Flapping dynamics of a piezoelectric membrane behind a circular cylinder

Abstract The flapping dynamics of a piezoelectric membrane placed behind a circular cylinder, which are closely related to its energy harvesting performance, were extensively studied near the critical regime by varying the distance between the cylinder and the membrane. A total of four configurations were used for the comparative study: the baseline configuration in the absence of the upstream circular cylinder, and three configurations with different distances ( S ) between the cylinder and the membrane ( S / D =0, 1, and 2). A polyvinylidene fluoride (PVDF) membrane was configured to flutter at its second mode in these experiments. The Reynolds number based on the membrane’s length was 6.35×10 4 to 1.28×10 5 , resulting in a full view of membrane dynamics in the subcritical, critical, and postcritical regimes. The membrane shape and the terminal voltage were simultaneously measured with a high-speed camera and an oscilloscope, respectively. The influence of the upstream cylinder on the membrane dynamics was discussed in terms of time-mean electricity, instantaneous variations and power spectra of terminal voltage and membrane shape, fluctuating voltage amplitude, and flapping frequency. The experimental results overwhelmingly demonstrated that the terminal voltage faithfully reflected various unsteady events embedded in the membrane’s flapping motion. For all configurations, dependency of the captured electricity on a flow speed beyond the critical status was found to follow the parabolic relationship. In the two configurations in which S / D =0 and 1, the extraneously induced excitation by the Karman vortex street behind the circular cylinder substantially reduced the critical flow speed, giving rise to effective energy capture at a lower flow speed and a relatively high gain in power output. However, in the configuration in which S / D =2, the intensified excitation by the Karman vortex street on the membrane considerably reduced the captured energy. Finally, a transient analysis of the membrane’s flapping dynamics in the configuration in which S / D =0 was performed in terms of phase-dependent variations of the membrane segment’s moving speed, membrane curvature, and terminal voltage; the analysis resulted in a full understanding of the energy harvesting process with consecutive inter transfer of elastic, kinetic, and electric energies.