## 3 Results and Discussion
### Analysis of Icing Characteristics  
For quantitatively characterizing the icing shape and the distribution of icing on the cylinder surface, several parameters are defined for the icing shape and the icing area. The evaluation method in the present study was based on previous studies that quantitatively analyzed the characteristics of icing on a cylinder rotating around a horizontal axis [25]. The parameters characterizing the features of icing on a rotating cylinder are shown in Figure 8.  
As shown in Figure 8, typical parameters include the icing area \(S\), the stagnation point thickness \(\delta\), the stagnation point deflection angle \(\alpha\), the left icing limit \(L_{I}\) and the right icing limit \(L_{r}\). The icing area \(S\) characterizes the area of the ice layer covering on the cylinder surface. The stagnation point thickness \(\delta\) is the vertical distance from the highest point on the ice layer to the cylinder surface. The stagnation point deflection angle \(\alpha\) is the included angle between the vertical center line and the straight line distance from the stagnation point to the center point of the cylinder. The rotation direction of the cylinder is the same as the deflection direction of the stagnation point deflection angle, and the linear velocity \(V\) is shown in Figure 8. With regard to the circumferential velocity of the cylinder, the clockwise direction is positive and the counterclockwise direction is negative. The parameter \(L_{1}\) is  
Figure 8: Typical parameters characterizing features of icing on a rotating cylinder. the left icing limit, which is the arc length covered by the ice layer on the left half. Similarly, the parameter \(L_{r}\) is the right icing limit. For comparatively analyzing the characteristics of icing on rotating cylinders with different diameters, the characteristic parameters defined above are nondimensionalized based on previous work [25]. The new sets of dimensionless parameters are defined in the following equations. \[\eta_{s}=\frac{S}{\pi{(d/2)}^{2}} \tag{2}\]  
\[\eta_{\delta}=\frac{\delta}{d} \tag{3}\]  
\[\eta_{L_{l}}=\frac{L_{l}}{\pi d/2} \tag{4}\]  
\[\eta_{L_{r}}=\frac{L_{r}}{\pi d/2} \tag{5}\]  
where \(\eta_{S}\) is the dimensionless icing area, \(\eta_{\delta}\) is the dimensionless stagnation point thickness, \(\eta_{LI}\) is the dimensionless left icing limit, \(\eta_{L}\) is the dimensionless right icing limit and d is the diameter of the cylinder. The icing areas and the dimensionless icing areas covering the cylinders with different diameters are shown in Figures 9 and 10. As shown in Figures 9 and 10, the icing areas and the dimensionless icing areas all increased with icing time. The experimental data show that the amount of icing on the rotating cylinder surface increased with the TSR or the rotational speed of the rotor. The  
Figure 10: Dimensionless icing areas of the rotating cylinders with different diameters: (**a**) \(d=20\) mm; (**b**) \(d=30\) mm; (**c**) \(d=40\) mm. Figure 9: Lcing areas covering the cylinder surfaces with different diameters: (**a**) \(d=20\) mm; (**b**) \(d=30\) mm; (**c**) \(d=40\) mm. reason for these results is that more super-cooled water droplets can be captured by the rotating cylinder per unit time with an increase in the TSR or the rotational speed. As shown in Figure 9, with the icing conditions held constant, the larger the diameter of the cylinder, the more water droplets are captured by the cylinder. The reason for this is that a cylinder with a larger diameter has a larger frontal area as it rotates. From Figure 10, it can be seen that the dimensionless icing area on the cylinder surface decreased with an increase in the cylinder diameter. The curvature of the profile of the ice layer decreased with an increase in the cylinder diameter. This shows that the diameter or the curvature of the cylinder has an effect on the dimensionless icing area. It indicates that a small cylinder with a large curvature is more easily affected by ice accretion.