Simulation of Undercooling Influence on Shape and Velocity of Seawater Freezing Process Using Phase Field Method

doi:10.16183/j.cnki.jsjtu.2020.077

Abstract

Abstract:

In order to study the microcosmic mechanism of ice formation in ship structure, a numerical simulation is conducted. Based on the Wheeler phase field model, the finite difference method is used to simulate the solidification shape of seawater at different undercoolings. In the process of simulation, sea water is regarded as the binary mixture of salt and pure water, and the authenticity of ice crystal growth is ensured by setting ice physical parameters and introducing crystal nucleus. In the calculation, four nuclei are set up to simulate the ice crystal growth, and the influence of different undercoolings on the ice crystal growth is discussed. The results show that the growth rate of ice crystal increases with the increase of undercooling, and it is linear with the change of undercooling. When the dimensionless undercooling is less than 0.85, the dendrite has only a few branches which are thin. When the dimensionless undercooling is higher than 0.85, the ice crystal has more than two-stages of branches which are obviously thicker. When the dimensionless undercooling reaches 1.0, the branches are squeezed by the main branches and lessned, and the crystal cores are finally filled.

Key words: phase field method, seawater icing, ice crystal growth, finite difference approach

CLC Number:

U661
O645.15

BAI Xu, YANG Sujie. Simulation of Undercooling Influence on Shape and Velocity of Seawater Freezing Process Using Phase Field Method[J]. Journal of Shanghai Jiao Tong University, 2021, 55(5): 513-520.

Figures/Tables 7

Tab.1

Physical properties of seawater solution

物理量	数值
c_p/(J·K^-1·cm³)	4.212
μ/(m·K^-1·S^-1)	7.4
σ/(J·cm²)	7.654×10^-6
T_M/K	269.75
K/(cm²·s^-1)	1.31×10^-3
L/(J·cm³)	333.5
D_s/(cm²·s^-1)	2.5×10^-7
D_l/(cm²·s^-1)	5.6×10^-6
k₀	0.8
$ε -$	0.005
m	0.035
α	405.3065

Tab.1

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

References 22

[1]	陆煊, 崔玫, 曹洪波, 等. 船舶防冻除冰技术现状与发展[J]. 船海工程, 2016, 45(2):37-39.
	LU Xuan, CUI Mei, CAO Hongbo, et al. Present situation and development of de-icing and prevent frostbite technology of ships[J]. Ship & Ocean Engineering, 2016, 45(2):37-39.
[2]	张明霞, 汪仕靖, 赵正彬. 极地航区船舶积冰预测研究进展[J]. 船海工程, 2018, 47(A1):113-120.
	ZHANG Mingxia, WANG Shijing, ZHAO Zhengbin. Research progress of ship icing prediction in polar waters[J]. China Ship Development and Design Center, 2018, 47(A1):113-120.
[3]	谢强, 陈海龙, 章继峰. 极地航行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.
	XIE Qiang, CHEN Hailong, ZHANG Jifeng. Research progress of anti-icing/deicing technologies for polar ships and offshore platforms[J]. Chinese Journal of Ship Research, 2017, 12(1):45-53.
[4]	刘永禄, 董韦敬. 舰船结冰预报方法研究[J]. 装备环境工程, 2016, 13(3):140-146.
	LIU Yonglu, DONG Weijing. Forecast methods for ship icing[J]. Equipment Environmental Engineering, 2016, 13(3):140-146.
[5]	陈尚海. 极地船海水系统冰晶生长特性研究[D]. 武汉: 武汉理工大学, 2017.
	CHEN Shanghai. Study on ice-crystal growth cha-racteristics of polar ship seawater system[D]. Wuhan: Wuhan University of Technology, 2017.
[6]	邓儒超. 极地船海水系统冰晶生长相场模拟及管道内流动特性研究[D]. 武汉: 武汉理工大学, 2016.
	DENG Ruchao. Phase-field simulation of ice crystal growth of polar ship seawater cooling system and flow characteristics study of ice slurry in the pipe[D]. Wuhan: Wuhan University of Technology, 2016.
[7]	COLLINS J B, LEVINE H. Diffuse interface model of diffusion-limited crystal growth[J]. Physical Review B, 1985, 31(9):6119. doi: 10.1103/PhysRevB.31.6119 URL
[8]	KOBAYASHI R. Modeling and numerical simulations of dendritic crystal growth[J]. Physica D: Nonlinear Phenomena, 1993, 63(3/4):410-423. doi: 10.1016/0167-2789(93)90120-P URL
[9]	WHEELER A A, MURRAY B T, SCHAEFER R J. Computation of dendrites using a phase field model[J]. Physica D: Nonlinear Phenomena, 1993, 66(1/2):243-262. doi: 10.1016/0167-2789(93)90242-S URL
[10]	FAN T H, LI J Q, MINATOVICZ B, et al. Phase-field modeling of freeze concentration of protein solutions[J]. Polymers, 2018, 11(1):1-10. doi: 10.3390/polym11010001 URL
[11]	YANG C, ZHU X Y, WANG X T, et al. Phase-field model of graphene aerogel formation by ice template method[J]. Applied Physics Letters, 2019, 115(11):1-5.
[12]	杨燕, 景伟强, 袁训锋. 过冷度影响冰晶生长的相场法研究[J]. 低温与超导, 2018, 46(9):67-71.
	YANG Yan, JING Weiqiang, YUAN Xunfeng. Study on under-cooling influence on ice crystal growth using phase-field method[J]. Cryogenics and Superconductivity, 2018, 46(9):67-71.
[13]	朱昌盛, 石可伟, 王智平, 等. 相场法模拟潜热的释放对多元合金凝固过程的影响[J]. 兰州理工大学学报, 2008, 34(2):6-10.
	ZHU Changsheng, SHI Kewei, WANG Zhiping, et al. Simulation of effect of latent heat release on solidification process of multicomponent alloys with phase-field method[J]. Journal of Lanzhou University of Technology, 2008, 34(2):6-10.
[14]	于艳梅, 杨根仓, 赵达文. 过冷熔体中枝晶生长的相场法数值模拟[D]. 西安: 西北工业大学, 2002.
	YU Yanmei, YANG Gencang, ZHAO Dawen. Phase-field simulation of the dendrite growth in undercooled melt[D]. Xi'an: Northwestern Polytechnical University, 2002.
[15]	韩端锋, 王永魁, 鞠磊, 等. 六角冰晶生长过程的相场模拟[J]. 哈尔滨工程大学学报, 2019, 40(9):1537-1542.
	HAN Duanfeng, WANG Yongkui, JU Lei, et al. Phase field simulation of the hexagonal ice crystal growth process[J]. Journal of Harbin Engineering University, 2019, 40(9):1537-1542.
[16]	韩端锋, 王永魁, 鞠磊, 等. 海水结冰过程中冰晶生长的相场模拟[J]. 哈尔滨工程大学学报, 2020, 41(1):1-8.
	HAN Duanfeng, WANG Yongkui, JU Lei, et al. Phase field simulation of ice crystal growth in seawater freezing process[J]. Journal of Harbin Engineering University, 2020, 41(1):1-8.
[17]	RYERSON C C, GOW A J. Crystalline structure and physical properties of ship superstructure spray ice[J]. Philosophical Transactions of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 2000, 358(1776):2847-2871.
[18]	SINGH J K, MÜLLER-PLATHE F. On the characterization of crystallization and ice adhesion on smooth and rough surfaces using molecular dynamics[J]. Applied Physics Letters, 2014, 104(2):021603. doi: 10.1063/1.4862257 URL
[19]	SULTANA K R, POPE K, MUZYCHKA Y S. Numerical predictions of solidification and water droplet impingement [C]//Arctic Technology Conference. Canada: Offshore Technology Conference, 2016, 1-15.
[20]	袁训锋. 强制对流影响凝固微观组织的相场法研究[D]. 兰州: 兰州理工大学, 2011.
	YUAN Xunfeng. Phase field method research on microstructure of solidification under forced flow[D]. Lanzhou: Lanzhou University of Technology, 2011.
[21]	雷鹏. 基于自适应有限元方法的相场模型模拟研究[D]. 兰州: 兰州理工大学, 2014.
	LEI Peng. Simulation and research of the phase-field model based on adaptive finite element method[D]. Lanzhou: Lanzhou University of Technology, 2014.
[22]	KENNETH G. The art of the snowflake: A photographic album[EB/OL]. (2018-12-07)[2020-03-22]. http://www.Snowcrystals.com/photos/photos.html