Session H6: Aerodynamics: Flexible Structures

Vibrating cantilever beam in a flowing soap film

We present an experimental study of the interaction between a flexible cantilever beam and a flowing fluid medium using a soap film. The vertically falling soap film is capable of attaining speeds ranging from 1.5 - 3 m/s with an operating test section width of 7.5 cm. Experiments were conducted for flexible cantilever beams of length L $\leq$ 10 mm yielding Reynolds number 5000 $<$ $Re$ $<$ 10000 and of cantilever beam thickness ranging from 0.03 - 0.08 mm were placed at angles of attack ranging from 10$^{\circ}$ - 50$^{\circ}$. We visualize the beam displacements and wake with a high-speed camera. Assuming small vibrational amplitudes, we consider the Euler-Bernoulli beam theory to understand the dynamics. From the analysis we find that the normalized average displacement is linear with respect to the square of the free-stream velocity. The vibrational amplitude is also discussed using a similar scaling. Finally, visualization of the downstream vortex structure is related to a beams displacement and vibrational frequency using dimensional analysis.   

Interaction of a highly flexible cantilever beam with grid-generated turbulent flow.

Experiments have been performed to study the fluid-structure interaction of a flexible cantilever beam with the free end facing upstream in anisotropic turbulent flow. Velocity fluctuations in the wind tunnel flow were generated by a turbulence grid. Time-Resolved Particle Image Velocimetry (TR-PIV) techniques were used to acquire velocity data on the plane of a CW laser illumination. Forces exerted on the beam were estimated based on the PIV data by analytically solving the Pressure Poisson Equation (PPE). Two types of interaction were observed. At a lower Reynolds number, fluid forces excite the beam into oscillations of small magnitude. At higher Reynolds number, the excitation is stronger, deflecting the beam sufficiently to cause flow separation and vortex shedding on one side of the beam. The resultant vortices exert additional forces on the beam producing large magnitude oscillations of the beam.   

Aeroelastic Flutter Behavior of a Cantilever and Elastically Mounted Plate within a Nozzle-Diffuser Geometry

Aeroelastic flutter arises when the motion of a structure and its surrounding flowing fluid are coupled in a constructive manner, causing large amplitudes of vibration in the immersed solid. A cantilevered beam in axial flow within a nozzle-diffuser geometry exhibits interesting resonance behavior that presents good prospects for internal flow energy harvesting. Different modes can be excited as a function of throat velocity, nozzle geometry, fluid and cantilever material parameters. Similar behavior has been also observed in elastically mounted rigid plates, enabling new designs for such devices. This work explores the relationship between the aeroelastic flutter instability boundaries and relevant non-dimensional parameters via experiments, numerical, and stability analyses. Parameters explored consist of a non-dimensional stiffness, a non-dimensional mass, non-dimensional throat size, and Reynolds number. A map of the system response in this parameter space may serve as a guide to future work concerning possible electrical output and failure prediction in harvesting devices.   

Wake reconfiguration downstream of an inclined flexible cylinder at the onset of vortex-induced vibrations

Slender flexible cylinders immersed in flow are common in nature (e.g. plants and trees in wind) and in engineering applications, for example in the domain of offshore engineering, where risers and mooring lines are exposed to ocean currents. Vortex-induced vibrations (VIV) naturally develop when the cylinder is placed at normal incidence but they also appear when the body is inclined in the current, including at large angles. In a previous work concerning a flexible cylinder inclined at 80 degrees, we found that the occurrence of VIV is associated with a profound alteration of the flow dynamics: the wake exhibits a slanted vortex shedding pattern in the absence of vibration, while the vortices are shed parallel to the body once the large-amplitude VIV regime is reached. The present study aims at bridging the gap between these two extreme configurations. On the basis of direct numerical simulations, we explore the intermediate states of the flow-structure system. We identify two dominant components of the flow: a high-frequency component that relates to the stationary body wake and a low-frequency component synchronized with body motion. We show that the scenario of flow reconfiguration is driven by the opposite trends of these two component contributions.   

Influence of flexible fins on vortex-induced load over a circular cylinder at low Reynolds number

Rigid fins/fairings are known to reduce the vortex induced periodic forces exerting on a cylinder by extending the shear layers interaction further downstream to avoid alternate oppositely-signed shed vortices in the afterbody region. In this work, we present a numerical analysis on the effect of flexible fins with their leading edges fixed tangentially to the cylinder and the trailing edges are free to flap in the wake of two-dimensional (2D) cylinder. Two-dimensional simulations are carried out with varying non-dimensional flexural rigidity, $K_B \in$ [0.01, 1] at a fixed a non-dimensional mass ratio, $m^*=0.1$ and Reynolds number, $Re$ = 100, defined based on the cylinder diameter. We investigate the role of flexibility in altering the wake flow and load generation over the cylinder body. As the $K_B$ is reduced, there exists a critical $K_B$ below which the flexible fins lose their stability to perform flapping and the drag acting on combined cylinder flexible fins begins to increase. However surprisingly, we observe that due to the flexible fin flapping the periodic lift forces acting on the cylinder drops significantly. We show that we can achieve an approx. 62.5\% decrease in the nett periodic lift forces when compared to the bare cylinder.   

Why do inverted-flags flap in a uniform steady flow?

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 \textit{et al.} J. Fluid Mech. \textbf{736}, R1 (2013) show that reversing the sheet's orientation, with the flow impinging on its free-edge, dramatically alters its dynamics. In this talk, we use a combination of mathematical theory, scaling analysis and measurement to explore the physical mechanisms driving the observed large-amplitude flapping motion of an inverted-flag. Flapping is found to be periodic predominantly, with a transition to chaos as flow speed increases. These findings have implications to leaf motion and other biological processes, such as the dynamics of individual hairs, because they also can present an inverted-flag configuration.   

Stability of low aspect ratio inverted flags and rods in a uniform flow

Cantilevered elastic plates and rods in an inverted configuration, where the leading edge is free to move and the trailing edge is clamped, undergo complex dynamics when subjected to a uniform flow. The stability of low aspect ratio inverted plates and rods is theoretically examined, showing that it is markedly different from that of their large aspect ratio counterpart. In the limit of zero aspect ratio, the undeflected equilibrium position is found to be stable for all wind speeds. A saddle-node bifurcation emerges at finite wind speed, giving rise to a strongly deflected stable and a weakly deflected unstable equilibria. This theory is compared to experimental measurements, where good agreement is found.   

Flow-Induced Flutter of Multi-Inverted Flag Configurations: Vortex Dynamics and Flutter Behaviors

Flow-induced flutter of ``inverted'' flags has potential application in energy-harvesting, enhanced mixing and heat transfer enhancement. While a number of previous studies have explored the dynamics of single inverted flags, the current study examines the issue of the coupled dynamics of multi-inverted flag configurations. The primary configurations investigated here have two inverted filaments in either side-by-side or tandem formations. The flapping behavior, dynamics, and flow-structure interaction of each filament as well as the synchronization between the dynamics of the filaments was studied. The investigation of the tandem configuration shows coupling of the flapping dynamics for a variety of separations as well as the ability of the trailing filament to drive the behavior of the leading filament. The behavior of the side-by-side configuration suggests the flapping dynamics in this configuration is dominated by the vortex shedding at the fixed trailing edges. The side-by-side configuration also exhibits multiple distinctive flutter behavior regimes depending on separation distance. Finally, simulations of flag formations with \textgreater 2 flags are also explored. Implication of the findings on energy-harvesting applications is discussed.   

The Stability of Tip Vortices Generated by a Flexible Wind Turbine

The influence of root-vortices and a trailing vortex sheet on tip-vortex dynamics of a flexible onshore and floating-offshore wind turbine configurations are investigated numerically. The rotor near-wake is generated using a lifting-line free vortex wake method, which is coupled to a finite element solver for linear flapwise bending deformations. A synthetic time series of rigid-body rotor motions emulates the offshore environment for the NREL 5MW reference wind turbine. To evaluate the influence of root vortices and the trailing vortex sheet, a linear stability analysis is first performed for a rotor wake consisting only of the tip vortices. The stability analysis is then modified to account for the presence of the root vortices and trailing vortex sheet. Stability trends of the two analyses are compared to identify any influence that the root vortices and the trailing vortex sheet have on the tip-vortex dynamics. Lastly, the aforementioned stability analyses are conducted for varying tip speed ratios to identify intrinsically stable helical structures.