﻿ 基于CFD的水下滑翔机水动力导数计算
 舰船科学技术  2023, Vol. 45 Issue (24): 38-46    DOI: 10.3404/j.issn.1672-7649.2023.24.007 PDF

1. 江苏科技大学 船舶与海洋工程学院，江苏 镇江 212003;
2. 上海交通大学 海洋工程国家重点实验室，上海 200240

Calculation of hydrodynamic derivatives of underwater glider based on CFD method
ZHANG Dai-yu1, CAO Lei1, ZHANG Bei2, WANG Zhi-dong1, LING Hong-jie1
1. School of Naval Architecture and Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China;
2. State Key Laboratory of Ocean Engineering, Shanghai Jiaotong University, Shanghai 200240, China
Abstract: The solution of hydrodynamic derivative is the basis of analyzing the maneuverability of underwater glider. In order to quickly predict the maneuverability of underwater glider, the calculation of hydrodynamic derivative of underwater glider is carried out based on CFD method. The captive model test is selected as the solution method of hydrodynamic derivatives, and its CFD numerical simulation method is given. Taking the SUBOFF submarine model as an example, the CFD numerical simulation and hydrodynamic derivative calculation of the captive model test are carried out. The calculation results show that the CFD numerical simulation method is an effective method to calculate the hydrodynamic derivative of the underwater vehicle. CFD method is used to simulate the yaw test, pure sway and pure yaw motion of the underwater glider, and the least square method is used to fit the simulation data to obtain the hydrodynamic derivatives of the underwater glider, which provides support for the analysis of handling performance.
Key words: underwater glider     hydrodynamic derivative     captive model test     oblique navigation experiment     planar motion mechanism.
0 引　言

1 水下潜器操纵模型

 图 1 固定坐标系和运动坐标系 Fig. 1 Fixed coordinate system and moving coordinate system

 $\begin{split} & X=m\left[(\dot{u}-v r+w q)-x_{\theta}\left(q^{2}+r^{2}\right)+y_{\theta}(p q-\dot{r})+z_{\theta}(p r+\dot{q})\right] ，\\ & Y=m\left[(\dot{v}-v p+u r)-y_{G}\left(r^{2}+p^{2}\right)+z_{\theta}(q r-\dot{p})+x_{G}\left(g_{p}+\ddot{r}\right)\right] ，\\ & Z=m\left[(\dot{w}-u q+v p) - z_{G}\left(p^{2}+q^{2}\right) + x_{G}(r p-\dot{q})+q_{G}(r q+\dot{p})\right] ，\\ & \left.K=I_{x} \dot{p}+\left(I_{u}-I_{v}\right) q r + m\left[y_{G}(\dot{w}+p v-q u)-z_{G}(\dot{v} + r u - p w\rangle\right)\right] ，\\ & M=I_{y} \dot{q}+\left(I_{x}-I_{z}\right) r p+m\left[z_{G}(\dot{u}+q w-r v)-x_{g}(\dot{w}+p-p)\right]，\\ & N=I_{s} \dot{r}+\left(I_{v}-I_{u}\right) p q+m\left[x_{G}(\dot{v}+r u-p w)-y_{G}(\dot{u}+q w-r v)\right] 。\end{split}$ (1)

2.2 纯横荡运动

 图 3 水下潜器的纯横荡运动示意图 Fig. 3 Schematic diagram of pure sway motion of underwater submersible
 $\left\{\begin{split} & \psi=r=0，\\ & y=a \sin \omega t，\\ & v=\dot{y}=a \omega \cos \omega t ，\\ & \dot{v}=\ddot{y}=-a \omega^{2} \sin \omega t 。\end{split} \right.$ (4)

 $\left\{\begin{split} &Y=Y_{\dot{v}}+Y_{v} v+Y_{0} ，\\ &N=N_{t} \dot{v}+N_{u} v+N_{0} 。\end{split} \right.$ (5)

 $\left\{\begin{split}&Y=-a \omega^{2} Y_{i} \sin \omega t+a \omega Y_{v} \cos \omega t+Y_{0}，\\ &N=-a \omega^{2} N_{i} \sin \omega t+a \omega N_{v} \cos \omega t+N_{0}。\end{split}\right.$ (6)

3 CFD数值模拟方法 3.1 控制方程

 $\begin{split} & \frac{\partial \bar{u}_{i}}{\partial x_{i}}=0 ，\\ & \rho \frac{\partial \bar{u}_{i}}{\partial t}+\rho \bar{u}_{j} \frac{\partial u_{i}}{\partial x_{j}}=-\frac{\partial \bar{p}_{i}}{\partial x_{i}}+\frac{\partial}{\partial x_{j}}\left(\mu \frac{\partial u_{i}}{\partial x_{j}}-\rho \overline{u_{j}^{j} x_{j}^{j}}\right)。\end{split}$ (10)

3.2 湍流模型

3.3 DFBI运动耦合求解

STAR-CCM+中的DFBI模块是流体与刚体之间耦合的动态流体相互作用，根据六自由度刚体的运动移动整个流体网格。对于纯横荡和纯首摇运动可以采用DFBI中的平面运动机构来计算。

DFBI中的平面运动机构用正弦摆动运动的形式预先指定$X-Y$平面中的运动，具体的体位置 $r$[7]

 $r=\left(\begin{array}{c} r_{x} \\ r_{y} \\ r_{x} \end{array}\right)=\left(\begin{array}{c} V_{0} \cdot t \\ y_{0} \cdot \sin (2 {\text{π}} f \cdot t) \\ z \end{array}\right) 。$ (12)

 $\left\{\begin{split} & \psi=\psi_{0}+\cos (2 {\text{π}} f+t) ，\\ & \psi_{0}=\arctan \left(\frac{y_{0}+2 {\text{π}} f}{V_{0}}\right)。\end{split} \right.$ (13)
4 SUBOFF模型验证 4.1 SUBOFF模型

 图 5 SUBOFF几何模型 Fig. 5 SUBOFF geometric model
4.2 计算域和网格划分

 图 6 SUBOFF计算区域 Fig. 6 SUBOFF calculation area

 图 7 SUBOFF计算区域网格划分 Fig. 7 Meshing of SUBOFF calculation area
4.3 求解器设定

4.4 水动力导数计算

1）斜航试验

 图 8 侧向力$Y$的拟合曲线图 Fig. 8 Fitting curve of lateral force $Y$

 图 9 首摇力矩$N$的拟合曲线图 Fig. 9 Fitting curve of bowing moment $N$

2）纯横荡运动

 图 10 侧向力$Y$的历时曲线图 Fig. 10 Time-lapse curve of lateral force $Y$

 图 11 首摇力矩$N$的历时曲线图 Fig. 11 Time-lapse curve of the yaw moment $N$

 图 16 水动力导数$Y_{r}^{\prime}$和$Y_{\dot r}^{\prime}$的拟合曲线 Fig. 16 Fitting curves of hydrodynamic derivatives $Y_{r}^{\prime}$ and $Y_{r}^{\prime}$

 图 17 水动力导数$N_{r}^{\prime}$和$N_{\dot r}^{\prime}$的拟合曲线 Fig. 17 Fitting curves of hydrodynamic derivatives $N_{r}^{\prime}$ and $N_{\dot r}^{\prime}$

4.5 计算结果分析

5 水下滑翔机水动力导数计算 5.1 水下滑翔机模型

 图 18 水下滑翔机几何模型 Fig. 18 Geometric model of underwater glider
5.2 计算域和网格划分

 图 19 水下滑翔机计算区域 Fig. 19 Underwater glider computing area

 图 20 水下滑翔机计算区域网格划分 Fig. 20 Grid division of underwater glider calculation area
5.3 斜航试验

 图 21 侧向力$Y$的拟合曲线图 Fig. 21 Fitting curve of lateral force $Y$

 图 22 首摇力矩$N$的拟合曲线图 Fig. 22 Fitting curve of bowing moment $N$

5.4 纯横荡运动

 图 23 侧向力$Y$的历时曲线图 Fig. 23 Time-lapse curve of lateral force $Y$

 图 24 首摇力矩$N$的历时曲线图 Fig. 24 Time-lapse curve of the yaw moment $N$

 图 29 水动力导数$Y_{r}^{\prime}$和$Y_{\dot r}^{\prime}$的拟合曲线 Fig. 29 Fitting curves of hydrodynamic derivatives $Y_{r}^{\prime}$ and $Y_{\dot r}^{\prime}$

 图 30 水动力导数$N_{r}^{\prime}$和$N_{\dot r}^{\prime}$的拟合曲线 Fig. 30 Fitting curves of hydrodynamic derivatives $N_{r}^{\prime}$ and $Y_{\dot r}^{\prime}$

6 结　语

1）SUBOFF潜艇模型的水动力导数计算值与试验值满足误差要求，证明了采用CFD方法数值模拟约束模型试验，可用于水下潜器的水动力导数计算。

2）基于CFD方法和约束模型试验可快速准确估算水下滑翔机的水动力导数，具有一定的工程实用价值，可为下一步水下滑翔机的操纵性仿真预报工作奠定基础。

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