﻿ 晃荡载荷作用下LNG船B型独立液货舱支撑结构受力分析
 舰船科学技术  2019, Vol. 41 Issue (8): 17-22 PDF

1. 华中科技大学 船舶与海洋工程学院，湖北 武汉 430074;
2. 高新船舶与深海开发装备协同创新中心，上海 200240;
3. 船舶和海洋水动力湖北省重点实验室，湖北 武汉 430074

Force analysis of support structure of LNG independent Type B tank under sloshing loads
DONG Wen1, YUAN Yi1, ZHANG Zheng-yi1,2,3, XIE De1,2,3
1. School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;
2. Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE), Shanghai 200240, China;
3. Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamics (HUST), Wuhan 430074, China
Abstract: To conduct the force analysis of the support structure of LNG independent Type B tank under sloshing loads, a two-dimensional finite element model with simplified support structure was established. The Abaqus was used to simulate the sloshing and calculate the force of the support structure under different cases based on arbitrary Lagrangian-Eulerian method and bulk modulus reduction technique. The following conclusions are drawn: 1. the periodic rolling motion results in the periodic support structure force; 2. the larger the rolling amplitude, the greater the range of the force variation; 3. in the same density and volume, the range of force variation caused by liquid cargo is greater than solid cargo; 4. the baffles in the cargo tank can reduce the range of force variation. The numerical methods and conclusions in this paper can contribute to the strength and fatigue analysis of the support structure during the preliminary design phase.
Key words: ALE method     bulk modulus reduction     independent type B tank     sloshing
0 引　言

1 研究对象

B型液货舱按形状可分为棱柱形（SPB型）和球形（MOSS型），如图1所示[7]。本文的研究对象是棱柱形液货舱，主要由耐低温的平面板材制成。

 图 1 B型独立液货舱 Fig. 1 Independent type B tank

 图 2 B型独立液货舱支撑结构 Fig. 2 Support structure of independent type B tank
2 数值仿真 2.1 数值方法

 $\frac{{\partial f\left( {{X_i},t} \right)}}{{\partial t}} = \frac{{\partial f\left( {{x_i},t} \right)}}{{\partial t}} + \frac{{\partial f\left( {{x_i},t} \right)}}{{\partial {x_i}}}{w_i} {\text{。}}$ (1)

 $\frac{{\partial \rho }}{{\partial t}} = - \rho \frac{{\partial {v_i}}}{{\partial {x_i}}} - {w_i}\frac{{\partial \rho }}{{\partial {x_i}}}{\text{，}}$ (2)
 $\rho \frac{{\partial {v_i}}}{{\partial t}} = {\sigma _{ij,j}} + \rho {b_i} - \rho {w_i}\frac{{\partial {v_i}}}{{\partial {x_j}}} {\text{，}}$ (3)
 $\rho \frac{{\partial E}}{{\partial t}} = {\sigma _{ij,j}}{v_{i,j}} + \rho {b_i}{v_i} - \rho {w_j}\frac{{\partial E}}{{\partial {x_j}}}{\text{。}}$ (4)

 $p - {p_{ref}} = \mathit{\Gamma} \rho \left( {e - {e_{ref}}} \right){\text{。}}$ (5)

 $\Gamma = \frac{1}{\rho }{\left. {\frac{{\partial p}}{{\partial e}}} \right|_\rho }{\text{。}}$ (6)

Abaqus引入了线性 ${U_S} - {U_P}$ Hugoniot 关系，可将 ${p_{ref}}$ 改写为[11-13]

 ${p_{ref}} = \frac{{{\rho _{ref}}c_0^2\eta }}{{{{\left( {1 - s\eta } \right)}^2}}}{\text{。}}$ (7)

 ${U_S} = {c_0} + s{U_P}{\text{。}}$ (8)

 $K = {\rho _{ref}}c_0^2{\text{，}}$ (9)

 $\Delta t \approx \frac{{{L_{\min }}}}{{{c_d}}}{\text{。}}$ (10)

 ${c_d} = \sqrt {\frac{{E\left( {1 - \mu } \right)}}{{\rho \left( {1 + \mu } \right)\left( {1 - 2\mu } \right)}}}{\text{。}}$ (11)

 $K = \frac{E}{{3\left( {1 - 2\mu } \right)}}{\text{，}}$ (12)

 ${c_d} = \sqrt {K\frac{{3\left( {1 - \mu } \right)}}{{\rho \left( {1 + \mu } \right)}}}{\text{。}}$ (13)

2.2 方法验证

 图 3 二维矩形容器晃荡算例 Fig. 3 Sloshing case of a two-dimensional container

 ${a_x}\left( t \right) = - {X_0}{\omega ^2}{\rm sin} \omega t{\text{。}}$ (14)

 图 4 自由液面上A点的波高变化 Fig. 4 Variation of wave height at point A

2.3 有限元模型

 图 5 B型独立液货舱有限元模型 Fig. 5 FE model of the independent type B tank

2.4 计算工况

 $\varphi = - {\varphi _0}\sin \omega t{\text{。}}$ (15)

3 计算结果

4个垂向支撑的总支持力与液货舱重力的误差小于1%，说明连接单元能够较好的模拟支撑结构，传递作用力。

 图 6 LC2和LC5工况支撑结构作用力对比 Fig. 6 Comparison of force on supports in LC2 and LC5

 图 7 LC3和LC6工况支撑结构作用力对比 Fig. 7 Comparison of forces on supports in LC3 and LC6

 图 8 LC2，LC3和LC4工况支撑结构作用力对比 Fig. 8 Comparison of forces on supports in LC2，LC3 and LC4

 图 9 LC5，LC6和LC7工况支撑结构作用力对比 Fig. 9 Comparison of forces on supports in LC5，LC6 and LC7
4 结　语

1）船体做周期性横摇运动时，支撑结构作用力也呈现出周期性变化，且在平衡位置附近波动；

2）船体横摇幅值越大，支撑结构作用力的变化范围越大；

3）由于液舱晃荡，装载液体货物时支撑结构作用力的变化范围大于装载相同密度和体积的固体货物时的变化范围；

4）液货舱内设置挡板能够降低支撑结构作用力的变化范围。

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