Three-dimensional flow and lift characteristics of a hovering ruby-throated hummingbird

A three-dimensional computational fluid dynamics simulation is performed for a ruby-throated hummingbird (Archilochus colubris) in hovering flight. Realistic wing kinematics are adopted in the numerical model by reconstructing the wing motion from high-speed imaging data of the bird. Lift history and the three-dimensional flow pattern around the wing in full stroke cycles are captured in the simulation. Significant asymmetry is observed for lift production within a stroke cycle. In particular, the downstroke generates about 2.5 times as much vertical force as the upstroke, a result that confirms the estimate based on the measurement of the circulation in a previous experimental study. Associated with lift production is the similar power imbalance between the two half strokes. Further analysis shows that in addition to the angle of attack, wing velocity and surface area, drag-based force and wing–wake interaction also contribute significantly to the lift asymmetry. Though the wing–wake interaction could be beneficial for lift enhancement, the isolated stroke simulation shows that this benefit is buried by other opposing effects, e.g. presence of downwash. The leading-edge vortex is stable during the downstroke but may shed during the upstroke. Finally, the full-body simulation result shows that the effects of wing–wing interaction and wing–body interaction are small.     

Analytical model for instantaneous lift and shape deformation of an insect-scale flapping wing in hover

In the analysis of flexible flapping wings of insects, the aerodynamic outcome depends on the combined structural dynamics and unsteady fluid physics. Because the wing shape and hence the resulting effective angle of attack are a priori unknown, predicting aerodynamic performance is challenging. Here, we show that a coupled aerodynamics/structural dynamics model can be established for hovering, based on a linear beam equation with the Morison equation to account for both added mass and aerodynamic damping effects. Lift strongly depends on the instantaneous angle of attack, resulting from passive pitch associated with wing deformation. We show that both instantaneous wing deformation and lift can be predicted in a much simplified framework. Moreover, our analysis suggests that resulting wing kinematics can be explained by the interplay between acceleration-related and aerodynamic damping forces. Interestingly, while both forces combine to create a high angle of attack resulting in high lift around the midstroke, they offset each other for phase control at the end of the stroke.     

Nonlinear flight dynamics and stability of hovering model insects

Current analyses on insect dynamic flight stability are based on linear theory and limited to small disturbance motions. However, insects'' aerial environment is filled with swirling eddies and wind gusts, and large disturbances are common. Here, we numerically solve the equations of motion coupled with the Navier–Stokes equations to simulate the large disturbance motions and analyse the nonlinear flight dynamics of hovering model insects. We consider two representative model insects, a model hawkmoth (large size, low wingbeat frequency) and a model dronefly (small size, high wingbeat frequency). For small and large initial disturbances, the disturbance motion grows with time, and the insects tumble and never return to the equilibrium state; the hovering flight is inherently (passively) unstable. The instability is caused by a pitch moment produced by forward/backward motion and/or a roll moment produced by side motion of the insect.     

柔性扑翼气动性能的数值研究

国内外对扑翼飞行的气动特性进行了大量研究,这些研究大多基于简谐扑动的刚性翼,然而大量观察发现鸟或昆虫飞行时,翅膀存在明显的柔性变形,这种变形对其气动性能具有显著的影响。该文针对一简化的二维柔性扑翼模型,采用数值求解N-S方程并耦合扑翼柔性变形方程的计算方法,研究了扑翼柔性变形对其气动性能的影响。结果显示扑翼的柔性变形改变了扑翼周围的涡结构,从而影响扑翼的气动性能;适当的柔性变形能延迟前缘涡的脱落,从而有效地改善扑翼的推进效率,但同时减弱了扑翼在低雷诺数环境中产生高升力的尾迹捕捉机制。     

The interplay of cell–cell and cell–substrate adhesion in collective cell migration

Collective cell migration often involves notable cell–cell and cell–substrate adhesions and highly coordinated motion of touching cells. We focus on the interplay between cell–substrate adhesion and cell–cell adhesion. We show that the loss of cell-surface contact does not significantly alter the dynamic pattern of protrusions and retractions of fast migrating amoeboid cells (Dictyostelium discoideum), but significantly changes their ability to adhere to other cells. Analysis of the dynamics of cell shapes reveals that cells that are adherent to a surface may coordinate their motion with neighbouring cells through protrusion waves that travel across cell–cell contacts. However, while shape waves exist if cells are detached from surfaces, they do not couple cell to cell. In addition, our investigation of actin polymerization indicates that loss of cell-surface adhesion changes actin polymerization at cell–cell contacts. To further investigate cell–cell/cell–substrate interactions, we used optical micromanipulation to form cell–substrate contact at controlled locations. We find that both cell-shape dynamics and cytoskeletal activity respond rapidly to the formation of cell–substrate contact.     

Role of cell polarity dynamics and motility in pattern formation due to contact-dependent signalling

A key challenge in biology is to understand how spatio-temporal patterns and structures arise during the development of an organism. An initial aggregate of spatially uniform cells develops and forms the differentiated structures of a fully developed organism. On the one hand, contact-dependent cell–cell signalling is responsible for generating a large number of complex, self-organized, spatial patterns in the distribution of the signalling molecules. On the other hand, the motility of cells coupled with their polarity can independently lead to collective motion patterns that depend on mechanical parameters influencing tissue deformation, such as cellular elasticity, cell–cell adhesion and active forces generated by actin and myosin dynamics. Although modelling efforts have, thus far, treated cell motility and cell–cell signalling separately, experiments in recent years suggest that these processes could be tightly coupled. Hence, in this paper, we study how the dynamics of cell polarity and migration influence the spatiotemporal patterning of signalling molecules. Such signalling interactions can occur only between cells that are in physical contact, either directly at the junctions of adjacent cells or through cellular protrusional contacts. We present a vertex model which accounts for contact-dependent signalling between adjacent cells and between non-adjacent neighbours through long protrusional contacts that occur along the orientation of cell polarization. We observe a rich variety of spatiotemporal patterns of signalling molecules that is influenced by polarity dynamics of the cells, relative strengths of adjacent and non-adjacent signalling interactions, range of polarized interaction, signalling activation threshold, relative time scales of signalling and polarity orientation, and cell motility. Though our results are developed in the context of Delta–Notch signalling, they are sufficiently general and can be extended to other contact dependent morpho-mechanical dynamics.     

A new twist on gyroscopic sensing: body rotations lead to torsion in flapping,flexing insect wings

Insects perform fast rotational manoeuvres during flight. While two insect orders use flapping halteres (specialized organs evolved from wings) to detect body dynamics, it is unknown how other insects detect rotational motions. Like halteres, insect wings experience gyroscopic forces when they are flapped and rotated and recent evidence suggests that wings might indeed mediate reflexes to body rotations. But, can gyroscopic forces be detected using only changes in the structural dynamics of a flapping, flexing insect wing? We built computational and robotic models to rotate a flapping wing about an axis orthogonal to flapping. We recorded high-speed video of the model wing, which had a flexural stiffness similar to the wing of the Manduca sexta hawkmoth, while flapping it at the wingbeat frequency of Manduca (25 Hz). We compared the three-dimensional structural dynamics of the wing with and without a 3 Hz, 10° rotation about the yaw axis. Our computational model revealed that body rotation induces a new dynamic mode: torsion. We verified our result by measuring wing tip displacement, shear strain and normal strain of the robotic wing. The strains we observed could stimulate an insect''s mechanoreceptors and trigger reflexive responses to body rotations.     

大展弦比夹芯翼大攻角颤振分析

首先导出大展弦比复合材料梁弯扭耦合模态的半解析解，对具有NACA0012翼型的大展弦比的夹芯翼，在模态空间内建立了运动方程。然后采用半经验的ONERA非线性气动力模型描述空气动力，形成了对大展弦比夹芯翼大攻角气动弹性问题的描述。通过结构求解器和空气动力求解器联合求解来完成非线性颧振边界的计算。为了验证非线性颤振边界的求解方法，还利用ONERA气动力模型中的线性部分建立了夹芯翼的线性颤振方程。结果表明：零翼根攻角时，线性颤振速度与用非线性颧振边界求解方法得到的颧振速度完全一致；颤振速度随翼根攻角的增加而迅速减小；复合层铺设方式对颤振速度有较大影响。     

Automatic monitoring of element shape quality in 2-D and 3-D computational mesh dynamics

One of the major problems in fluid–structure interaction using the arbitrary Lagrangian Eulerian approach lies in the area of dynamic mesh generation. For accurate fluid-dynamic computations, meshes must be generated at each time step. The fluid mesh must be regenerated in the deformed fluid domain in order to account for the displacements of the elastic body computed by the structural dynamics solver. In the elasticity-based computational dynamic mesh procedure, the fluid mesh is modeled as a pseudo-elastic solid the deformation of which is based on the displacement boundary conditions, resulting from the solution of the computational structural dynamics problem. This approach has a distinct advantage over other mesh-movement algorithms in that it is a very general, physically based approach that can be applied to both structured and unstructured meshes. The major drawback of the linear elastostatic solver is that it does not guarantee the absence of severe element distortion. This paper describes a novel mesh-movement procedure for mesh quality control of 2-D and 3-D dynamic meshes based on solving a pseudo-nonlinear elastostatic problem. An inexpensive distortion measure for different types of elements is introduced and used for controlling the element shape quality. The mesh-movement procedure is illustrated with several examples (large-displacement and free-boundary problems) that highlight its advantages in terms of performance, mesh quality, and robustness. It is believed that the resulting scheme will result in a more economical simulation of the motion of complex geometry, 3-D elastic bodies immersed in temporally and spatially evolving flows. Received 20 April 2000     

Wing and body motion and aerodynamic and leg forces during take-off in droneflies

Here, we present a detailed analysis of the take-off mechanics in droneflies performing voluntary take-offs. Wing and body kinematics of the insects during take-off were measured using high-speed video techniques. Based on the measured data, the inertia force acting on the insect was computed and the aerodynamic force of the wings was calculated by the method of computational fluid dynamics. Subtracting the aerodynamic force and the weight from the inertia force gave the leg force. In take-off, a dronefly increases its stroke amplitude gradually in the first 10–14 wingbeats and becomes airborne at about the 12th wingbeat. The aerodynamic force increases monotonously from zero to a value a little larger than its weight, and the leg force decreases monotonously from a value equal to its weight to zero, showing that the droneflies do not jump and only use aerodynamic force of flapping wings to lift themselves into the air. Compared with take-offs in insects in previous studies, in which a very large force (5–10 times of the weight) generated either by jumping legs (locusts, milkweed bugs and fruit flies) or by the ‘fling’ mechanism of the wing pair (butterflies) is used in a short time, the take-off in the droneflies is relatively slow but smoother.     

Effect of flapping kinematics on aerodynamic force of a flapping two-dimensional flat plate

Potential applications of flapping-wing micro-aerial vehicles (MAVs) have prompted enthusiasm among the engineers and researchers to understand the flow physics associated with flapping flight. An incompressible Navier–Stokes solver that is capable of handling flapping flight kind of moving boundary problem is developed. Arbitrary Lagrangian–Eulerian (ALE) method is used to handle the moving boundaries of the problem. The solver is validated with the results of problems like inline oscillation of a circular cylinder in still fluid and a flat plate rapidly accelerating at constant angle of attack. Numerical simulations of flapping flat plate mimicking the kinematics of those like insect wings are simulated, and the unsteady fluid dynamic phenomena that enhance the aerodynamic force are studied. The solution methodology provides the velocity field and pressure field details, which are used to derive the force coefficients and the vorticity field. Time history of force coefficients and vortical structures gives insight into the unsteady mechanism associated with the unsteady aerodynamic force production. The scope of the work is to develop a computational fluid dynamic (CFD) solver with the ALE method that is capable of handling moving boundary problems, and to understand the flow physics associated with the flapping-wing aerofoil kinematics and flow parameters on aerodynamic forces. Results show that delayed stall, wing–wake interaction and rotational effect are the important unsteady mechanisms that enhance the aerodynamic forces. Major contribution to the lift force is due to the presence of leading edge vortex in delayed stall mechanism.     

Gull-inspired joint-driven wing morphing allows adaptive longitudinal flight control

Birds dynamically adapt to disparate flight behaviours and unpredictable environments by actively manipulating their skeletal joints to change their wing shape. This in-flight adaptability has inspired many unmanned aerial vehicle (UAV) wings, which predominately morph within a single geometric plane. By contrast, avian joint-driven wing morphing produces a diverse set of non-planar wing shapes. Here, we investigated if joint-driven wing morphing is desirable for UAVs by quantifying the longitudinal aerodynamic characteristics of gull-inspired wing-body configurations. We used a numerical lifting-line algorithm (MachUpX) to determine the aerodynamic loads across the range of motion of the elbow and wrist, which was validated with wind tunnel tests using three-dimensional printed wing-body models. We found that joint-driven wing morphing effectively controls lift, pitching moment and static margin, but other mechanisms are required to trim. Within the range of wing extension capability, specific paths of joint motion (trajectories) permit distinct longitudinal flight control strategies. We identified two unique trajectories that decoupled stability from lift and pitching moment generation. Further, extension along the trajectory inherent to the musculoskeletal linkage system produced the largest changes to the investigated aerodynamic properties. Collectively, our results show that gull-inspired joint-driven wing morphing allows adaptive longitudinal flight control and could promote multifunctional UAV designs.     

Sequentially-coupled space–time FSI analysis of bio-inspired flapping-wing aerodynamics of an MAV

We present a sequentially-coupled space–time (ST) computational fluid–structure interaction (FSI) analysis of flapping-wing aerodynamics of a micro aerial vehicle (MAV). The wing motion and deformation data, whether prescribed fully or partially, is from an actual locust, extracted from high-speed, multi-camera video recordings of the locust in a wind tunnel. The core computational FSI technology is based on the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) formulation. This is supplemented with using NURBS basis functions in temporal representation of the wing and mesh motion, and in remeshing. Here we use the version of the DSD/SST formulation derived in conjunction with the variational multiscale (VMS) method, and this version is called “DSD/SST-VMST.” The structural mechanics computations are based on the Kirchhoff–Love shell model. The sequential-coupling technique is applicable to some classes of FSI problems, especially those with temporally-periodic behavior. We show that it performs well in FSI computations of the flapping-wing aerodynamics we consider here. In addition to the straight-flight case, we analyze cases where the MAV body has rolling, pitching, or rolling and pitching motion. We study how all these influence the lift and thrust.     

弹性机翼跨音速静气动弹性问题研究

在非结构网格基础上,采用有限体积法求解了Euler方程;在结构网格基础上,采用有限差分方法求解了N-S方程。同时采用结构影响系数法计及机翼结构系统的弹性影响,计算了弹性机翼的结构变形和气动力载荷。计算结果表明:后掠机翼结构系统的弹性使弹性机翼产生了正的挠度和负的剖面扭转角;负的扭转角使弹性机翼的有效迎角减小;有效迎角的减小又使得弹性机翼的有效气动力载荷减小。针对算例机翼结构系统的弹性使弹性机翼的升力相对刚性机翼的升力减小27.9%。     

Unified fluid–structure interpolation and mesh motion using radial basis functions

A multivariate interpolation scheme, using radial basis functions, is presented, which results in a completely unified formulation for the fluid–structure interpolation and mesh motion problems. The method has several significant advantages. Primarily, all volume mesh, structural mesh, and flow‐solver type dependence is removed, and all operations are performed on totally arbitrary point clouds of any form. Hence, all connectivity and user‐input requirements are removed from the computational fluid dynamics–computational structural dynamics (CFD–CSD) coupling problem, as only point clouds are required to determine the coupling. Also, it may equally well be applied to structured and unstructured grids, or structural and aerodynamic grids that intersect, again because no connectivity information is required. Furthermore, no expensive computations are required during an unsteady simulation, just matrix–vector multiplications, since the required dependence relations are computed only once prior to any simulation and then remain constant. This property means that the method is both perfectly parallel, since only the data relevant to each structured block or unstructured partition are required to move those points, and totally independent from the flow solver. Hence, a completely generic ‘black box’ tool can be developed, which is ideal for use in an optimization approach. Aeroelastic behaviour of the Brite–Euram MDO wing is analysed in terms of both static deflection and dynamic responses, and it is demonstrated that responses are strongly dependent on the exact CFD–CSD interpolation used. Mesh quality is also examined during the motion resulting from a large surface deformation. Global grid quality is shown to be preserved well, with local grid orthogonality also being maintained well, particularly at and near the moving surface, where the original orthogonality is retained. Copyright © 2007 John Wiley & Sons, Ltd.     

Metal–organic frameworks for electronics: emerging second order nonlinear optical and dielectric materials

Metal–organic frameworks (MOFs) have been intensively studied over the past decade because they represent a new category of hybrid inorganic–organic materials with extensive surface areas, ultrahigh porosity, along with the extraordinary tailorability of structure, shape and dimensions. In this highlight, we summarize the current state of MOF research and report on structure–property relationships for nonlinear optical (NLO) and dielectric applications. We focus on the design principles and structural elements needed to develop potential NLO and low dielectric (low-κ) MOFs with an emphasis on enhancing material performance. In addition, we highlight experimental evidence for the design of devices for low-dielectric applications. These results motivate us to develop better low-dielectric and NLO materials and to perform in-depth studies related to deposition techniques, patterning and the mechanical performance of these materials in the future.     

Phasing of dragonfly wings can improve aerodynamic efficiency by removing swirl

Dragonflies are dramatic, successful aerial predators, notable for their flight agility and endurance. Further, they are highly capable of low-speed, hovering and even backwards flight. While insects have repeatedly modified or reduced one pair of wings, or mechanically coupled their fore and hind wings, dragonflies and damselflies have maintained their distinctive, independently controllable, four-winged form for over 300Myr. Despite efforts at understanding the implications of flapping flight with two pairs of wings, previous studies have generally painted a rather disappointing picture: interaction between fore and hind wings reduces the lift compared with two pairs of wings operating in isolation. Here, we demonstrate with a mechanical model dragonfly that, despite presenting no advantage in terms of lift, flying with two pairs of wings can be highly effective at improving aerodynamic efficiency. This is achieved by recovering energy from the wake wasted as swirl in a manner analogous to coaxial contra-rotating helicopter rotors. With the appropriate fore–hind wing phasing, aerodynamic power requirements can be reduced up to 22 per cent compared with a single pair of wings, indicating one advantage of four-winged flying that may apply to both dragonflies and, in the future, biomimetic micro air vehicles.     

Wing‐kinematics measurement and flight modelling of the bamboo weevil C. buqueti

Insects are one of the most agile flyers in nature, and studying the kinematics of their wings can provide important data for the design of insect‐like wing‐flapping micro aerial vehicles. This study integrates high‐speed photogrammetry and three‐dimensional (3D) force measurement system to explore the kinematics of Cyrtotrachelus buqueti during the wing‐flapping flight. The tracking point at the wing tip of the hind wing was recorded using high‐speed videography. The lift‐thrust force characteristic of wing‐flapping motion was obtained by the 3D force sensor. Quantitative measurements of wing kinematics show that the wing‐flapping pattern of the hind wing of C. buqueti was revealed as a double figure‐eight trajectory. The kinematic modelling of the wing‐flapping pattern was then established by converting the flapping motion into rotational motion about the pivoting wing base in the reference coordinate system. Moreover, the lift force generated by C. buqueti during the wing‐flapping flight is sufficient to support its body weight without the need to use thrust force to compensate for the lack of lift force.Inspec keywords: video recording, force sensors, photogrammetry, kinematics, force measurement, aerospace componentsOther keywords: kinematic modelling, pivoting wing base, wing‐flapping flight, insect‐like wing‐flapping microaerial vehicles, high‐speed videography, 3D force sensor, Cyrtotrachelus buqueti, wing kinematics measurement, wing‐flapping motion pattern, lift‐thrust force characteristics, bamboo weevil C. buqueti, high‐speed photogrammetry, three‐dimensional force measurement system, 3D force measurement system, double figure‐eight trajectory     

Time-resolved vortex wake of a common swift flying over a range of flight speeds

The wake of a freely flying common swift (Apus apus L.) is examined in a wind tunnel at three different flight speeds, 5.7, 7.7 and 9.9 m s⁻¹. The wake of the bird is visualized using high-speed stereo digital particle image velocimetry (DPIV). Wake images are recorded in the transverse plane, perpendicular to the airflow. The wake of a swift has been studied previously using DPIV and recording wake images in the longitudinal plane, parallel to the airflow. The high-speed DPIV system allows for time-resolved wake sampling and the result shows features that were not discovered in the previous study, but there was approximately a 40 per cent vertical force deficit. As the earlier study also revealed, a pair of wingtip vortices are trailing behind the wingtips, but in addition, a pair of tail vortices and a pair of ‘wing root vortices’ are found that appear to originate from the wing/body junction. The existence of wing root vortices suggests that the two wings are not acting as a single wing, but are to some extent aerodynamically detached from each other. It is proposed that this is due to the body disrupting the lift distribution over the wing by generating less lift than the wings.