The influence of wing–wake interactions on the production of aerodynamic forces in flapping flight

We used two-dimensional digital particle image velocimetry (DPIV) to visualize flow patterns around the flapping wing of a dynamically scaled robot for a series of reciprocating strokes starting from rest. The base of the wing was equipped with strain gauges so that the pattern of fluid motion could be directly compared with the time history of force production. The results show that the development and shedding of vortices throughout each stroke are highly stereotyped and influence force generation in subsequent strokes. When a wing starts from rest, it generates a transient force as the leading edge vortex (LEV) grows. This early peak, previously attributed to added-mass acceleration, is not amenable to quasi-steady models but corresponds well to calculations based on the time derivative of the first moment of vorticity within a sectional slice of fluid. Forces decay to a stable level as the LEV reaches a constant size and remains attached throughout most of the stroke. The LEV grows as the wing supinates prior to stroke reversal, accompanied by an increase in total force. At stroke reversal, both the LEV and a rotational starting vortex (RSV) are shed into the wake, forming a counter-rotating pair that directs a jet of fluid towards the underside of the wing at the start of the next stroke. We isolated the aerodynamic influence of the wake by subtracting forces and flow fields generated in the first stroke, when the wake is just developing, from those produced during the fourth stroke, when the pattern of both the forces and wake dynamics has reached a limit cycle. This technique identified two effects of the wake on force production by the wing: an early augmentation followed by a small attenuation. The later decrease in force is consistent with the influence of a decreased aerodynamic angle of attack on translational forces caused by downwash within the wake and is well explained by a quasi-steady model. The early effect of the wake is not well approximated by a quasi-steady model, even when the magnitude and orientation of the instantaneous velocity field are taken into account. Thus, the wake capture force represents a truly unsteady phenomenon dependent on temporal changes in the distribution and magnitude of vorticity during stroke reversal

On the estimation of swimming and flying forces from wake measurements

The transfer of momentum from an animal to fluid in its wake is fundamental to many swimming and flying modes of locomotion. Hence, properties of the wake are commonly studied in experiments to infer the magnitude and direction of locomotive forces. The determination of which wake properties are necessary and sufficient to empirically deduce swimming and flying forces is currently made ad hoc. This paper systematically addresses the question of the minimum number of wake properties whose combination is sufficient to determine swimming and flying forces from wake measurements. In particular, it is confirmed that the spatial velocity distribution (i.e. the velocity field) in the wake is by itself insufficient to determine swimming and flying forces, and must be combined with the fluid pressure distribution. Importantly, it is also shown that the spatial distribution of rotation and shear (i.e. the vorticity field) in the wake is by itself insufficient to determine swimming and flying forces, and must be combined with a parameter that is analogous to the fluid pressure. The measurement of this parameter in the wake is shown to be identical to a calculation of the added-mass contribution from fluid surrounding vortices in the wake, and proceeds identically to a measurement of the added-mass traditionally associated with fluid surrounding solid bodies. It is demonstrated that the velocity/pressure perspective is equivalent to the vorticity/vortex-added-mass approach in the equations of motion. A model is developed to approximate the contribution of wake vortex added-mass to locomotive forces, given a combination of velocity and vorticity field measurements in the wake. A dimensionless parameter, the wake vortex ratio (denoted Wa), is introduced to predict the types of wake flows for which the contribution of forces due to wake vortex added-mass will become non-negligible. Previous wake analyses are reexamined in light of this parameter to infer the existence and importance of wake vortex added-mass in those cases. In the process, it is demonstrated that the commonly used time-averaged force estimates based on wake measurements are not sufficient to prove that an animal is generating the locomotive forces necessary to sustain flight or maintain neutral buoyancy

Preferential accumulation of bubbles in Couette-Taylor flow patterns

We investigate the migration of bubbles in several flow patterns occurring within the gap between a rotating inner cylinder and a concentric fixed outer cylinder. The time-dependent evolution of the two-phase flow is predicted through three-dimensional Euler-Lagrange simulations. Lagrangian tracking of spherical bubbles is coupled with direct numerical simulation of the Navier-Stokes equations. We assume that bubbles do not influence the background flow (one-way coupling simulations). The force balance on each bubble takes into account buoyancy, added-mass, viscous drag and shear-induced lift forces. For increasing velocities of the rotating inner cylinder, the flow in the fluid gap evolves from the purely azimuthal steady Couette flow to Taylor toroidal vortices and eventually a wavy vortex flow. The migration of bubbles is highly dependent on the balance between buoyancy and centripetal forces (mostly due to the centripetal pressure gradient) directed toward the inner cylinder and the vortex cores. Depending on the rotation rate of the inner cylinder, bubbles tend to accumulate alternatively along the inner wall, inside the core of Taylor vortices or at particular locations within the wavy vortices. A stability analysis of the fixed points associated with bubble trajectories provides a clear understanding of their migration and preferential accumulation. The location of the accumulation points is parameterized by two dimensionless parameters expressing the balance of buoyancy, centripetal attraction toward the inner rotating cylinder, and entrapment in Taylor vortices. A complete phase diagram summarizing the various regimes of bubble migration is built. Several experimental conditions considered by Djéridi et al.1 are reproduced; the numerical results reveal a very good agreement with the experiments. When the rotation rate is further increased, the numerical results indicate the formation of oscillating bubble strings, as observed experimentally by Djéridi et al.2. After a transient state, bubbles collect at the crests or troughs of the wavy vortices. An analysis of the flow characteristics clearly indicates that bubbles accumulate in the low-pressure regions of the flow field

The aerodynamic effects of wing–wing interaction in flapping insect wings

We employed a dynamically scaled mechanical model of the small fruit fly Drosophila melanogaster (Reynolds number 100–200) to investigate force enhancement due to contralateral wing interactions during stroke reversal (the 'clap-and-fling'). The results suggest that lift enhancement during clap-and-fling requires an angular separation between the two wings of no more than 10–12°. Within the limitations of the robotic apparatus, the clap-and-fling augmented total lift production by up to 17%, but depended strongly on stroke kinematics. The time course of the interaction between the wings was quite complex. For example, wing interaction attenuated total force during the initial part of the wing clap, but slightly enhanced force at the end of the clap phase. We measured two temporally transient peaks of both lift and drag enhancement during the fling phase: a prominent peak during the initial phase of the fling motion, which accounts for most of the benefit in lift production, and a smaller peak of force enhancement at the end fling when the wings started to move apart. A detailed digital particle image velocimetry (DPIV) analysis during clap-and-fling showed that the most obvious effect of the bilateral 'image' wing on flow occurs during the early phase of the fling, due to a strong fluid influx between the wings as they separate. The DPIV analysis revealed, moreover, that circulation induced by a leading edge vortex (LEV) during the early fling phase was smaller than predicted by inviscid two-dimensional analytical models, whereas circulation of LEV nearly matched the predictions of Weis-Fogh's inviscid model at late fling phase. In addition, the presence of the image wing presumably causes subtle modifications in both the wake capture and viscous forces. Collectively, these effects explain some of the changes in total force and lift production during the fling. Quite surprisingly, the effect of clap-and-fling is not restricted to the dorsal part of the stroke cycle but extends to the beginning of upstroke, suggesting that the presence of the image wing distorts the gross wake structure throughout the stroke cycle