David Lentink

Biofluiddynamic scaling of flapping, spinning and translating fins and wings

SUMMARY Organisms that swim or fly with fins or wings physically interact with the surrounding water and air. The interactions are governed by the morphology and kinematics of the locomotory system that form boundary conditions to the Navier–Stokes (NS) equations. These equations represent Newtons law of motion for the fluid surrounding the organism. Several dimensionless numbers, such as the Reynolds number and Strouhal number, measure the influence of morphology and kinematics on the fluid dynamics of swimming and flight. There exists, however, no coherent theoretical framework that shows how such dimensionless numbers of organisms are linked to the NS equation. Here we present an integrated approach to scale the biological fluid dynamics of a wing that flaps, spins or translates. Both the morphology and kinematics of the locomotory system are coupled to the NS equation through which we find dimensionless numbers that represent rotational accelerations in the flow due to wing kinematics and morphology. The three corresponding dimensionless numbers are (1) the angular acceleration number, (2) the centripetal acceleration number, and (3) the Rossby number, which measures Coriolis acceleration. These dimensionless numbers consist of length scale ratios, which facilitate their geometric interpretation. This approach gives fundamental insight into the physical mechanisms that explain the differences in performance among flapping, spinning and translating wings. Although we derived this new framework for the special case of a model fly wing, the method is general enough to make it applicable to other organisms that fly or swim using wings or fins.

Influence of wing kinematics on aerodynamic performance in hovering insect flight

The influence of different wing kinematic models on the aerodynamic performance of a hovering insect is investigated by means of two-dimensional time-dependent Navier–Stokes simulations. For this, simplified models are compared with averaged representations of the hovering fruit fly wing kinematics. With increasing complexity, a harmonic model, a Robofly model and two more-realistic fruit fly models are considered, all dynamically scaled at Re = 110. To facilitate the comparison, the parameters of the models were selected such that their mean quasi-steady lift coefficients were matched. Details of the vortex dynamics, as well as the resulting lift and drag forces, were studied. The simulation results reveal that the fruit fly wing kinematics result in forces that differ significantly from those resulting from the simplified wing kinematic models. In addition, light is shed on the effect of different characteristic features of the insect wing motion. The angle of attack variation used by fruit flies increases aerodynamic performance, whereas the deviation is probably used for levelling the forces over the cycle.

Leading-Edge Vortices Elevate Lift of Autorotating Plant Seeds

Helicopter Seed Lift The “helicopter” seeds of maple trees and other similar autorotating seeds detach from their parent tree under windy conditions and gyrate as they are dispersed by the wind. The reproductive success of the tree depends on the flight performance of its seeds. Autorotating seeds are known to generate high lift as they slowly descend through the air, but the means by which they do so is unclear. Lentink et al. (p. 1438, see the cover) have elucidated the aerodynamic mechanism for high lift in autorotating seeds using a robot model seed and a three-dimensional flow measurement technique. Maple seeds and a hornbeam seed create a prominent leading-edge vortex that is similar to the flow structures that are responsible for the high lift generated by the wings of hovering insects and bats. Thus, both animals and plants have converged on an identical aerodynamic solution for generating lift. Winged plant seeds use leading edge vortices to create lift, in the same way that flying animals do. As they descend, the autorotating seeds of maples and some other trees generate unexpectedly high lift, but how they attain this elevated performance is unknown. To elucidate the mechanisms responsible, we measured the three-dimensional flow around dynamically scaled models of maple and hornbeam seeds. Our results indicate that these seeds attain high lift by generating a stable leading-edge vortex (LEV) as they descend. The compact LEV, which we verified on real specimens, allows maple seeds to remain in the air more effectively than do a variety of nonautorotating seeds. LEVs also explain the high lift generated by hovering insects, bats, and possibly birds, suggesting that the use of LEVs represents a convergent aerodynamic solution in the evolution of flight performance in both animals and plants.

Automated visual tracking for studying the ontogeny of zebrafish swimming

SUMMARY The zebrafish Danio rerio is a widely used model organism in studies of genetics, developmental biology, and recently, biomechanics. In order to quantify changes in swimming during all stages of development, we have developed a visual tracking system that estimates the posture of fish. Our current approach assumes planar motion of the fish, given image sequences taken from a top view. An accurate geometric fish model is automatically designed and fit to the images at each time frame. Our approach works across a range of fish shapes and sizes and is therefore well suited for studying the ontogeny of fish swimming, while also being robust to common environmental occlusions. Our current analysis focuses on measuring the influence of vertebra development on the swimming capabilities of zebrafish. We examine wild-type zebrafish and mutants with stiff vertebrae (stocksteif) and quantify their body kinematics as a function of their development from larvae to adult (mutants made available by the Hubrecht laboratory, The Netherlands). By tracking the fish, we are able to measure the curvature and net acceleration along the body that result from the fishs body wave. Here, we demonstrate the capabilities of the tracking system for the escape response of wild-type zebrafish and stocksteif mutant zebrafish. The response was filmed with a digital high-speed camera at 1500 frames s–1. Our approach enables biomechanists and ethologists to process much larger datasets than possible at present. Our automated tracking scheme can therefore accelerate insight in the swimming behavior of many species of (developing) fish.

The Scalable Design of Flapping Micro-Air Vehicles Inspired by Insect Flight

Here we explain how flapping micro air vehicles (MAVs) can be designed at different scales, from bird to insect size. The common believe is that micro fixed wing airplanes and helicopters outperform MAVs at bird scale, but become inferior to flapping MAVs at the scale of insects as small as fruit flies. Here we present our experience with designing and building micro flapping air vehicles that can fly both fast and slow, hover, and take-off and land vertically, and we present the scaling laws and structural wing designs to miniaturize these designs to insect size. Next we compare flapping, spinning and translating wing performance to determine which wing motion results in the highest aerodynamic performance at the scale of hummingbirds, house flies and fruit flies. Based on this comparison of hovering performance, and our experience with our flapping MAV, we find that flapping MAVs are fundamentally much less energy efficient than helicopters, even at the scale of a fruit fly with a wing span of 5 mm. We find that insect-sized MAVs are most energy effective when propelled by spinning wings.

Vortex-wake interactions of a flapping foil that models animal swimming and flight.

SUMMARY The fluid dynamics of many swimming and flying animals involves the generation and shedding of vortices into the wake. Here we studied the dynamics of similar vortices shed by a simple two-dimensional flapping foil in a soap-film tunnel. The flapping foil models an animal wing, fin or tail in forward locomotion. The vortical flow induced by the foil is correlated to (the resulting) thickness variations in the soap film. We visualized these thickness variations through light diffraction and recorded it with a digital high speed camera. This set-up enabled us to study the influence of foil kinematics on vortex-wake interactions. We varied the dimensionless wavelength of the foil (λ*=4–24) at a constant dimensionless flapping amplitude (A*=1.5) and geometric angle of attack amplitude (Aα,geo=15°). The corresponding Reynolds number was of the order of 1000. Such values are relevant for animal swimming and flight. We found that a significant leading edge vortex (LEV) was generated by the foil at low dimensionless wavelengths (λ*<10). The LEV separated from the foil for all dimensionless wavelengths. The relative time (compared with the flapping period) that the unstable LEV stayed above the flapping foil increased for decreasing dimensionless wavelengths. As the dimensionless wavelength decreased, the wake dynamics evolved from a wavy von Kármán-like vortex wake shed along the sinusoidal path of the foil into a wake densely packed with large interacting vortices. We found that strongly interacting vortices could change the wake topology abruptly. This occured when vortices were close enough to merge or tear each other apart. Our experiments show that relatively small changes in the kinematics of a flapping foil can alter the topology of the vortex wake drastically.

Power reduction and the radial limit of stall delay in revolving wings of different aspect ratio

Airplanes and helicopters use high aspect ratio wings to reduce the power required to fly, but must operate at low angle of attack to prevent flow separation and stall. Animals capable of slow sustained flight, such as hummingbirds, have low aspect ratio wings and flap their wings at high angle of attack without stalling. Instead, they generate an attached vortex along the leading edge of the wing that elevates lift. Previous studies have demonstrated that this vortex and high lift can be reproduced by revolving the animal wing at the same angle of attack. How do flapping and revolving animal wings delay stall and reduce power? It has been hypothesized that stall delay derives from having a short radial distance between the shoulder joint and wing tip, measured in chord lengths. This non-dimensional measure of wing length represents the relative magnitude of inertial forces versus rotational accelerations operating in the boundary layer of revolving and flapping wings. Here we show for a suite of aspect ratios, which represent both animal and aircraft wings, that the attachment of the leading edge vortex on a revolving wing is determined by wing aspect ratio, defined with respect to the centre of revolution. At high angle of attack, the vortex remains attached when the local radius is shorter than four chord lengths and separates outboard on higher aspect ratio wings. This radial stall limit explains why revolving high aspect ratio wings (of helicopters) require less power compared with low aspect ratio wings (of hummingbirds) at low angle of attack and vice versa at high angle of attack.

Flapping wing aerodynamics: from insects to vertebrates.

ABSTRACT More than a million insects and approximately 11,000 vertebrates utilize flapping wings to fly. However, flapping flight has only been studied in a few of these species, so many challenges remain in understanding this form of locomotion. Five key aerodynamic mechanisms have been identified for insect flight. Among these is the leading edge vortex, which is a convergent solution to avoid stall for insects, bats and birds. The roles of the other mechanisms – added mass, clap and fling, rotational circulation and wing–wake interactions – have not yet been thoroughly studied in the context of vertebrate flight. Further challenges to understanding bat and bird flight are posed by the complex, dynamic wing morphologies of these species and the more turbulent airflow generated by their wings compared with that observed during insect flight. Nevertheless, three dimensionless numbers that combine key flow, morphological and kinematic parameters – the Reynolds number, Rossby number and advance ratio – govern flapping wing aerodynamics for both insects and vertebrates. These numbers can thus be used to organize an integrative framework for studying and comparing animal flapping flight. Here, we provide a roadmap for developing such a framework, highlighting the aerodynamic mechanisms that remain to be quantified and compared across species. Ultimately, incorporating complex flight maneuvers, environmental effects and developmental stages into this framework will also be essential to advancing our understanding of the biomechanics, movement ecology and evolution of animal flight. Summary: By comparing flapping flight across insects and vertebrates, we identify how their morphology and kinematics govern both shared and distinct aerodynamic mechanisms, and highlight open research questions in animal flight.

Vortex interactions with flapping wings and fins can be unpredictable

As they fly or swim, many animals generate a wake of vortices with their flapping fins and wings that reveals the dynamics of their locomotion. Previous studies have shown that the dynamic interaction of vortices in the wake with fins and wings can increase propulsive force. Here, we explore whether the dynamics of the vortex interactions could affect the predictability of propulsive forces. We studied the dynamics of the interactions between a symmetrically and periodically pitching and heaving foil and the vortices in its wake, in a soap-film tunnel. The phase-locked movie sequences reveal that abundant chaotic vortex-wake interactions occur at high Strouhal numbers. These high numbers are representative for the fins and wings of near-hovering animals. The chaotic wake limits the forecast horizon of the corresponding force and moment integrals. By contrast, we find periodic vortex wakes with an unlimited forecast horizon for the lower Strouhal numbers (0.2–0.4) at which many animals cruise. These findings suggest that swimming and flying animals could control the predictability of vortex-wake interactions, and the corresponding propulsive forces with their fins and wings.

Biomimetics: Flying like a fly

When biologists unravelled the principles of insect flight, they inspired a generation of engineers to build on their aerodynamic feats. Thanks to a revolution in micro-manufacturing techniques, the first robotic fly now flies.