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Analysis of Vibration Characteristics Induced by Water Hammer of Ship’s Longitudinal Inclination and Balance System
DOI: 10.12677/APF.2020.104005, PDF, HTML, XML, 下载: 269  浏览: 587

Abstract: In the process of underwater navigation, it is necessary to move water in the longitudinal inclina-tion and balance tank frequently. Water hammer often occurs, which induces high-intensity tran-sient vibration and transient noise of the system. The transient load force is output through Flow Master, and the model of water transfer system is established in CAESAR II for time history analysis and calculation. At the same time, the influence of support height, support stiffness, fixing mode and support spacing on the vibration of longitudinal inclination and balance system is calculated and analyzed, which provides support for the subsequent three-dimensional design of pipeline system.

1. 引言

2. 水锤基本理论与数学模型

2.1. 水锤基本方程

2.1.1. 运动方程

Figure 1. Forces on small water bodies

$-\frac{\partial \left(H-Z\right)\cdot \Delta xA}{\partial x}-\rho g\Delta x\mathrm{sin}\alpha -{\tau }_{0}\pi D\Delta x=\rho A\Delta x\frac{\text{d}V}{\text{d}t}$ (2.1)

$\frac{\text{d}V}{\text{d}t}=\frac{\partial V}{\partial t}+\frac{\partial V}{\partial x}\frac{\partial x}{\partial t}=\frac{\partial V}{\partial t}+V\frac{\partial V}{\partial x}$ (2.2)

$g\frac{\partial H}{\partial x}+V\frac{\partial V}{\partial x}+\frac{\partial V}{\partial t}+\frac{4{\tau }_{0}}{\rho D}=0$ (2.3)

${\tau }_{0}=\frac{1}{8}\rho f{V}^{2}$ (2.4)

$\frac{\partial H}{\partial x}+\frac{V}{g}\frac{\partial V}{\partial x}+\frac{1}{g}\frac{\partial V}{\partial t}+\frac{fV}{2gD}|V|=0$ (2.5)

2.1.2. 连续性方程

$-\frac{\partial }{\partial x}\left(\rho AV\text{d}t\right)\text{d}x=\frac{\partial }{\partial t}\left(\rho A\text{d}x\right)\text{d}t$ (2.6)

$\frac{\partial \left(\rho A\right)}{\partial t}+\frac{\partial \left(\rho AV\right)}{\partial x}=0$ (2.7)

$-\frac{\partial V}{\partial x}=\frac{1}{A}\frac{\text{d}A}{\text{d}t}+\frac{1}{\rho }\frac{\text{d}\rho }{\text{d}t}$ (2.8)

$\frac{\partial H}{\partial t}+V\frac{\partial H}{\partial x}+\frac{{a}^{2}}{g}\frac{\partial V}{\partial x}=0$ (2.9)

V——管道中流体的流速(m/s)；

$\alpha$ ——水锤波波速(m/s)。

$\frac{\partial H}{\partial x}\ll \frac{\partial H}{\partial t}$ (2.10)

$\frac{\partial H}{\partial t}+\frac{{a}^{2}}{g}\frac{\partial V}{\partial x}=0$ (2.11)

3. 系统建模

Figure 2. Overall system model

Figure 3. Flange—valve model

4. 纵倾移水系统水锤激振时间历程分析

Table 1. Displacement under maximum impact pressure

5. 管系振动影响因素研究

5.1. 支撑高度

Figure 4. Original calculation results

Figure 5. Peak vibration displacement deformation of water hammer in front of valve

Figure 6. Peak vibration displacement deformation of water hammer behind valve

Figure 7. Cloud chart of peak stress of water hammer in front of valve

Figure 8. Cloud chart of peak stress of water hammer behind valve

Table 2. Maximum displacement of flange and support near valve at 520 mm height

Table 3. Maximum displacement of flange and support near valve at 1020 mm height

Table 4. Maximum displacement of flange and support near valve at 1520 mm height

5.2. 支撑刚度

Table 5. Maximum displacement of flange and support near valve under 1000 N/cm stiffness

Table 6. Maximum displacement of flange and support near valve under 2500 N/cm stiffness

Table 7. Maximum displacement of flange and support near valve under 5000 N/cm stiffness

Table 8. Maximum displacement of flange and support near valve under 10000 N/cm stiffness

5.3. 固定方式

Table 9. Maximum displacement of flange and support near the valve when fixed support is adopted

Table 10. Maximum displacement of flange and support near valve when original support is adopted

5.4. 支撑间隔

Table 11. Maximum displacement of flange and support near valve with support interval of 4 m

Table 12. Maximum displacement of flange and support near valve when original support is adopted

6. 小结

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