenomena of a fruit fly model in both surging upwind and zigzagging crosswind cases. The unsteady flow generated by flapping wings perturbs the odor plume structure and significantly impacts the odor intensity at the olfactory receptors (i.e., antennae). During zigzagging crosswind flight, the differences in odor perception time and peak odor intensity at the receptors potentially help create stereo odorant mapping to track odor source.more »Our simulation results will provide new insights into the mechanism of how fruit flies perceive odor landscape and inspire the future design of odor-guided micro aerial vehicles (MAVs) for surveillance and detection missions.

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

   https://doi.org/10.1115/DETC2020-22638  

   Reade, Joseph ; Jankauski, Mark A. ( August 2020 , ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference)

   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 formore »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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5. Quasi three-dimensional deformable blade element and unsteady vortex lattice reduced-order modeling of fluid–structure interaction in flapping wings

   https://doi.org/10.1063/5.0129128  

   Schwab, R. ; Reade, J. ; Jankauski, M. ( December 2022 , Physics of Fluids)

   Flapping, flexible insect wings deform under inertial and fluid loading. Deformation influences aerodynamic force generation and sensorimotor control, and is thus important to insect flight mechanics. Conventional flapping wing fluid–structure interaction models provide detailed information about wing deformation and the surrounding flow structure, but are impractical in parameter studies due to their considerable computational demands. Here, we develop two quasi three-dimensional reduced-order models (ROMs) capable of describing the propulsive forces/moments and deformation profiles of flexible wings. The first is based on deformable blade element theory (DBET) and the second is based on the unsteady vortex lattice method (UVLM). Both rely on a modal-truncation based structural solver. We apply each model to estimate the aeromechanics of a thin, flapping flat plate with a rigid leading edge, and compare ROM findings to those produced by a coupled fluid dynamics/finite element computational solver. The ROMs predict wing deformation with good accuracy even for relatively large deformations of 25% of the chord length. Aerodynamic loading normal to the wing's rotation plane is well captured by the ROMs, though model errors are larger for in-plane loading. We then perform a parameter sweep to understand how wing flexibility and mass affect peak deflection, mean lift andmore »average power. All models indicate that flexible wings produce less lift but require lower average power to flap. Importantly, these studies highlight the computational efficiency of the ROMs—compared to the convention modeling approach, the UVLM and DBET ROMs solve 4 and 6 orders of magnitude faster, respectively.

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