**1. Introduction**

In recent years, the development of flow-induced vibrations (FIV) energy harvesters has increased rapidly to offer a new source of energy. Due to the large strains and geometric deformations during FIV, they have traditionally been classified as a destructive phenomenon. One of the well-known examples of flutter-induced destruction is the Tacoma Narrows Bridge collapse in 1940, where torsional flutter at sufficiently large amplitudes caused catastrophic failure of the entire bridge. However, common and accessible FIV could be considered as a way to extract energy. Bernitsas et al. [1] have developed a device that uses the vortex induced vibration (VIV) phenomenon to generate electricity. Contrary to the VIV phenomenon, where significant oscillations develop in a small range of flow velocities and with limited oscillation amplitudes, other aeroelastic instabilities like flutter occur for an infinite range of flow velocities and without a self-limited response beyond the critical flow velocity which makes the flutter more promising for generating energy.

For instance, Hobbs and Hu [2] tested micro-watt energy harvesters inspired by tree trunks swaying in the wind. Their converter consists of four pivoted cylinders which affixed to the ground via a piezoelectric transducer. Yoshitake et al. [3] generated minuscule amounts of energy, using a device composed of Hula-Hoops and an electro magnetic transducer mechanism, in air flow. To study the aerodynamic efficiency of a drag assisted energy-harvesting device, Sung et al. [4] investigated the effects of the cylinder cross-sectional shape on the VIV. Their numerical simulations have demonstrated that an elliptical cylinder undergoes much larger displacements than a circular one. Nevertheless, their research mainly focuses on improving maximum displacement or amplitude rather than the angular velocity of the vibration.

**Citation:** Arionfard, H.; Mohammadi, S. Numerical Investigation of the Geometrical Effect on Flow-Induced Vibration Performance of Pivoted Bodies. *Energies* **2021**, *14*, 1128. https://doi. org/10.3390/en14041128

Academic Editor: Adam Adamkowski

Received: 16 January 2021 Accepted: 16 February 2021 Published: 20 February 2021

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In an attempt to study the performance of FIV, Arionfard and Nishi [5] carried out an experiment on a pivoted cylinder instead of a transitionally moving one. Being assisted by the drag force, the pivoting cylinder showed an increase in performance comparing to transitional VIV of a cylinder. As a result, different configurations with one and two cylinders were considered in the following researches to increase the performance by utilizing different mechanisms of vibrations [6–8]. However, an important way to improve the FIV performance is through the geometry of the bluff body and enhancement of the geometrical parameters is necessary in order to increase energy extraction performance. For several years great effort has been devoted to the study the effect of cross sections on FIV. However, common cross sections in aviation and civil engineering has attracted much more attention; Airfoil flutter [9], galloping of square, triangular, and semicircular sections [10], rectangular and D-sections[11,12] are some examples. However, to the author's best knowledge, very few publications are available in the literature that discuss the role of the geometrical parameters of the bluff body on the performance of the vibration. This paper reports geometrical effects on FIV performance of pivoted cylinders. Six cross section shapes are compared in which the circular cylinder is checked with our experimental data for validating the numerical simulation.

The present paper is organized as follows. The case is described in Section 2 followed by details of the numerical method, domains, and boundary conditions. Verification and validations is reported in Section 4, and the results are presented in in Section 5. We make conclusive remarks in Section 6.
