﻿ 复杂外形潜水器的动力学建模
 舰船科学技术  2017, Vol. 39 Issue (9): 23-28 PDF

Dynamic modeling of complex-shaped underwater vehicle
XU Meng-meng, FENG Zheng-ping, BI An-yuan, PAN Wan-jun
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, China
Abstract: As a complex-shaped underwater vehicle, DOE HD2+2 remotely operated vehicle (ROV) is chosen as an object to compute hydrodynamic parameters. It is necessary for nonlinear modeling of complex-shaped underwater vehicle and model-based control system design. Damping coefficients and added mass coefficients are determined by computational fluid dynamics (CFD) viscous flow method and panel method. Instead of tetrahedral mesh, polyhedral mesh is adopted to improve the computational time. And mesh is optimized to reduce the total number of grids in the flow domain. Due to the asymmetry of geometry shape of ROV, the curves of damping force and moment versus velocity are piecewise fitted. Finally, the dynamic simulation model of ROV is established by Matlab Simulink based on hydrodynamic coefficients determined by CFD, and the validity of dynamic model is validated by pool experiment.
Key words: complex-shaped     underwater vehicle     coupling     pool experiment
0 引 言

1 阻尼矩阵计算 1.1 DOE HD2+2 ROV的几何建模

DOE HD2+2 ROV重量为128 kg，长1.4 m，宽0.686 m，高0.673 m，最大作业深度为300 m。它有4个水平推进器，控制ROV的前进和回转运动，1个侧向推进器控制ROV的侧向运动，1个垂向推进器控制ROV的升沉运动，其本体结构从上往下主要为防撞框架、浮力块、推进器、配平铅块等。

xG=xB=0 m，yG=yB=0 m，zG≈0.054 m，Ix≈6.104 kg·m2Iy≈13.315 kg·m2Iz≈14.213 kg·m2Ixy=Iyz≈0 kg·m2Izx≈–0.858 kg·m2

 图 1 DOE HD2+2 ROV示意图 Fig. 1 Schematic diagram of DOE HD2+2 ROV
1.2 流体域建立

1.3 网格划分

 图 2 模拟ROV平移和转动的计算域 Fig. 2 Computation domain of simulating ROV translational and rotational motion

 图 3 计算域切面与ROV壁面多面体网格示意图 Fig. 3 Polyhedral mesh of cut surface in the flow domain and near-wall surface

STAR-CCM+中ROV壁面的y+值基本在30～100之间，如图4（a）ROV壁面Y+图所示，第 1 层网格高度在湍流区域内。由图4（b）右压强云图可以看出DOE HD2+2 ROV的迎流面压强大，明显阻碍水流的运动。由图5速度云图可知旋转域内水流速度的大小与半径成正比，与文献[16]潜艇的速度云图不同，流经ROV的尾流速度在很长的流域内都不能恢复到进流段的流态，这是因为潜艇为流线型，对流体阻碍作用小，而ROV外形复杂，对壁面附近水流速度阻碍显著。

 图 4 纵向来流1 m/s时ROV壁面的Y+值与压强云图 Fig. 4 Scalar contour of near wall domain when ROV surge motion at 1 m/s speed

 图 5 角速度为0.06 rad/s时旋转域平面的速度云图 Fig. 5 Velocity contour at ω=0.06 rad/s around the model
1.4 网格独立性验证

 图 6 不同网格数量下纵向来流时ROV所受的垂向力和纵倾力矩 Fig. 6 Heave force and pitch moment for surge motion for grid independence study

 图 7 不同网格数量下侧向来流时ROV所受的垂向力和回转力矩 Fig. 7 Heave force and yaw moment for sway motion for grid independence study
1.5 耦合的阻尼矩阵

 ${ D}\left( { V} \right) = - \left[ {\begin{array}{*{20}{l}}{{X_u} + {X_{u\left| u \right|}}\left| u \right|} & {{X_v} + {X_{vv}}v} & {{X_w} + {X_{ww}}w} & 0 & 0 & 0\\{{Y_u} + {Y_{uu}}u} & {{Y_v} + {Y_{v\left| v \right|}}\left| v \right|} & {{Y_w} + {Y_{ww}}w} & {{Y_P}} & 0 & {{Y_r}}\\{{Z_u} + {Z_{uu}}u} & {{Z_v} + {Z_{vv}}v} & {{Z_w} + {Z_{w\left| w \right|}}\left| w \right|} & 0 & {{Z_q}} & 0\\{{K_u} + {K_{uu}}u} & {{K_v} + {K_{v\left| v \right|}}\left| v \right|} & {{K_w} + {K_{ww}}w} & {{K_P}} & 0 & 0\\{{M_u} + {M_{u\left| u \right|}}\left| u \right|} & {{M_v} + {M_{vv}}v} & {{M_w} + {M_{w\left| w \right|}}\left| w \right|} & 0 & {{M_q}} & 0\\{{N_u} + {N_{u\left| u \right|}}\left| u \right|} & {{N_v} + {N_{v\left| v \right|}}v} & {{N_w} + {N_{ww}}w} & 0 & 0 & {{N_r}}\end{array}} \right]\text{。}$ (1)
2 附加质量矩阵计算 2.1 面元法

 $\left\{ {\begin{split}& {{\nabla ^2}\varphi \left( {x, y, z, t} \right) = 0,\; \left( {{\text{在整个流场}}} \right)}\text{，} \\& {\displaystyle\frac{{\partial \varphi }}{{\partial n}} = {V_n},\; \left( {{\text{在物面上}}} \right)}\text{，} \\& {\nabla \varphi = 0,\; \left( {{\text{无穷远处}}} \right)}\text{。} \end{split}} \right.$ (2)

 ${\lambda _{ij}} = - \rho \iint_{{s_0}} {{\varphi _j}\frac{{\partial {\varphi _i}}}{{\partial n}}{\rm d}{S_0}}\text{，}$ (3)

2.2 WAMIT计算

 图 8 MultiSurf建立的ROV几何模型示意图 Fig. 8 Geomtry model of ROV in Multisurf

2.3 耦合的附加质量矩阵

 ${{ M}_A} = \left[ {\begin{array}{*{20}{l}}{ - 33.481} & 0 & { - 1.510} & 0 & { - 2.009} & 0\\0 & { - 110.894} & 0 & {3.448} & 0 & {4.921}\\{ - 1.510} & 0 & { - 141.576} & 0 & { - 7.19} & 0\\0 & {3.448} & 0 & { - 5.843} & 0 & { - 0.792}\\{ - 2.009} & 0 & { - 7.190} & 0 & { - 11.746} & 0\\0 & {4.921} & 0 & { - 0.792} & 0 & { - 12.75}\end{array}} \right]\text{。}$ (4)
3 实验与仿真结果对比

 图 9 纵向推力下ROV高度随时间的运动变化 Fig. 9 Variations of altitude under longitudinal thrust

 图 10 侧向推力下ROV首向角随时间的运动变化 Fig. 10 Variations of heading angle under lateral thrust

 图 11 回转力矩下首向角随时间的运动变化 Fig. 11 Variations of heading angle under yaw moment

 图 12 垂向推力下ROV高度随时间的运动变化 Fig. 12 Variations of altitude under vertical thrust

ROV在高速运动下，其非线性模型是高度耦合的，涉及到更多非线性耦合项，难以预测。本文只是对比了ROV较低速下的运动响应，而且由于没有速度传感器和定位设备，只能通过ROV姿态变化验证DOE HD2+2 ROV动力学模型的有效性。

4 结 语

1）具有不规则、不对称外形的潜水器，正负方向运动所引起的水动力有差别，而且有耦合力产生。

2）通过开环操控实验与仿真对比，可证明建立的ROV动力学模型及采用CFD方法计算复杂外形的潜水器水动力有效。在保证计算结果精度的前提下，基于多面体网格的数值计算及面元法都大大提高了计算效率，该方法同样适用于其他潜水器的水动力计算。

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