﻿ 基于最小阻力的双体无人船优化设计
 舰船科学技术  2018, Vol. 40 Issue (8): 27-32 PDF

1. 华南理工大学 土木与交通学院，广东 广州 510640;
2. 广州市顺海造船有限公司，广东 广州 511440

Research on optimization design of catamaran unmanned surface vehicle based on the minimum resistance
YANG Xian-yuan1, WU Jia-ming1, LI Lin-hua2
1. School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, China;
2. Guangzhou Shunhai Shipyards Ltd., Guangzhou 511440, China
Abstract: In order to reduce the resistance of catamaran unmanned surface vehicle in waves, various design which take length-width ratio, demihull spacing and longitudinal center of gravity as design variables are developed by the principle of the uniform design, and the relationship between resistance and design parameter is obtained after the calm water resistance and added resistance-in-wave at head seas of each cases is analyzed by means of numerical method. Finally, a new design with better resistance performance in waves taken overall consideration of the limitation of general arrangement on ship design and based on the minimum total resistance.
Key words: catamaran     unmanned surface vehicle     calm water resistance     added resistance-in-wave     optimization design
0 引　言

1 细长体理论与波浪增阻 1.1 细长体理论

 $\begin{split}\!\!\!\!\!\!&{R_{\rm{w}}} = \frac{{4\rho {g^2}}}{{{\rm{\pi }}{v^2}}}\mathop \int_1^\infty ({I^2} + {J^2})\frac{{{\lambda ^2}}}{{\sqrt {{\lambda ^2} - 1} }}{\rm{d}}\lambda \text{，} \\ & I = \int_0^\infty \int_{ - \infty }^\infty f(x,z){e^{\displaystyle\frac{{ - {\lambda ^2}gz}}{{{v^2}}}}}\displaystyle\frac{{\cos \lambda gx}}{{{v^2}}}\operatorname{d}\!x{\rm{d}}z \text{，} \quad\quad\quad(1) \\ & J = \int_0^\infty \int _{ - \infty }^\infty f(x,z){e^{\displaystyle\frac{{ - {\lambda ^2}gz}}{{{v^2}}}}}\frac{{\sin \lambda gx}}{{{v^2}}}{\rm{d}}x{\rm{d}}z \text{，} \\ & \lambda = \frac{{m{v^2}}}{g} \text{。} \end{split}$

 $\sigma = \frac{{{U_x}}}{{2{\rm{\pi }}}}\frac{{{\rm{d}}y}}{{{\rm{d}}x}} \cdot {S'_0}\text{，}$ (2)

 $\sigma = \frac{{ - 1}}{{2{\rm{\pi }}}}\hat n \cdot U \cdot {S_0}\text{，}$ (3)

 ${R_{{\rm{wp}}}} \!=\! \frac{{\rho gB}}{4}\left\{ \begin{gathered} \zeta _0^2\left[ {1 - \frac{{2{k_0}H}}{{\sinh (2{k_0}H)}}} \right] + \hfill \\ \mathop \sum \limits_{m = 1}^\infty \zeta _m^2\left[ {1 \!-\! \frac{{{{\cos }^2}{\theta _m}}}{2}\left( {1 \!+\! \frac{{2{k_m}H}}{{\sinh (2{k_m}H)}}} \right)} \right] \hfill \\ \end{gathered} \right\}\text{，}$ (4)

 $\begin{gathered} \left| {\begin{array}{*{20}{c}} {{\xi _m}} \\ {{\eta _m}} \end{array}} \right| = \frac{{16{\rm{\pi }}U}}{{Bg}} \cdot \frac{{\bar k + {k_m}{{\cos }^2}{\theta _m}}}{{1 + {{\sin }^2}{\theta _m} - \bar kH{\rm{sech}}\left( {{k_m}H} \right)}} \times \hfill \\ \mathop \sum \limits_\sigma \left[ \begin{gathered} {\sigma _\sigma }{e^{ - {k_m}H}} \cdot \hfill \\ \cosh \left[ {{k_m}(H + {z_\sigma })} \right]\left| {\begin{array}{*{20}{c}} {\cos ({k_m}{x_\sigma }\cos {\theta _m})} \\ {\sin ({k_m}{x_\sigma }\cos {\theta _m})} \end{array}} \right|\left| {\begin{array}{*{20}{c}} {\cos \displaystyle\frac{{m{\rm{\pi }}{y_\sigma }}}{B}} {\sin \displaystyle\frac{{m{\rm{\pi }}{y_\sigma }}}{B}} \end{array}} \right| \hfill \\ \end{gathered} \right] \text{。}\hfill \\ \end{gathered}$ (5)

Michell积分以流动为对称绕流、船体长宽比足够大为前提条件，因此，对于双体船，每个船体应关于各自的中纵剖面左右对称且均拥有足够大的长宽比，以保证足够的计算精度。

1.2 波浪增阻

 $\overline {{R_{aw}}} = 2\int_0^\infty {{C_{aw}}} \cdot {S_\zeta }({\omega _e}){\kern 1pt} \;\partial {\omega _e}\text{，}$ (6)
 ${C_{aw}}{\rm{ = }}\frac{{{R_{aw}}({\omega _e})}}{{\zeta _0^2}}\text{。}$ (7)

 ${R_{aw}}{\rm{ = }}\frac{{ik}}{2}({\eta _3}{\hat F_3} + {\eta _5}{\hat F_5}) + {R_7}\text{，}$ (8)

 ${\hat F_3} = \zeta {\int e ^{ - ik\xi }}{e^{ - kz}}[c(\xi ) - {\omega _0}({\omega _e}{a_{33}}(\xi ) - i{b_{33}}(\xi ))]{\rm d}\xi \text{，}$ (9)
 ${\hat F_5} \!=\! - \zeta {\int e ^{ - ik\xi }}{e^{ - kz}}[c(\xi ) - {\omega _0}(\xi + \frac{{iU}}{{{\omega _e}}})({\omega _e}{a_{33}}(\xi ) - i{b_{33}}(\xi ))]{\rm d}\xi \text{，}$ (10)
 ${R_7}{\rm{ = }}\frac{{{\zeta ^2}k{\omega _0}^2}}{{2{\omega _e}}}\int {{e^{ - 2kz}}} {b_{33}}(\xi ){\rm d}\xi \text{。}$ (11)

2 计算模型与计算方法

 $(1 + \beta {k_h}) = 3.03{({L_{wl}}/{\nabla ^{1/3}})^{ - 0.4}}\text{。}$ (12)

 图 1 计算模型与船体坐标系 Fig. 1 The model for calculation and ship coordinate system

 图 2 细长体网格 Fig. 2 The slender body mesh

 图 3 船体切片 Fig. 3 The hull section
3 片体长宽比对双体无人船阻力的影响研究 3.1 片体长宽比对阻力的影响

 图 4 不同Lwl/Bwl静水阻力曲线 Fig. 4 Calm water resistance curves of different Lwl/Bwl

 图 5 不同Lwl/Bwl波浪增阻曲线 Fig. 5 Added resistance-in-wave curves of different Lwl/Bwl

 图 6 不同Lwl/Bwl总阻力曲线图 Fig. 6 Total resistance curves of different Lwl/Bwl

 图 7 V=4.5 kn时阻力与长宽比关系曲线 Fig. 7 Relationship curves of resistance and Lwl/Bwlat V=4.5 kn
3.2 储能锂电池对片体水线宽度限制

4 片体间距对双体无人船阻力的影响研究

 图 8 不同K/Bwl兴波阻力系数曲线 Fig. 8 Wave-making resistance coefficient curves of different K/Bwl

 图 9 不同K/Bwl下静水阻力曲线 Fig. 9 Calm water resistance curves of different K/Bwl

 图 10 不同K/Bwl下波浪增阻曲线 Fig. 10 Added resistance-in-wave curves of different K/Bwl

 图 11 不同K/Bwl下总阻力曲线 Fig. 11 Total resistance curves of different K/Bwl
4.1 柔性太阳能薄膜对片体间距限制

5 LCG对双体无人船阻力的影响研究

LCG与无人船纵倾角密切相关进而影响无人船的阻力性能。求解片体长宽比及片体相对中心距优化结果在不同重心纵向坐标LCG下双体无人船纵倾角，如表2所示。根据纵倾角建立各重心纵向坐标LCG对应的船体曲面模型并分别计算不同重心纵向坐标LCG下双体无人船静水阻力以及波浪增阻。

 图 12 不同LCG静水阻力曲线 Fig. 12 Calm water resistance curves of different LCG

 图 13 不同LCG下波浪增阻曲线 Fig. 13 Added resistance-in-wave curves of different LCG

 图 14 不同LCG总阻力曲线 Fig. 14 Total resistance curves of different LCG

 图 15 V=4.5 kn下阻力与LCG关系曲线 Fig. 15 Relationship curves of resistance and LCG at V=4.5 kn
6 结　语

1）较大的细长比对降低双体无人船总阻力较有利。在等排水量的前提下，细长的片体对降低高速静水阻力、波浪增阻均有利，因而设计中宜采用大长宽比片体；但考虑到于片体内部锂电池布置对片体水线宽度的限制等因素，双体无人船片体宽度又不宜过小。片体长宽比最终优选为20.48。

2）从总阻力最小的角度考虑，较小的片体间距对降低总阻力较有利。片体间距对静水阻力的影响与航速有关，低航速下片体间距对静水阻力影响不小明显，航速较高时片体间距与静水阻力正相关或负相关；而较大的片体间距不利于减小波浪增阻。

3）较靠后的重心对降低总阻力较有利。结果显示，适当的尾倾可以降低双体无人船波浪增阻从而降低总阻力。

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