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Two-dimensional numerical simulations are used to study the coupled fluid-structureelectric interaction of a simple model of an inverted piezoelectric flag, and to investigate the dynamics of the flow-structure interaction of this configuration as well as its energy harvesting performance. In particular, the dynamic response of the inverted flag as well as the associated flow patterns are examined for a range of inertia, bending stiffness and Reynolds numbers, and categorized into distinct vibrational states based on the symmetry of the motion as well as the amplitude. Simulations indicate that large-amplitude vibrations can be achieved over a large range of parameters and there is also evidence of lock-on between the flag flutter and the intrinsic wake shedding phenomenon. The initial inclination of the flag to the prevailing flow is found to significantly affect the flutter performance for inclination angles exceeding 15 • . The state with large symmetric flutter is identified as being most promising for energy harvesting, and the effect of piezoelectric material parameters on the energy harvesting performance of this flutter state is examined in detail. The maximum energy efficiency of the flags is found to be approximately 7 %, and the maximum occurs when there is a match between the time scales of flutter and the intrinsic time scale of the piezoelectric circuit. The simulations are used to examine a simple scaling law that could be used to predict the energy harvesting performance of such devices.

SUMMARYWe examine numerically the performance of a thin foil reinforced by embedded rays resembling the caudal fins of many fishes. In our study, the supporting rays are depicted as nonlinear Euler-Bernoulli beams with three-dimensional deformability. This structural model is then incorporated into a boundary-element hydrodynamic model to achieve coupled fluid-structure interaction simulation. Kinematically, we incorporate both a homocercal mode with dorso-ventral symmetry and a heterocercal mode with dorso-ventral asymmetry. Using the homocercal mode, our results demonstrate that the anisotropic deformability of the rayreinforced fin significantly increases its capacity of force generation. This performance enhancement manifests as increased propulsion efficiency, reduced transverse force and reduced sensitivity to kinematic parameters. Further reduction in transverse force is observed by using the heterocercal mode. In the heterocercal model, the fin also generates a small lifting force, which may be important in vertical maneuvers. Via three-dimensional flow visualization, a chain of vortex rings is observed in the wake. Detailed features of the wake, e.g. the orientation of the vortex rings in the heterocercal mode, agree with predictions based upon particle image velocimetry (PIV) measurements of flow around live fish.

The flow-induced fluttering motion of a flexible reed inside a heated channel is modeled numerically and used to investigate the relationship between the aeroelastic vibration of the reed and heat-transfer enhancement. An immersed boundary method is developed to solve the coupled flow-structure-thermal problem, and the simulations show that the vibrating reed significantly increases the mean heat flux through the channel, as well as the thermal performance, quantified in terms of the thermal enhancement factor. The effect of reed material properties on vibratory dynamics and heat transfer is studied. Changes in material properties produce a rich variety of vibratory behavior, and the thermal performance is found to depend more strongly on the reed inertia than its bending stiffness. The effects of both the Reynolds number and channel confinement are examined and it is found that the thermal performance is maximized when the reed creates large modulations in the boundary layer of the channel, while at the same time avoiding the creation of strong vortices.

A numerical model of a ray-reinforced fin is developed to investigate the relation between its structural characteristics and its force generation capacity during flapping motion. In this two-dimensional rendition, the underlying rays are modelled as springs, and the membrane is modelled as a flexible but inextensible plate. The fin kinematics is characterized by its oscillation frequency and the phase difference between different rays (which generates a pitching motion). An immersed boundary method (IBM) is applied to solve the fluid–structure interaction problem. The focus of the current paper is on the effects of ray flexibility, especially the detailed distribution of ray stiffness, upon the capacity of thrust generation. The correlation between thrust generation and features of the surrounding flow (especially the leading edge separation) is also examined. Comparisons are made between a fin with rigid rays, a fin with identical flexible rays, and a fin with flexible rays and strengthened leading edge. It is shown that with flexible rays, the thrust production can be significantly increased, especially in cases when the phase difference between different rays is not optimized. By strengthening the leading edge, a higher propulsion efficiency is observed. This is mostly attributed to the reduction of the effective angle of attack at the leading edge, accompanied by mitigation of leading edge separation and dramatic changes in characteristics of the wake. In addition, the flexibility of the rays causes reorientation of the fluid force so that it tilts more towards the swimming direction and the thrust is thus increased.

The stability of a thin flexible plate confined inside an inviscid two-dimensional channel is examined using a nonlinear eigenvalue analysis method. A new Green's function for the vortex wake of the flexible plate inside the channel, as well as its rapidly convergent series approximation, is proposed. Comparison with a fully coupled Navier-Stokes fluid-structure interaction model indicates that the current inviscid model successfully predicts the flutter boundary for a confined flexible plate. The analysis also shows that confinement has a destabilizing effect on heavy plates. Furthermore, as the confinement is increased, the oscillating frequency of the plate increases and new peaks appear in its stability curve. Asymmetric placement of the plate within the channel, especially when the plate is very close to one wall, also modifies the stability curve of the system by shifting the mode transition points toward smaller fluid-to-plate inertia ratios. Our study suggests that the degree of confinement and asymmetric placement of the plate in the channel could be used to alter the flutter instability of the plate, and to adjust the frequency of flutter.

The deformability of insect wings is associated with the embedded skeleton (venation). In this paper, the aerodynamic performance of wings with nonuniform flexibility is computationally investigated. By using a two-dimensional rendition, the underlying veins are modeled as springs, and the membrane is modeled as a flexible plate. The focus is on the effects of the detailed distribution of vein flexibility upon the performance of such a wing in the generation of lift force. Specifically, we are interested in finding the importance of leading edge strengthening. Towards this end, the aerodynamic performances of three wings, a rigid wing, a flexible wing with identical veins, and a flexible wing with strengthened leading edge, are studied and compared against each other. It is shown that the flexible wing with leading edge strengthening is capable of producing significantly higher lift force without consuming more energy. This is found to be related to the stabilizing and cambering effects at the leading edge, which enhances the leading edge vortices. In addition, in contrast to the other two wings, which show sensitivity to kinematic parameters, the wing with strengthened leading edge perform well over a wide range of parameters.

SUMMARYWe numerically examine the fluid-structure interaction and force generation of a skeleton-reinforced fin that geometrically, structurally and kinematically resembles the pectoral fin of a fish during labriform swimming. This fin contains a soft membrane with negligible bending stiffness and 12 embedded rays (modeled as beams). A potential flow-based boundary element model is applied to solve the fluid flow around the fin, in which the vorticity field is modeled as thin vorticity sheets shed from prescribed locations (the sharp trailing edge). The fin motion is actuated by dorsoventral and anteroposterior rotations of the rays (the motion of each ray is controlled individually), as well as pitching motion of the baseline. Consequently, the fin undergoes a combination of flapping (lift-based) and rowing (drag-based) motions typical in labriform swimming. The fin motion contains two strokes: a recovery stroke and a power stroke. The performance of the fin depends upon kinematic parameters such as the Strouhal number, the phase lag between rays, the pitching motion of the baseline and the passive deformations of the rays. The most interesting finding is that the strengthening of the ray at the leading edge plays a pivotal role in performance enhancement by reducing the effective angle of attack and decreasing the power expenditure during the recovery stroke. Supplementary material available online at