﻿ 基于Rankine源函数的船舶兴波阻力计算
 舰船科学技术  2023, Vol. 45 Issue (11): 51-54    DOI: 10.3404/j.issn.1672-7619.2023.11.010 PDF

Calculation of ship wavemaking resistance based on rankine source function solution
YUAN Xiao-ping
Science and Technology College Gannan Normal University, Gannan 341000, China
Abstract: The paper use the Rankine source function based on the Green's function to calculate the wave making resistance in ship motion, in order to improve the calculation accuracy of the direct method and ensure the safety of ship travel.
Key words: Rankine source function     wave making resistance     computational solution
0 引　言

1 船舶坐标系和定义运动量的描述

1.1 空间坐标系o0x0y0z0

1.2 运动坐标系GXGYGZ

1.3 平动坐标系oxyz

2 船舶兴波阻力运动方程的构建 2.1 纵摇、垂荡耦合运动方程

 ${\zeta ^*} = {e^{ - k{T_m}}}{\zeta _A}\cos (kx\cos \beta - ky\sin \beta + {\omega _e}t) \text{，}$

 $F_{1}^{\prime}=-2 \rho g b\left(z-X \theta-\zeta^{*}\right) \text{，}$

 $F_{2}^{\prime}=-N_{H}\left(\bar{z}-X \bar{\theta}+V \theta-\zeta^{*}\right) \text{，}$

 $\begin{array}{l} F_{z}=\int_{L}\left(F_{1}^{\prime}+F_{2}^{\prime}+F_{3}^{\prime}\right){\rm{ d}} X，\\ M_{\theta}=\int_{L} X\left(F_{1}^{\prime}+F_{2}^{\prime}+F_{3}^{\prime}\right) {\rm{d}} X 。\end{array}$

 $\begin{array}{l} \frac{D}{g} z=F_{z} ，\\ I_{y \bar{\theta}}=M_{\theta}。\end{array}$
2.2 横摇运动方程

 $-I_{x x \bar{\varphi}}^{\prime}-2 N \bar{\varphi}-D h \varphi+D h a_{m}=0 \text{，}$

 $I_{x x \bar{\varphi}}^{\prime}+2 N \dot{\varphi}+D h \varphi=D h a_{m 0} \sin \omega t \text{，}$

 $\begin{array}{l} 2 v=\frac{2 N}{I_{x x}^{\prime}} ，\\ \omega_{\varphi}^{2}=\frac{D h}{I_{x x}^{\prime}}。\end{array}$

 $\bar{\varphi}+2 v \bar{\varphi}+\omega_{\varphi}^{2} \varphi=a_{m 0} \omega_{\varphi}^{2} \sin \omega t \text{。}$
3 基于Rankine源函数的船舶兴波阻力计算 3.1 波浪设置

 ${C_\psi } = \int_R {\frac{{{{\left| {\mathop{\hat{ \psi}} \limits (\omega )} \right|}^2}}}{{\left| \omega \right|}}} {\rm{d}}\omega < \infty \text{。}$

 ${\psi _{a,b}}(t) = \frac{1}{{\sqrt {\left| a \right|} }}\psi \left(\frac{{t - b}}{a}\right)，a,b \in R；a \ne 0 \text{。}$

 ${W_f}(a,b) = \left\langle {f,{\psi _{a,b}}} \right\rangle = {\left| a \right|^{ - 1/2}}\int\limits_R {f(t) {\psi \left(\frac{{t - b}}{a}\right)} } {\rm{d}}t \text{。}$

 ${W_f}(a,b - \tau ) \text{，}$

 $\frac{1}{{\sqrt c }}{W_f}(ca,cb) c > 0 \text{。}$
3.2 不同风浪条件下的耐波性结果分析

 图 1 高风浪向下耐波性分析 Fig. 1 Analysis of downward seakeeping in high wind and waves

 图 2 低风浪向下耐波性分析 Fig. 2 Analysis of downward seakeeping in low wind and waves

 图 3 无90°高风浪向下的耐波性分析 Fig. 3 Seakeeping analysis without 90° high wind and waves downward
3.3 横摇结果分析

 图 4 不同浪向下横摇幅值曲线 Fig. 4 Different waves swing down the amplitude curve

3.4 纵摇结果分析

 图 5 不同浪向下纵摇幅值曲线 Fig. 5 Different waves roll down the amplitude curve

4 结　语

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