## Characteristics and Optimization Objectives of a Galloping Bluff Body  
### Characteristics of a Galloping Bluff Body  
The aerodynamic shape of a galloping bluff body plays a dominant role in the efficiency of converting wind energy into vibration energy. The efficiency of energy harvesting can be improved significantly by optimizing the aerodynamic shape of the bluff body. The bluff body cross-sections of early galloping wind energy harvesters had typical bluff body sections, such as square, D-shape, or triangle [32]. Based on these typical sections, the cross-sections were modified for improving the efficiency of WEHs. Figure 1 shows cross-sections of a few optimized galloping bluff bodies.  
In the process of the aerodynamic modification of the galloping bluff bodies, one optimization method is to add fins near the leading edge. The fins form sharp protrusions, resulting in stronger flow separation. A square prism with leading-edge fins [7] is shown in Figure 1a. Circular cylinders with different shape attachments [43; 44] are shown in Figure 1b. A circular cylinder with roughness strips [45] is shown in Figure 1c.  
Another optimization method is to add a plate near the trailing edge. Adding a plate increases the depth of the bluff body, resulting in increasing cross-wind force. A square prism with a Y-shaped plate near the trailing edge [36] is shown in Figure 1d. A circular cylinder with a splitter plate [35] is shown in Figure 1e.  
In summary, the optimized aerodynamic shape of a galloping bluff body has the characteristics of a wide windward surface with sharp protrusions, and overall lengthening with a plate at the tail. As shown in Figure 1f, the blade bluff body has the characteristics of the optimized shape, and, hence, a blade-shaped bluff body has excellent galloping performance [40; 46].  
Figure 1: The aerodynamic shapes of optimized galloping bluff bodies, such as (**a**) square prism with leading-edge fins; (**b**) circular cylinder with different shape attachments; (**c**) circular cylinder with roughness strips; (**d**) square prism with Y-shaped fins near the trailing edge; (**e**) circular cylinder with a splitter plate; (**f**) blade bluff bodies.  
In order to systematically investigate the performance of the blade bluff body, an arc-plate bluff body, consisting of an arc and a plate at the tail, is proposed, as shown in Figure 2. The windward width \(D\) of the different bluff bodies is identical. The geometry of the arc-plate-shaped bluff body is described by two variables, \(a_{1}\) and \(a_{2}\), ranging from 0 to 1. The arc angle \(\beta=2\pi a_{1}\), and the tail plate length \(L_{t}=2 Da_{2}\). Changing the two variables can create a variety of different shapes. For instance, when the arc angle \(\beta\) is \(2\pi\) and the plate length \(L_{t}\) is 0, the bluff body is a circular cylinder; when the arc angle \(\beta\) is \(2\pi\) and the plate length \(L_{t}\) is not 0, the bluff body is a circular cylinder with a plate, following the aerodynamic shape studied by [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] [35]. When the angle \(\beta\) is \(\pi/2\) and the plate length \(L_{t}\) is 0, the bluff body follows the aerodynamic shape studied by [PERSON], [PERSON], and [PERSON] [40]. Therefore, the proposed arc-plate bluff body has a good ability to create a variety of aerodynamic shapes using two variables.