## 4 Contrast Analyses between Different Rotation Modes  
In previous studies [25], the characteristics of icing on a cylinder rotating around the horizontal axis were studied, and the icing results are shown in Figure 17. In this section, icing events occurring on the cylinders are analyzed for two rotation modes. In the rotation mode of Figure 17, the relative wind speed, which is the vector difference between the wind speed and the linear speed of the cylinder, and its direction vary with the rotational speed of the cylinder, as shown in Figure 18 [25]. Figure 16: Variation of the thickness of ice layer along the cylinder surface: (**a**) \(\lambda\) = 0.2; (**b**) \(\lambda\) = 0.6; (**c**) \(\lambda\) = 1.0; (**d**) \(\lambda\) = 1.5; (**e**) \(\lambda\) = 2.5; (**f**) \(\lambda\) = 3.5. Figure 17: Icing on a cylinder rotating around the horizontal axis: (**a**) 100 rpm; (**b**) 200 rpm; (**c**) 400 rpm; (**d**) 600 rpm; (**e**) 800 rpm. As shown in Figure 18, when the wind speed is constant, the relative wind speed \(W\)i and its direction vary with the linear speed of the cylinder \(V_{i}\). When the rotational speed increases, the relative wind speed also increases. Then, the included angle between the relative wind speed and the linear speed of the cylinder decreases. The variation of the direction of the relative wind speed \(W\) with the rotational speed of the cylinder is shown in Figure 19.  
The reason for the variation shown in Figure 19 is that the linear velocity of the cylinder is perpendicular to the wind speed at all times. When the rotational speed of the cylinder increases, the direction of the relative wind speed changes. However, no matter how the rotational speed changes, the frontal area of the cylinder toward the relative wind speed remains constant. For this reason, the icing region on the rotating cylinder surface is always concentrated on half the surface of the cylinder, as shown in Figure 17, and the icing region changes with the direction of the relative wind speed. In contrast, the rotation state of the cylinder rotating around the vertical axis is different from that of the cylinder rotating around the horizontal axis. When the cylinder rotates around the horizontal axis, the trajectory plane of the cylinder is vertical to the wind direction. However, when the cylinder rotates around the vertical axis, the trajectory plane of the cylinder is parallel to the wind direction. It is found that the relative position of the cylinder and the incoming flow varies all the time in a circle, as shown in Figure 20.  
Figure 19: Variation of the direction of the relative wind speed at different rotation speeds [29]. Figure 18: Sketch map of the direction of relative wind speed. In Figure 20, \(U\) is the wind speed, \(V\) is the linear velocity of the cylinder and \(W\) is the relative wind speed. The region enclosed by the trajectory of the cylinder, can be divided into two regions, i.e., the forward motion region and the backward motion region. In this rotation mode, the whole cylinder surface is covered by the ice layer at a low tip speed ratio (TSR), e.g., a TSR lower than 1. The reason for this result is that when the cylinder rotates into the forward motion region, the front surface of the cylinder captures the super-cooled water droplets. Then the ice layer occurs on the front surface. Similarly, as the cylinder rotates into the backward motion region, the super-cooled water droplets impinge on the back surface of the cylinder, because the linear speed of the cylinder is lower than the wind speed. Hence, the whole cylinder surface is covered by the ice layer. When the tip speed ratio (TSR) is high, e.g., a TSR higher than 1, only the front surface of cylinder is covered by the ice layer, as shown in Figure 6. The reason for this result is that when the cylinder rotates into the forward motion region, the front surface captures the super-cooled water droplets and is covered by the ice layer, which is similar to the result under the low TSR condition.