﻿ 舰船管道泄漏振动信号研究
 舰船科学技术  2020, Vol. 42 Issue (6): 55-60    DOI: 10.3404/j.issn.1672-7649.2020.06.011 PDF

1. 海军工程大学教务处，湖北 武汉 430033;
2. 海军工程大学动力工程学院，湖北 武汉 430033

Research on leakage vibration signal of pipeline on ship
LIU Gui-feng1, LIU Jing-bin2, ZHANG Tao2, LIU Shu-yong2
1. Academic Sericice Section, Wuhan 430033, China;
2. College of Power Engineering, Naval Universitg of Engineering, Wuhan 430033, China
Abstract: Turbulent flow and cavitation collapse of ship water supply pipeline will produce strong vibration signal.To study the relationship between vibration and boundary conditions such as pressure and velocity.In this paper, the mathematical expression of vibration response is established based on theoretical analysis.The correctness of the expression is verified by simulation and experiment.It lays a foundation for further research on identification and location of pipeline leakage.
Key words: leakage identification     vibration model     simulation experiment
0 引　言

1 泄漏管道振动产生机理

1.1 空化现象产生的振动

 $f = \frac{1}{{2{\text{π}} r}}\sqrt {\frac{{3\gamma P}}{\rho }} \text{。}$ (1)

 ${r_{\max}} = \sqrt {\frac{{2P}}{{3\rho }}{t_g}}\text{。}$ (2)

 图 1 气泡溃灭阶段半径随时间的变化情况 Fig. 1 The variation of the radius of the bubble collapse phase with time

 \begin{aligned} & p\left( {r,l} \right) = \frac{\sigma }{l}\left[ {{{\left( {\frac{{{R_0}}}{r}} \right)}^2} - 3} \right] + \frac{{{p_\infty } - {p_v}}}{l}\left\{ {\frac{{4r}}{3}\left[ {{{\left( {\frac{{{R_0}}}{r}} \right)}^3} - 1} \right] - \frac{{R_0^3}}{{{r^2}}}} \right\} - \\ & \frac{{{P_1}}}{{\left( {1 - \gamma } \right)l}}\left\{ {\frac{{4r}}{3}\left[ {{{\left( {\frac{{{R_0}}}{r}} \right)}^3} - {{\left( {\frac{{{R_0}}}{r}} \right)}^{3\gamma }}} \right] - \frac{{R_0^3}}{{{r^2}}} + \frac{{\gamma R_0^{3\gamma }}}{{{r^{\left( {3\gamma - 1} \right)}}}}} \right\} \text{。} \\[-17pt] \end{aligned} (3)

 ${c_v} = \frac{{{P_\infty } - {P_v}}}{{\rho v_\infty ^2/2}}$ (4)

1.2 湍流产生的振动

 $p \approx C\frac{{\rho {v^8}{L^2}}}{{2{c^5}}}\text{。}$ (5)

2 管壁上测点的振动响应方程

 $x\left( t \right) = \mathop \sum \limits_{i = 1}^{{\rm{i}} \to \infty } {a_i}\sin \left( {2{\text{π}} {f_i}t + {\theta _i}} \right)$ (6)

 $x\left( t \right) = \mathop \sum \limits_{i = tl}^{tg} {a_{ti}}\sin \left( {2{\text{π}} {f_{ti}}t + {\theta _{ti}}} \right) + \mathop \sum \limits_{i = kl}^{kg} {a_{ki}}\sin \left( {2{\text{π}}{f_{ki}}t + {\theta _{ki}}} \right) + y\left( t \right)\text{。}$ (7)

 ${a_{ti}} = {b_{ti}}C\rho {v^8}{L^2}/2{c^5} = {C_t}{b_{ti}}{d_i}{v^8}\text{。}$ (8)

 ${a_{ki}} = {C_k}{b_{ki}}{p_{ki}}/{v^2}\text{。}$ (9)

 $\begin{split} & x\left( t \right) = \mathop \sum \limits_{i = tl}^{tg} {C_t}{b_{ti}}{d_i}{v^8}\sin \left( {2{\text{π}} {f_{ti}}t + {\theta _{ti}}} \right)+ \\ & \mathop \sum \limits_{i = kl}^{kg} \left( {{C_k}{b_{ki}}{p_{ki}}/{v^2}} \right)\sin \left( {2{\text{π}}{f_{ki}}t + {\theta _{ki}}} \right) + y\left( t \right)\text{。} \end{split}$ (10)

 $\begin{split} & x\left( {l,t} \right) = \mathop \sum \limits_{i = tl}^{tg} {C_t}{b_{ti}}{d_i}{v^8}sin\left[ {2{\text{π}}{f_{ti}}\left( {t + \frac{l}{c}} \right) + {\theta _{ti}}} \right] + \\ & \mathop \sum \limits_{i = kl}^{kg} \left( {{C_k}{b_{ki}}{p_{ki}}/{v^2}} \right)\sin \left[ {2{\text{π}} {f_{ki}}\left( {t + \frac{l}{c}} \right) + {\theta _{ki}}} \right] + y\left( {t + \frac{l}{c}} \right) \text{。} \end{split}$ (11)

3 管道泄漏仿真分析

 图 2 泄漏管道三维模型 Fig. 2 Three-dimensional model of leaking pipeline
3.1 管内压力对泄漏振动的影响

 图 3 不同管内压力情况下泄漏处流场压力分布 Fig. 3 Flow field pressure distribution at the leak in different tube pressures

 图 4 不同管内压力情况下流场湍流动能等值线 Fig. 4 Flow field turbulent energy contours under different tube pressures

 $k = \frac{1}{2}m\left( {{{\overline {u'} }^2} + {{\overline {v'} }^2} + {{\overline {w'} }^2}} \right)\text{。}$ (12)
 $\overline {u'} = \frac{1}{T}\int_{{t_0} - \frac{T}{2}}^{{t_0} + \frac{T}{2}} {\left( {u - \bar u} \right){\rm d}t}\text{。}$ (13)

 $\overline u = \frac{Q}{{A'}} = \frac{{\sqrt {\Delta P/\rho gSL} }}{{A'}}\text{。}$ (14)

3.2 流速对泄漏振动的影响

 图 5 不同管内流速情况下流场压力等值线 Fig. 5 Flow field pressure contours for different flow rates

 图 6 不同管内流速情况下流场湍流动能等值线 Fig. 6 Flow field turbulent energy contours in different tube flow rates

4 实　验

 图 7 不同情况下在管壁采集的振动信号 Fig. 7 Vibration signals collected by the pipe wall under different circumstances
5 结　语

 [1] 刘景斌, 王基, 刘树勇. 基于振动分析的损伤识别方法综述[C]. 全国声学设计与噪声振动控制工程学术会议.2017. [2] 杨进, 文玉梅, 李平. 泄漏声振动传播信道辨识及其在泄漏点定位中的应用[J]. 振动工程学报, 2007, 20(3): 260-267. DOI:10.3969/j.issn.1004-4523.2007.03.010 [3] MINNARERT M. Musical air-bubbles and the sound of running water[J]. Philosophical Magazine, 1933, 16. [4] RAYLEIGH L. Pressure Developed in a Liquid During the Collapse of a Spherical Cavity[J]. Philosophical Magatine, 1917, 34(199): 94-98. [5] 陶跃群, 蔡军, 刘斌, 等. 湍流作用下空化泡的动力学分析和溃灭瞬间自由基产量计算[J]. 中国科学院大学学报, 2017, 34(2): 191-197. [6] 王国玉, 曹树良, 赵令家, 等. 高速水流中旋涡空化所引起的空蚀和振动[J]. 工程热物理学报, 2002, 23(6): 707-710. DOI:10.3321/j.issn:0253-231X.2002.06.014 [7] 黄景泉. 空泡起始和溃灭阶段的噪声[J]. 应用数学和力学, 1990, 11(8): 725-730. [8] MANI R. The influence of jet flow on jet noise. Part I. The noise of unheated jets[J]. Journal of Fluid Mechanics, 1976, 73(4): 753-778. DOI:10.1017/S0022112076001602 [9] 黄继汤. 空化与空蚀的原理及应用[M]. 北京: 清华大学出版社, 1991.