## 3 Characteristics of Ice Accretion on Diverse Members
### Ice Accretion on Pipeline
#### 3.1.2 Influence of Icing Duration  
The ice profiles of typical pipelines are shown in Figures 8-11, and the thickness \(\delta_{\theta}\), icing range \(\mu\), and icicle length \(l\) for different cases are shown in Figures 12 and 13. Figure 11: _Cont._  
Figure 10: Profiles of ice accretions for various \(N\) (\(D\) = 150 mm). Figure 9: Profiles of ice accretions for various \(N\) (\(D\) = 50 mm). Figure 11: Profiles of ice accretions for various \(N\) (\(D\) = 1000 mm). Figure 12: _Cont._  
Figure 12: Thickness of radial ice at various \(N\): (**a**) \(D\) = 25 mm, (**b**) \(D\) = 50 mm, (**c**) \(D\) = 100 mm, (**d**) \(D\) = 150 mm, (**e**) \(D\) = 200 mm, (**f**) \(D\) = 300 mm, (**g**) \(D\) = 400 mm, (**h**) \(D\) = 600 mm, (**i**) \(D\) = 800 mm, and (**j**) \(D\) = 1000 mm. The key observations and analyses can be summarized as follows:  
1. The ice profile changed with increasing \(N\). A thin layer of annular-shaped ice formed at the early stage, the ice profile then changed from a crescent shape to a sector shape and finally to a D shape with increasing \(N\), which can be simplified as the models shown in Figure 14. The annular-shaped ice had almost the same ice thickness at different positions. The crescent-shaped ice could be simplified as an arc, which could be characterized by several parameters: \(g\) (the thicknesses at the end point of the radial ice), \(\delta_{0}\), and \(\mu\). The sector-shaped ice can be divided into three curved segments: _ad, be,_ and _dce_, and the ice thicknesses at points \(d\), \(c\), and \(e\) were the same. The D-shaped ice could also be divided into three curved segments: _ad, be_, and _dce_, which had a smaller thickness at point \(c\) than that at points \(d\) and \(e\). The annular-shaped ice was similar to the ice shape in [PERSON] et al. [14] for high airstream velocities \(U\) = 30 m/s and \(T\) = \(-\)1 \({}^{\circ}\)C. The crescent-shaped and sector-shaped ice profiles were similar to those presented by [PERSON] et al. [26] (\(U\) = 6 and 10 m/s, \(T\) = \(-\)15 \({}^{\circ}\)C) and [PERSON] et al. [14] (\(U\) = 10 m/s and 20 m/s, \(T\) = \(-\)1 to \(-\)15 \({}^{\circ}\)C). The D-shaped ice was similar to the reverse-triangular ice presented by [PERSON] et al. [26] for \(U\) = 10 and 20 m/s, \(T\) = \(-\)15 \({}^{\circ}\)C. 2 It is speculated that the larger diameter pipelines required longer times to form a specific type of radial ice under the same conditions. For example, for a pipeline with \(D\) = 25 mm (Figure 8), the ice profile was crescent shape when \(N\) = 20-40, and it became into sector shape when \(N\) = 60-160. For a pipeline with \(D\) = 150 mm (Figure 10), the ice profile was an annular shape when \(N\) = 20, and it became a crescent shape when \(N\) = 40 and 60, it became a sector shape when \(N\) = 80-140 and finally became D shape when \(N\) = 160. For a pipeline with \(D\) = 1000 mm (Figure 11), the ice profile was annular shape when \(N\) = 20-100, and it became crescent shape when \(N\) = 120-240. 3 \(\delta\), \(\mu\), and \(l\) increased with increasing \(N\) (Figures 12 and 13). The shape of the icicle changed with increasing \(N\). For \(D\) = 150 mm (Figure 10), the top and bottom diameters of the linear part of the icicle were almost the same at \(N\) = 20, which could be simplified as a circular cylinder, it was similar to icicle shape presented by [PERSON] et al. [26] (\(U\) = 6 m/s, \(T\) = \(-\)15 \({}^{\circ}\)C, 5 min elapsed);  
Figure 14: Engineering geometric models of radial ice: (**a**) annular shaped, (**b**) crescent shaped, (**c**) sector shaped, and (**d**) D shaped. the top diameter then increased faster than the bottom diameter, and the linear part could be simplified as a circular truncated cone at \(N=60\), which was were similar to icicle shape presented by [PERSON] et al. (2016) (\(U=6\) m/s, \(T=-15\)\({}^{\circ}\)C, 20 min elapsed); the linear part could be simplified as an elliptical cone since the transverse size of the icicle grew faster than the longitudinal size at \(N=160\).