﻿ 三维对称楔形体入水的水弹性力学分析
 舰船科学技术  2018, Vol. 40 Issue (3): 19-25 PDF

Hydroelasticity analysis of 3D symmetrical wedge water entry
WANG Ling, ZHU Ren-qing, LI Hong-yan
School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China
Abstract: Water entry slamming is a complicated hydroelastic problem, which is paid more and more attention in the field of naval architecture and ocean engineering. A systematic study on the process of water entry slamming is performed with the aid of model test and Ansys numerical simulation software technology. Firstly, a reduced scale structure model and test device are designed. The slamming pressure during the structure water entry is measured in real time through the sensors arranged on the wedge structure. The effective and feasibility of the numerical simulation method is validated by model test. Finally, based on the result of the test, numerical simulations of water entry for 3D flexible wedge is conducted. We can obtain both the contours of pressure and von mises stress of the wedge and the contours of velocity of the fluid. The points of flexible wedge and test are compared and analyzed, which proves the feasibility and validity of the numerical simulation method.
Key words: water entry     numerical simulation     hydroelasticity     model test     wedge
0 引　言

1 入水问题的数学模型和数值模型 1.1 结构入水水弹性力学的微分控制方程

 图 1 弹性体与液体耦合图 Fig. 1 The sketch diagram of a plastic structure coupled with liquid

 ${\rho _s}\frac{{{\operatorname{D} ^2}{u_i}}}{{\operatorname{D} {t^2}}} = {\sigma _{ij,j}} + {F_i}\text{。}$ (1)

 ${e_{ij}} = \frac{1}{2}\left( {{u_{i,j}} + {u_{j,i}}} \right)\text{。}$ (2)

 ${\sigma _{ij}} = {{\lambda }}{e_{kk}}{\delta _{ij}} + 2\mu {e_{ij}}\text{。}$ (3)

 ${{\lambda }} = \frac{{E{{\nu }}}}{{\left( {1 + {{\nu }}} \right)\left( {1 - 2{{\nu }}} \right)}}{{,}}\;{{\mu }} = \frac{E}{{\left( {1 + 2{{\nu }}} \right)}}\text{。}$ (4)

 ${\rho _L}\frac{{{D^2}{u_i}}}{{D{t^2}}} = {\rho _L}\left( {\frac{\partial }{{\partial t}} + {u_j}\frac{\partial }{{\partial {x_j}}}} \right){u_i} = {F_i} + \frac{{\partial {p_{ij}}}}{{\rho \partial {x_j}}}\text{。}$ (5)

 ${p_{ij}} = - p{\delta _{ij}} + 2\mu \left( {{s_{ij}} - \frac{1}{3}{s_{kk}}{\delta _{ij}}} \right)\text{。}$ (6)

 $\frac{{D{\rho _L}}}{{{D_t}}} + {\rho _L}{u_{i,i}} = 0\text{，}$ (7)

 ${\rho _L} = {\text{常数}}\text{。}$ (8)

 ${\left( {\frac{{p + B}}{{{p_0} + B}}} \right)^{\frac{1}{A}}} = \frac{{{\rho _L}}}{{{\rho _{{L_0}}}}}\text{。}$ (9)

 $p = \frac{{k\left( {\rho - {\rho _0}} \right)}}{{{\rho _0}}}\text{。}$ (10)

 ${\left( {{{\dot u}_i}{n_i}} \right)_s} = {\left( {{{\dot u}_i}{n_i}} \right)_L}\;\; \text{。}$ (11)

1.2 入水问题的数值模型

1）控制方程的离散方法

 $\frac{\partial }{{\partial t}}\left( {\rho \varphi } \right) + \nabla \cdot \left( {\rho {{u}}\varphi } \right) = \nabla \cdot \left( {{\Gamma _\varphi }\nabla \varphi } \right) + {{{S}}_\varphi }\text{，}$ (12)

 $\int\nolimits_{\Delta V} {\nabla \cdot \left( {\rho {{u}}\varphi } \right)} { d}V = \int\nolimits_{\Delta V} {\nabla \cdot \left( {{\Gamma _\varphi }\nabla \varphi } \right)} { d}V + \int\nolimits_{\Delta V} {{{{S}}_\varphi }{ d}V}\text{，}$ (13)

 $\int\nolimits_{\Delta V} {\nabla \cdot {{a}}{ d}V} = \int\nolimits_A {{{n}} \cdot {{a}}{ d}A} \text{，}$ (14)

 $\int\nolimits_A {{{n}} \cdot \left( {\rho {{u}}\varphi } \right)} { d}A = \int\nolimits_A {{{n}} \cdot \left( {{\Gamma _\varphi }\nabla \varphi } \right)} { d}A + \int\nolimits_{\Delta V} {{{{S}}_\varphi }} { d}V\text{。}$ (15)

 $\sum\limits_f^{{N_{faces}}} {{\rho _f}{{{u}}_f}{\varphi _f} \cdot {A_f} = \sum {{\Gamma _\varphi }{{\left( {\nabla \varphi } \right)}_n} \cdot {A_f}} } + {{{S}}_\varphi }V{\text{。}}$ (16)

2）流场的求解方法

3）流场与结构耦合方程

 ${{F}}\left[ {{X}} \right] \equiv \left[ {\begin{array}{*{20}{c}} {{{{F}}_f}\left[ {{{{X}}_f},{{\underline {{d}} }_s}\left( {{{{X}}_s}} \right)} \right]} \\ {{{{F}}_s}\left[ {{{{X}}_s},{{{\tau }}_f}\left( {{{{X}}_f}} \right)} \right]} \end{array}} \right] = 0\text{。}$ (17)

2 楔形体入水砰击试验 2.1 试验目的

2.2 试验模型

 图 2 模型正视图 Fig. 2 Model front view

 图 3 模型成品图 Fig. 3 Figure of finished mode

2.3 测点布置

 图 4 测点布置图 Fig. 4 Measuring point layout

2.4 试验仪器

2.5 试验装置和试验方案

 图 5 模型入水装置示意图 Fig. 5 Schematic diagram of the model into water

2.6 实验过程及结果分析

 图 6 模型落水过程 Fig. 6 Model drowning process

 图 7 0.5 m高度各点落水砰击压力时间历程图 Fig. 7 The pressure time history diagram of each pointfrom 0.5 m height

 图 8 1 m高度各点落水砰击压力时间历程图 Fig. 8 The pressure time history diagram of each pointfrom 1 m height

3 三维柔性楔形体入水 3.1 几何建模及网格划分

 图 9 计算域和结构平面图 Fig. 9 The sketch diagram of computational domain and structure plan

 图 10 网格划分 Fig. 10 Meshing
3.2 计算求解

3.3 弹性体入水的响应分析

 图 11 楔形体不同时刻的压力分布云图（h=1 m） Fig. 11 Contours of surface pressure of wedge in different time (h=1 m)

 图 12 楔形体不同时刻的等效应力云图（h=1 m） Fig. 12 Contours of von mises stress of wedge in different time (h=1 m)

 图 13 流体不同时刻的速度云图（h=1 m） Fig. 13 Contours of velocity of fluid in different time (h=1 m)

 图 14 测点的砰击压力图 Fig. 14 Slamming pressure peak of test points

4 结　语

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