﻿ 有压管道内关阀水锤的三维模拟研究 A Three-Dimensional Simulation about Water Hammer Caused by Valve Closure in Pressure Pipeline

Modeling and Simulation
Vol.07 No.03(2018), Article ID:26269,9 pages
10.12677/MOS.2018.73017

A Three-Dimensional Simulation about Water Hammer Caused by Valve Closure in Pressure Pipeline

Yun Cao1, Ling Zhou1*, Tiecheng Li2, Haiping Hu2, Deyou Liu1, Yue Zhao1

1College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing Jiangsu

2Baishan Pumped Storage Power Station, State Grid Xinyuan Company LTD., Huadian Jilin

Received: Jul. 10th, 2018; accepted: Jul. 25th, 2018; published: Aug. 6th, 2018

ABSTRACT

In this paper we study the case that ball is closing in a pressure pipeline. The main research method is computational fluid dynamics software; here we introduce the source term: the compressibility of water. The target of building model and simulation for three-dimensional water hammer are accomplished. Experimental results are used to verify that the three-dimensional model can simulate the pressure of water hammer accurately when valve is closing. Compared with one-dimensional model, three-dimensional model is more precise, and the three-dimensional flow fluid during the direct water hammer can also be demonstrated vividly. The shape of valve and the valve closure time are also studied. On the basis of three-dimensional model, we can simulate the water hammer more accurately and precisely. The results have important theoretical value and practical engineering value.

Keywords:Ball Valve, Instantaneous Closure, 3D Simulation, Direct Water Hammer, Closing Time

1河海大学，水利水电学院，江苏 南京

2国网新源控股有限公司白山抽水蓄能电站，吉林 桦甸

1. 研究背景

2. 物理模型

Figure 1. Schematic diagram of experimental set-up

3. 数学模型

3.1. 控制方程

1) 三维动量和连续性方程

$\frac{\partial \rho }{\partial t}+\frac{\partial \rho {u}_{x}}{\partial x}+\frac{\partial \rho {u}_{y}}{\partial y}+\frac{\partial \rho {u}_{z}}{\partial z}={S}_{m}$ (1)

$\frac{\partial }{\partial t}\left(\rho {u}_{i}\right)+\frac{\partial }{\partial {x}_{i}}\left(\rho {u}_{i}{u}_{j}\right)=-\frac{\partial P}{\partial {x}_{i}}+\frac{\partial }{\partial {x}_{i}}\mu \left(\frac{\partial {u}_{i}}{\partial {x}_{j}}+\frac{\partial {u}_{j}}{\partial {x}_{i}}\right)+\rho {g}_{i}+{F}_{i}$ (2)

2) 湍流模型

$\frac{\partial }{\partial t}\left(\rho k\right)+\frac{\partial }{\partial {x}_{i}}\left(\rho k{u}_{i}\right)=\frac{\partial }{\partial {x}_{i}}\left({\Gamma }_{k}\frac{\partial k}{\partial {x}_{i}}\right)+{G}_{k}-{Y}_{k}+{S}_{k}$ (3)

$\frac{\partial }{\partial t}\left(\rho \omega \right)+\frac{\partial }{\partial {x}_{i}}\left(\rho \omega {u}_{i}\right)=\frac{\partial }{\partial {x}_{j}}\left({\Gamma }_{\omega }\frac{\partial \omega }{\partial {x}_{j}}\right)+{G}_{\omega }+{Y}_{\omega }+{D}_{\omega }+{S}_{k}$ (4)

3) 液体状态方程

${\rho }_{l}={\rho }_{l,0}{\left(\frac{K}{{{K}^{\prime }}_{l,0}}\right)}^{1/n}$ (5)

$K={{K}^{\prime }}_{l,0}+n\Delta {p}_{l}^{*}$ (6)

$\Delta {p}_{l}^{*}={p}_{l}^{*}-{\rho }_{l,0}^{*}$ (7)

3.2. 模型求解

3.3. 几何模型和边界条件

4. 三维计算结果

4.1. 模型验证

4.2. 阀门形状对直接水锤的影响

4.3. 阀门关闭时间对直接水锤的影响

Figure 2. Comparative analysis of 3D, 1D and experiment

(a) (b)

Figure 3. Schematic plots for different shape of valve: (a) Plane; (b) Sphere

Figure 4. Comparative analysis of the results between different shape of valve and experiment

Figure 5. Comparative analysis of the results between different closing time and experiment

1) 0 s关闭的球阀是一组附加的参考对比值，采用0 s关阀相对于采用盲端作为对比更具有代表性，也可以排除一些不必要的干扰，从而使对比具有更高的可信度。

2) 0.009 s的球阀关闭时间是实验中采用的关阀时间，这种关阀时间在最大程度上保持了与实验的一致性，这组数值模拟对实验的还原度最高，所以具有很高的参考价值。

3) 0.018 s的球阀关闭时间也是一组附加的参考对比值，因为之前的数值模拟数据和实验数据的对比过程中，发现数值模拟数据在时间上总是与实验数据有较大差异，这种差异有两点很明显的表现：第一点是水锤波的产生时间比实验测得要早，第二点是水锤波的周期2 L/a会随着时间增长。所以我们尝试将关阀时间延长，以期得到与实验数据比较接近的数值模拟结果。

$2L/a=2×37.2÷1319\approx 0.05641\text{s}$

Figure 6. Magnification of Figure 5, part one

Figure 7. Magnification of Figure 5, part two

Figure 8. Velocity field of fluid during the ball valve is closing

4.4. 三维流场

5. 结论

A Three-Dimensional Simulation about Water Hammer Caused by Valve Closure in Pressure Pipeline[J]. 建模与仿真, 2018, 07(03): 136-144. https://doi.org/10.12677/MOS.2018.73017

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