﻿ 水下滑翔机外形设计与水动力计算
 舰船科学技术  2017, Vol. 39 Issue (3): 107-112 PDF

Configuration and hydrodynamic performance calculation of an underwater glider
YANG Lei, CAO Jun-jun, YAO Bao-heng, LIAN Lian
Naval Architecture and Ocean Engineering National Laboratory, Shanghai Jiaotong University, Shanghai 200240, China
Abstract: Underwater gliders are a class of autonomous underwater vehicles which don't use external active propulsion systems. By changing its net buoyancy and the center of buoyancy, it can glide in sawtooth motion and spiraling motion. Therefore, a good hydrodynamic performance is extremely important to design a glider. The configuration of an underwater glider designed by our laboratory was described in this paper. The hydrodynamics of the glider in linear and turning motion were calculated by CFD software. The calculated results are in good agreement with the towing experimental results. Furthermore, the glider completed a series of sawtooth motions and spiraling motions in the lake experiment. It indicates that the hydrodynamic results are accuracy and satisfy the engineering requirement. The results provide guidance and reference for the design of an underwater glider.
Key words: underwater glider     hydrodynamic coefficient     towing experiment
0 引　言

1 水下滑翔机外形设计

1.1 阻力

 图 1 “海鸥一号”设计外形 Fig. 1 The design hull of the Seagull-1 glider

 图 2 “海鸥一号”机翼外形 Fig. 2 The wing of the Seagull-1 glider

 ${y_e} = \frac{{{D_0}}}{2} \times {\left( {1 - {{\left( {\frac{x}{{{L_e}}}} \right)}^{{n_e}}}} \right)^{\frac{1}{{{n_e}}}}} {n_e} = 1.7\text{，}$ (1)
 ${y_r} = \frac{{{D_0}}}{2} \times {\left( {1 - {{\left( {\frac{x}{{{L_r}}}} \right)}^{{n_r}}}} \right)^{\frac{1}{{{{\rm{n}}_r}}}}} {n_r} = 3\text{。}$ (2)
1.2 升力

1.3 水动力表达式

 ${{F}} = \left[ {\begin{array}{*{20}{c}}{ - D}\\{SF}\\{ - L}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{({K_{D0}} + {K_D}{\alpha ^2}){{{v}}^2}}\\[6pt]{{K_\beta }\beta {{{v}}^2}}\\[6pt]{({K_{L0}} + {K_L}\alpha ){{{v}}^2}}\end{array}} \right]\text{，}$ (3)
 ${{T}} = \left[ {\begin{array}{*{20}{c}}{{T_1}}\\{{T_2}}\\{{T_3}}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{({K_{MY}}\beta + {K_p}p){{{v}}^2}}\\[6pt]{({K_{M0}} + {K_M}\alpha + {K_q}q){{{v}}^2}}\\[6pt]{({K_{MZ}}\beta + {K_r}r){{{v}}^2}}\end{array}} \right]\text{。}$ (4)

 图 3 水下滑翔机坐标系 Fig. 3 Frame illustration of the underwater glider
2 数值计算求解原理及过程 2.1 湍流模型

 \left\{ \begin{aligned} \frac{{\partial (\rho k)}}{{\partial t}} + \frac{{\partial (\rho k{u_i})}}{{\partial {x_i}}} = \frac{\partial }{{\partial {x_j}}}\left[ {{\alpha _k}{\mu _{eff}}\frac{{\partial k}}{{\partial {x_j}}}} \right] + {G_k} + \rho \varepsilon \text{，}\qquad (5)\\ \frac{{\partial (\rho \varepsilon )}}{{\partial t}} \!+\! \frac{{\partial (\rho \varepsilon {u_i})}}{{\partial {x_i}}} \!=\! \frac{\partial }{{\partial {x_j}}}\left[ {{\alpha _\varepsilon }{\mu _{eff}}\frac{{\partial \varepsilon }}{{\partial {x_j}}}} \right] \!+\! \frac{{C_{1\varepsilon }^ * \varepsilon }}{k}{G_k} \!-\! {C_{2\varepsilon }}\rho \frac{{{\varepsilon ^2}}}{k}\text{。}\end{aligned} \right.
 \left\{ \begin{aligned}& \frac{\partial }{{\partial t}}(\rho k) + \frac{\partial }{{\partial {x_i}}}(\rho k{u_i}) = \frac{\partial }{{\partial {x_j}}}({\Gamma _k}\frac{{\partial k}}{{\partial {x_j}}}) + {G_k} - {Y_k} + {S_k}\text{，}\\& \frac{\partial }{{\partial t}}(\rho \omega ) \!+\! \frac{\partial }{{\partial {x_i}}}(\rho \omega {u_i}) = \frac{\partial }{{\partial {x_j}}}({\Gamma _\omega }\frac{{\partial \omega }}{{\partial {x_j}}}) \!+\! {G_\omega } \!-\! {Y_\omega } \!+\! {S_\omega }\text{。}\end{aligned} \right. (6)
2.2 网格划分

CFD 计算中，通常计算域越大，其计算精度越高，但计算域增大将会增加计算时间，对计算机要求也更加苛刻。因此，对水下滑翔机斜航运动进行仿真时，同时采用结构化网格和非结构化网格。其中计算域分成两部分，内部流场采用非结构化网格，因为非结构化网格贴体性强，适应复杂外形的求解，同时非结构化网格生成过程中不断进行优化判断，因而生成高质量网格；外部流场则采用结构化网格，从而减少网格数量，提高网格质量，加快运算时间。计算域范围为：– 6Lx ≤ 6L，– 3Ly ≤ 3L，– 3Lz ≤ 3L

 图 4 斜航运动网格划分 Fig. 4 The grid of the glider in linear motion

 图 5 定常回转运动网格划分 Fig. 5 The grid of the glider in turning motion
2.3 边界条件

2.4 数值求解

3 计算结果及分析 3.1 计算工况

 图 6 不同攻角下阻力变化 Fig. 6 The drag force with respect to α

 图 7 不同攻角下升力变化 Fig. 7 The lift force with respect toα

 图 8 不同攻角下纵倾力矩变化 Fig. 8 MomentT2 with respect toα

 图 9 不同漂角下横向力变化 Fig. 9 The side force with respect toβ

3.2 拖曳试验

3.3 计算结果与分析

 图 6 不同攻角下阻力变化 Fig. 6 The drag force with respect to α

 图 10 不同漂角下偏航力矩变化 Fig. 10 MomentT3 with respect toβ

 图 11 不同攻角下升阻比变化 Fig. 11 Ration of lift and drag force

 图 12 “海鸥一号”千岛湖湖试 Fig. 12 The Qiandao lake experiments

 图 13 “海鸥一号”锯齿运动水深变化曲线 Fig. 13 The depth of glider in sawtooth motion
4 结　语

1）“海鸥一号”使用的外形具有优良的水动力性能，其中通过将天线置于尾舵中以达到减少附体阻力的效果，所使用的回转体外形曲线配合 NACA 翼型较大多数滑翔机配合平板翼在升阻比方面有了很大的提升。对以后水下滑翔机的设计和优化有一定的指导和借鉴意义。

2）本文采用 RNGk-ε 湍流模型模拟海鸥一号的斜航运动，同时利用结构化网格和非结构化网格，预报结果与拖曳试验相比，偏差较小，具有一定的工程实用价值，为水下滑翔机的前期设计和工程求解提供了指导。

3）本文采用 SSTk-ω 湍流模型模拟海鸥一号的定常回转运动，使用 Fluent 软件的 UDF 分别添加动量源项和设置边界条件完成仿真，其结果与相似外形的滑翔机结果进行对比，结果在同一数量级。此外，在湖试中“海鸥一号”也顺利实现锯齿运动和螺旋下潜运动，证明该方法同样适用于水下滑翔机。

 [1] ﻿叶效伟. 水下滑翔机设计、优化及运动模拟[D].上海交通大学, 2013. [2] 范双双. 洋流影响下的水下滑翔机动力学建模、运动分析与控制器设计研究[D]. 浙江大学, 2013. [3] 李志伟, 崔维成. 水下滑翔机水动力外形研究综述[J]. 船舶力学, 2012, 16(7): 831–832. LI Zhi-wei, CUI Wei-cheng. Overview on the hydrodynamic performance of underwater gliders, [J]. Journal of Ship Mechanics, 2012, 16(7): 831–832. [4] SHERMAN J, DAVIS RE, OWENS WB, et al. " The autonomous underwater glider ‘Spray, ’” [C]// IEEE Journal of Oceanic Engineering, 2001, 26(4):437–446. [5] WEBB D C, SIMONETTI P J, and JONES C P, SLOCUM: an underwater glider propelled by environmental energy, [C]// IEEE Journal of Oceanic Engineering, 2001, 26(4):447–452. [6] ERIKSEN C C, OSSE T J, LIGHT R D, et al. Seaglider: a long-range autonomous underwater vehicle for oceanographic research, [C]// IEEE Journal of Oceanic Engineering, 2001, 26(4):424–436. [7] 王蕾. 太阳能水下滑翔机器人载体的水动力计算[D]. 沈阳: 沈阳工业大学, 2014. [8] 诸敏. 水下滑翔机设计优化与运动分析[D]. 杭州: 浙江大学, 2007. [9] CAO Jun-jun, CAO Jun-liang, YAO Bao-heng, et al. Three dimensional model, hydrodynamics analysis and motion simulation of an underwater glider, [C]// IEEE OCEANS, Genova, 2015. [10] 郑力铭. 流体计算从入门到精通[M]. 北京: 电子工业出版社, 2015. [11] 肖昌润, 刘瑞杰, 许可, 等. 潜艇旋臂回转试验数值模拟[J]. 江苏科技大学学报, 2014, 28(4): 314–315. XIAO Chang-run, LIU Rui-jie, XU Ke, et al. Simulation for submarine rotating-arm tests [J].Journal of Jiangsu University of Science and Technology, 2014, 28(4): 314–315. [12] ZHANG Shao-wei, YU Jiang-cheng, ZHANG Ai-qun, et al. Spiraling motion of underwater gliders: Modeling, analysis, and experimental results [J]. Ocean Engineering. 2013(60): 1–13.