Benjamin Thiria

Rather than resonance, flapping wing flyers may play on aerodynamics to improve performance

Saving energy and enhancing performance are secular preoccupations shared by both nature and human beings. In animal locomotion, flapping flyers or swimmers rely on the flexibility of their wings or body to passively increase their efficiency using an appropriate cycle of storing and releasing elastic energy. Despite the convergence of many observations pointing out this feature, the underlying mechanisms explaining how the elastic nature of the wings is related to propulsive efficiency remain unclear. Here we use an experiment with a self-propelled simplified insect model allowing to show how wing compliance governs the performance of flapping flyers. Reducing the description of the flapping wing to a forced oscillator model, we pinpoint different nonlinear effects that can account for the observed behavior—in particular a set of cubic nonlinearities coming from the clamped-free beam equation used to model the wing and a quadratic damping term representing the fluid drag associated to the fast flapping motion. In contrast to what has been repeatedly suggested in the literature, we show that flapping flyers optimize their performance not by especially looking for resonance to achieve larger flapping amplitudes with less effort, but by tuning the temporal evolution of the wing shape (i.e., the phase dynamics in the oscillator model) to optimize the aerodynamics.

Passive elastic mechanism to mimic fish- muscle action in anguilliform swimming

Swimmers in nature use body undulations to generate propulsive and manoeuvring forces. The anguilliform kinematics is driven by muscular actions all along the body, involving a complex temporal and spatial coordination of all the local actuations. Such swimming kinematics can be reproduced artificially, in a simpler way, by using the elasticity of the body passively. Here, we present experiments on self-propelled elastic swimmers at a free surface in the inertial regime. By addressing the fluid–structure interaction problem of anguilliform swimming, we show that our artificial swimmers are well described by coupling a beam theory with the potential flow model of Lighthill. In particular, we show that the propagative nature of the elastic wave producing the propulsive force is strongly dependent on the dissipation of energy along the body of the swimmer.

Vortex-induced drag and the role of aspect ratio in undulatory swimmers

During cruising, the thrust produced by a self-propelled swimmer is balanced by a global drag force. For a given object shape, this drag can involve skin friction or form drag, both being well-documented mechanisms. However, for swimmers whose shape is changing in time, the question of drag is not yet clearly established. We address this problem by investigating experimentally the swimming dynamics of undulating thin flexible foils. Measurements of the propulsive performance together with full recording of the elastic wave kinematics are used to discuss the general problem of drag in undulatory swimming. We show that a major part of the total drag comes from the trailing longitudinal vortices that roll-up on the lateral edges of the foils. This result gives a comparative advantage to swimming foils of larger span thus bringing new insight to the role of aspect ratio for undulatory swimmers.

Large-amplitude undulatory swimming near a wall

The propulsive dynamics of a flexible undulating foil in a self-propelled swimming configuration near a wall is studied experimentally. Measurements of the swimming speed and the propulsive force are presented, together with image acquisition of the kinematics of the foil and particle image velocimetry (PIV) in its wake. The presence of the wall enhances the cruising velocity in some cases up to 25% and the thrust by a 45% , for swept angles of 160 and 240°. The physical mechanisms underlying this effect are discussed by studying the vorticity dynamics in the wake of the foil. Proper orthogonal decomposition is applied to the PIV measurements in order to analyse the kinetic energy modal distribution in the flow and to relate it to the propulsion generated by the foil.

Synchronization and collective swimming patterns in fish (Hemigrammus bleheri)

In this work, we address the case of red nose tetra fish Hemigrammus bleheri swimming in groups in a uniform flow, giving special attention to the basic interactions and cooperative swimming of a single pair of fish. We first bring evidence of synchronization of the two fish, where the swimming modes are dominated by ‘out-phase’ and ‘in-phase’ configurations. We show that the transition to this synchronization state is correlated with the swimming speed (i.e. the flow rate), and thus with the magnitude of the hydrodynamic pressure generated by the fish body during each swimming cycle. From a careful spatio-temporal analysis corresponding to those synchronized modes, we characterize the distances between the two individuals in a pair in the basic schooling pattern. We test the conclusions of the analysis of fish pairs with a second set of experiments using groups of three fish. By identifying the typical spatial configurations, we explain how the nearest neighbour interactions constitute the building blocks of collective fish swimming.

Propagating waves in bounded elastic media: Transition from standing waves to anguilliform kinematics

Confined geometries usually involve reflected waves interacting together to form a spatially stationary pattern. A recent study on bio-locomotion, however, has reported that propagating wave kinematics can naturally emerge in a forced elastic rod, even with boundary conditions involving significant reflections. It has been shown that this particular behavior is observed only in the presence of strong damping. Based on those observations, this study aims at giving a quantitative description of the mechanism involved to prevent the build-up of standing waves and generate traveling solutions. The question is discussed here in the framework of handmade artificial swimmers as an example of practical application but we believe that its potential is beyond this scope.

Simple phalanx pattern leads to energy saving in cohesive fish schooling

Significance Fish school structures are firstly based on social life or prey–predator interactions, but another idea has often been raised by hydrodynamicists, claiming that fish could take advantage of schooling behavior from a locomotion efficiency perspective. By using a controlled swimming experiment with real schools, the present work shows that fish swimming together effectively need a less demanding stroke rate to sustain high swimming velocities, using, however, a different collective strategy compared with the usually suggested diamond pattern predicted by vortex-based interactions. The observed strategy, simply consisting of synchronized side-by-side swimming with nearest neighbors, finally, appears to be a lot more convenient for reaching an energy-saving regime. The question of how individuals in a population organize when living in groups arises for systems as different as a swarm of microorganisms or a flock of seagulls. The different patterns for moving collectively involve a wide spectrum of reasons, such as evading predators or optimizing food prospection. Also, the schooling pattern has often been associated with an advantage in terms of energy consumption. In this study, we use a popular aquarium fish, the red nose tetra fish, Hemigrammus bleheri, which is known to swim in highly cohesive groups, to analyze the schooling dynamics. In our experiments, fish swim in a shallow-water tunnel with controlled velocity, and stereoscopic video recordings are used to track the 3D positions of each individual in a school, as well as their tail-beating kinematics. Challenging the widespread idea of fish favoring a diamond pattern to swim more efficiently [Weihs D (1973) Nature 241:290–291], we observe that when fish are forced to swim fast—well above their free-swimming typical velocity, and hence in a situation where efficient swimming would be favored—the most frequent configuration is the “phalanx” or “soldier” formation, with all individuals swimming side by side. We explain this observation by considering the advantages of tail-beating synchronization between neighbors, which we have also characterized. Most importantly, we show that schooling is advantageous as compared with swimming alone from an energy-efficiency perspective.

Resistive thrust production can be as crucial as added mass mechanisms for inertial undulatory swimmers.

In this Rapid Communication, we address a crucial point regarding the description of moderate to high Reynolds numbers aquatic swimmers. For decades, swimming animals have been classified in two different families of propulsive mechanisms based on the Reynolds number: the resistive swimmers, using local friction to produce the necessary thrust force for locomotion at low Reynolds number, and the reactive swimmers, lying in the high Reynolds range, and using added mass acceleration (described by perfect fluid theory). However, inertial swimmers are also systems that dissipate energy, due to their finite size, therefore involving strong resistive contributions, even for high Reynolds numbers. Using a complete model for the hydrodynamic forces, involving both reactive and resistive contributions, we revisit here the physical mechanisms responsible for the thrust production of such swimmers. We show, for instance, that the resistive part of the force balance is as crucial as added mass effects in the modeling of the thrust force, especially for elongated species. The conclusions brought by this work may have significant contributions to the understanding of complex swimming mechanisms, especially for the future design of artificial swimmers.

Modelling of an actuated elastic swimmer

We study the force production dynamics of undulating elastic plates as a model for fish-like inertial swimmers. Using a beam model coupled with Lighthills large-amplitude elongated-body theory, we explore different localised actuations at one extremity of the plate (heaving, pitching, and a combination of both) in order to quantify the reactive and resistive contributions to the thrust. The latter has the form of a quadratic drag in large Reynolds number swimmers and has recently been pointed out as a crucial element in the thrust force balance. We validate the output of a weakly nonlinear solution to the fluid--structure model using thrust force measurements from an experiment with flexible plates subjected to the three different actuation types. The model is subsequently used in a self-propelled configuration ---with a skin friction model that balances thrust to produce a constant cruising speed--- to map the reactive versus resistive thrust production in a parameter space defined by the aspect ratio and the actuation frequency. We show that this balance is modified as the frequency of excitation changes and the response of the elastic plate shifts between different resonant modes, the pure heaving case being the most sensitive to the modal response with drastic changes in the reactive/resistive contribution ratio along the frequency axis. We analyse also the role of the phase lag between the heaving and pitching components in the case of combined actuation, showing in particular a non-trivial effect on the propulsive efficiency.

Bioinspired turbine blades offer new perspectives for wind energy

Wind energy is becoming a significant alternative solution for future energy production. Modern turbines now benefit from engineering expertise, and a large variety of different models exists, depending on the context and needs. However, classical wind turbines are designed to operate within a narrow zone centred around their optimal working point. This limitation prevents the use of sites with variable wind to harvest energy, involving significant energetic and economic losses. Here, we present a new type of bioinspired wind turbine using elastic blades, which passively deform through the air loading and centrifugal effects. This work is inspired from recent studies on insect flight and plant reconfiguration, which show the ability of elastic wings or leaves to adapt to the wind conditions and thereby to optimize performance. We show that in the context of energy production, the reconfiguration of the elastic blades significantly extends the range of operating regimes using only passive, non-consuming mechanisms. The versatility of the new turbine model leads to a large increase of the converted energy rate, up to 35%. The fluid/elasticity mechanisms involved for the reconfiguration capability of the new blades are analysed in detail, using experimental observations and modelling.