﻿ 一种水下非均质拖曳线列阵动力学仿真方法及试验验证
 舰船科学技术  2017, Vol. 39 Issue (3): 127-130 PDF

A dynamic simulation method and experimental verification of underwater heterogeneous towed linear array
YE Fan-tao, CHEN Yan-yong, SHAO Yong-yong, ZHU Min
Kunming Branch of the 705 Research Institute of CSIC, Kunming 650118, China
Abstract: Based on Ablow and Schechter's classical difference method, the underwater heterogeneous towed linear array’s motion control equation is set up for analyzing the force on the array. To obtain the towed linear array’s dynamic characteristic, central difference method is used to discretize the control equation, then this un-linear equation is iterated and solved on both time and spatial domain by Newton iteration method. On this basis, an experiment is designed and ran by using a prototype of the array in the lake, and a comparison analysis of the test and simulation data is given. The results show that the mathematical simulation method given by this paper is feasible, and it can be an useful technological mean to analyze the dynamic characteristic of the underwater heterogeneous towed linear array.
Key words: linear array     dynamics simulation     towing experiment
0 引　言

1 线列阵拖缆动力学仿真 1.1 拖缆仿真模型建立

 图 1 惯性坐标系与局部坐标系的建立 Fig. 1 Establish inertia frame and local frame

 ${ M}\vec { y}' = { N}\dot {\vec { y}} + {q}{\text{，}}$ (1)

 $\vec { y} = \left( {T,{V_t},{V_n},{V_b},\theta ,\varphi } \right),$
 ${ M} \!=\! \left[\!\! {\begin{array}{*{20}{c}}1&0&0&0&0&0\\0&1&0&0&{ - {V_b}\cos \varphi }&{ - {V_{\rm{n}}}}\\0&0&1&0&{ - {V_b}\sin \varphi }&{{V_t}}\\0&0&0&1&{{V_t}\cos \varphi + {V_n}\sin \varphi }&0\\0&0&0&0&{T\cos \varphi }&0\\0&0&0&0&0&T\end{array}}\!\! \right],$
 ${{N}} \!=\! \left[ \!\!{\begin{array}{*{20}{c}}{ \!-\! \frac{{em{V_{\rm{t}}}}}{{1 + eT}}}\!&\!m\!&\!0\!&\!0\!&\!{ - {m_1}{V_b}\cos \varphi }\!&\!{{m_1}{V_n}}\\e\!&\!0\!&\!0\!&\!0\!&\!0\!&\!0\!\\0\!&\!0\!&\!0\!&\!0\!&\!0\!&\!{1 + eT}\\0\!&\!0\!&\!0\!&\!0\!&\!{\left( {1 + eT} \right)\cos \varphi }\!&\!0\\{ \!-\! \frac{{e{m_1}{V_b}}}{{1 + eT}}}\!&\!0\!&\!0\!&\!{{m_1}}\!&\!{{m_1}{V_n}\sin \varphi + m{V_t}\cos \varphi }\!&\!0\\{ \!-\! \frac{{e{m_1}{V_n}}}{{1 \!+\! eT}}}\!&\!0\!&\!{{m_1}}\!&\!0\!&\!{ - {m_1}{V_b}\sin \varphi }\!&\!{m{V_t}}\end{array}}\!\! \right],$
 ${ q} \!=\! \left[\!\! {\begin{array}{*{20}{c}}{ - w\sin \varphi + \frac{1}{2}\rho d{{\left( {1 + \varepsilon } \right)}^{\frac{1}{2}}}\pi {C_t}{U_t}\left| {{U_t}} \right|}\\0\\0\\0\\{\frac{1}{2}\rho d{{\left( {1 + \varepsilon } \right)}^{\frac{1}{2}}}\pi {C_n}{U_b}{{\left( {{U_{\rm{b}}}^2 + {U_n}^2} \right)}^{\frac{1}{2}}}}\\{w\cos \varphi + \frac{1}{2}\rho d{{\left( {1 + \varepsilon } \right)}^{\frac{1}{2}}}{C_n}{U_n}{{\left( {{U_{{b}}}^2 + {U_n}^2} \right)}^{\frac{1}{2}}}}\end{array}} \!\!\right]\text{。}$

1）拖缆上端点边界条件

 $\left\{ \begin{array}{l}{V_t} = {V_i}\cos \theta \cos \varphi - {V_j}\sin \theta \cos \varphi + {V_k}\sin \varphi{\text{，}} \\{V_n} = {V_i}\cos \theta \sin \varphi - {V_j}\sin \theta \sin \varphi - {V_{\rm{k}}}\cos \varphi {\text{，}}\\{V_b} = {V_i}\sin \varphi - {V_j}\cos \theta {\text{。}}\end{array} \right.$ (2)

2）拖缆下端点边界条件

 $\left\{ \begin{array}{l}T = 0{\text{，}}\\ - w\cos \varphi - \frac{1}{2}\rho d{\left( {1 + \varepsilon } \right)^{\frac{1}{2}}}{C_n}{U_n}{\left( {{U_n}^2 + {U_b}^2} \right)^{\frac{1}{2}}}=\\ {m_1}{{\dot V}_n} + m{V_t}\dot \varphi - {m_1}{V_b}\dot \theta \sin \varphi{\text{，}} \\ - \frac{1}{2}\rho d{\left( {1 + \varepsilon } \right)^{\frac{1}{2}}}{C_n}{U_b}{\left( {{U_n}^2 + {U_b}^2} \right)^{\frac{1}{2}}}=\\ {m_1}{{\dot V}_b} + m{V_t}\dot \theta \cos \varphi + {m_1}{V_n}\dot \theta \sin \varphi {\text{。}}\end{array} \right.$ (3)
1.2 动力学仿真计算

 图 2 线列阵外形示意图 Fig. 2 Sketch map of the linear array

 图 3 不同航速下线列阵拖缆的运动姿态 Fig. 3 The motion posture of the linear array on different speed

2 线列阵阻力特性试验研究 2.1 试验对象

 图 4 线列阵实尺度模型图 Fig. 4 Prototype of the linear array
2.2 试验方法

 图 5 试验装置整体示意图 Fig. 5 Sketch map of the experimental facility

2.3 试验结果分析

 图 6 水平直拖试验拖缆位形 Fig. 6 Configuration of linear array by towing straightly

将仿真结果表 2 与试验所得数据表 3 进行比较，如图 7 所示，可以看出两者相差不大，最大误差在 10% 以内，且变化趋势一致，验证了数学仿真手段的可靠性。从图中可以看到，低航速时两者基本重合，在高航速时仿真值略大。分析其原因是由于建立线列阵拖缆模型时进行了简化所致。线列阵拖缆的阻力系数与航速及其和水平面的夹角有关。航速越高，阻力系数越小；夹角越大，其阻力系数则越大。但在一定范围内总体变化不大。仿真时因为线列阵拖缆为零浮力，在水中其姿态近乎水平，所以为了简化模型，采用固定阻力系数进行仿真，从而导致仿真值比试验结果偏大。

 图 7 拖缆在不同航速下仿真与试验阻力值对比 Fig. 7 Comparison of the resistance of the linear array on different speed between simulation and experiment
3 结　语

1）通过仿真分析结果，发现随着航速的提高，线列阵在拖点处拉力不断增大，即其受到的阻力不断增大；整体线列阵拖缆的深度变化逐渐变小，每一小段的深度波动也变小，即整根线列阵拖缆变得越来越平直。

2）仿真结果与试验数据对比分析可知，两者相差不大，最大误差在 10% 以内，且变化趋势一致，验证了本文针对分均质拖曳线列阵提出的仿真方法有效可靠。在高航速时仿真值略大，其原因是由于仿真时对模型进行了简化处理。

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