﻿ 计算流体力学在船舶操纵运动仿真中的应用
 舰船科学技术  2022, Vol. 44 Issue (14): 40-43    DOI: 10.3404/j.issn.1672-7649.2022.14.009 PDF

Application of the computational fluid dynamics in ship maneuvering simulation
CHEN Huang, LIN Xiong-ping
Chengyi University College, Jimei University, Xiamen 361000, China
Abstract: The maneuvering motion characteristics of ships include ship speed control, steering control, resistance characteristics and so on, which are related to the navigation safety and economy of ships. As a new branch of hydrodynamics in recent years, computational fluid dynamics, combined with fluent and other software, has been widely used in ship hydrodynamics calculation and optimization. This paper introduces the basic analysis steps and principles of computational fluid dynamics, establishes the hydrodynamic models of hull and propeller respectively, and simulates the ship maneuvering motion combined with the simulation software.
Key words: computational fluid dynamics     manipulation movement     simulation     finite element
0 引　言

1 计算流体力学原理

1）计算域的定义和模型搭建；

2）控制方程构建；

3）有限元离散和仿真；

4）数值求解。

 图 1 基于计算流体力学的船舶操纵运动仿真流程 Fig. 1 Simulation flow of ship maneuvering motion based on computational fluid dynamics

1）海水湍流方程

 $\begin{gathered} \frac{{\partial \left( {\rho k} \right)}}{{\partial t}} = \frac{\partial }{{\partial {x_i}}}\left\{ {\left( {{\mu _t} + \frac{{{\mu _t}}}{{{\sigma _k}}}} \right)\frac{{{\text{δ}} k}}{{{\text{δ}} {x_i}}}} \right\} + {G_k} - \rho \varepsilon ，\\ \frac{{\partial \left( {\rho \varepsilon } \right)}}{{\partial t}} = \frac{\partial }{{\partial {x_j}}}\left\{ {\left( {{\mu _t} + \frac{{{\mu _t}}}{{{\sigma _\varepsilon }}}} \right)\frac{{{\text{δ}} \varepsilon }}{{{\text{δ}} {x_j}}}} \right\} + {G_k} - \rho \frac{{{\varepsilon ^2}}}{k}。\\ \end{gathered}$

 ${\mu _t} = {C_0}\frac{\varepsilon }{\rho }\left( {\frac{{{k^2}}}{\varepsilon }} \right) 。$

2）海水连续性方程

 $\frac{\partial }{{\partial t}}\iiint\limits_V {}{\rm{d}}x{\rm{d}}y{\rm{d}}z + \oint {\rho {V_t}{n_t}{\rm{d}}A} = 0 。$

 $\frac{{{\text{δ}} \vec Vt}}{{{\text{δ}}\rho }} + {\rm{div}}\left( {\sum\limits_{i = 1}^n {{A_i}} } \right) = 0 。$

2 计算流体力学的有限体积法

 $\frac{{\rm{d}}}{{{\rm{d}}t}}\int_V \rho \phi {\rm{d}}s + \int_A \rho {\mathbf{v}}\phi \cdot {\rm{d}}s = \int_A {} \nabla \phi {\rm{d}}s + \int_V {{S_\phi }} {\rm{d}}s \text{，}$

 $\nabla = \left( {\frac{\partial }{{\partial x}},\frac{\partial }{{\partial y}},\frac{\partial }{{\partial z}}} \right) 。$

 图 2 有限体积法的离散示意图 Fig. 2 Discrete diagram of finite volume method
3 基于计算流体力学的船舶操纵运动仿真 3.1 船舶运动系统建模

 图 3 船舶操纵运动坐标系 Fig. 3 Ship maneuvering motion coordinate system

 $\left\{ {\begin{array}{*{20}{l}} {\dfrac{{\rm{d}}}{{{\rm{d}}t}}{x_0} = u\cos \psi - v\cos \phi \sin \psi } ，\\ {\dfrac{{\rm{d}}}{{{\rm{d}}t}}{y_0} = u\sin \psi + v\cos \phi \cos \psi } ，\\ {\dot \psi = r\cos \phi }，\\ {\dot \phi = w} 。\end{array}} \right.$

 $\vec V = v + u 。$

 $\left\{ {\begin{array}{*{20}{l}} {\left( {m + {m_x}} \right)\dot u - \left( {m + {m_y}} \right)vr = {X_H} + {X_P} + {X_R} + {X_w}}，\\ {\left( {m + {m_y}} \right)\dot v + \left( {m + {m_x}} \right)ur = {Y_H} + {Y_P} + {Y_R} + {Y_{{\text{wind }}}}}，\\ {\left( {{I_z} + {J_z}} \right)\dot r = {N_H} + {N_P} + {N_R} + {N_{{\text{wind }}}} + {N_{{\text{wave }}}}}，\\ {\left( {{I_x} + {J_x}} \right)\dot w = {L_H} + {L_P} + {L_R} + {L_{{\text{wind }}}} + {L_{{\text{wave }}}}} 。\end{array}} \right.$

3.2 船体附加质量及附加惯性矩

 $M = \left| {\begin{array}{*{20}{c}} {{m_x}}&0&0 \\ 0&{{m_y}}&{{m_y}{\alpha _x}} \\ 0&{{m_y}{\alpha _x}}&{{J_z}} \end{array}} \right| 。$

 $\left\{ {\begin{array}{*{20}{l}} {{K_x} = {m_x}u} ，\\ {{K_y} = {m_y}v + {m_y}{\alpha _x}r} ，\\ {{I_z} = {m_y}{\alpha _x}v + {J_z}r} 。\end{array}} \right.$

 $\left\{ {\begin{array}{*{20}{l}} {{m_x} = {k_x}\frac{{4\text{π} }}{3}\rho L{b^2}}，\\ {{m_y} = {k_y}\frac{{4\text{π} }}{3}\rho L{d^2}} ，\\ {{J_z} = {k_z}\frac{{4\text{π} }}{{15}}\rho L{d^2}\left( {{L^2} + {d^2}} \right)} 。\end{array}} \right.$

 图 4 惯性矩系数关系示意图 Fig. 4 Schematic diagram of moment of inertia coefficient
3.3 基于计算流体力学的船舶螺旋桨推力数学模型

 $\left\{ {\begin{array}{*{20}{l}} {T = {t_p}\rho \left[ {{V_A} + {{(0.7\text{π} nD)}^2}} \right]\dfrac{\text{π} }{4}{D^2}{M_T}C_T^{}(\beta )} ，\\ {\beta = {{\tan }^{ - 1}}\dfrac{{\left( {1 - {\omega _p}} \right)}}{{0.7 \text{π} nD}}} 。\end{array}} \right.$

 图 5 不同螺旋桨转速下的扭矩系数与推力系数的关系曲线 Fig. 5 Relationship between torque coefficient and thrust coefficient at different propeller speeds
4 基于计算流体力学的船舶操纵运动仿真

1）建立船体和螺旋桨的有限元模型

 图 6 船尾位置有限元模型示意图 Fig. 6 Schematic diagram of finite element model of stern position

2）模型解算

3）仿真数据显示与输出

 图 7 一段时间内船舶航迹角度的仿真曲线 Fig. 7 Simulation curve of ship track angle in a period of time
5 结　语

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