Vibrissa inspired geometries enhance sensitivity of wake-induced vibrations

Abstract

We report on experiments designed to characterize the vortex-induced vibration (VIV) and wake-induced vibration (WIV) experienced by bluff bodies immersed in both steady and unsteady flows. Using a real-time Cyber-Physical System (CPS) we systematically prescribe the virtual mass, spring constant, and damping of elastically mounted models. This allows us to characterize the forces and displacements of the free vibration of a circular cylinder, elliptical cylinder, and a seal whisker inspired vibrissa model with undulating elliptical geometry. In a free flow, the circular cylinder exhibits high VIV, while the reduced aspect ratio objects have minimal vibration across all structural frequencies. When a flow disturbance of a pitching and heaving hydrofoil is introduced, the reduced aspect ratio objects are excited by WIV with highest amplitude oscillations occurring when structural frequency of the test object matches wake frequency of the upstream foil. To further understand the benefits of an undulated geometry over a classic elliptical cylinder, we assess the nonlinear fluid damping experienced by each test object by comparing experimental data to quadratic drag and Van der Pol damping models. Our results show that the amplitude dependent Van der Pol damping model better describes the physical system for both test objects by capturing the suppression of large amplitude WIV, but recovering small amplitude VIV. However, the strength of the fitted Van der Pol damping coefficient is greater for the elliptical cylinder than the vibrissa. We find the vibrissa experiences lower damping than the elliptical cylinder across all tested structural frequencies, indicating how the vibrissa geometry may serve as a higher sensitivity sensor.

Figures (7)

• Figure 1: Experimental set-up. (a) Top view of the experimental set-up. (b) Schematic demonstrating the connection between the physical components of the downstream-mounted body and the cyber-physical system governing its motion. Values $k$, $b$, and $m$ are the commanded spring constant, damping constant, and mass, respectively, while $M$ is true physical mass.
• Figure 2: Vortex-induced vibration response of test models in free flow. Y-axis displacement and fluid force measurements plotted together over 20 cycles for circular cylinder trials conducted at (a) $U^*=7$ and (b) $U^*=4.5$. (c) Complete $U^*$ sweeps from $U^*=2$ to $U^*=11$ for circular cylinder, elliptical cylinder and vibrissa models.
• Figure 3: Vortex-induced vibration response of the circular cylinder is independent from Reynolds number. $U^*$ sweep results for the circular cylinder at Re $\sim$ 16k, 10k and 8k.
• Figure 4: Wake-induced vibration response of test models in a vortical thrust wake. (a) Complete $U^*$ sweeps from $U^*=2$ to $U^*=11$ for circular cylinder, elliptical cylinder and vibrissa models with an upstream wake frequency $f_w=0.79$ Hz. Y-axis displacement and fluid force measurements plotted together over 5 cycles for vibrissa trials with an upstream wake frequency $f_w=0.79$ Hz such that $f_w/f_s=1$ at $U^*=7$, conducted at (b) $U^*=6$ ($f_w/f_s<1$), (c) $U^*=7$ ($f_w/f_s=1$), and (d) $U^*=8$ ($f_w/f_s>1$).
• Figure 5: Comparison of damping metrics in ringdown experiments. (a) Mean and standard deviation of damping ratios calculated using the method of logarithmic decrement by Equation \ref{['eq:logdec']} from ringdown trials at each tested structural frequency. (b) An example of a single ringdown experiment for both models at $f_s=0.79$ Hz. (c) Mean and standard deviation of quadratic drag coefficient $b_f$ calculated by optimization of damping equation \ref{['eq:quad']}. (d) Mean and standard deviation of Van der Pol damping coefficient $\mu$ calculated by optimization of damping equation \ref{['eq:vdp']}. Predicted and measured (e) position and (f) force for both damping models for $f_s=1.1$ Hz.