Flexibility effects on vortex formation of translating plates

Vortex structures made by impulsively translating low aspect-ratio plates are studied experimentally using defocusing digital particle image velocimetry. The investigation of translating plates with a 90° angle of attack is important since it is a fundamental model for a better understanding of drag-based propulsion systems. Rectangular flat rigid, flexible and curved-rigid thin plates with the same aspect ratio are studied in order to develop qualitative and quantitative understanding of their vortex structures and hydrodynamic forces. We find that the vortex formation processes of all three cases are drastically different from each other. The interaction of leading-edge vortices and tip flow near the tip region is an important mechanism to distinguish vortex patterns among these three cases. The drag trends of three cases are correlated closely with vortex structure and circulation. The initial peak of hydrodynamic force in the flexible plate case is not as large as the initial peak of the flat and curved rigid plate cases during the acceleration phase. However, after the initial peak, the flexible plate generates a large force comparable to that of the flat-rigid plate case in spite of its deformed shape, which results from the slow development of the vortex structure

3D vortex formation of rigid and flexible plates in impulsively starting motion

This fluid dynamics video shows three-dimensional vortex formation process for plates in impulsive motion which is investigated experimentally by using defocusing digital particle image velocimetry (DDPIV). Rigid and flexible plate cases are compared in order to study the effect of flexibility on 3D vortex formation and associated hydrodynamic forces. This study was motivated by the general question of how the flexibility of flapping propulsors in flying and swimming animals affects vortex formation and propulsive force. For translating and rotating motion, the flexible plate generates a vortex morphology which is drastically different from that of the rigid plate. We identified the deflection of the tip region as the source of this difference. The flexible plate does not produce a large peak for the hydrodynamic force at the impulsive start and stop. This force trend is correlated with smooth vortex formation and shedding processes

Vortex dynamics of clapping plates

Vortex formation and force generation of clapping plates with various aspect ratios (AR) and stroke angles were investigated. Experiments were performed with a pair of hinged rectangular plates that were rotated symmetrically in a static fluid, and defocusing digital particle image velocimetry was employed to measure the three-dimensional flow field. Single-plate cases were also studied to compare with clapping plate cases. As AR decreases, both circulation of the tip vortex and area enclosed by the vortex loop increase inversely. An empirical power-law relationship with a negative exponent is found between total impulse and AR for a given stroke angle. The sensitivity of the force generated by the plates to the change of AR is larger at the smaller stroke angle because of faster acceleration and deceleration. The increase in impulse per plate from the single-plate case to the clapping double-plate case is larger for lower AR. These results reveal that low AR wings are more efficient in propulsive force generation in some specific modes of unsteady flapping flight. The evolution of the wake structures is found to depend on AR and stroke angle

Wall-bounded periodic snap-through and contact of a buckled sheet

Fluid flow passing a post-buckled sheet placed between two close confining walls induces periodic snap-through oscillations and contacts that can be employed for triboelectric energy harvesting. The responses of a two-dimensional sheet to a uniform flow and wall confinement in both equilibrium and post-equilibrium states are numerically investigated by varying the distance between the two ends of the sheet, gap distance between the confining walls, and flow velocity. Cases with strong interactions between the sheet and walls are of most interest for examining how contact with the walls affects the dynamics of the sheet and flow structure. At equilibrium, contact with the wall displaces the sheet to form a nadir on its front part, yielding a lower critical flow velocity for the transition to snap-through oscillations. However, reducing the gap distance between the walls below a certain threshold distinctly shifts the shape of the sheet, alters pressure distribution, and eventually leads to a notable delay in the instability. The contact between the oscillating sheet and the walls at post-equilibrium is divided into several distinct modes, changing from sliding/rolling contact to bouncing contact with increasing flow velocity. During this transition, the time-averaged contact force exerted on the sheet decreases with the flow velocity. The vortices generated at the extrema of the oscillating sheet are annihilated by direct contact with the walls and merging with the shear layers formed by the walls, resulting in a wake structure dominated by the unstable shear layers.Comment: 30 pages, 14 figures, 4 Movie

Large-amplitude flapping of an inverted flag in a uniform steady flow – a vortex-induced vibration

The dynamics of a cantilevered elastic sheet, with a uniform steady flow impinging on its clamped end, have been studied widely and provide insight into the stability of flags and biological phenomena. Recent measurements by Kim et al. (J. Fluid Mech., vol. 736, 2013, R1) show that reversing the sheet’s orientation, with the flow impinging on its free edge, dramatically alters its dynamics. In contrast to the conventional flag, which exhibits (small-amplitude) flutter above a critical flow speed, the inverted flag displays large-amplitude flapping over a finite band of flow speeds. The physical mechanisms giving rise to this flapping phenomenon are currently unknown. In this article, we use a combination of mathematical theory, scaling analysis and measurement to establish that this large-amplitude flapping motion is a vortex-induced vibration. Onset of flapping is shown mathematically to be due to divergence instability, verifying previous speculation based on a two-point measurement. Reducing the sheet’s aspect ratio (height/length) increases the critical flow speed for divergence and ultimately eliminates flapping. The flapping motion is associated with a separated flow – detailed measurements and scaling analysis show that it exhibits the required features of a vortex-induced vibration. Flapping is found to be periodic predominantly, with a transition to chaos as flow speed increases. Cessation of flapping occurs at higher speeds – increased damping reduces the flow speed range where flapping is observed, as required. These findings have implications for leaf motion and other biological processes, such as the dynamics of hair follicles, because they also can present an inverted-flag configuration

Flapping dynamics of an inverted flag

The dynamics of an inverted flag are investigated experimentally in order to find the conditions under which self-excited flapping can occur. In contrast to a typical flag with a fixed leading edge and a free trailing edge, the inverted flag of our study has a free leading edge and a fixed trailing edge. The behaviour of the inverted flag can be classified into three regimes based on its non-dimensional bending stiffness scaled by flow velocity and flag length. Two quasi-steady regimes, straight mode and fully deflected mode, are observed, and a limit-cycle flapping mode with large amplitude appears between the two quasi-steady regimes. Bistable states are found in both straight to flapping mode transition and flapping to deflected mode transition. The effect of mass ratio, relative magnitude of flag inertia and fluid inertia, on the non-dimensional bending stiffness range for flapping is negligible, unlike the instability of the typical flag. Because of the unsteady fluid force, a flapping sheet can produce elastic strain energy several times larger than a sheet of the deformed mode, improving the conversion of fluid kinetic energy to elastic strain energy. According to the analysis of the leading-edge vortex formation process, the time scale of optimal vortex formation correlates with efficient conversion to elastic strain energy during bending

Characteristics of Three-dimensional Vortex Formation and Propulsive Performance in Flapping Locomotion

Three-dimensional vortex formation and propulsive performance were studied experimentally to identify some of the main characteristic mechanisms of flapping locomotion. Mechanical models with thin plates were used to simulate flapping and translating motions of animal propulsors. Three-dimensional flow fields were mapped quantitatively using defocusing digital particle image velocimetry. First, vortex structures made by impulsively translating low aspect-ratio plates were studied. The investigation of translating plates with a 90 degree angle of attack is important since it is a fundamental model for a better understanding of drag-based propulsion systems. Rectangular flat-rigid, flexible, and curved-rigid thin plastic plates with the same aspect ratio were used to compare their vortex structures and hydrodynamic forces. The interaction of the tip flow and the nearby vortex is a critical flow phenomenon to distinguish vortex patterns among these three cases. In the flexible plate case, slow development of the vortex structure causes a small initial peak in hydrodynamic force during the acceleration phase. However, after the initial peak, the flexible plate generates large force magnitude comparable to that of the flat-rigid plate case. Drag-based paddling propulsion was also studied to explain some of the fundamental differences in vortex formation of lift-based and drag-based propulsions. While the temporal change of the inner area enclosed by the vortex loop is an important factor in thrust generation of lift-based propulsion, the temporal change of the vortex strength becomes more important in drag-based propulsion. Spanwise flow behind the paddling plate plays an important role in tip vortex motion and thrust generation. The distribution of spanwise flow depends on the propulsor shape and the Reynolds number. A delta-shaped propulsor generates strong spanwise flow compared to a rectangular propulsor. For the low Reynolds number case, the spanwise flow is not as strong as that of the high Reynolds number case. The flexible propulsor can smooth out force peaks during impulsive motions without sacrificing total impulse, which is advantageous in avoiding structural failures and stabilizing body motion. The role of the stopping vortex was addressed in optimizing a stroke angle of paddling animals. In addition, vortex formation of clapping propulsion was investigated by varying aspect ratio and stroke angle. A low aspect-ratio propulsor produces larger total impulse than a high aspect-ratio propulsor. As the aspect ratio increases, circulation of the vortex is strengthened, and the inner area enclosed by the vortex structure tends to enlarge. Moreover, in terms of thrust, the advantage of a single plate over double clapping plates is larger for the lower aspect-ratio case. These results offer information to better understand the benefit of low aspect-ratio wings in force generation under specific locomotion modes. When a pair of plates claps, a vortex loop forms from two counter-rotating tip vortices by a reconnection process. The dynamics of wake structures are dependent on the aspect ratio and the stroke angle. Vortex formation and vorticity transport processes of translating and rotating plates with a 45 degree angle of attack were investigated as well. In both translating and rotating cases, the spanwise flow over the plate and the vorticity tilting process inside the leading-edge vortex were observed. The distribution of spanwise flow is a prominent distinction between the vortex structures of these two cases. While spanwise flow is confined inside the leading-edge vortex for the translating case, it is widely present over the plate and the wake region of the rotating case. As the Reynolds number decreases, due to the increase in viscosity, leading-edge and tip vortices tend to spread inside the area swept by the rotating plate, which results in lower lift force generation. Lastly, for translating motion, the dynamics of the vortex in corner regions was compared among three different corner shapes. For a large corner angle, the forward movement of the vortex tends to be uniform along the plate edges. However, for a small corner angle, the vortex close to the corner moves forward following the plate while the vortex away from the corner retards its forward movement.</p