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1. 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)

   null (Ed.)

   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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2. 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 and 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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3. A Novel Fluid–Structure Interaction Framework for Flapping, Flexible Wings

   https://doi.org/10.1115/1.4044268  

   Schwab, Ryan; Johnson, Erick; Jankauski, Mark (December 2019, Journal of Vibration and Acoustics)

   Fluid–structure interaction (FSI) plays a significant role in the deformation of flapping insect wings. However, many current FSI models are high-order and rely on direct computational methods, thereby limiting parametric studies as well as insights into the physics governing wing dynamics. We develop a novel flapping wing FSI framework that accommodates general wing geometry and fluid loading. We use this framework to study the unilaterally coupled FSI of an idealized hawkmoth forewing considering two fluid models: Reynolds-averaged Navier–Stokes computational fluid dynamics (RANS CFD) and blade element theory (BET). We first compare aerodynamic modal forces estimated by the low-order BET model to those calculated via high fidelity RANS CFD. We find that for realistic flapping kinematics, BET estimates modal forces five orders of magnitude faster than CFD within reasonable accuracy. Over the range flapping kinematics considered, BET and CFD estimated modal forces vary maximally by 350% in magnitude and approximately π/2 radians in phase. The large reduction in computational time offered by BET facilitates high-dimensional parametric design of flapping-wing-based technologies. Next, we compare the contributions of aerodynamic and inertial forces to wing deformation. Under the unilateral coupling assumption, aerodynamic and inertial-elastic forces are on the same order of magnitude—however, inertial-elastic forces primarily excite the wing’s bending mode whereas aerodynamic forces primarily excite the wing’s torsional mode. This suggests that, via conscientious sensor placement and orientation, biological wings may be able to sense independently inertial and aerodynamic forces. 

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4. Experimental studies suggest differences in the distribution of thorax elasticity between insects with synchronous and asynchronous musculature

   https://doi.org/10.1098/rsif.2023.0029  

   Casey, Cailin; Heveran, Chelsea; Jankauski, Mark (April 2023, Journal of The Royal Society Interface)

   Insects have developed diverse flight actuation mechanisms, including synchronous and asynchronous musculature. Indirect actuation, used by insects with both synchronous and asynchronous musculature, transforms thorax exoskeletal deformation into wing rotation. Though thorax deformation is often attributed exclusively to muscle tension, the inertial and aerodynamic forces generated by the flapping wings may also contribute. In this study, a tethered flight experiment was used to simultaneously measure thorax deformation and the inertial/aerodynamic forces acting on the thorax generated by the flapping wing. Compared to insects with synchronous musculature, insects with asynchronous muscle deformed their thorax 60% less relative to their thorax diameter and their wings generated 2.8 times greater forces relative to their body weight. In a second experiment, dorsalventral thorax stiffness was measured across species. Accounting for weight and size, the asynchronous thorax was on average 3.8 times stiffer than the synchronous thorax in the dorsalventral direction. Differences in thorax stiffness and forces acting at the wing hinge led us to hypothesize about differing roles of series and parallel elasticity in the thoraxes of insects with synchronous and asynchronous musculature. Specifically, wing hinge elasticity may contribute more to wing motion in insects with asynchronous musculature than in those with synchronous musculature. 

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5. Flapping dynamics and wing flexibility enhance odor detection in blue bottle flies

   https://doi.org/10.1088/1748-3190/adb822  

   Haider, Naeem; Lou, Zhipeng; Hsu, Shih-Jung; Cheng, Bo; Li, Chengyu (March 2025, Bioinspiration & Biomimetics)

   Abstract One of the most ancient and evolutionarily conserved behaviors in the animal kingdom involves utilizing wind-borne odor plumes to track essential elements such as food, mates, and predators. Insects, particularly flies, demonstrate a remarkable proficiency in this behavior, efficiently processing complex odor information encompassing concentrations, direction, and speed through their olfactory system, thereby facilitating effective odor-guided navigation. Recent years have witnessed substantial research explaining the impact of wing flexibility and kinematics on the aerodynamics and flow field physics governing the flight of insects. However, the relationship between the flow field and olfactory functions remains largely unexplored, presenting an attractive frontier with numerous intriguing questions. One such question pertains to whether flies intentionally manipulate the flow field around their antennae using their wing structure and kinematics to augment their olfactory capabilities. To address this question, we first reconstructed the wing kinematics based on high-speed video recordings of wing surface deformation. Subsequently, we simulated the unsteady flow field and odorant transport during the forward flight of blue bottle flies (Calliphora vomitoria) by solving the Navier–Stokes equations and odorant advection–diffusion equations using an in-house computational fluid dynamics solver. Our simulation results demonstrated that flexible wings generated greater cycle-averaged aerodynamic forces compared to purely rigid flapping wings, underscoring the aerodynamic advantages of wing flexibility. Additionally, flexible wings produced 25% greater odor intensity, enhancing the insect’s ability to detect and interpret olfactory cues. This study not only advances our understanding of the intricate interplay between wing motion, aerodynamics, and olfactory capabilities in flying insects but also raises intriguing questions about the intentional modulation of flow fields for sensory purposes in other behaviors. 

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