## 3 Results and Discussion
### Analysis of Icing Characteristics
The relative amount of icing, i.e., the dimensionless icing area, is larger than that on the cylinder with a larger diameter. This means that small-scale VAWTs are more affected by icing accretion than large-scale ones, because the small-scale blade has a large curvature profile. The variations of the stagnation point thicknesses and the dimensionless stagnation point thicknesses with icing time under the different TSRs are shown in Figures 11 and 12. As shown in Figure 11, when the diameter of the cylinder is constant, the stagnation point thickness increases with the rotational speed or the TSR. Similarly, when the TSR or the rotational speed is constant, the stagnation point thickness also increases with the icing time. However, the diameter of the cylinder has little effect on the stagnation point thickness. The stagnation point thicknesses are approximately the same for different diameters. The reason for this result is that the diameter has little effect on the quantity of super-cooled droplets captured by the unit arc length on the cylinder surface. It only significantly affects the icing area, because a cylinder with a large diameter or small  
Figure 11: Variations of the stagnation point thickness with the icing time: (**a**) \(d=20\) mm; (**b**) \(d=30\) mm; (**c**) \(d=40\) mm. Figure 8.0 Variations of the dimensionless stagnation point thickness with the icing time: (**a**) \(d=20\) mm; (**b**) \(d=30\) mm; (**c**) \(d=40\) mm. curvature has a long arc length at the cross section, which can capture more super-cooled water droplets. As shown in Figure 12, it was found that the dimensionless stagnation point thicknesses also increased with the rotational speed and the icing time. However, when the rotational speed or the TSR was constant, the dimensionless stagnation point thickness decreased with an increase in the diameter of the cylinder. This also indicates that icing on a cylinder with a large diameter or a small curvature has little effect on the profile of the cylinder. The variations in the left icing limit and the right icing limit on the cylinder surfaces are shown in Figures 13 and 14. As shown in Figures 13 and 14, the limits of icing on the left and the right sides of the cylinder reached 100% for low rotational speeds. This means that the surface of the cylinder was completely covered by the ice layer. As the rotational speed increased, both the icing limits gradually decreased and approached approximately 50%. This showed that the diameter of the cylinder and the icing time both had small effects on the icing limit. According to these data, it was found that the icing limits for each size of cylinder rapidly reached the maximum values in a short time from the beginning of the icing time. Then, they changed only a little with icing time. For quantitatively analyzing the distribution of the ice layer thickness on the cylinder surface, the profile of the cylinder was divided into 200 parts and unfolded. A coordinate system for the cylinder surface was established, and a sketch map of this is shown in Figure 8.1  
As shown in Figure 15, the origin of the coordinate system is located at the highest point in the figure, which is the forefront point of the cylinder against the wind. The positive direction of the coordinate system is clockwise and the negative direction is counterclockwise. The range of coordinate values characterizing the relative positions of the points on the cylinder surface is from \(-0.2\) to \(0.2\). The thickness of the ice layer at each point along the cylinder surface was characterized using the coordinate system, as shown in Figure 8.2  
Figure 8.3 _Cont._  
Figure 8.4 Coordinate system for the cylinder surface. As shown in Figure 16, the main icing region was near the origin position on the cylinder surface. When the rotational speed or the TSR was low, e.g., 0.2, the ice layer symmetrically covered the whole cylinder surface.