﻿ 基于数值方法的AUV近水面运动特性研究
 舰船科学技术  2023, Vol. 45 Issue (10): 85-90    DOI: 10.3404/j.issn.1672-7649.2023.10.017 PDF

1. 东北大学 机械工程与自动化学院，辽宁 沈阳 110819;
2. 中国科学院沈阳自动化研究所机器人学国家重点实验室，辽宁 沈阳 110016;
3. 中国科学院机器人与智能制造创新研究院，辽宁 沈阳 110169;
4. 中国人民解放军32033部队，海南 海口 570000

Research on the motion characteristics of AUV near water surface based on numerical method
WANG Xu-hui1,2,3, LIN Yang2,3, WANG Ding-qian4, MENG Ling-shuai2,3, GAO Hao2,3, CAO Xin-xing1,2,3, GU Hai-tao2,3
1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China;
2. Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110169, China;
3. Institute of Robotics and Intelligent Manufacturing Innovation, Chinese Academy of Sciences, Shenyang 110169, China;
4. No. 32033 Unit of PLA, Haikou 570000, China
Abstract: In order to clarify the motion characteristics of an AUV in the process of water surface recovery, firstly, using numerical methods as the main tool, the influence of free liquid on AUV motion was analyzed by the method of controlling variables. Secondly, the motion equation of the AUV near the water surface was established. Thirdly, through numerical simulation of PMM, all the hydrodynamic coefficients required for the AUV near-water motion equation were obtained. Finally, the accuracy of the obtained AUV near-water motion equation was verified by the cross-comparison of the water surface straight trajectory based on the motion equation and the CFD method. The results show that the obtained AUV motion equation near the water surface has good accuracy, which can provide a reference for the motion control and other follow-up work in the AUV water surface recovery process.
Key words: AUV     numerical methods     kinematic properties
0 引　言

1 模型 1.1 AUV参数

 图 1 便携式AUV Fig. 1 Portable AUV

 图 2 简化模型 Fig. 2 Simplified model of AUV
1.2 数值计算方法

RANS方程可写为：

 $\begin{split} & \nabla \cdot\left[\rho U\right]=0，\\ & \quad\quad\frac{\partial \left[\rho U\right]}{\partial t}+\nabla \cdot\left\{\rho UU\right\}=-\nabla p+\left[\nabla \cdot\left\{\left(\tau +{\tau }^{R}\right)\right\}\right]，\end{split}$ (1)

 $\frac{\partial }{\partial t}\left(\rho k\right)+\nabla \cdot\left(\rho k\overline{v}\right)=\nabla \cdot\left[\left(\mu +\frac{{\mu }_{t}}{{\sigma }_{k}}\right)\nabla k\right]+{P}_{k}-\rho \left(\epsilon -{\epsilon }_{0}\right)+{S}_{k} ，$ (2)
 $\begin{split} &\frac{\partial }{\partial t}\left(\rho \epsilon \right)+\nabla \cdot\left(\rho \epsilon \overline{v}\right)=\nabla \cdot\left[\left(\mu +\frac{{\mu }_{t}}{{\sigma }_{\epsilon }}\right)\nabla \epsilon \right]+\\ & \quad\quad \frac{1}{{T}_{e}}{C}_{\epsilon 1}{P}_{\epsilon }-{C}_{\epsilon 2}{f}_{2}\rho \left(\frac{\epsilon }{{T}_{e}}-\frac{{\epsilon }_{0}}{{T}_{0}}\right)+{S}_{\epsilon }。\end{split}$ (3)
1.3 AUV运动方程

 图 3 坐标系示意图 Fig. 3 Schematic of the coordinate system

 $m\left( {\dot u - vr + wq} \right) = X_{\dot u}^{}\dot u + X_{uu}^{}{u^2} ，$ (4)
 $m\left( {\dot v - wp + ur} \right) = Y_{\dot v}^{}\dot v + Y_{\dot r}^{}\dot r + Y_v^{}uv + Y_r^{}ur ，$ (5)
 $m\left( {\dot w - uq + vp} \right) = Z_w^{}uw + Z_{\dot w}^{}\dot w + Z_{\dot q}^{}\dot q + Z_q^{}uq，$ (6)
 ${I_{xx}}\dot p + \left( {{I_{xx}} - {I_{yy}}} \right)qr = {\text{0}} ，$ (7)
 ${I_{yy}}\dot q + \left( {{I_{xx}} - {I_{zz}}} \right)rp = M_w^{}uw + M_q^{}uq + M_{\dot w}^{}\dot w + M_{\dot q}^{}\dot q ，$ (8)
 ${I_{zz}}\dot r + \left( {{I_{yy}} - {I_{xx}}} \right)pq = N_{\dot r}^{}\dot r{\text{ + }}N_{\dot v}^{}\dot v{\text{ + }}N_v^{}uv + N_r^{}ur 。$ (9)

1.4 仿真环境

 图 4 仿真场景示意 Fig. 4 Illustration of the simulation scene

 图 5 计算域示意 Fig. 5 Illustration of the computed domain
1.5 网格无关性与精度

CFD方法求解水动力问题需要消耗大量计算资源。本文采用的求解方法是RANS方法，对于RANS方法，由于湍流模型的引入，当网格达到一定密度之后，继续增加网格密度对计算结果影响不大。同时，由于离散误差的存在，网格密度过大时误差反而可能增大。为了合理利用计算资源，首先进行网格无关性验证，即在误差合理的情况下，用最粗糙的网格进行计算。为了保证更改网格密度后网格质量不变，最优方法是成倍数加密网格，但是对于三维问题来说，每次网格量需要至少增加8倍，这种方法在实际操作中不可行。本文验证网格无关性的方法如下：首先按照经验大致划分一套初始网格；再根据网格情况通过调整基础尺寸的方式调整网格密度，将不同网格密度下的计算结果进行比较；选取最合理的一套网格为最终的计算网格。

 $\left\{ \begin{gathered} {e_{xi}} = \left| {\frac{{{X_i} - {X_{i - 1}}}}{{{X_i}}}} \right| \times {\text{100\% }},i = 1,2,3,4 ，\\ {e_{zi}} = \left| {\frac{{{Z_i} - {Z_{i - 1}}}}{{{Z_i}}}} \right| \times {\text{100\% }},i = 1,2,3,4 。\\ \end{gathered} \right.$ (10)

2 数值计算过程

x，y，z分别为AUV随体坐标系在惯性坐标系下的坐标；u，v，w分别为AUV速度V在随体坐标系3个坐标轴上的投影；pq，r分别为AUV角速度 $\Omega$ 在随体坐标系3个轴上的投影； $\varphi$ $\theta$ $\psi$ 分别为横倾角、纵倾角和首向角。

2.1 自由液面对运动的影响

 图 6 轴向力与垂向力变化情况 Fig. 6 Changes in axial and vertical forces

2.2 直航运动

2.3 PMM运动

PMM属于拘束船模试验的一种，通过强制AUV作规定运动，获取AUV受到的力与力矩，从而求得AUV的水动力系数。通过数值模拟横荡、首摇、纵荡、纵摇4种运动，求解相应的水动力系数，运动规律如下式：

 $\left\{ \begin{gathered} y = a\sin \omega t ，\\ v = \dot y = a\omega \cos \omega t ，\\ \dot v = - a{\omega ^2}\sin \omega t 。\\ \end{gathered} \right.$ (11)

 $R_i^2 = \frac{{\displaystyle\sum {SS{R_i}} }}{{\displaystyle\sum {SS{T_i}} }},{\text{ }}i = 1,2,3 。$ (12)

3 结果与验证 3.1 水动力系数

 图 7 拟合精度汇总图 Fig. 7 Fit the accuracy summary graph

3.2 轨迹仿真验证

 图 8 CFD直航模拟场景 Fig. 8 CFD direct flight simulation scenario

 图 9 运动方程模拟仿真模型 Fig. 9 Simulation model of the equation of motion simulation

 图 10 直航轨迹仿真结果图 Fig. 10 Trajectory simulation result graph

4 结　语

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