Session M21: Bio: Dynamic Mechanisms of Insect Flight

Toward understanding the mechanics of hovering in insects, hummingbirds and bats

We present results on the dynamical characteristics of two different mechanisms of hovering, corresponding to the behavior of hummingbirds and bats. Using a Lagrangian formulation, we have developed a dynamical model of a body (trunk) and two rectangular wings. The trunk has 3 degrees of freedom (x, z and pitch angle) and each wing has 3 modes of actuation: flapping, pronation/supination, and wingspan extension/flexion (only present for bats). Wings can be effectively massless (hummingbird and insect wings) or relatively massive (important in the case of bats). The aerodynamic drag and lift forces are calculated using a quasi-steady blade-element model. The regions of state space in which hovering is possible are computed by over an exhaustive range of parameters. The effect of wing mass is to shrink the phase space available for viable hovering and, in general, to require higher wingbeat frequency. Moreover, by exploring hovering energy requirements, we find that the pronation angle of the wings also plays a critical role. For bats, who have relatively heavy wings, we show wing extension and flexion is critical in order to maintain a plausible hovering posture with reasonable power requirements. Comparisons with biological data show good agreement with our model predictions.   

Effects of altitude on the climbing performance of Monarch butterflies

Millions of Monarchs annually travel up to 4,000km, the longest migration distance among insects. They fly and overwinter at high altitudes. However, the aerodynamic mechanism enabling the long-range flight of Monarch butterflies is unknown. To study the effects of altitude on the aerodynamic performance of Monarch butterflies, a unique combination of a motion tracking system and a variable pressure chamber that allows controlling the density is used. The condition inside the chamber is systematically varied to simulate high altitude conditions up to 3,000 m. An optical tracking technique is used to characterize the climbing trajectories of freely flying Monarch butterflies. Customized reflective markers are designed to minimize the effects of marker addition. Flapping amplitude and frequency as well as climbing trajectories are measured. Lift acting on the butterfly is also determined by considering the force balance. Results show that the average flight speed and the Reynolds number, in general, decreased with the altitude, whereas, interestingly, the lift coefficient increased with the altitude. More detailed measurements and analyses will be performed in the future to explain the lift enhancement by flying at higher altitudes.   

Bats dynamically change wingspan to enhance lift and efficiency

Bats can dynamically change the wingspan by controlling the joints on the wings. This work focuses on the effect of dynamically changing wingspan on the lift and efficiency in slow-flying bats. The geometry and kinematics of the bat model is constructed based on the experimental measurements of Wolf et al. (J. Exp. Biol. 213, 2142--2153). The Navier-Stokes equations for incompressible flows are solved numerically to investigate the 3D unsteady flows around the bat model. It is found that the dynamically changing wingspan can significantly enhance the lift and efficiency. The lift enhancement is contributed by both lifting surface area extended during the downstroke and the vortex force associated with the leading-edge vortices intensified by the dynamically changing wingspan. The nonlinear interaction between the dynamically changing wing and the vortex structures plays an important role in the lift enhancement of a slow-flying bat in addition to the geometrical effect of changing the lifting-surface area in a flapping cycle.   

Investigation of Body-involved Lift Enhancement in Bio-inspired Flapping Flight

Previous studies found that insects and birds are capable of using many unsteady aerodynamic mechanisms to augment the lift production. These include leading edge vortices, delayed stall, wake capture, clap-and-fling, etc. Yet the body-involved lift augmentation has not been paid enough attention. In this work, the aerodynamic effects of the wing-body interaction on the lift production in cicada and hummingbird forward flight are computationally investigated. 3D wing-body systems and wing flapping kinematics are reconstructed from the high-speed videos or literatures to keep their complexity. Vortex structures and associated aerodynamic performance are numerically studied by an in-house immersed-boundary-method-based flow solver. The results show that the wing-body interaction enhances the overall lift production by about 20{\%} in the cicada flight and about 28{\%} in the hummingbird flight, respectively. Further investigation on the vortex dynamics has shown that this enhancement is attributed to the interactions between the body-generated vortices and the flapping wings. The output from this work has revealed a new lift enhancement mechanism in the flapping flight.   

Role of passive deformation on propulsion through a lumped torsional flexibility model

Scientists and biologists have been affianced in a deeper examination of insect flight to develop an improved understanding of the role of flexibility on aerodynamic performance. Here, we mimic a flapping wing through a fluid-structure interaction framework based upon a lumped torsional flexibility model. The developed fluid and structural solvers together determine the aerodynamic forces and wing deformation, respectively. An analytical solution to the simplified single-spring structural dynamics equation is established to substantiate simulations. It is revealed that the dynamics of structural deformation is governed by the balance between inertia, stiffness and aerodynamics, where the former two oscillate at the plunging frequency and the latter oscillates at twice the plunging frequency. We demonstrate that an induced phase difference between plunging and passive pitching is responsible for a higher thrust coefficient. This phase difference is also shown to be dependent on aerodynamics to inertia and natural to plunging frequency ratios. For inertia dominated flows, pitching and plunging always remain in phase. As the aerodynamics dominates, a large phase difference is induced which is accountable for a large passive deformation and higher thrust.   

The role of resonance in propulsion of an elastic pitching wing with or without inertia

Flapping wings of insects and undulating fins of fish both experience significant elastic deformations during propulsion, and it has been shown that in both cases, the deformations are beneficial to force enhancement and power efficiency. In fish swimming, the inertia of the fin structure is negligible and the hydrodynamic force is solely responsible for the deformation. However, in insect flight, both the wing inertia and aerodynamic force can be important factors leading to wing deformation. This difference raises the question about the role of the system (fluid-structure) resonance in the performance of propulsion. In this study, we use a 2D pitching foil as a model wing and vary its bending rigidity, pitching frequency, and mass ratio to investigate the fluid-structure interaction near resonance. The results show that at low mass ratios, i.e., a scenario of swimming, the system resonance greatly enhances thrust production and power efficiency, which is consistent with previous experimental results. However, at high mass ratios, i.e., a scenario of flying, the system resonance leads to overly large deformation that actually does not bring benefit any more. This conclusion thus suggests that resonance plays different roles in flying and in swimming.   

Bristles reduce force required to fling wings apart in small insects.

The smallest flying insects commonly possess wings with long bristles. Little quantitative information is available on the morphology of these bristles, and the functional importance of these bristles remains a mystery. In this study, we used the immersed boundary method to determine via numerical simulation if bristled wings reduced the force required to fling the wings apart during ``clap and fling''. The challenge of studying the fluid dynamics of bristles was in resolving the fluid flow between the bristles. The effects of Reynolds number, angle of attack, bristle spacing, and wing-wing interactions were investigated. We found that a bristled wing experiences less force than a solid wing, however bristled wings may act more like solid wings at lower angles of attack than they do at higher angles of attack. In wing-wing interactions, bristled wings significantly decrease the drag required to fling two wings apart compared with solid wings, especially at lower Reynolds numbers. These results support the idea that bristles may offer an aerodynamic benefit during clap and fling by reducing the force required to fling the wings apart in tiny insects.   

Flapping flight using bristled wings: effects of varying gap to diameter ratios

The smallest flying insects with body lengths under 1 mm, such as thrips, show a preferential adaptation for fringed or bristled wings. In addition, these tiny insects have been observed to use wing-wing interaction via the clap and fling mechanism. We have previously shown that the use of bristled wings can lower forces required to clap the wings together and fling them apart. Tremendous variation is observed in bristled wing design among tiny insects. In this study, we examine the role of ratio of bristle gap to diameter (G/D) on force generation and flow structures at Reynolds numbers on the order of 10. A dynamically scaled robotic model was developed for this study, in which physical models of bristled wings were programmed to execute a 2D clap and fling kinematics. Bristled wing models with G/D ranging from 5 through 17 were examined. Lift and drag forces were measured using strain gages and phase-locked particle image velocimetry was used to visualize flow structures generated from the flapping motion. The results showed reductions in the size of the leading edge vortex and drag force with increasing G/D. The effects of increasing G/D on leakiness through the bristles will be presented.   

Hovering and targeting flight simulations of a dragonfly-like flapping wing-body model by IB-LBM

Hovering and targeting flights of the dragonfly-like flapping wing-body model are numerically investigated by using the immersed boundary-lattice Boltzmann method (IB-LBM). The governing parameters of the problem are the Reynolds number $Re$, the Froude number $Fr$, and the non-dimensional mass $m$. We set the parameters at $Re=200$, $Fr=15$, and $m=51$. % First, we simulate free flights of the model for various values of the phase difference angle $\phi$ between the forewing and the hindwing motions and for various values of the stroke angle $\beta$ between the stroke plane and the horizontal plane. We find that the vertical motion of the model depends on the phase difference angle $\phi$, and the horizontal motion of the model depends on the stroke angle $\beta$. % Secondly, using the above results we try to simulate the hovering flight by dynamically changing the phase difference angle $\phi$ and the stroke angle $\beta$. The hovering flight can be successfully simulated by a simple proportional controlleres of the phase difference angle and the stroke angle. % Finally, we simualte targeting flight by dynamically changing the stroke angle $\beta$.