﻿ 考虑风载荷的客滚船纯横移运动分析
 舰船科学技术  2023, Vol. 45 Issue (19): 77-81    DOI: 10.3404/j.issn.1672-7649.2023.19.014 PDF

Crabbing analysis of ropax considering wind load
FU He-he, YU Jian, Bayartu, CHEN Deng
China Merchants Cruise Research Institute (Shanghai) Co., Ltd., Shanghai 200011, China
Abstract: Crabbing is special ship maneuvering characteristics, it can determine whether a combination of main propellers and lateral thrusters resist environmental forces. A good crabbing ability can effectively reduce harbor time for ship and improve port operation efficiency. Ship yards need to estimate the power of thrusters at preliminary design stage. In this paper, crabbing mathematical model of ropax considering wind load based on MMG model is provided, the thrust allocation is determined by the maximum value of the sum of the percent thrust of each propeller and thruster, wind speed is modified based on measuring height. The calculation results and the model test results of a ropax in the literature are compared and verified to be consistent, proved to be validity. At last, three ropax are predicted, the power of thrusters based on crabbing ability in contract design stage is provided.
Key words: crabbing     thruster     ropax     wind load     thrust allocation
0 引　言

1 计算原理

 图 1 环境力干扰下的双桨船纯横移运动示意图 Fig. 1 Crabbing for twin screw ship against environmental forces

 \left\{ {\begin{aligned} & {\left( {m + {m_x}} \right)\dot u - \left( {m + {m_y}} \right)vr = X}{\text{,}}\\ & {\left( {m + {m_y}} \right)\dot v - \left( {m + {m_x}} \right)ur = Y}{\text{,}}\\ & {\left( {{I_{zz}} + {J_{zz}}} \right)\dot r = N}{\text{。}} \end{aligned}} \right. (1)

 \left\{ {\begin{aligned} & {X = {X_H} + {X_P} + {X_R} + {X_A} + {X_T} ，}\\ & {Y = {Y_H} + {Y_P} + {Y_R} + {Y_A} + {Y_T}，}\\ & {N = {N_H} + {N_P} + {N_R} + {N_A} + {N_T} }{\text{。}} \end{aligned}} \right. (2)

2 计算步骤

 图 2 纯横移运动计算步骤 Fig. 2 Crabbing calculation procedure
2.1 船体上流体力和力矩

 \left\{ \begin{aligned} & {c}{X}_{{H}} = {\frac{1}{2}\rho Ld{V}^{2}(X'} _{{u}{u}}{u}{{'}} \left|{u}{{'}}\right| + {X}_{{u}{v}{v}}{{'}} {u}{{'}} {{v}{{'}}}^{2} + {X}_{{u}{u}{u}{v}{v}}{{'}}{{u}{{'}}}^{2}{{v}{{'}}}^{2} + {X}_{{v}{v}}{{'}}{{v}{{'}}}^{2} ),\\ & {Y}_{{H}}=\frac{1}{2}\rho Ld{V}^{2}\left({Y}_{{u}{u}{v}}{{'}}{{u}{{'}}}^{2}{v}{{'}}+{Y}_{{u}{u}{v}{v}{v}}{{'}}{{u}{{'}}}^{2}{{v}{{'}}}^{3}+{Y}_{{v}{v}{v}}{{'}}{{v}{{'}}}^{3}\right),\\ & {N}_{{H}} = \frac{1}{2}\rho {L}^{2}d{V}^{2} ({N}_{{u}{v}}{{'}}{{u}{{'}}v}{{'}} + {N}_{{u}{u}{v}}{{'}} {{u}{{'}}}^{2}{v}{{'}} + {N}_{{u}{u}{v}{v}{v}}{{'}} {{u}{{'}}}^{2} {{v}{{'}}}^{3} + {N}_{{v}{v}{v}}{{'}} {{v}{{'}}}^{3} )。\end{aligned}\right. (3)

2.2 推进器的推力模型

 ${X}_{{P}}=\frac{{\text{π}} }{8}\rho {D}_{{P}}^{2}({u}_{{P}}^{2}+{\left(0.7{\text{π}} n{D}_{{P}}\right)}^{2}){C}_{{T}}\left({\beta }_{{P}{R}}\right) {\text{,}}$ (4)
 ${P}_{{P}}=\frac{{{\text{π}} }^{2}}{4}\rho {D}_{{P}}^{3}({u}_{{P}}^{2}+{\left(0.7{\text{π}} n{D}_{{P}}\right)}^{2})n{C}_{{Q}}\left({\beta }_{{P}{R}}\right){\text{。}}$ (5)

2.3 舵的流体动力模型

 $\left\{ {\begin{array}{*{20}{c}} {{X_{{R}}} = (1 - {t_{{R}}}){F_{{N}}}{\rm{sin}}\delta }，\\ {{Y_{{R}}} = (1 + {a_{{H}}}){F_{{N}}}{\rm{cos}}\delta }。\end{array}} \right.$ (6)

2.4 风力模型及风速和高度转换

 \left\{ {\begin{aligned} & {{X_{{w}}} = 0.5{\rho _{{a}}}{A_{{f}}}U_{{w}}^2{c_{{{wx}}}}}{\text{,}}\\ & {{Y_{{w}}} = 0.5{\rho _{\rm{a}}}{A_{{s}}}U_{{w}}^2{c_{{{wy}}}}}{\text{,}}\\ & {{N_{{w}}} = 0.5{\rho _{{a}}}{A_{{s}}}L_{oa}U_{{w}}^2{c_{{{wn}}}}}{\text{。}} \end{aligned}} \right. (7)

2.5 推力分配

3 算例验证和预报 3.1 3200客位客滚船验证

 图 3 文献算例验证 Fig. 3 The crabbing capability chart for verification
3.2 3100 m车道/1000人次客滚船验证

3 100 m车道/1000人次客滚船的主要参数见表1。根据TU Hamburg-Harburg报告提供的参数计算船舶向右横移1 m/s时的风速极限，得到风速极限对比如图4所示的。可以看出，计算值与TU Hamburg-Harburg计算值吻合较好，在180°～190°的计算值偏差较大，但此区域为风速极值较大 的区域，对整体评估的影响不大。结果显示最危险的工况出现在风向为311°，风速为12.1 m/s，而TU给出的结果为风向315°，风速极限在12.5 m/s，说明计算能力能较好的模拟风速极限情况，在应用上是可靠的。船舶向左横移1 m/s的风速极限图与船舶向右横移的趋势基本对称，风速最大值出现在风向为349°，风速极限值为41.3 m/s，最小的风速极限值出现在风向49.3°，风速极限值为11.7 m/s。结合船舶横移的2个工况，当风向在40°～120°以及240°～320°时，船舶能承受的风速较小，风速在11.7～14.9 m/s之间。

 图 4 3100 m车道客滚船验证 Fig. 4 The crabbing capability of 3 100 m ropax for verification
3.3 3580 m车道/1300人次客滚船预报

 图 5 3580 m车道客滚船预报 Fig. 5 Estimation for 3580LM Ropax based on crabbing capability

3.4 5100 m车道豪华客滚船预报

 图 6 5100 m车道客滚船预报 Fig. 6 Estimation for 5 100 m Ropax based on crabbing capability

4 结　语

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