Shock and Vibration

Volume 2016 (2016), Article ID 2346025, 13 pages

http://dx.doi.org/10.1155/2016/2346025

## A Water Hammer Protection Method for Mine Drainage System Based on Velocity Adjustment of Hydraulic Control Valve

^{1}Research Institute of Machinery and Electronics, Taiyuan University of Technology, Taiyuan 030024, China^{2}Key Laboratory of Advanced Transducers & Intelligent Control System, Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China^{3}Taiyuan University of Technology College of Mechanical Engineering, Mine Fluid Control Engineering Research Center (Laboratory) in Shanxi Province, Taiyuan 030024, China

Received 3 June 2015; Accepted 28 September 2015

Academic Editor: Mario Terzo

Copyright © 2016 Yanfei Kou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Water hammer analysis is a fundamental work of pipeline systems design process for water distribution networks. The main characteristics for mine drainage system are the limited space and high cost of equipment and pipeline changing. In order to solve the protection problem of valve-closing water hammer for mine drainage system, a water hammer protection method for mine drainage system based on velocity adjustment of HCV (Hydraulic Control Valve) is proposed in this paper. The mathematic model of water hammer fluctuations is established based on the characteristic line method. Then, boundary conditions of water hammer controlling for mine drainage system are determined and its simplex model is established. The optimization adjustment strategy is solved from the mathematic model of multistage valve-closing. Taking a mine drainage system as an example, compared results between simulations and experiments show that the proposed method and the optimized valve-closing strategy are effective.

#### 1. Introduction

Mine drainage system is an important part in the safety production of coal mine [1]. Due to the limited space and the high cost of equipment changing, water hammer is a common phenomenon in mine drainage system and its harm is inestimable [2, 3]. The minor injuries of water hammer can cause severe shock or even pipes breaking, and the major injuries can cause equipment damaging, pumping station flooding, or even injuries to underground staff. There are several traditional water hammer protection methods such as installing vacuum valves, exhaust valve, and pressure tank. However, when these water hammer protection methods are used to mine drainage system, the original piping arrangement has to be changed because additional equipment is needed. It is unenforceable to do this in this limited mine space and the cost is too high. In this situation, controlling the time and velocity of valve-closing is an effective means to protect water hammer in mine drainage system. A water hammer is easily to be formed in pipeline if the valve-closing is fast. On the contrary, the capability of pumps is inefficient if the valve-closing is too slow because pumps in mine drainage system are centrifugal. This inefficient operation has damage for pumps, because power provided by pumps is converted into heat. Therefore, it is important for us to research the critical valve-closing velocity for Hydraulic Control Valve (HCV). Researches of theoretical system and engineering applications for water hammer protection of pipeline fluid delivery areas are increasingly improved [4–6]. But it is still a difficult problem in mine drainage system because of the limited mine space [7, 8].

At present, the theories and methods of water hammer and its protection means become more and more mature. In summary, researches about this problem are mainly in three aspects: hydraulic transient modeling, the calculation, and protection methods of water hammer.

*(1**) Hydraulic Transient Modeling*. For the research on hydraulic transient, from the mathematical derivation of the 18th century to the graphical analysis of the mid-20th century and to the current computer digital simulation, scholars have already made a lot of research results. The major achievements are getting the relationship between multiphase and multicomponent transient flow equations, water hammer equations, and the control equations, such as Joukowsky equation [9]. Based on the transient flow simulation theory, Colombo et al. [10] proposed an aqueducts fault detection technology, Lee et al. [11] proposed the pipe network leak and deterioration over time detection technology by the time domain reflectometry (TDR), Arbon et al. [12] proposed pipeline corrosion and blockage detection technology, Gong et al. [13] proposed a detection technology for pipe friction, wall thickness, velocity, position, and the length of the pipes, and Ferrante et al. [14] presented a leak detection method with coupling wavelet analysis and a Lagrangian model techniques. Meniconi et al. [15] presented a pipe system diagnosis method with the small amplitude sharp pressure waves.

*(2**) The Calculation Methods of Hydraulic Transient for Water Hammer*. The calculation methods of hydraulic transient for water hammer include arithmetic method, graphic method, and numerical method.

*(i) Arithmetic Method*. Before the 1930s, the hydraulic transient calculation of water hammer used Allievi equations mostly [16]. Allievi equations can be called Arithmetic method which is used to solve the problems of water hammer that with simple boundary conditions and its workload is very large.

*(ii) Graphic Method*. Graphic method is developed in 1930s to 1960s. Bergeron, Parmakian, and so forth [17] are committed to develop this method. Boundary conditions and the process of water hammer fluctuation are expressed through coordinate graphics of and according to this method. Due to the graphics, it is simple and intuitive for the hydraulic transient calculation of water hammer. However, the accuracy is not high because this method is restricted by calculating means and assumptions.

*(iii) Numerical Method*. From 1960s, some numerical methods appeared that can be aided by computers, such as Characteristic (MOC) [18], Wave Characteristic Method (WCM) [19], Implicit Method [20, 21], and Finite Element Method (FEM) [22, 23]. The WCM can solve water hammer problems of complex piping systems and boundary conditions. It is the most common method because of the high accuracy and computing. The Implicit Method divides pipeline into several segments and solves equations of the entire pipeline system simultaneously in each segment. The advantage of Implicit Method can be described in a way that a longer segment is selected and the number of calculations is reduced. However, there is more time needed for calculation in large and complex pipeline network system [24]. FEM with flexibility is used in pipe network system which have complex boundary conditions. However, it has a limitation in solving hydraulic transient problems.

*(3**) Water Hammer Protection*. Prevention and controlling means for water hammer are researched with the development of their theory and calculation. Wylie [25–27] has researched several protective devices for water hammer, such as air valves, check valves, pressure tank, and surge tank. Lee [28] and Stephenson [29] discussed the performances of air valves in water hammer protection. However, these researches have not given a quantitative calculation for the problem of water hammer protection.

This paper proposed a water hammer protection method based on velocity adjustment of HCV to deal with the problem of valve-closing water hammer in mine drainage system. The mathematic model of water hammer fluctuations is founded based on MOC according to the hydraulic transient. Then, boundary conditions of water hammer controlling for mine drainage system are determined and the simplex model is established. Finally, the optimization adjustment strategy is solved with simulation and experiment.

The remainder of this paper is organized as follows. Section 2 provides the mathematic model of the propagation and superposition model for water hammer fluctuations. Section 3 provides an optimization method to determine the adjustment strategy for HCV. Section 4 presents a case study. Concluding remarks are offered in the last section of this paper.

#### 2. The Process of Water Hammer Fluctuations

##### 2.1. Mathematic Model

*(1**) Foundation Equations*. The momentum equations of transient flow can be expressed aswhere is longitudinal mean velocity, is pressure head, is friction factor, is diameter of pipeline, is gravitational acceleration, is propagation distance along pipe, and is time.

The left of the equation represents the time-varying inertia force in a unit volume. In the right, the first item represents the pressure in a unit volume of fluid. The second item is friction loss pressure in a unit length of pipe, and the third item is pressure of transient flow.

The continuity equation is used to describe transient flow and it can be expressed as follows:where is propagation speed of water hammer wave and is the angle between the axis of pipe and the horizontal line.

*(2**) The Process of Water Hammer Fluctuations*. Pressures that are caused by friction loss and transient flow velocity are ignored. Furthermore, is considered for continuity equations. Then, the foundation equations can be simplified as

The second-order partial differential equations about and are obtained through the partial derivative and are taken for variables and in (3). Therefore, the momentum equations for water hammer wave in pipeline drainage system are expressed as

The functions and are introduced along with characteristic lines . Then, the general solution of (4) can be described aswhere is the initial pressure head, is the initial flow velocity, and and are direct and reflection fluctuation functions.

##### 2.2. Propagation and Superposition Model of Water Hammer Wave Based on Characteristic Line Method

Pumps and valves are the generating sources of water hammer wave in hydraulic transition process of pipeline fluid delivery system. These two kinds of water hammer wave start at the same time and propagation directions are superimposed. The superposition leads to strengthening of fluctuations for water hammer. In order to control the water hammer pressure effectively, the superposition effects of water hammer wave need to be weakened as much as possible.

The fundamental equations of water hammer can be rewritten as

These equations are combined linearly using an unknown multiplier . Let be the linear combination. The coefficient can be determined by

In the constraint of characteristic line equation , (6) converts to ordinary differential equation as follows:

and are negligible when and the tilt angle of pipeline is less than 25°. The average flow velocity is replaced by flow . The characteristic equations are changed intowhere is the characteristic line of forward wave in -axis, is the characteristic line of reflected wave in -axis, and is cross-sectional area of pipe.

The integral operation and differential conversion are introduced to (9). The discrete characteristic equations of water hammer are obtained as follows. Equation (10) and the characteristic line grid are shown in Figure 1: