﻿ 平整冰推挤抗冰结构物的数值模拟和作用规律研究
 舰船科学技术  2022, Vol. 44 Issue (10): 55-60    DOI: 10.3404/j.issn.1672-7649.2022.10.011 PDF

1. 上海交通大学 海洋工程国家重点实验室，上海 200240;
2. 上海交通大学 船舶海洋与建筑工程学院，上海 200240;
3. 上海交通大学 海洋装备研究院，上海 200240

Research of numerical simulation and action law of anti-ice structure pushed by flat ice
REN Yu-pei1,2,3, HE Yan-ping1,2,3, CHEN Zhe1,2,3, LIU Ya-dong1,2,3, YU Long1,2,3
1. State Key Laboratory of Ocean Engineering, Shanghai Jiaotong University, Shanghai 200240, China;
2. School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, China;
3. Institute of Marine Equipment, Shanghai Jiaotong University, Shanghai 200240, China
Abstract: To reduce the pushing load caused by the movement of level ice, platforms in ice zone are usually equipped with anti-ice structures like ice cone or other structures with inclined surface. The pushing load caused by flat ice is an important technical index for the design of platform in ice area. It is of great significance to simulate the load characteristic relation of flat ice pushing structures and the accumulation patterns of crushing ice accurately. In this paper, FEM-SPH coupling algorithm and finite element method (FEM) were used to simulate the process, in which a ice cone were pushed by a flat ice, and the influence of the diameter of ice cone on the morphology of broken ice and the pushing load is analyzed. The results showed that, compared with FEM, FEM-SPH coupling algorithm can not only accurately predict the dynamic load of flat ice pushing structure, but also visually reproduce the accumulation of broken ice, which is helpful to understand and analyze the interaction law between flat ice and structure. In addition, the model and analysis conclusions about FEM-SPH coupling algorithm can provide reference for the research and design of structures in ice zone.
Key words: ice cone     FEM-SPH     accumulation of crushed ice     numerical simulation
0 引　言

1 基础理论 1.1 FEM-SPH耦合算法

FEM-SPH耦合算法将有限元法（FEM）与光滑粒子流体动力学（SPH）法相结合。在有限元网格失效后生成的光滑粒子将遵守质量守恒原则，以SPH法计算原理继续参与后续计算，模拟出碎冰或其他碎片飞散、堆积效果。FEM-SPH耦合算法在保证计算效率的同时，避免了有限元法存在的网格畸变等问题。单元转化过程如图1所示。

 图 1 FEM-SPH耦合算法单元转化示意图 Fig. 1 Transformation process of units in FEM-SPH coupling algorithm

1.2 Croasdale理论模型

 $\mathrm{F}={C}_{1}D{\sigma }_{f}{\left(\frac{{\rho }_{w}g{h}^{5}}{E}\right)}^{\frac{1}{4}}\left(1+\frac{{{\text{π}} }^{2}{I}_{c}}{4D}\right)+{C}_{2}Dzh({\rho }_{w}-{\rho }_{i})g 。$ (1)

${C}_{1}$ ${C}_{2}$ 为与锥体倾角 $\alpha$ 、摩擦系数 $\, \mu$ 相关的2个常数：

 ${C}_{1}=0.68\frac{\mathrm{sin}\alpha +\mu \mathrm{cos}\alpha }{\mathrm{cos}\alpha -\mu \mathrm{sin}\alpha }，$ (2)
 ${C}_{2}=\left(\mathrm{sin}\alpha +\mu \mathrm{cos}\alpha \right)\left(\frac{\mathrm{sin}\alpha +\mu \mathrm{cos}\alpha }{\mathrm{cos}\alpha -\mu \mathrm{sin}\alpha }+\frac{\mathrm{cos}\alpha }{\mathrm{sin}\alpha }\right)，$ (3)

${I}_{c}$ 为冰的特征长度：

 ${I}_{c}={\left(\frac{E{h}^{3}}{12{\rho }_{w}g\left(1-{\upsilon }^{2}\right)}\right)}^{\frac{1}{4}} 。$ (4)

 ${F}={C}_{1}D{\sigma }_{f}{\left(\frac{{\rho }_{w}g{h}^{5}}{E}\right)}^{\frac{1}{4}}\left(1+\frac{{\text{π}}^{2}{I}_{c}}{4D}\right) 。$ (5)
2 仿真模型

 图 2 仿真模型 Fig. 2 Simulation model

 图 3 应变率 $\dot{\epsilon }=0.001\;{{\rm{s}}}^{-1}$ 时塑性应变阶段应力-应变曲线 Fig. 3 Relationship between yield stress and strain in tension and compression when $\dot{\epsilon }=0.001\;{{\rm{s}}}^{-1}$

 图 4 压缩屈服应力比例因子-应变率曲线 Fig. 4 Relationship between strain rates and compressive yield stress scale factors

FEM-SPH耦合算法与有限元法在有限元部分设置相同，有限元冰排面向抗冰锥的一边自由，其余三边均刚性固定，以抗冰锥为主动面，平整冰为从动面，建立两者间接触关系。FEM-SPH耦合算法中，除抗冰锥与平整冰间接触外，还需建立抗冰锥与SPH粒子、SPH粒子与SPH粒子间的接触关系。因上述接触关系的建立均独立进行，推挤载荷可从仿真结果中直接读取。

 ${F}_{b}=\left\{\begin{array}{l} 0{z}_{p}\geqslant 0，\\ {\rho }_{w}g\times \dfrac{4}{3}{\text{π}} {r}^{3}{z}_{p} < 0。\end{array}\right.$ (6)

 ${F}_{d}={c}_{d}\times \frac{1}{2}{\rho }_{w}{v}^{2}\times \mathrm{\pi }{r}^{2}。$ (7)

3 结果分析 3.1 网格无关性分析

 图 5 平均推挤载荷与网格尺寸关系 Fig. 5 Relationship between mean pushing load and grid size

 图 6 0.5m网格尺寸仿真结果 Fig. 6 Simulation result when grid size equals to 0.5m

3.2 模拟结果分析

 图 7 仿真结果 Fig. 7 Simulation result

3.3 水线面直径对堆积现象影响

 图 8 冰堆积参数拟合图 Fig. 8 Fitting curves of parameters from crushing ice accumulation

2条拟合曲线相关系数r均不低于0.99，且决定系数R2均达到0.99。上述数据说明，在误差允许范围内，碎冰平均深度与碎冰宽度均与抗冰锥的水线面直径呈正比关系。

 图 9 不同水线面直径主视图 Fig. 9 Main view of ice cone with different diameters

 图 10 不同水线面直径俯视图 Fig. 10 Top view of ice cone with different diameters

3.4 水线面直径对作用力影响

 图 11 水线面直径与推挤载荷关系曲线 Fig. 11 Relationship between diameters of ice cone and pushing load

4 结　语

FEM-SPH耦合算法与有限元法模拟的抗冰锥冰载荷均随着水线面直径增加而增大，计算结果均与Croasdale理论公式接近。其中FEM-SPH耦合算法的精度略优于有限元法。

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