﻿ 三体船型阻力和运动性能分析
 舰船科学技术  2022, Vol. 44 Issue (9): 53-56    DOI: 10.3404/j.issn.1672-7649.2022.09.011 PDF

Resistance and motion performance analysis of trimaran based on finite element analysis technology
SHI Xiao, CAO Ai-xia, LI Dan
College of Intelligent Manufacturing, Qingdao Huanghai University, Qingdao 266427, China
Abstract: Compared with the traditional ship type, trimaran has better hydrodynamic characteristics, so it has higher navigation speed and less navigation resistance. At present, as a special ship, trimaran has more applications in military field, scientific research and exploration and competitive field. This paper introduces the basic theory of computational fluid dynamics and finite element analysis technology, establishes the finite element model of trimaran and navigation liquid environment, analyzes the grid convergence characteristics of the finite element model, establishes the boundary conditions required for the resistance and motion performance analysis of trimaran, and completes the resistance and motion characteristics analysis of trimaran in STAR CCM + software.
Key words: finite element analysis     computational fluid dynamics     mesh convergence     STAR-CCM+
0 引　言

1 三体船的运动坐标系建立及基本CFD理论

 图 1 三体船运动坐标系 Fig. 1 Trimaran motion coordinate system

 ${\Delta ^2}\psi {\text{ = }}0 \text{，}$

 $m\frac{{\partial \left( {\rho {u_x}} \right)}}{{\partial t}} + m\frac{{\partial \left( {\rho {u_x}{u_y}} \right)}}{{\partial t}} = m\frac{\partial }{{\partial t}}\left[ {\mu \left( {\frac{{\partial {u_x}}}{{\partial y}} + \frac{{\partial {u_y}}}{{\partial x}}} \right)} \right] + {F_i} \text{。}$

2 基于有限元分析的三体船型阻力和运动性能分析 2.1 三体船阻力和运动性能分析的自由液面处理

 $\rho * \frac{{{\rm{d}}V}}{{{\rm{d}}t}} + \frac{{\delta \left( {\rho l} \right)}}{{\delta y}} + \frac{{\delta \left( {\rho m} \right)}}{{\delta z}} + \frac{{\delta \left( {\rho n} \right)}}{{\delta x}} = 0 \text{。}$

 $\left\{ {\begin{array}{*{20}{l}} {\dfrac{{\partial l}}{{\partial t}} + {m_0}\dfrac{{\partial m}}{{\partial {t_{}}}} = \dfrac{\partial }{{\partial y}}\left[ {\left( {v + {\sigma _k}l} \right)\dfrac{{\partial n}}{{\partial t}}} \right] + {\beta ^*} \times {P_k}}，\\ {\dfrac{{\partial {P_k}}}{{\partial t}} = \dfrac{\partial }{{\partial t}}\left[ {\left( {V + {\sigma _k}l} \right)\dfrac{{\partial m}}{{\partial t}}} \right] + 2(1 - {F_i})} 。\end{array}} \right.$

 $\alpha \left( {x,t} \right) = \left\{ \begin{gathered} 0，\;\;x \in {V_1} ，\hfill \\ 1，\;\;\;x \in {V_2}，\hfill \\ \end{gathered} \right.$

 $\frac{{\partial \alpha }}{{\partial t}} + u\frac{{\partial \alpha }}{{\partial x}} + v\frac{{\partial \alpha }}{{\partial y}} + w\frac{{\partial \alpha }}{{\partial z}} = 0 \text{，}$

 ${\varphi _{}} = \frac{1}{{\Delta {V_{ij}}}}\int_{{V_{}}} \alpha (x,t){\rm{d}}V \text{，}$

 $\frac{{\partial \varphi }}{{\partial t}} + u\frac{{\partial \varphi }}{{\partial x}} + v\frac{{\partial \varphi }}{{\partial y}} + w\frac{{\partial \varphi }}{{\partial z}} = 0 。$

$\varphi = 1$ 时，网格中不含流体，当 $\varphi = 0$ 时，自由液面穿过该网格，示意图如图2所示。

 图 2 VOF函数及自由液面interface示意图 Fig. 2 Schematic diagram of VOF function and free surface interface

 $\int\limits_S {\frac{\partial }{{\partial {t^{}}}}\left( {{\rho _0}\varphi } \right){\rm{d}}V + \int\limits_{}^{} {div\left( {{\rho _0}\bar \varphi } \right){\rm{d}}V} = } S\left( V \right) \text{，}$

${\rho _0}$ 为流体的密度。

 ${\rho _0}\frac{{{\rm{d}}\frac{1}{2}{{\bar u}_i}}}{{{\rm{d}}t}} = \frac{\partial }{{\partial t}}\left\{ {\frac{{\delta {{\bar u}_i}}}{{\delta t}}} \right\} - {\rho _0}\varepsilon 。$

2.2 三体船阻力和运动性能分析的网格及收敛算法

 图 3 船体及船舶周围流场的有限元模型 Fig. 3 Finite element model of flow field around hull and ship

 $\begin{gathered} {\tau _1} = {S_1} - {S_2}，\hfill \\ {\tau _2} = {S_2} - {S_3}，\hfill \\ \end{gathered}$

 $\kappa = \frac{{{\tau _1}}}{{{\tau _2}}} 。$

$\kappa$ 满足 $0 < \kappa < 1$ 时，有限元网格单调收敛，此时可计算网格疏密程度导致的船舶流体仿真导致的误差。

 ${\kappa _o} = \frac{{{\varepsilon _1}}}{{{\varepsilon _2}}} = \frac{{0.000\;086}}{{0.000\;127}} = 0.677 \text{，}$

 ${P_G} = \frac{{\ln \left( {{\varepsilon _2}/{\varepsilon _1}} \right)}}{{\ln \kappa }} = 1.025 \text{。}$
2.3 三体船阻力和运动性能分析的边界条件及仿真

 图 4 海浪余弦规则波示意图 Fig. 4 Schematic diagram of wave cosine regular wave

 $\xi(t)=\sum_{i=1}^{n} \xi \cos \left(k \psi \pm \omega t+\varepsilon_{i}\right) 。$

 图 5 航速一定下的三体船阻力特性变化曲线 Fig. 5 Resistance characteristic curve of trimaran at a certain speed
3 结　语

 [1] 陈京普, 朱德祥, 何术龙. 双体船/三体船兴波阻力数值预报方法研究[J]. 船舶力学, 2006, 10(2): 7. [2] 卢晓平, 郦云, 董祖舜. 高速三体船研究综述[J]. 海军工程大学学报, 2005, 17(2): 7. [3] 欧阳宽, 陈明华, 王固祺, 等. 高速三体船於环流水槽实验之阻力性能探讨[J]. 台北海洋技术学院学报, 2012, 5(1): 61-77. [4] 李培勇, 裘泳铭, 顾敏童, 等. 超细长三体船耐波性试验研究[J]. 海洋工程, 2002, 20(4): 5. DOI:10.3969/j.issn.1005-9865.2002.04.002 [5] 郦云, 卢晓平. 高速三体船阻力性能研究[J]. 船舶力学, 2007, 11(2): 8. [6] 吴广怀, 吴培德, 蒋耀军, 等. 基于兴波阻力的三体船片体位置快速优化方法[J]. 船舶力学, 2005, 9(4): 8. [7] 卢晓平, 王中, 孙永华, 等. Rankine源Dawson型方法求解三体船兴波阻力[J]. 华中科技大学学报:自然科学版, 2008, 36(11): 5.