﻿ 基于船模水池试验的船舶顺浪纯稳性损失计算扩展模式
 舰船科学技术  2017, Vol. 39 Issue (9): 45-48 PDF

Extended model for calculation of the pure stability loss of ships in following waves based on ship model basin test
LI Dong, SHI Ai-guo, XUE Ya-dong, YANG Bo, ZHANG Xin-yu, XI Wen-tao
Dalian Naval Academy, Dalian 116018, China
Abstract: Research on pure loss of stability of ships sailing in following waves is becoming one of the subjects of international navigation and International Maritime Organization (IMO). Based on Ю.И. Nechaev’s method[1] of the calculation of pure stability loss of ships sailing in following waves according to ship model tank test of 28 fishing ships and transport ships, an extended model is proposed, which extends the scope of application of the original algorithm, and the example of ship with large ratio of length to width is given. Also the programming of the extended model is implemented, and a practical software is generated. Finally, the reliability of the extended model is verified by comparing with the results obtained from the CFD test method and the general theoretical calculation method.
Key words: pure loss of stability     following waves     extended model     ship model basin test
0 引 言

1）水池试验法：优点是更加贴近海上实际；缺点是试验的次数、船型等受经费的约束较大[35]

2）计算法：优点是适用性比较好，不受时空等限制；缺点是计算繁琐，至少要计算4个自由度的摇荡，并且所计算的水动力受到诸多约制，譬如傅汝德-克里洛夫（Frude-Krylov）力和斯密斯（Smith）效应，误差较大[68]

1 涅法数模化

 $\Delta l\left( \theta \right) = B\left[ {\phi \left( {\frac{h}{\lambda };\theta } \right) + \sum\limits_{m = 1}^{14} {{A_m}{f_m}\left( \theta \right)} } \right],$ (1)

 图 1 随浪在波峰时稳性力臂增量函数 Fig. 1 The stability arm increment function on the peak in following waves
 \left\{ \begin{aligned}&\phi \left( {\frac{h}{\lambda };10} \right) = - 3428.6{\left( {\frac{h}{\lambda }} \right)^5} \!\!\!+ 975.93{\left( {\frac{h}{\lambda }} \right)^4} \!\!\!- 93.86{\left( {\frac{h}{\lambda }} \right)^3} \!\!\!+ \\&\quad \quad\quad\;\;\;\;3.487{\left( {\frac{h}{\lambda }} \right)^2} - 0.102\frac{h}{\lambda } - 0.0033, \\ & \phi \left( {\frac{h}{\lambda };20} \right) = - 987.25{\left( {\frac{h}{\lambda }} \right)^5} \!\!\!+\! 125.58{\left( {\frac{h}{\lambda }} \right)^4} \!\!\!+\! 13.448{\left( {\frac{h}{\lambda }} \right)^3} \!\!\!- \\&\quad \quad\quad\;\;\;\;2.0048{\left( {\frac{h}{\lambda }} \right)^2} - 0.0752\frac{h}{\lambda } - 0.0054, \\ & \phi \left( {\frac{h}{\lambda };30} \right) = 6481.2{\left( {\frac{h}{\lambda }} \right)^5} \!\!\!- 2059.7{\left( {\frac{h}{\lambda }} \right)^4} \!\!\!+ 229.69{\left( {\frac{h}{\lambda }} \right)^3}\!\!\! - \\&\quad \quad\quad\;\;\;\;9.4139{\left( {\frac{h}{\lambda }} \right)^2} - 0.117\frac{h}{\lambda } - 0.007, \\ & \phi \left( {\frac{h}{\lambda };40} \right) = 7592.9{\left( {\frac{h}{\lambda }} \right)^5} \!\!- 2395.7{\left( {\frac{h}{\lambda }} \right)^4} \!\!+ 262.6{\left( {\frac{h}{\lambda }} \right)^3} - \\&\quad \quad\quad\;\;\;\;10.1932{\left( {\frac{h}{\lambda }} \right)^2} - 0.1461\frac{h}{\lambda } - 0.008, \\ & \phi \left( {\frac{h}{\lambda };50} \right) = 7782.4{\left( {\frac{h}{\lambda }} \right)^5} \!\!\!- 2428.3{\left( {\frac{h}{\lambda }} \right)^4} \!\!\!+\! 264.996{\left( {\frac{h}{\lambda }} \right)^3} \!\!\!- \\&\quad \quad\quad\;\;\;\;10.5842{\left( {\frac{h}{\lambda }} \right)^2} - 0.1152\frac{h}{\lambda } - 0.0076, \\ & \phi \left( {\frac{h}{\lambda };60} \right) = 6813.3{\left( {\frac{h}{\lambda }} \right)^5} \!\!\!- 2163{\left( {\frac{h}{\lambda }} \right)^4} \!\!\!+ 242.0232{\left( {\frac{h}{\lambda }} \right)^3} \!\!\!-\\& \quad \quad\quad\;\;\;\;10.1331{\left( {\frac{h}{\lambda }} \right)^2} - 0.0974\frac{h}{\lambda } - 0.0065\text{。}\end{aligned} \right. (2)

 \left\{ \begin{aligned}& {A_1} = \displaystyle\frac{L}{B} \!-\! {\left( {\frac{L}{B}} \right)_0},\!\begin{array}{*{20}{c}}\!\!\!\!\!\!\!{}&{{A_2} = \displaystyle\frac{B}{T} \!-\! {{\left( {\frac{B}{T}} \right)}_0},\!\begin{array}{*{20}{c}}\!\!\!\!\!\!\!{}&{{A_3} = \displaystyle\frac{H}{T} - {{\left( {\frac{H}{T}} \right)}_0}},\!\end{array}}\end{array}\\& {A_4} =\!\! x - {x_0},\!\!\! \begin{array}{*{20}{c}}{}{{A_5} = \varphi - {\varphi _0},\!\!\! \begin{array}{*{20}{c}}{}{{A_6} = Fr - F{r_0},\!\! \;\begin{array}{*{20}{c}}{}{{A_7} = A_1^2}, \end{array}}\end{array}}\end{array}\\& {A_8} = A_2^2,\begin{array}{*{20}{c}}{}&{{A_9} = A_3^2,\!\begin{array}{*{20}{c}}{}&{{A_{10}} = A_5^2,\!\begin{array}{*{20}{c}}{}&{{A_{11}} = A_6^2},\!\end{array}}\end{array}}\end{array}\\& {A_{12}} = {A_2}{A_3},\!\begin{array}{*{20}{c}}{}&{{A_{13}} = {A_2}{A_4},\!\begin{array}{*{20}{c}}{}&{{A_{14}} = {A_1}{A_6}}\text{。}\end{array}}\end{array}\end{aligned}\!\!\! \right.\!\!\! (3)

 \left\{ \begin{aligned}& {\left( {\displaystyle\frac{L}{B}} \right)_0}{\rm{ = }}4.820, \begin{array}{*{20}{c}}{}&{{{\left( {\displaystyle\frac{B}{T}} \right)}_0}{\rm{ = 2}}.{\rm{67}}0}, \end{array}\\& {\left( {\displaystyle\frac{H}{T}} \right)_0}{\rm{ = }}1.300, \begin{array}{*{20}{c}}{}&{{x_0}{\rm{ = }}0.700}, \end{array}\\& {\varphi _0}{\rm{ = 0}}{\rm{.692}}, \begin{array}{*{20}{c}}{}&{F{r_0}{\rm{ = }}0.280}\text{。}\end{array}\end{aligned} \right. (4)

${f_m}\left( \theta \right)$ 为横倾角函数，每个函数都对应着固定的值，文献[9]以表格的形式给出，本文在程序设计时录入所有的数值存于可读文件便于直接访问。

2 扩展适用范围

1）骑浪状态舰艇纯稳性损失的计算，取决于A1A14等参数，可归结为 $\displaystyle\frac{L}{B}$ 等六参数；

2）设每一参数对纯稳性损失的影响权重相同；

3）超过表1所述适用范围的船舶，其参数值如大于范围上限则扩展值为负值，小于下限则扩展值为正值。

 $\begin{split}{l}&\left( {1 - K} \right) \cdot \Delta l\left( \theta \right) = \\&\left( {1 - K} \right) \cdot B\left[ {\phi \left( {\displaystyle\frac{h}{\lambda };\theta } \right) + \sum\limits_{m = 1}^{14} {{A_m}{f_m}\left( \theta \right)} } \right],\end{split}$ (5)

 $K = \sum\limits_i^6 {\frac{1}{6}} \left( {\frac{{{M_i} - {M_{0i}}}}{{{M_{0i}}}}} \right)\text{。}$ (6)

 \begin{aligned}K & {\rm{ = }}\frac{1}{6}\left( {\frac{{9.1 - 4.820}}{{4.820}} + \frac{{3.45 - 2.670}}{{2.670}} + \frac{{0.399 - 0.280}}{{0.280}}} \right)=\\ & 0.268,\\ & 1 - K = 0.732\text{。}\end{aligned}

$\Delta l\left( \theta \right)$ 按一般计算的结果须乘以0.732，所得值为某舰顺浪航行船中骑浪状态下的稳性力臂损失。扩展后的稳性力臂损失值与后文中CFD数值模拟结果的吻合较好，表明该扩展模式适用于水面舰艇。

3 扩展至船舶顺浪航行任意状态

 $\Delta l{\left( \theta \right)_t} = \frac{1}{2}\left[ {\Delta l{{\left( \theta \right)}_f} + \Delta l{{\left( \theta \right)}_g}} \right]\cos \left( {{\omega _e}t - \varepsilon } \right){\text{。}}$ (7)

4 应用软件化

1）判断“扩展模式”是否被选择，若是，修正超范围参数后转步骤2；若否，且存在超范围参数则报输入错误并退出程序，参数皆符合范围则转步骤2；

 图 2 扩展模式界面 Fig. 2 Interface of extended mode

2）根据涅查耶夫算法分别计算10°，20°，30°，40°，50°，60°对应的纯稳性损失，如果“扩展模式”被选中，则按照第2节的思路对这6个值进行修正，转步骤3；否则，直接转步骤3;

3）对步骤2得到的6个点做函数拟合，根据输入的 $\theta$ 值得到函数的值即为最后的结果。

5 验证及结论

 图 3 三种稳性计算方式结果对比图 Fig. 3 Contrast diagram of three different methods of stability calculation

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