﻿ 极地航行船舶桅杆积冰预报
 舰船科学技术  2023, Vol. 45 Issue (12): 8-13    DOI: 10.3404/j.issn.1672-7619.2023.12.002 PDF

Prediction of mast icing on polar ships
LIU Zhu, ZHANG Ji-feng
College of Aerospace and Architecture Engineering, Harbin Engineering University, Harbin 150001, China
Abstract: In carrying out scientific research activities and shipping for polar navigation ships, the cold and foggy environment is straightforward to cause mast icing, which affects navigation safety. Fluent and Fensap-ice are used to forecast the ice accretion on the mast, and the ice accretion distribution under different meteorological conditions is studied. The numerical simulation results show that with the increase of wind speed from 2 m/s to 10 m/s, the amount of ice on the mast increases from 0.10 g to 3.66 g. With the rise of liquid water content, the amount of ice on the mast increases from 1.11 g to 5.55 g, and it increases linearly. However, the liquid water content will not change the water droplet collection coefficient on the mast surface. With the increase of average droplet diameter, the amount of ice on the mast surface increases. The research content of this paper has specific guiding significance for increasing the navigation safety of polar navigation ships.
Key words: polar ship mast     ice accumulation prediction     stability     navigation safety
0 引　言

1 积冰数值模拟计算方法 1.1 空气流场计算方法

 $\frac{{\partial \rho }}{{\partial {t}}} + \frac{{\partial \rho {u_j}}}{{\partial {x_j}}} = 0，$ (1)

 $\frac{\partial }{{\partial t}}\left( {\rho {u_i}} \right) + \frac{\partial }{{\partial {x_j}}}\left( {\rho {u_i}{u_j}} \right) = \frac{\partial }{{\partial {x_j}}}\left( {{\tau _{ij}}} \right) ，$ (2)

 $\begin{split} & \frac{\partial }{{\partial t}}\left( {\rho H - p} \right) + \frac{\partial }{{\partial {x_j}}}\left( {\rho {u_j}H} \right) = \\ & \frac{\partial }{{\partial {x_j}}}\left( {{u_i}{\tau _{ij}}} \right) - \frac{\partial }{{\partial {x_j}}}\left( {\frac{\mu }{{Pr }}\frac{{\partial h}}{{\partial {x_j}}}} \right)。\end{split}$ (3)

 $\frac{{\partial \overline \rho }}{{\partial t}} + \frac{{\partial \rho {{\widetilde u}_j}}}{{\partial {x_j}}} = 0，$ (4)

 $\begin{split} &\frac{\partial }{{\partial t}}\left( {\overline \rho \widetilde ui} \right) + \frac{\partial }{{\partial xj}}(\overline \rho {\widetilde u_i}\widetilde uj + \overline p {\delta _{ij}}) = \\ & \frac{\partial }{{\partial {x_j}}}\left[ {(u + {u_t})\left( {\frac{{\partial \widetilde ui}}{{\partial xj}} + \frac{{\partial {{\widetilde u}_j}}}{{\partial {x_i}}}} \right) + \lambda \frac{{{{\widetilde u}_k}}}{{{x_k}}}{\delta _{ij}}} \right] ，\end{split}$ (5)

 $\begin{split} & \frac{\partial }{{\partial t}}\left( {\overline \rho \widetilde H - \overline p } \right) + \frac{\partial }{{\partial {x_j}}}\left( {\overline \rho {{\widetilde u}_j}\widetilde H} \right) = \\ & \frac{\partial }{{\partial {x_j}}}\left[ {\left( {\frac{\mu }{{\Pr }} + \frac{{{\mu _t}}}{{{{\Pr }_t}}}} \right)\frac{{\partial \widetilde h}}{{\partial {x_j}}}} \right] + \\ &\frac{\partial }{{\partial {x_j}}}\left\{ {{{\widetilde u}_i}\left[ {\left( {\mu + {\mu _i}} \right)\left( {\frac{{\partial {{\widetilde u}_i}}}{{\partial {x_j}}} + \frac{{\partial {{\widetilde u}_j}}}{{\partial {x_i}}}} \right) + \lambda \frac{{\partial {{\widetilde u}_k}}}{{\partial {x_k}}}{\delta _{ij}}} \right]} \right\} - \\ & \frac{\partial }{{\partial {x_j}}}\left[ {\left( {\mu + \frac{{{\mu _t}}}{{{\sigma _k}}}} \right)\frac{{\partial k}}{{\partial {x_j}}}} \right]。\end{split}$ (6)

1.2 水滴撞击特性计算方法

1）水滴在运动过程中始终为球体；

2）水滴在运动过程中只受到重力和空气阻力；

3）水滴在运动过程中，不考虑水滴的传质传热；

4）水滴在撞击壁面时，不发生反弹与飞溅现象。

 $\dfrac{{{\rm{d}}u}}{{{\rm{d}}t}} = \frac{{18{\mu _a}{C_D}{Re} }}{{24\rho d_p^2}}({u_a} - u) + \frac{{\rho - {\rho _a}}}{\rho }g。$ (7)

 ${Re} = \frac{{{\rho _a}\left| {u{}_a - u} \right|{d_p}}}{{{\mu _a}}}。$ (8)

 $\begin{split} & \frac{{\partial \left( {\alpha u} \right)}}{{\partial t}} + \nabla \cdot \left( {\alpha uu} \right) = \\ & \frac{{18{\mu _a}{C_D}{Re} }}{{24\rho d_p^2}}\alpha \left( {{u_a} - u} \right) + \alpha \frac{{\rho - {\rho _a}}}{\rho }g，\end{split}$ (9)
 $\frac{{\partial \alpha }}{{\partial t}} + \nabla \cdot \left( {\alpha u} \right) = 0 。$ (10)

 $\alpha = \frac{{LWC}}{\rho }。$ (11)

 $\beta = \frac{{\left( {{u_n} \cdot {\boldsymbol{n}}} \right){\alpha _n}}}{{\left| {{u_\infty }} \right|{\alpha _\infty }}} 。$ (12)

1.3 积冰生成计算方法

 图 1 控制单元内的质量和能量交换示意图 Fig. 1 Schematic diagram of mass and energy exchange within a control unit.

 ${M_{in}} + {M_{im}} + {M_{ev}} + {M_{out}} + {M_{ice}} = 0 ，$ (13)
 ${Q_{in}} + {Q_{im}} - {Q_{ev}} - {Q_{out}} - {Q_{fre}} - {Q_{conv}} = 0。$ (14)

 $f = \frac{{{M_{ice}}}}{{{M_{in}} + {M_{im}}}}。$ (15)

 ${f_1} = \frac{{{M_{ice,1}}}}{{{M_{im,1}}}}。$ (16)

$f = 1$ 时，表明此控制体单元内所有可冻结的水全部冻结；当 $f \in \left( {0,1} \right)$ 时，表明只有部分水冻结；当 $f = 0$ 时，表明没有水冻结。计算完第1个控制体单元的冻结系数 ${f_1}$ ，就可以计算下一个控制体单元的冻结系数 ${f_2},{f_3},...,{f_n},...$ 直至最后一个控制体单元。

 ${M}_{ice}=f\cdot\left({M}_{in}+{M}_{im}\right) 。$ (17)
1.4 方法验证

 图 2 圆柱体网格划分情况 Fig. 2 Cylinder meshing situation.

 图 3 数值模拟结果与冰风洞试验结果对比 Fig. 3 Comparison between numerical simulation results and ice wind tunnel experimental results.
2 模型建立与网格划分

 图 4 模型建立 Fig. 4 Model establishment.

 图 5 桅杆及外流场网格划分情况 Fig. 5 Meshing of mast and outer flow field.
3 气象条件对桅杆积冰的影响

3.1 风速对桅杆积冰的影响

 图 6 不同风速条件下桅杆表面水滴收集系数 Fig. 6 Collection coefficient of water droplets on the mast surface under different wind speeds.

 图 7 不同风速条件下桅杆表面积冰 Fig. 7 Ice accretion on mast surface under different wind speeds.
3.2 液态水含量对桅杆积冰的影响

 图 8 不同液态水含量条件下桅杆表面水滴收集系数 Fig. 8 Collection coefficient of water droplets on mast surface under different liquid water content.

 图 9 不同液态水含量下桅杆表面积冰 Fig. 9 Ice accretion on mast surface under different liquid water content.
3.3 水滴直径对桅杆积冰的影响

 图 10 不同水滴直径条件下桅杆表面水滴收集系数 Fig. 10 The collection coefficient of water droplets on the mast surface under the condition of different droplet diameters.

 图 11 不同水滴直径条件下桅杆表面积冰 Fig. 11 Ice accretion on mast surface under different droplet diameters.
4 结　语

1）所选桅杆的Ⅰ 区域与Ⅱ 区域是积冰最为严重的部位，在进行积冰防护与清理时，尤其要注意该部位。

2）随着风速从2 m/s增加到10 m/s，桅杆表面的最大水滴收集系数从0.13增加到0.57，积冰质量从0.10 g增加到3.66 g。同时，背风面的积冰厚度和范围增加。

3）随着液态水含量的增加，积冰质量从1.11 g增加到5.55 g，并且是呈线性增加。但液态水含量不会改变桅杆表面的水滴收集系数。

4）随着水滴直径的增加，撞击到桅杆表面水滴的质量增加，桅杆迎风面积冰范围和积冰质量增加，但水滴直径越大，水滴和空气一起运动时偏离气流流线的能力越强，参与回流的水滴数量减少，导致桅杆背风面的积冰范围减少。

 [1] 谢强, 陈海龙, 章继峰. 极地船舶及海洋平台防冰和除冰技术研究进展[J]. 中国舰船研究, 2017, 12(1): 45-53. [2] NG A K Y, ANDREWS J, BABB D, et al. Implications of climate change for shipping: Opening the Arctic seas[J]. Wiley Interdisciplinary Reviews:Climate Change, 2018, 9(2): e507. [3] 刁端信, 陈豪. 国外海军集成桅杆技术发展浅析[J]. 船舶, 2015, 26(3): 6. [4] POURYOUSSEFI S G, MIRZAEI M, NAZEMI M, et al. Experimental study of ice accretion effects on aerodynamic performance of an NACA 23012 airfoil[J]. Chinese Journal of Aeronautics, 2016, 29(3): 585-595. DOI:10.1016/j.cja.2016.03.002 [5] JANJUA Z A, TURNBULL B, HIBBERD S, et al. Mixed ice accretion on aircraft wings[J]. Physics of Fluids, 2018, 30(2): 027101. DOI:10.1063/1.5007301 [6] BHATIA D. A numerical investigation into the impact of icing on the aerodynamic performance of aerofoils[C]//IOP Conference Series: Materials Science and Engineering. IOP Publishing, 2020, 831(1): 012007. [7] KALYULIN S L, MODORSKII V Y, CHEREPANOV I E. Numerical modeling of the influence of the gas-hydrodynamic flow parameters on streamlined surface icing[C]//AIP Conference Proceedings. AIP Publishing LLC, 2018, 2027(1): 030180. [8] JIN J Y, VIRK M S. Study of ice accretion along symmetric and asymmetric airfoils[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2018, 179: 240-249. DOI:10.1016/j.jweia.2018.06.004 [9] TAKAHASHI T, FUKUDOME K, MAMORI H, et al. Effect of characteristic phenomena and temperature on super-cooled large droplet icing on NACA0012 airfoil and axial fan blade[J]. Aerospace, 2020, 7(7): 92. DOI:10.3390/aerospace7070092 [10] WANG J Y, HU X J. Application of RNG k-ε turbulence model on numerical simulation in vehicle external flow field[C]//Applied Mechanics and Materials. Trans Tech Publications Ltd, 2012, 170: 3324-3328. [11] 沈杰, 白旭. 风速对寒区船舶杆件结构霜冰结冰的影响分析[J]. 舰船科学技术, 2020, 42(9): 56-60. [12] 孟繁鑫, 陈维建, 梁青森, 等. 引射式积冰风洞内圆柱积冰试验[J]. 航空动力学报, 2013, 28(7): 1467-1474.