﻿ 基于SPH-FEM算法的浮冰-水-船耦合作用数值模拟方法
 舰船科学技术  2023, Vol. 45 Issue (11): 28-32    DOI: 10.3404/j.issn.1672-7619.2023.11.006 PDF

1. 中国船级社，山东 威海 264200;
2. 哈尔滨工程大学船舶工程学院，黑龙江 哈尔滨 150000;
3. 烟台哈尔滨工程大学研究院，山东 烟台 264000;
4. 中国船舶集团有限公司，上海 200011

Application of SPH-FEM coupling algorithm in ice-water-ship numerical simulation model making problem
BI Dong-kui1, WANG Xiang-yu2, SUN Shu-zheng3, CHEN Rui-tong2, YU Feng4, YOU Tingting4
1. China Classification Society, Weihai 264200, China;
2. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150000, China;
3. Yantai Research Institute of Harbin Engineering University, Yantai 264000 China;
4. China State Shipbuilding Corporation Limited, Shanghai 200011, China
Abstract: In order to simulate the nonlinearity and randomness of the polar ship under the influence of both floating ice and sea water, the smoothed particle hydrodynamics and finite element method are proposed in this paper. SPH-FEM coupling algorithm is applied to the dynamic process simulation of an LNG ship colliding with ice floes while sailing in the ice pool test. The basic theory and implementation method of the coupling algorithm are described. Then, the working conditions of floating ice with different concentrations are simulated, the value of ice resistance to the hull is monitored respectively, the movement of floating ice is observed, and the variation law of resistance with time when LNG ships collide with floating ice with different concentrations is analyzed, and compared with the empirical formula. The results show that the coupling algorithm simulated the LNG ship sailing in each floating ice condition is consistent with the real situation, and the results have high accuracy, which provides a strong basis for the subsequent ice load research of polar ships.
Key words: ship-ice interaction     floating ice     SPH     ice model
0 引　言

1 数值模型

SPH的基本原理为拉格朗日法。将连续的海水与浮冰离散成诸多粒子质点，这些粒子拥有独立的质量、位置坐标、速度、加速度等物理量。随后求解整体的动力学方程，跟随每个质点的各项物理参数随时间的变化情况，最终综合所有质点得到整个流场与冰体的物理情况。

SPH方程构造首先采用核函数逼近的方法，将描述场的函数转化成积分表达式，然后粒子近似，实现了对核函数近似积分表达式的粒子离散。

 ${\Pi ^h}f(x) = \int {f(y)W(x - y,h){\rm{d}}y}，$ (1)

 $W(x,h) = \frac{1}{{h{{(x)}^d}}}\theta (x) 。$ (2)

SPH方程最常用的光滑内核是三次B-样条函数，由下式定义：

 $\theta (u) = C \times \left\{ {\begin{array}{*{20}{l}} {1 - \displaystyle\frac{3}{2}{u^2} + \displaystyle\frac{3}{4}{u^3}}，&{{\rm{for}}{\text{ }}\left| u \right| \leqslant 1}，\\ {\displaystyle\frac{1}{4}{{(2 - u)}^3}}，&{{\rm{for}}{\text{ }}1 \leqslant \left| u \right| \leqslant 2}，\\ 0，&{{\rm{for}}{\text{ }}2 < \left| u \right|。} \end{array}} \right.$ (3)

 ${f_n} = - k\ln ，$ (4)
 $l = h - {r_{sp}} ，$ (5)
 ${f_t} = \eta (\frac{{\partial u}}{{\partial t}} - \upsilon )，$ (6)
 ${f_{\rm{con}}} = {f_n} + {f_t} 。$ (7)
2 计算模型 2.1 LNG船体模型

2.2 浮冰域

 $p = \frac{{{\rho _0}{C_1}^2\mu [1 + (1 - \displaystyle\frac{{{\gamma _0}}}{2})\mu - \displaystyle\frac{\alpha }{2}{\mu ^2}]}}{{{{[1 - ({S_1} - 1)\mu - {S_2}\displaystyle\frac{{{\mu ^2}}}{{(\mu + 1)}} - {S_3}\displaystyle\frac{{{\mu ^3}}}{{{{(\mu + 1)}^2}}}]}^2}}} + ({\gamma _0} + \alpha \mu )E 。$ (8)

 图 1 静置10 s水线位置 Fig. 1 Let it sit for 10 seconds at the waterline position

 图 2 浮力-时间曲线 Fig. 2 Buoyancy-time curve
2.3 浮冰工况与结果对比

 ${R}_{\rm{ice}}={p}_{1}A+{p}_{2}\phi {F}_{n}\cdot n。$ (9)

 $A = \frac{1}{4}{B^2}\sqrt {r{h_{\rm ice}}} {\rho _{\rm ice}}\left(1 + 2\frac{L}{B}{f_0}{\alpha _H}\right) ，$ (10)
 $\phi = r{h_{\rm ice}}{\rho _{\rm ice}}B\left[{f_0} + \tan {\alpha _0}\left({\alpha _H} + \frac{L}{B}\tan {\alpha _0}\right)\right]。$ (11)

3 计算结果分析 3.1 浮冰应变云图分析

 图 3 40%浮冰密集度的应变云图 Fig. 3 Strain cloud map of 40% ice floe density

 图 4 60%浮冰密集度的应变云图 Fig. 4 Strain cloud map of 60% ice floe density

 图 5 80%浮冰密集度的应变云图 Fig. 5 Strain cloud map of 80% ice floe density

3.2 浮冰运动状态分析

 图 6 浮冰不同运动状态 Fig. 6 Floating ice in different motion states

3.3 不同密集度下冰力随时间变化曲线

 图 7 40%浮冰密集度冰力−时间曲线 Fig. 7 40% Ice density ice force time curve

 图 8 60%浮冰密集度冰力−时间曲线 Fig. 8 60% Ice density ice force time curve

 图 9 80%浮冰密集度冰力−时间曲线 Fig. 9 80% Ice density ice force time curve

 图 10 浮冰阻力均值和经验公式值与浮冰密集度的散点图 Fig. 10 Scatter plot of mean and empirical formula values of floating ice resistance and floating ice density
4 结　语

1）基于FEM-SPH耦合算法对LNG船在水中与浮冰碰撞过程有很好的模拟效果。

2）在LNG船航行过程中，浮冰与船体接触被破坏区域主要在船首与肩部，船身处浮冰应变变化不大。浮冰运动状态主要有推积、贴体和平移，密集度小的工况中推积与贴体较少，浮冰平移较多。

3）冰力−时间曲线可反映船体与浮冰碰撞全过程。浮冰密集度小的工况中船体所受平均冰力较小，与DuBrovin经验公式对比，整体变化趋势一致，在高密集度工况下仿真结果偏大。

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