Research ArticleA Water Hammer Protection Method for Mine Drainage SystemBased on Velocity Adjustment of Hydraulic Control Valve

Yanfei Kou12 Jieming Yang12 and Ziming Kou3

1Research Institute of Machinery and Electronics Taiyuan University of Technology Taiyuan 030024 China2Key Laboratory of Advanced Transducers amp Intelligent Control System Ministry of Education Taiyuan University of TechnologyTaiyuan 030024 China3Taiyuan University of Technology College of Mechanical Engineering Mine Fluid Control Engineering Research Center(Laboratory) in Shanxi Province Taiyuan 030024 China

Correspondence should be addressed to Jieming Yang jmyang666163com

Received 3 June 2015 Accepted 28 September 2015

Academic Editor Mario Terzo

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

Water hammer analysis is a fundamental work of pipeline systems design process for water distribution networks The maincharacteristics for mine drainage system are the limited space and high cost of equipment and pipeline changing In order to solvethe protection problem of valve-closing water hammer for mine drainage system a water hammer protection method for minedrainage system based on velocity adjustment of HCV (Hydraulic Control Valve) is proposed in this paperThemathematic modelof water hammer fluctuations is established based on the characteristic line method Then boundary conditions of water hammercontrolling for mine drainage system are determined and its simplex model is established The optimization adjustment strategyis solved from the mathematic model of multistage valve-closing Taking a mine drainage system as an example compared resultsbetween 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 safetyproduction of coal mine [1] Due to the limited space andthe high cost of equipment changing water hammer is acommon phenomenon inmine drainage system and its harmis inestimable [2 3]Theminor injuries of water hammer cancause severe shock or even pipes breaking and the majorinjuries can cause equipment damaging pumping stationflooding or even injuries to underground staff There areseveral traditional water hammer protection methods suchas installing vacuum valves exhaust valve and pressure tankHowever when these water hammer protection methods areused to mine drainage system the original piping arrange-ment has to be changed because additional equipment isneeded It is unenforceable to do this in this limited minespace and the cost is too high In this situation controllingthe time and velocity of valve-closing is an effective meansto protect water hammer in mine drainage system A waterhammer is easily to be formed in pipeline if the valve-closing

is fast On the contrary the capability of pumps is inefficient ifthe valve-closing is too slow because pumps inmine drainagesystem are centrifugal This inefficient operation has damagefor pumps because power provided by pumps is convertedinto heat Therefore it is important for us to research thecritical valve-closing velocity for Hydraulic Control Valve(HCV) Researches of theoretical system and engineeringapplications for water hammer protection of pipeline fluiddelivery areas are increasingly improved [4ndash6] But it is stilla difficult problem in mine drainage system because of thelimited mine space [7 8]

At present the theories and methods of water hammerand its protection means become more and more mature Insummary researches about this problem are mainly in threeaspects hydraulic transient modeling the calculation andprotection methods of water hammer

(1) Hydraulic Transient Modeling For the research onhydraulic transient from the mathematical derivation ofthe 18th century to the graphical analysis of the mid-20th

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 2346025 13 pageshttpdxdoiorg10115520162346025

2 Shock and Vibration

century and to the current computer digital simulationscholars have alreadymade a lot of research resultsThemajorachievements are getting the relationship betweenmultiphaseandmulticomponent transient flow equations water hammerequations and the control equations such as Joukowskyequation [9] Based on the transient flow simulation theoryColombo et al [10] proposed an aqueducts fault detectiontechnology Lee et al [11] proposed the pipe network leakand deterioration over time detection technology by the timedomain reflectometry (TDR) Arbon et al [12] proposedpipeline corrosion and blockage detection technology Gonget al [13] proposed a detection technology for pipe frictionwall thickness velocity position and the length of the pipesand Ferrante et al [14] presented a leak detection methodwith coupling wavelet analysis and a Lagrangian modeltechniques Meniconi et al [15] presented a pipe systemdiagnosis method with the small amplitude sharp pressurewaves

(2) The Calculation Methods of Hydraulic Transient for WaterHammer The calculation methods of hydraulic transient forwater hammer include arithmetic method graphic methodand numerical method

(i) Arithmetic Method Before the 1930s the hydraulic tran-sient calculation of water hammer used Allievi equationsmostly [16] Allievi equations can be called Arithmeticmethod which is used to solve the problems of water hammerthatwith simple boundary conditions and itsworkload is verylarge

(ii) Graphic Method Graphic method is developed in 1930s to1960s Bergeron Parmakian and so forth [17] are committedto develop thismethod Boundary conditions and the processof water hammer fluctuation are expressed through coordi-nate graphics of119867 and119881 according to thismethodDue to thegraphics it is simple and intuitive for the hydraulic transientcalculation of water hammer However the accuracy is nothigh because this method is restricted by calculating meansand assumptions

(iii) Numerical Method From 1960s some numerical meth-ods appeared that can be aided by computers such as Char-acteristic (MOC) [18] Wave Characteristic Method (WCM)[19] Implicit Method [20 21] and Finite Element Method(FEM) [22 23]TheWCM can solve water hammer problemsof complex piping systems and boundary conditions It isthe most common method because of the high accuracy andcomputingThe Implicit Method divides pipeline into severalsegments and solves equations of the entire pipeline systemsimultaneously in each segment The advantage of ImplicitMethod can be described in a way that a longer segment isselected and the number of calculations is reduced Howeverthere is more time needed for calculation in large andcomplex pipeline network system [24] FEMwith flexibility isused in pipe network system which have complex boundaryconditions However it has a limitation in solving hydraulictransient problems

(3) Water Hammer Protection Prevention and controllingmeans for water hammer are researched with the devel-opment of their theory and calculation Wylie [25ndash27] hasresearched several protective devices for water hammer suchas air valves check valves pressure tank and surge tankLee [28] and Stephenson [29] discussed the performancesof air valves in water hammer protection However theseresearches have not given a quantitative calculation for theproblem of water hammer protection

This paper proposed a water hammer protection methodbased on velocity adjustment of HCV to deal with the prob-lem of valve-closing water hammer in mine drainage systemThe mathematic model of water hammer fluctuations isfounded based onMOC according to the hydraulic transientThen boundary conditions of water hammer controlling formine drainage system are determined and the simplex modelis established Finally the optimization adjustment strategy issolved with simulation and experiment

The remainder of this paper is organized as followsSection 2 provides the mathematic model of the propagationand superposition model for water hammer fluctuationsSection 3 provides an optimization method to determine theadjustment strategy for HCV Section 4 presents a case studyConcluding remarks are offered in the last section of thispaper

2 The Process of Water Hammer Fluctuations

21 Mathematic Model

(1) Foundation Equations The momentum equations of tran-sient flow can be expressed as

minus1

119892

120597119881

120597119905=120597119867

120597119909+119891

119863

1198812

2119892+120597

120597119909(1198812

2119892) (1)

where 119881 is longitudinal mean velocity119867 is pressure head 119891is friction factor 119863 is diameter of pipeline 119892 is gravitationalacceleration 119909 is propagation distance along pipe and 119905 istime

The left of the equation represents the time-varyinginertia force in a unit volume In the right the first itemrepresents the pressure in a unit volume of fluid The seconditem is friction loss pressure in a unit length of pipe and thethird item is pressure of transient flow

The continuity equation is used to describe transient flowand it can be expressed as follows

120597119867

120597119905+ 119881

120597119867

120597119909+1198862

119892

120597119881

120597119909minus 119881 sin 120579 = 0 (2)

where 119886 is propagation speed of water hammer wave and 120579 isthe angle between the axis of pipe and the horizontal line

(2) The Process of Water Hammer Fluctuations Pressures thatare caused by friction loss and transient flow velocity areignored Furthermore 119881 ≪ 119886 is considered for continuity

Shock and Vibration 3

equations Then the foundation equations can be simplifiedas

120597119867

120597119909+1

119892

120597119881

120597119905= 0

120597119867

120597119905+1198862

119892

120597119881

120597119909= 0

(3)

The second-order partial differential equations about119867(119909 119905) and119881(119909 119905) are obtained through the partial derivativeand are taken for variables 119909 and 119905 in (3) Therefore themomentum equations for water hammer wave in pipelinedrainage system are expressed as

1205971198672

1205971199092=1

1198862

1205971198672

1205971199052

1205971198812

1205971199092=1

1198862

1205971198812

1205971199052

(4)

The functions 119865(119909 119905) and 119891(119909 119905) are introduced alongwith characteristic lines 119889119909 = plusmn119889119905 Then the general solutionof (4) can be described as

119867 minus1198670= 119865(119905 minus

119909

119886) + 119891(119905 +

119909

119886)

119881 minus 1198810= minus

119892

119886[119865(119905 minus

119909

119886) minus 119891(119905 +

119909

119886)]

(5)

where 1198670is the initial pressure head 119881

0is the initial flow

velocity and 119865(119909 119905) and 119891(119909 119905) are direct and reflectionfluctuation functions

22 Propagation and Superposition Model of Water HammerWave Based on Characteristic Line Method Pumps andvalves are the generating sources of water hammer wavein hydraulic transition process of pipeline fluid deliverysystem These two kinds of water hammer wave start at thesame time and propagation directions are superimposedThesuperposition leads to strengthening of fluctuations for waterhammer In order to control the water hammer pressureeffectively the superposition effects of water hammer waveneed to be weakened as much as possible

The fundamental equations of water hammer can berewritten as

1198711= 119892

120597119867

120597119905+ 119881

120597119881

120597119909+120597119881

120597119905+119891119881 |119881|

2119863= 0

1198712=120597119867

120597119905+ 119881

120597119881

120597119909+1198862

119892

120597119881

120597119909minus 119881 sin 120579 = 0

(6)

These equations are combined linearly using an unknownmultiplier 120582 Let 119871 = 119871

1+1205821198712be the linear combinationThe

coefficient 120582 can be determined by

120582 = plusmn119892

119886 (7)

t

2Δt

Δt

t = 0

1 Δx i minus 1 i i + 1 N + 1 x

P

C+ Cminus

A B

Figure 1 Characteristic line grid for water hammer calculation

In the constraint of characteristic line equation 119889119909119889119905 =119881plusmn119886 (6) converts to ordinary differential equation as follows

119862+

119889119867

119889119905+119886

119892

119889119881

119889119905minus 119881 sin 120579 +

119891119886119881 |119881|

2119892119863= 0

119889119909

119889119905= 119881 + 119886

119862minus

119889119867

119889119905minus119886

119892

119889119881

119889119905minus 119881 sin 120579 minus

119891119886119881 |119881|

2119892119863= 0

119889119909

119889119905= 119881 minus 119886

(8)

119881 and119881sin120579 are negligible when119881 ≪ 119886 and the tilt angleof pipeline is less than 25∘ The average flow velocity 119881 isreplaced by flow 119876 The characteristic equations are changedinto

119862+

119889119867

119889119905+

119886

119892119860

119889119876

119889119905+119891119886119876 |119876|

21198921198631198602= 0

119889119909

119889119905= +119886

119862minus

minus119889119867

119889119905+

119886

119892119860

119889119876

119889119905+119891119886119876 |119876|

21198921198631198602= 0

119889119909

119889119905= minus119886

(9)

where 119862+ is the characteristic line of forward wave in 119909-axis119862minus is the characteristic line of reflected wave in 119909-axis and119860

is cross-sectional area of pipeThe integral operation and differential conversion are

introduced to (9) The discrete characteristic equations ofwater hammer are obtained as follows Equation (10) and thecharacteristic line grid are shown in Figure 1

119867119875minus 119867119860+

119886

119892119860(119876119875minus 119876119860) +

119891Δ119909119876119860

10038161003816100381610038161198761198601003816100381610038161003816

21198921198631198602= 0

119867119875minus 119867119861+

119886

119892119860(119876119875minus 119876119861) +

119891Δ119909119876119861

10038161003816100381610038161198761198611003816100381610038161003816

21198921198631198602= 0

(10)

4 Shock and Vibration

By solving the above equations transient variables 119867119875

and119876119875in the node 119894 of the pipe over the timeΔ119905 are expressed

as

119867119875=(119862119875+ 119862119872)

2

119876119875=(119862119875minus 119867119875)

119861

(11)

where 119861 = 119886119892119860Consider

119862119875= 119867119860+ 119861119876119860minus

119891Δ119909

21198921198631198602119876119860

10038161003816100381610038161198761198601003816100381610038161003816

119862119872= 119867119861minus 119861119876119860minus

119891Δ119909

21198921198631198602119876119861

10038161003816100381610038161198761198611003816100381610038161003816

(12)

The initial condition of water hammer is that of a steadyflow 119862

119875and 119862

119872in (11) are known and the parameters on

each time step can be solvedHydraulic characteristics of HCV can be described

through loss coefficient 120585 and capacity coefficient119862 Consider

119876119891=119860

radic120585

radic2119892Δ119867119891

119876119891= 119862radicΔ119867119891

(13)

where 119860 is cross-sectional area of the upstream of HCV andΔ119867119891is the pressure difference of HCV in upper and lower

Let 120591 = (1198621198620)(120591 = radic120585

0120585) be the relative opening

displacement of HCVThe dimensionless flow through HCVcan be described as

119902119891=

119876119891

1198761198910

= 120591radicΔℎ119891 (14)

where Δℎ119891is pressure difference on HCV It can be solved

as Δ119867119891Δ1198671198910 The subscript ldquo0rdquo represents HCV being open

completely

3 Optimization Method for VelocityAdjustment of HCV

31 Boundary Conditions Boundary conditions for pumpof outlet are shown in Figure 2 If the inlet loss of pumpis ignored the inlet of pool pump and HCV can becombined and dealt with as a boundary of characteristic linein foundational equations of water hammer

The equilibrium condition for water head is established inthis boundary It can be described as

119867119891+ 119867 minus119867

119897= 119867119901 (15)

where 119867119891is the depth of pool inlet 119867 is the work lift of the

pump 119867119897is the transient resistance loss of HCV and 119867

119901is

the pressure head of HCV outletWe take the balance equations of water head which in

the characteristic line 119862minusand inertia equations of pump unit

Pump Valve

Q1

B

Cminus

P

Figure 2 Boundary conditions of pump outlet

together And then the boundary conditions can be expressedas follows based on the characteristic lines of pumps

119909 = 120587 + arctan119902

120572

119882119867 (119909) =ℎ

1205722 + 1199022

119882119861 (119909) =120573

1205722 + 1199022

(16)

where the pump-lift is ℎ = 119867119867119877 The flow of pump is

119902 = 119876119876119877 The rotational speed is 120572 = 119899119899

119877 The torque is

120573 = 119879119879119877The subscript represents ratedworking conditions

Then (16) is generated as follows

1198651= 119867119895minus 119862119872minus 119861119876119877119902 + 119867

119877(1205722+ 1199022)119882119867(119909)

minus

119867119891011990210038161003816100381610038161199021003816100381610038161003816

1205912= 0

1198652= (1205722+ 1199022)119882119861 (119909) + 120573

0minus 1198701(1205720minus 120572) = 0

(17)

where 1198701= 2119870119899

119877119879119877 119870 = 120587119866119863

2120119892 and 119866119863

2 isrotational inertia 120572

0and 120573

0are rotational speed and torque

in the initial stateThen (17) can be rewritten as follows whenvariables 120572 and 119902 are introduced

1198651+ 1198651119902Δ119902 + 119865

1120572Δ120572 = 0

1198652+ 1198652119902Δ119902 + 119865

2120572Δ120572 = 0

(18)

The problem is solved as follows

120572(119896+1)

= 120572(119896)+ Δ120572

119902(119896+1)

= 119902(119896)+ Δ119902

(19)

in which Δ120572 and Δ119902 are solved through (18)The iterative errors should meet (19) Consider

|Δ120572| +1003816100381610038161003816Δ119902

1003816100381610038161003816 le 120576 (120576 = 00002) (20)

32 OptimizationMethod ofHCVAdjustment Theboundaryconditions of multistage valve-closing are introduced in thecharacteristic line calculation of water hammer for which

Shock and Vibration 5

the best procedure for multistage valve-closing is consideredThe displacement of valve-closing at any time can be deter-mined through linear procedure in multistage valve closure

Through a large number of practical tests the valveclosure with a uniform or uniform variable speed is foundto have a small influence on the water hammer in the front23 of valve-closing stroke while there is a large influenceon the later 13 of valve-closing stroke Therefore the valveclosure process is divided into multistage By doing so the

uniform and uniform variable speeds are both introduced tovalve closure process In the following section we will discussuniform or uniform variable speed calculation method invalve closure process

Assuming that the times of valve-closing in multi-stageare 1198791 1198792 119879

119894 119879

119899 the corresponding displacements of

valve-closing are 1199041 1199042 119904

119894 119904

119899 Then the displacements

of valve-closing at any time 119905 are determined as follows

119904119894

=

1199041

1198791

119905 le 1198791 The 1st stage of valve-closing

1199041+1199042

1198792

(119905 minus 1198791) 119879

1le 119905 le 119879

1+ 1198792 The 2nd stage of valve-closing

1199041+ 1199042+ sdot sdot sdot + 119904

119894minus1+119904119894

119879119894

(119905 minus 119879119894minus1) 119879

1+ 1198792+ sdot sdot sdot + 119879

119894minus1le 119905 le 119879

1+ 1198792+ sdot sdot sdot + 119879

119894 The 119894 stage of valve-closing

1199041+ 1199042+ sdot sdot sdot + 119904

119894+ sdot sdot sdot +

119904119899

119879119899

(119905 minus 119879119899minus1) 1198791+ 1198792+ sdot sdot sdot + 119879

119894+ sdot sdot sdot + 119879

119899minus1le 119905 le 119879

1+ 1198792+ sdot sdot sdot + 119879

119894+ sdot sdot sdot + 119879

119899 The 119899 stage of valve-closing

1199041+ 1199042+ sdot sdot sdot + 119904

119894+ 119904119899= 119878 119905 gt 119879

1+ 1198792+ sdot sdot sdot + 119879

119894+ 119879119899 valve-closing is completed

(21)

where 119904119894is displacement of valve-closing at 119905 and 119878 is the total

stroke of valve-closingFor the valve-closing displacement 119904

119894at any time 119905 we

can calculate the dimensionless opening degree 120591 using (21)through linear interpolation according to equidistantΔ119904

119894and

its input value

120591 = 120591 (119894) +119906(119896)

2[120591 (119894 + 1) minus 119896120591 (119894)] 120591 (119894)

+119906(119896minus1)

2[120591 (119894 + 1) minus (119896 minus 1) 120591 (119894)] + sdot sdot sdot

+1199062

2[120591 (119894 + 1) minus 2120591 (119894)]

+119906

2[120591 (119894 + 1) minus 120591 (119894)]

119906 =119904119894minus 1199040

Δ119904119894

minus 1

(22)

In the scope of velocity adjustment for HCV the velocitydisplacement and time of valve-closing have various combi-nations This paper adopts a multistage adjustment strategyaccording to simulation results of water hammer

The valve closure time for the first stage is equal or closeto the time of the flow of pump that is zero The valve closuretime for the following stages is one in four of the previousstage Consequently the initial valve closure procedure isdetermined Then search computing is taken to determinethe optimization valve closure procedure

4 Case Study and Experiment

41Working Conditions Themine with normal water qualitywas consideredThewater normal inflowwas 50m3h and themaximum inflow was 250m3h Water was discharged into

ground by two drain pipes of which the specifications wereD273times 12 respectively (one was used and another was spare)The pipes in this existing and antiquated mine drainagesystem were seamless steel pipe The allowed pressure was aslower at 64MPa The wellhead elevation was 997991m andthe borehole inclination was 20∘ There were three multistagecentrifugal pumps and two HCVs were used in Figure 3And the specification of pumps was MD280-65 times 6 (119876 =

280m3h119867 = 390m) One pump was used and others weremaintenance when themine was with a normal inflow or twopumps were used and one was spare when the mine was witha maximum inflow

The automatic drainage system was chosen in this mineCheck valves were installed in pump outlet There are HCVsin pipeline shown in Figure 3(a)where the strokewas 220mmwith the structure of HCV shown in Figure 4 During normalpump stoppingHCVswere closed first and then pumpswerestopped The water hammer phenomenon was significant indrains pipeline during this processTherefore we should takesome measures to prevent the water hammer phenomenon

42 Simulations An algorithm was developed using com-mercial simulation software Fluent63 based on the waterhammer theory described in Section 2 The accelerationamplitude pipeline pressure and valve closure displacementwere obtained in the cases of uniform and uniform variablespeed through transient simulation for water hammer Thecorrectness of simulation and the proposed theory werethen verified against experimental results We simulated thevalve-closing in single-stage with a constant velocity and inmultistage with a variable velocity based on the proposedtheory

(1) The Simulation of Valve-Closing in Single-Stage with aConstant Velocity The velocity V = 001ms of valve-closingin single-stage was determined through repeated simulation

6 Shock and Vibration

HCVs

Pump

(a) (b)

Figure 3 Diagram of drain pipes

(1)

(1) Hydraulic system

(2)

(2) Explosion-proof motors

(3)

(3) Valve body

Figure 4 Structure diagram of HCV

Then times of equipment in this situation were obtainedusing (20) to (21) as shown in Table 1

The simulation results of valve-closing parameters insingle-stage with 001ms are shown in Figures 5ndash12

For Figures 5ndash12 the static pressure of pipeline wasat 306MPa for pump stopping After the vacuum wascompleted the pump was started and HCV was open witha constant velocity At this moment pipeline pressure wasincreased alongwith the valve-opening displacement ofHCVThen pressure fluctuations appearedThe valve-opening dis-placement of HCV was 426mm and the maximum pressurewas 384MPa when 119905 = 12148 s After this momentthe pressure was steady The valve-opening displacement ofHCV was 702mm and the maximum pressure was 325MPawhen 119905 = 15244 s The drainage system pressure reacheda steady state along with the increasing of valve-openingdisplacement The pressure of pipeline began to drop when119905 = 62436 s and valve-closing displacement was 534mmWater hammer phenomenon appeared when 119905 = 67211 sWhen 119905 = 706 s the maximum boost of water hammer wasΔ119867 = 152m and the pressure of pipeline at this moment

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

x

Figure 5 Acceleration in 119909

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

x

S(m

m)

Figure 6 Amplitude in 119909

was 477Mpa It is 147 times the normal discharge pressure(325MPa) and the pressure increased by 50 suddenly Theacceleration and amplitude of pipeline in directions of 119909119910 and 119911 were changed significantly when water hammeroccurred Maximum acceleration in directions of 119909 119910 and119911 was 483ms2 646ms2 and 545ms2 and the maximumamplitude was 158mm 258mm and 153mm respectivelyAdditionally the total stroke of HCV was assumed to be 119878Valve-closing with rapid and constant velocity were taken

Shock and Vibration 7

Table 1 Times of equipment in single-stage valve-closing

Equipment actions Pump start Valve-opening Full open Valve-closing Valve closed Water hammer finished Total timesTimes 119905 (s) 4128 7883 31590 46007 67934 110500 21927

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

y

Figure 7 Acceleration in 119910

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

y

S(m

m)

Figure 8 Amplitude in 119910

z

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

Figure 9 Acceleration in 119911

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

z

S(m

m)

Figure 10 Amplitude in 119911

0 10 20 30 40 50 60 70 80 90 100 11010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

Figure 11 Pressure in pipeline

0 10 20 30 40 50 60 70 80 90 100t (s)

020406080

100120140160180200220240260

S(m

m)

Figure 12 Amplitude of HCV

8 Shock and Vibration

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus10minus9minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

x

Figure 13 Acceleration in 119909

in the former 21198783 and a variable velocity was taken in thelatter 1198783 according to the simulation results of valve-closingwater hammer Due to the velocity of valve-closing that hasa large impact on water hammer parameters it is an effectiveapproach to protect water hammer by choosing a reasonablevelocity for valve-closing

The allowed pressure of pipe is lower and its value was64MPa However the pressure of pipeline reached 48MPain the case of 22 s valve-closing from the above analysis Thisvalue is near to the allowed pressure of pipe with the pressurebeing not high and the water hammer phenomenon was notsignificant compared with other mine drainage systems Inorder to reduce the pressure of pipeline to protection pipelineit is necessary to develop water hammer protection

(2) The Simulation of Valve-Closing in Multistage with aVariable Velocity The optimization strategy of valve-closingadjustment for HCV is generated using boundary condi-tions according to optimization method of valve-closingadjustment that is proposed in this paper It is a multistagevalve-closing with a variable velocity In the front 23 ofvalve-closing stroke the velocity is constant and its value is001ms In the later 13 of valve-closing stroke the velocity isa variable (the deceleration is constant) and the initial value is001ms The total time of valve-closing is 43823 s Times ofequipment in multistage valve-closing are shown in Table 2

The simulation results of valve-closing parameters inmultistage are shown in Figures 13ndash20

The pipeline pressuring acceleration and amplitude inthe directions of 119909 119910 and 119911 are significantly reducedin multistage valve-closing with a variable velocity Valve-closing with a constant velocity is started at 46007 s andvalve-closing with a variable velocity is started at 606 s TheHCVs are closed and pumps are stopped at 8983 s In thisprocess themaximumpressure ofwater hammer is 349MPaNo effect of water hammer occurred under this situation

43 Experiments The experimental devices include multi-function data acquisition instrument vibration sensor pres-sure sensors and cable displacement encoder Multifunction

x

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

S(m

m)

Figure 14 Amplitude in 119909

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus10minus9minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

y

Figure 15 Acceleration in 119910

data acquisition instrument has 16 channels and its acqui-sition frequency is 1024 kHz Data of acceleration ampli-tude flow pressure and displacement of valve-closing wereacquired by this multifunction data acquisition instrumentVibration sensor was used to measure piping vibration underthe influence of water hammer It was disposed along withthe 119909 119910 and 119911 direction of the pipe Pressure sensors wereused to measure pipeline pressure Its measurement accuracyand range are 0ndash10MPa and plusmn05 FS Cable displacementencoder was used to posit the displacement of valve-closingThe arrangement diagram of sensors and flow chart of pumpsare shown in Figures 21 and 22

HCVs control system was designed in this experimentwhich is shown in Figure 23 Sensors were used to collectsignals of pressure and acceleration in pipeline PLC unitwas used to analyze pipeline pressure and vibration for waterhammer on the basis of pressure and acceleration signalsAn expected running speed was given to HCVs And thenvoltage current power and fault protection informationof pumps pressure flow temperature vacuum and HCVsstatus information were monitored at real time These multi-parameter data were integrated using of fuzzy control theorywith calculus and control strategy The HCVs control system

Shock and Vibration 9

Table 2 Times of equipment in multistage valve-closing

Equipment actions Pump start Valve-opening Full open Valve-closing Valve closed Water hammer finished Total timesTimes 119905 (s) 4128 85 39504 46007 89830 128816 43823

y

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20minus15minus10minus5

05

1015202530

t (s)

S(m

m)

Figure 16 Amplitude in 119910

0 10 20 30 40 50 60 70 80 90 100 110 120 130

minus9minus10

minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

z

Figure 17 Acceleration in 119911

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

S(m

m)

z

t (s)

Figure 18 Amplitude in 119911

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

Figure 19 Pressure in pipeline

020406080

100120140160180200220240260280

S(m

m)

0 10 20 30 40 50 60 70 80 90 100 110t (s)

Figure 20 Displacement of HCV

can control starting and stopping of pumps automatically andcan monitor the signals in system running process timely

For the total stroke of valve 119878 the experimental conditionsare as follows In the front 23 of the stroke the velocitywas constant and its value was 001ms In the later 13the velocity is variable (the deceleration is constant) andthe initial value was 001ms The full valve-closing timeswere 44 s Measured values of water hammer parameters inmultistage are shown in Table 3

10 Shock and Vibration

sensor

sensor

Pressuresensor

Pressuregauge

Negativepressure sensor

Jet valves Hydrostatic pipe

Flow sensor Pressure sensor

Drain pipe

Drain pipe

Drain pipe

A-A

X vibration

Z vibration

Y vibration sensor

Figure 21 Arrangement diagram of sensors

Data collection isbeginning

Pump start

Valve start

Full valve opening

Normal drainage

Valve-closing start

Valve closed

Pump stop

Water hammer is finishedData collection is finished

Phase 1

Pump start

Phase 2Pump running

Phase 3Pump stopping

Figure 22 The flow chart of test for pumps

Shock and Vibration 11

HCVs PLC unit

Acceleration sensor

Pressure sensor

PC

Other sensors and execution system

Opticalfiber

Closed-loop control of waterhammer protection

Figure 23 Composition of HCVs control system

Table 3 Measured values of water hammer parameters

Measured parameters Acceleration (ms2) Displacement (mm) Pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Valve-closing times (s)22 48308 64582 54457 157662 285192 153051 4586525 48207 64581 54453 157515 285139 153012 4556428 47986 63215 54394 157495 284632 152036 4495231 45689 61265 52563 136938 268576 130369 4467833 45389 61063 51935 135963 246985 126325 4461236 43236 59638 50632 126985 238965 117652 4267539 17231 11023 16352 92514 63656 113251 3561542 17016 10363 15426 90356 61563 109968 3542344 16987 08692 14112 89482 59354 106432 3500648 16886 08629 14003 89235 59139 106365 35006

5 Results and Discussion

The reliability and effectiveness are illustrated through thecomparison between the results of simulation and experi-ment

(1) Results of Valve-Closing in Single-Stage with a ConstantVelocity and in Multistage with a Variable Velocity AreCompared Pipeline pressures and displacements of valve-opening under these two conditions are shown in Figures 24and 25 respectively The red curves represent the variationsin single-stage with a constant velocity while the black curvesrepresent the variations formultistagewith a variable velocity

Figures 24 and 25 show a significant water hammer effectin single-stage valve-closing with a constant velocity andthe valve-closing time is shorter (22 s) On the other handwater hammer phenomenon was found to be considerablyimproved for multistage valve-closing condition with a vari-able velocity and the valve-closing timewas extended (44 s) Itshows that valve-closing inmultistage with a variable velocitycan control the water hammer phenomenon effective inminedrainage system

(2) Results of the Simulation and Experiment Are Also Com-pared Results for valve-closing with a variable velocity areshown in Table 4

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

PZCPZD

Figure 24 Pressure in pipeline

It can be seen from Table 4 that the simulation forvalve-closing with a variable velocity shows good agreementwith the experiment The errors between simulation andexperiment are less than 5 Therefore the valve-closing in

12 Shock and Vibration

Table 4 Results comparison of simulation and experiment

Parameters Max acceleration (ms2) Max displacement (mm) Max pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Simulation 45830 62672 52341 165122 273335 148726 45798Experiment 48308 64582 54457 157660 285192 153051 45867Errors 46 29 39 47 42 28 02Simulation 16876 08446 13651 86395 56689 104653 34901Experiment 16987 08692 14112 89482 59354 106432 35006Errors 07 28 33 34 44 17 03

0 10 20 30 40 50 60 70 80 90 1000

20406080

100120140160180200220240

t (s)

S(m

m)

S1(FM)S2(FM)

Figure 25 Displacement of HCV

multistagewith a variable velocity can reduce the impact fromwater hammer in mine drainage system

6 Conclusions and Future Work

Limited space and high cost of equipment changing arethe main characteristics for mine drainage system For theproblem of valve-closing water hammer protection in minedrainage system this paper proposed a protection methodbased on velocity adjustment of HCVs The mathematicmodel of valve-closing water hammer is established basedon fundamental equations The strategy of valve-closing inmultistage with a variable velocity is obtained by velocityadjustment strategy of HCVs and it is effective in protect-ing the valve-closing water hammer without change pipingarrangement or addition equipment The results of simula-tions and experiments in different adjustment velocity arecomparedWe obtained that the water hammer phenomenonis not obvious with valve-closing velocity in the front 23 of itsstroke and it is very seriously within the later 13 Thereforewe take a two-stage valve-closing strategy In the first stagethe velocity is constant and its value is 001ms In the secondstage the velocity is variable (the deceleration is constant) andthe initial value is 001ms

Extending errors in the theoretical wave speed havean important influence on prediction of the closure rate

before a water hammer occurs in the actual pipeline A verychallenging mathematical task is variable This is beyond thescope of this paper and may be considered as a future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National 125 Tech-nology Support Program of China under Grant noSQ2012BAJY3504

References

[1] M Sun X-R Ru and L-F Zhai ldquoIn-situ fabrication ofsupported iron oxides from synthetic acid mine drainage highcatalytic activities and good stabilities towards electro-Fentonreactionrdquo Applied Catalysis B Environmental vol 165 pp 103ndash110 2015

[2] A Kaliatka M Vaisnoras and M Valincius ldquoModelling ofvalve induced water hammer phenomena in a district heatingsystemrdquo Computers amp Fluids vol 94 pp 30ndash36 2014

[3] N Jeong D Chi and J Yoon ldquoAnalytic estimation of the impactpressure in a beam-tube due to water-hammer effectrdquo Journalof Nuclear Science and Technology vol 50 no 12 pp 1139ndash11492013

[4] W S Yi J Jiang D D Li G Lan and Z Zhao ldquoPump-stoppingwater hammer simulation based on RELAP5rdquo IOP ConferenceSeries Materials Science and Engineering vol 52 no 7 ArticleID 072009 2013

[5] Q W Yong M Jiang and Y Tang ldquoStudy on liquid pipelinewater hammer and protective device with gas concentrationrdquoAdvanced Materials Research vol 616ndash618 pp 774ndash777 2013

[6] J Zhang J Gao M Diao W Wu T Wang and S Qi ldquoA casestudy on risk assessment of long distance water supply systemrdquoProcedia Engineering vol 70 pp 1762ndash1771 2014

[7] K I M Sang-Gyun L E E Kye-Bock and K I M Kyung-YupldquoWater hammer in the pump-rising pipeline system with an airchamberrdquo Journal of Hydrodynamics Series B vol 26 no 6 pp960ndash964 2015

[8] M A Bouaziz M A Guidara C Schmitt E Hadj-Taıeb and ZAzari ldquoWater hammer effects on a gray cast iron water networkafter adding pumpsrdquo Engineering Failure Analysis vol 44 pp1ndash16 2014

Shock and Vibration 13

[9] M S Ghidaoui M Zhao D A McInnis and D H AxworthyldquoA review of water hammer theory and practicerdquo AppliedMechanics Reviews vol 58 no 1ndash6 pp 49ndash76 2005

[10] A F Colombo P Lee and B W Karney ldquoA selective literaturereview of transient-based leak detection methodsrdquo Journal ofHydro-Environment Research vol 2 no 4 pp 212ndash227 2009

[11] P J Lee M F Lambert A R Simpson J P Vıtkovsky andD Misiunas ldquoLeak location in single pipelines using transientreflectionsrdquo Australian Journal of Water Resources vol 11 no 1pp 53ndash65 2007

[12] N S Arbon M F Lambert A R Simpson andM L StephensldquoField test investigations into distributed fault modeling inwater distribution systems using transient testingrdquo in Proceed-ings of the World Environmental and Water Resources CongressTampa Fla USA May 2007

[13] J Gong A R SimpsonM F Lambert A C Zecchin Y-I Kimand A S Tijsseling ldquoDetection of distributed deteriorationin single pipes using transient reflectionsrdquo Journal of PipelineSystems Engineering and Practice vol 4 no 1 pp 32ndash40 2013

[14] M Ferrante B Brunone and S Meniconi ldquoLeak detectionin branched pipe systems coupling wavelet analysis and aLagrangian modelrdquo Journal of Water Supply Research andTechnology vol 58 no 2 pp 95ndash106 2009

[15] S Meniconi B Brunone and M Ferrante ldquoWater-hammerpressure waves interaction at cross-section changes in series inviscoelastic pipesrdquo Journal of Fluids and Structures vol 33 pp44ndash58 2012

[16] W H Hager ldquoSwiss contributions to water hammer theoryrdquoJournal of Hydraulic Research vol 39 no 1 pp 3ndash7 2001

[17] M S Ghidaoui and B W Karney ldquoModified transformationand integration of 1D wave equationsrdquo Journal of HydraulicEngineering vol 121 no 10 pp 758ndash760 1995

[18] A Adamkowski and M Lewandowski ldquoCavitation character-istics of shutoff valves in numerical modeling of transientsin pipelines with column separationrdquo Journal of HydraulicEngineering vol 141 no 2 2015

[19] E Yao G Kember and D Hansen ldquoAnalysis of water hammerattenuation in applications with varying valve closure timesrdquoJournal of Engineering Mechanics vol 141 no 1 Article ID04014107 2014

[20] R Korbar Z Virag and M Savar ldquoTruncated method of char-acteristics for quasi-two-dimensional water hammer modelrdquoJournal of Hydraulic Engineering vol 140 no 6 Article ID04014013 2014

[21] M Rohani and M H Afshar ldquoSimulation of transient flowcaused by pump failure point-implicit method of characteris-ticsrdquo Annals of Nuclear Energy vol 37 no 12 pp 1742ndash17502010

[22] A Triki ldquoMultiple-grid finite element solution of the shallowwater equations water hammer phenomenonrdquo Computers ampFluids vol 90 pp 65ndash71 2014

[23] A Keramat A S Tijsseling Q Hou and A Ahmadi ldquoFluid-structure interactionwith pipe-wall viscoelasticity during waterhammerrdquo Journal of Fluids and Structures vol 28 pp 434ndash4552012

[24] S-G Kim K-B Lee and K-Y Kim ldquoWater hammer in thepump-rising pipeline system with an air chamberrdquo Journal ofHydrodynamics vol 26 no 6 pp 960ndash964 2014

[25] E B Wylie and V L Streeter Fluid Transients McGraw-HillNew York NY USA 1978

[26] W Wan W Huang and C Li ldquoSensitivity analysis for theresistance on the performance of a pressure vessel for waterhammer protectionrdquo Journal of Pressure Vessel TechnologymdashTransactions of the ASME vol 136 no 1 Article ID 011303 2014

[27] G De Martino F De Paola N Fontana and M GiugnildquoDiscussion of lsquosimple guide for design of air vessels forwater hammer protection of pumping linesrsquo by D StephensonrdquoJournal of Hydraulic Engineering vol 130 no 3 pp 273ndash2752004

[28] T S Lee ldquoAir influence on hydraulic transients on fluid systemwith air valvesrdquo Journal of Fluids Engineering vol 121 no 3 pp646ndash650 1999

[29] D Stephenson ldquoEffects of air valves and pipework on waterhammer pressuresrdquo Journal of Transportation Engineering vol123 no 2 pp 101ndash106 1997

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Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

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Civil EngineeringAdvances in

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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DistributedSensor Networks

International Journal of

2 Shock and Vibration

century and to the current computer digital simulationscholars have alreadymade a lot of research resultsThemajorachievements are getting the relationship betweenmultiphaseandmulticomponent transient flow equations water hammerequations and the control equations such as Joukowskyequation [9] Based on the transient flow simulation theoryColombo et al [10] proposed an aqueducts fault detectiontechnology Lee et al [11] proposed the pipe network leakand deterioration over time detection technology by the timedomain reflectometry (TDR) Arbon et al [12] proposedpipeline corrosion and blockage detection technology Gonget al [13] proposed a detection technology for pipe frictionwall thickness velocity position and the length of the pipesand Ferrante et al [14] presented a leak detection methodwith coupling wavelet analysis and a Lagrangian modeltechniques Meniconi et al [15] presented a pipe systemdiagnosis method with the small amplitude sharp pressurewaves

(2) The Calculation Methods of Hydraulic Transient for WaterHammer The calculation methods of hydraulic transient forwater hammer include arithmetic method graphic methodand numerical method

(i) Arithmetic Method Before the 1930s the hydraulic tran-sient calculation of water hammer used Allievi equationsmostly [16] Allievi equations can be called Arithmeticmethod which is used to solve the problems of water hammerthatwith simple boundary conditions and itsworkload is verylarge

(ii) Graphic Method Graphic method is developed in 1930s to1960s Bergeron Parmakian and so forth [17] are committedto develop thismethod Boundary conditions and the processof water hammer fluctuation are expressed through coordi-nate graphics of119867 and119881 according to thismethodDue to thegraphics it is simple and intuitive for the hydraulic transientcalculation of water hammer However the accuracy is nothigh because this method is restricted by calculating meansand assumptions

(iii) Numerical Method From 1960s some numerical meth-ods appeared that can be aided by computers such as Char-acteristic (MOC) [18] Wave Characteristic Method (WCM)[19] Implicit Method [20 21] and Finite Element Method(FEM) [22 23]TheWCM can solve water hammer problemsof complex piping systems and boundary conditions It isthe most common method because of the high accuracy andcomputingThe Implicit Method divides pipeline into severalsegments and solves equations of the entire pipeline systemsimultaneously in each segment The advantage of ImplicitMethod can be described in a way that a longer segment isselected and the number of calculations is reduced Howeverthere is more time needed for calculation in large andcomplex pipeline network system [24] FEMwith flexibility isused in pipe network system which have complex boundaryconditions However it has a limitation in solving hydraulictransient problems

(3) Water Hammer Protection Prevention and controllingmeans for water hammer are researched with the devel-opment of their theory and calculation Wylie [25ndash27] hasresearched several protective devices for water hammer suchas air valves check valves pressure tank and surge tankLee [28] and Stephenson [29] discussed the performancesof air valves in water hammer protection However theseresearches have not given a quantitative calculation for theproblem of water hammer protection

This paper proposed a water hammer protection methodbased on velocity adjustment of HCV to deal with the prob-lem of valve-closing water hammer in mine drainage systemThe mathematic model of water hammer fluctuations isfounded based onMOC according to the hydraulic transientThen boundary conditions of water hammer controlling formine drainage system are determined and the simplex modelis established Finally the optimization adjustment strategy issolved with simulation and experiment

The remainder of this paper is organized as followsSection 2 provides the mathematic model of the propagationand superposition model for water hammer fluctuationsSection 3 provides an optimization method to determine theadjustment strategy for HCV Section 4 presents a case studyConcluding remarks are offered in the last section of thispaper

2 The Process of Water Hammer Fluctuations

21 Mathematic Model

(1) Foundation Equations The momentum equations of tran-sient flow can be expressed as

minus1

119892

120597119881

120597119905=120597119867

120597119909+119891

119863

1198812

2119892+120597

120597119909(1198812

2119892) (1)

where 119881 is longitudinal mean velocity119867 is pressure head 119891is friction factor 119863 is diameter of pipeline 119892 is gravitationalacceleration 119909 is propagation distance along pipe and 119905 istime

The left of the equation represents the time-varyinginertia force in a unit volume In the right the first itemrepresents the pressure in a unit volume of fluid The seconditem is friction loss pressure in a unit length of pipe and thethird item is pressure of transient flow

The continuity equation is used to describe transient flowand it can be expressed as follows

120597119867

120597119905+ 119881

120597119867

120597119909+1198862

119892

120597119881

120597119909minus 119881 sin 120579 = 0 (2)

where 119886 is propagation speed of water hammer wave and 120579 isthe angle between the axis of pipe and the horizontal line

(2) The Process of Water Hammer Fluctuations Pressures thatare caused by friction loss and transient flow velocity areignored Furthermore 119881 ≪ 119886 is considered for continuity

Shock and Vibration 3

equations Then the foundation equations can be simplifiedas

120597119867

120597119909+1

119892

120597119881

120597119905= 0

120597119867

120597119905+1198862

119892

120597119881

120597119909= 0

(3)

The second-order partial differential equations about119867(119909 119905) and119881(119909 119905) are obtained through the partial derivativeand are taken for variables 119909 and 119905 in (3) Therefore themomentum equations for water hammer wave in pipelinedrainage system are expressed as

1205971198672

1205971199092=1

1198862

1205971198672

1205971199052

1205971198812

1205971199092=1

1198862

1205971198812

1205971199052

(4)

The functions 119865(119909 119905) and 119891(119909 119905) are introduced alongwith characteristic lines 119889119909 = plusmn119889119905 Then the general solutionof (4) can be described as

119867 minus1198670= 119865(119905 minus

119909

119886) + 119891(119905 +

119909

119886)

119881 minus 1198810= minus

119892

119886[119865(119905 minus

119909

119886) minus 119891(119905 +

119909

119886)]

(5)

where 1198670is the initial pressure head 119881

0is the initial flow

velocity and 119865(119909 119905) and 119891(119909 119905) are direct and reflectionfluctuation functions

22 Propagation and Superposition Model of Water HammerWave Based on Characteristic Line Method Pumps andvalves are the generating sources of water hammer wavein hydraulic transition process of pipeline fluid deliverysystem These two kinds of water hammer wave start at thesame time and propagation directions are superimposedThesuperposition leads to strengthening of fluctuations for waterhammer In order to control the water hammer pressureeffectively the superposition effects of water hammer waveneed to be weakened as much as possible

The fundamental equations of water hammer can berewritten as

1198711= 119892

120597119867

120597119905+ 119881

120597119881

120597119909+120597119881

120597119905+119891119881 |119881|

2119863= 0

1198712=120597119867

120597119905+ 119881

120597119881

120597119909+1198862

119892

120597119881

120597119909minus 119881 sin 120579 = 0

(6)

These equations are combined linearly using an unknownmultiplier 120582 Let 119871 = 119871

1+1205821198712be the linear combinationThe

coefficient 120582 can be determined by

120582 = plusmn119892

119886 (7)

t

2Δt

Δt

t = 0

1 Δx i minus 1 i i + 1 N + 1 x

P

C+ Cminus

A B

Figure 1 Characteristic line grid for water hammer calculation

In the constraint of characteristic line equation 119889119909119889119905 =119881plusmn119886 (6) converts to ordinary differential equation as follows

119862+

119889119867

119889119905+119886

119892

119889119881

119889119905minus 119881 sin 120579 +

119891119886119881 |119881|

2119892119863= 0

119889119909

119889119905= 119881 + 119886

119862minus

119889119867

119889119905minus119886

119892

119889119881

119889119905minus 119881 sin 120579 minus

119891119886119881 |119881|

2119892119863= 0

119889119909

119889119905= 119881 minus 119886

(8)

119881 and119881sin120579 are negligible when119881 ≪ 119886 and the tilt angleof pipeline is less than 25∘ The average flow velocity 119881 isreplaced by flow 119876 The characteristic equations are changedinto

119862+

119889119867

119889119905+

119886

119892119860

119889119876

119889119905+119891119886119876 |119876|

21198921198631198602= 0

119889119909

119889119905= +119886

119862minus

minus119889119867

119889119905+

119886

119892119860

119889119876

119889119905+119891119886119876 |119876|

21198921198631198602= 0

119889119909

119889119905= minus119886

(9)

where 119862+ is the characteristic line of forward wave in 119909-axis119862minus is the characteristic line of reflected wave in 119909-axis and119860

is cross-sectional area of pipeThe integral operation and differential conversion are

introduced to (9) The discrete characteristic equations ofwater hammer are obtained as follows Equation (10) and thecharacteristic line grid are shown in Figure 1

119867119875minus 119867119860+

119886

119892119860(119876119875minus 119876119860) +

119891Δ119909119876119860

10038161003816100381610038161198761198601003816100381610038161003816

21198921198631198602= 0

119867119875minus 119867119861+

119886

119892119860(119876119875minus 119876119861) +

119891Δ119909119876119861

10038161003816100381610038161198761198611003816100381610038161003816

21198921198631198602= 0

(10)

4 Shock and Vibration

By solving the above equations transient variables 119867119875

and119876119875in the node 119894 of the pipe over the timeΔ119905 are expressed

as

119867119875=(119862119875+ 119862119872)

2

119876119875=(119862119875minus 119867119875)

119861

(11)

where 119861 = 119886119892119860Consider

119862119875= 119867119860+ 119861119876119860minus

119891Δ119909

21198921198631198602119876119860

10038161003816100381610038161198761198601003816100381610038161003816

119862119872= 119867119861minus 119861119876119860minus

119891Δ119909

21198921198631198602119876119861

10038161003816100381610038161198761198611003816100381610038161003816

(12)

The initial condition of water hammer is that of a steadyflow 119862

119875and 119862

119872in (11) are known and the parameters on

each time step can be solvedHydraulic characteristics of HCV can be described

through loss coefficient 120585 and capacity coefficient119862 Consider

119876119891=119860

radic120585

radic2119892Δ119867119891

119876119891= 119862radicΔ119867119891

(13)

where 119860 is cross-sectional area of the upstream of HCV andΔ119867119891is the pressure difference of HCV in upper and lower

Let 120591 = (1198621198620)(120591 = radic120585

0120585) be the relative opening

displacement of HCVThe dimensionless flow through HCVcan be described as

119902119891=

119876119891

1198761198910

= 120591radicΔℎ119891 (14)

where Δℎ119891is pressure difference on HCV It can be solved

as Δ119867119891Δ1198671198910 The subscript ldquo0rdquo represents HCV being open

completely

3 Optimization Method for VelocityAdjustment of HCV

31 Boundary Conditions Boundary conditions for pumpof outlet are shown in Figure 2 If the inlet loss of pumpis ignored the inlet of pool pump and HCV can becombined and dealt with as a boundary of characteristic linein foundational equations of water hammer

The equilibrium condition for water head is established inthis boundary It can be described as

119867119891+ 119867 minus119867

119897= 119867119901 (15)

where 119867119891is the depth of pool inlet 119867 is the work lift of the

pump 119867119897is the transient resistance loss of HCV and 119867

119901is

the pressure head of HCV outletWe take the balance equations of water head which in

the characteristic line 119862minusand inertia equations of pump unit

Pump Valve

Q1

B

Cminus

P

Figure 2 Boundary conditions of pump outlet

together And then the boundary conditions can be expressedas follows based on the characteristic lines of pumps

119909 = 120587 + arctan119902

120572

119882119867 (119909) =ℎ

1205722 + 1199022

119882119861 (119909) =120573

1205722 + 1199022

(16)

where the pump-lift is ℎ = 119867119867119877 The flow of pump is

119902 = 119876119876119877 The rotational speed is 120572 = 119899119899

119877 The torque is

120573 = 119879119879119877The subscript represents ratedworking conditions

Then (16) is generated as follows

1198651= 119867119895minus 119862119872minus 119861119876119877119902 + 119867

119877(1205722+ 1199022)119882119867(119909)

minus

119867119891011990210038161003816100381610038161199021003816100381610038161003816

1205912= 0

1198652= (1205722+ 1199022)119882119861 (119909) + 120573

0minus 1198701(1205720minus 120572) = 0

(17)

where 1198701= 2119870119899

119877119879119877 119870 = 120587119866119863

2120119892 and 119866119863

2 isrotational inertia 120572

0and 120573

0are rotational speed and torque

in the initial stateThen (17) can be rewritten as follows whenvariables 120572 and 119902 are introduced

1198651+ 1198651119902Δ119902 + 119865

1120572Δ120572 = 0

1198652+ 1198652119902Δ119902 + 119865

2120572Δ120572 = 0

(18)

The problem is solved as follows

120572(119896+1)

= 120572(119896)+ Δ120572

119902(119896+1)

= 119902(119896)+ Δ119902

(19)

in which Δ120572 and Δ119902 are solved through (18)The iterative errors should meet (19) Consider

|Δ120572| +1003816100381610038161003816Δ119902

1003816100381610038161003816 le 120576 (120576 = 00002) (20)

32 OptimizationMethod ofHCVAdjustment Theboundaryconditions of multistage valve-closing are introduced in thecharacteristic line calculation of water hammer for which

Shock and Vibration 5

the best procedure for multistage valve-closing is consideredThe displacement of valve-closing at any time can be deter-mined through linear procedure in multistage valve closure

Through a large number of practical tests the valveclosure with a uniform or uniform variable speed is foundto have a small influence on the water hammer in the front23 of valve-closing stroke while there is a large influenceon the later 13 of valve-closing stroke Therefore the valveclosure process is divided into multistage By doing so the

uniform and uniform variable speeds are both introduced tovalve closure process In the following section we will discussuniform or uniform variable speed calculation method invalve closure process

Assuming that the times of valve-closing in multi-stageare 1198791 1198792 119879

119894 119879

119899 the corresponding displacements of

valve-closing are 1199041 1199042 119904

119894 119904

119899 Then the displacements

of valve-closing at any time 119905 are determined as follows

119904119894

=

1199041

1198791

119905 le 1198791 The 1st stage of valve-closing

1199041+1199042

1198792

(119905 minus 1198791) 119879

1le 119905 le 119879

1+ 1198792 The 2nd stage of valve-closing

1199041+ 1199042+ sdot sdot sdot + 119904

119894minus1+119904119894

119879119894

(119905 minus 119879119894minus1) 119879

1+ 1198792+ sdot sdot sdot + 119879

119894minus1le 119905 le 119879

1+ 1198792+ sdot sdot sdot + 119879

119894 The 119894 stage of valve-closing

1199041+ 1199042+ sdot sdot sdot + 119904

119894+ sdot sdot sdot +

119904119899

119879119899

(119905 minus 119879119899minus1) 1198791+ 1198792+ sdot sdot sdot + 119879

119894+ sdot sdot sdot + 119879

119899minus1le 119905 le 119879

1+ 1198792+ sdot sdot sdot + 119879

119894+ sdot sdot sdot + 119879

119899 The 119899 stage of valve-closing

1199041+ 1199042+ sdot sdot sdot + 119904

119894+ 119904119899= 119878 119905 gt 119879

1+ 1198792+ sdot sdot sdot + 119879

119894+ 119879119899 valve-closing is completed

(21)

where 119904119894is displacement of valve-closing at 119905 and 119878 is the total

stroke of valve-closingFor the valve-closing displacement 119904

119894at any time 119905 we

can calculate the dimensionless opening degree 120591 using (21)through linear interpolation according to equidistantΔ119904

119894and

its input value

120591 = 120591 (119894) +119906(119896)

2[120591 (119894 + 1) minus 119896120591 (119894)] 120591 (119894)

+119906(119896minus1)

2[120591 (119894 + 1) minus (119896 minus 1) 120591 (119894)] + sdot sdot sdot

+1199062

2[120591 (119894 + 1) minus 2120591 (119894)]

+119906

2[120591 (119894 + 1) minus 120591 (119894)]

119906 =119904119894minus 1199040

Δ119904119894

minus 1

(22)

In the scope of velocity adjustment for HCV the velocitydisplacement and time of valve-closing have various combi-nations This paper adopts a multistage adjustment strategyaccording to simulation results of water hammer

The valve closure time for the first stage is equal or closeto the time of the flow of pump that is zero The valve closuretime for the following stages is one in four of the previousstage Consequently the initial valve closure procedure isdetermined Then search computing is taken to determinethe optimization valve closure procedure

4 Case Study and Experiment

41Working Conditions Themine with normal water qualitywas consideredThewater normal inflowwas 50m3h and themaximum inflow was 250m3h Water was discharged into

ground by two drain pipes of which the specifications wereD273times 12 respectively (one was used and another was spare)The pipes in this existing and antiquated mine drainagesystem were seamless steel pipe The allowed pressure was aslower at 64MPa The wellhead elevation was 997991m andthe borehole inclination was 20∘ There were three multistagecentrifugal pumps and two HCVs were used in Figure 3And the specification of pumps was MD280-65 times 6 (119876 =

280m3h119867 = 390m) One pump was used and others weremaintenance when themine was with a normal inflow or twopumps were used and one was spare when the mine was witha maximum inflow

The automatic drainage system was chosen in this mineCheck valves were installed in pump outlet There are HCVsin pipeline shown in Figure 3(a)where the strokewas 220mmwith the structure of HCV shown in Figure 4 During normalpump stoppingHCVswere closed first and then pumpswerestopped The water hammer phenomenon was significant indrains pipeline during this processTherefore we should takesome measures to prevent the water hammer phenomenon

42 Simulations An algorithm was developed using com-mercial simulation software Fluent63 based on the waterhammer theory described in Section 2 The accelerationamplitude pipeline pressure and valve closure displacementwere obtained in the cases of uniform and uniform variablespeed through transient simulation for water hammer Thecorrectness of simulation and the proposed theory werethen verified against experimental results We simulated thevalve-closing in single-stage with a constant velocity and inmultistage with a variable velocity based on the proposedtheory

(1) The Simulation of Valve-Closing in Single-Stage with aConstant Velocity The velocity V = 001ms of valve-closingin single-stage was determined through repeated simulation

6 Shock and Vibration

HCVs

Pump

(a) (b)

Figure 3 Diagram of drain pipes

(1)

(1) Hydraulic system

(2)

(2) Explosion-proof motors

(3)

(3) Valve body

Figure 4 Structure diagram of HCV

Then times of equipment in this situation were obtainedusing (20) to (21) as shown in Table 1

The simulation results of valve-closing parameters insingle-stage with 001ms are shown in Figures 5ndash12

For Figures 5ndash12 the static pressure of pipeline wasat 306MPa for pump stopping After the vacuum wascompleted the pump was started and HCV was open witha constant velocity At this moment pipeline pressure wasincreased alongwith the valve-opening displacement ofHCVThen pressure fluctuations appearedThe valve-opening dis-placement of HCV was 426mm and the maximum pressurewas 384MPa when 119905 = 12148 s After this momentthe pressure was steady The valve-opening displacement ofHCV was 702mm and the maximum pressure was 325MPawhen 119905 = 15244 s The drainage system pressure reacheda steady state along with the increasing of valve-openingdisplacement The pressure of pipeline began to drop when119905 = 62436 s and valve-closing displacement was 534mmWater hammer phenomenon appeared when 119905 = 67211 sWhen 119905 = 706 s the maximum boost of water hammer wasΔ119867 = 152m and the pressure of pipeline at this moment

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

x

Figure 5 Acceleration in 119909

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

x

S(m

m)

Figure 6 Amplitude in 119909

was 477Mpa It is 147 times the normal discharge pressure(325MPa) and the pressure increased by 50 suddenly Theacceleration and amplitude of pipeline in directions of 119909119910 and 119911 were changed significantly when water hammeroccurred Maximum acceleration in directions of 119909 119910 and119911 was 483ms2 646ms2 and 545ms2 and the maximumamplitude was 158mm 258mm and 153mm respectivelyAdditionally the total stroke of HCV was assumed to be 119878Valve-closing with rapid and constant velocity were taken

Shock and Vibration 7

Table 1 Times of equipment in single-stage valve-closing

Equipment actions Pump start Valve-opening Full open Valve-closing Valve closed Water hammer finished Total timesTimes 119905 (s) 4128 7883 31590 46007 67934 110500 21927

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

y

Figure 7 Acceleration in 119910

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

y

S(m

m)

Figure 8 Amplitude in 119910

z

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

Figure 9 Acceleration in 119911

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

z

S(m

m)

Figure 10 Amplitude in 119911

0 10 20 30 40 50 60 70 80 90 100 11010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

Figure 11 Pressure in pipeline

0 10 20 30 40 50 60 70 80 90 100t (s)

020406080

100120140160180200220240260

S(m

m)

Figure 12 Amplitude of HCV

8 Shock and Vibration

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus10minus9minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

x

Figure 13 Acceleration in 119909

in the former 21198783 and a variable velocity was taken in thelatter 1198783 according to the simulation results of valve-closingwater hammer Due to the velocity of valve-closing that hasa large impact on water hammer parameters it is an effectiveapproach to protect water hammer by choosing a reasonablevelocity for valve-closing

The allowed pressure of pipe is lower and its value was64MPa However the pressure of pipeline reached 48MPain the case of 22 s valve-closing from the above analysis Thisvalue is near to the allowed pressure of pipe with the pressurebeing not high and the water hammer phenomenon was notsignificant compared with other mine drainage systems Inorder to reduce the pressure of pipeline to protection pipelineit is necessary to develop water hammer protection

(2) The Simulation of Valve-Closing in Multistage with aVariable Velocity The optimization strategy of valve-closingadjustment for HCV is generated using boundary condi-tions according to optimization method of valve-closingadjustment that is proposed in this paper It is a multistagevalve-closing with a variable velocity In the front 23 ofvalve-closing stroke the velocity is constant and its value is001ms In the later 13 of valve-closing stroke the velocity isa variable (the deceleration is constant) and the initial value is001ms The total time of valve-closing is 43823 s Times ofequipment in multistage valve-closing are shown in Table 2

The simulation results of valve-closing parameters inmultistage are shown in Figures 13ndash20

The pipeline pressuring acceleration and amplitude inthe directions of 119909 119910 and 119911 are significantly reducedin multistage valve-closing with a variable velocity Valve-closing with a constant velocity is started at 46007 s andvalve-closing with a variable velocity is started at 606 s TheHCVs are closed and pumps are stopped at 8983 s In thisprocess themaximumpressure ofwater hammer is 349MPaNo effect of water hammer occurred under this situation

43 Experiments The experimental devices include multi-function data acquisition instrument vibration sensor pres-sure sensors and cable displacement encoder Multifunction

x

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

S(m

m)

Figure 14 Amplitude in 119909

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus10minus9minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

y

Figure 15 Acceleration in 119910

data acquisition instrument has 16 channels and its acqui-sition frequency is 1024 kHz Data of acceleration ampli-tude flow pressure and displacement of valve-closing wereacquired by this multifunction data acquisition instrumentVibration sensor was used to measure piping vibration underthe influence of water hammer It was disposed along withthe 119909 119910 and 119911 direction of the pipe Pressure sensors wereused to measure pipeline pressure Its measurement accuracyand range are 0ndash10MPa and plusmn05 FS Cable displacementencoder was used to posit the displacement of valve-closingThe arrangement diagram of sensors and flow chart of pumpsare shown in Figures 21 and 22

HCVs control system was designed in this experimentwhich is shown in Figure 23 Sensors were used to collectsignals of pressure and acceleration in pipeline PLC unitwas used to analyze pipeline pressure and vibration for waterhammer on the basis of pressure and acceleration signalsAn expected running speed was given to HCVs And thenvoltage current power and fault protection informationof pumps pressure flow temperature vacuum and HCVsstatus information were monitored at real time These multi-parameter data were integrated using of fuzzy control theorywith calculus and control strategy The HCVs control system

Shock and Vibration 9

Table 2 Times of equipment in multistage valve-closing

Equipment actions Pump start Valve-opening Full open Valve-closing Valve closed Water hammer finished Total timesTimes 119905 (s) 4128 85 39504 46007 89830 128816 43823

y

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20minus15minus10minus5

05

1015202530

t (s)

S(m

m)

Figure 16 Amplitude in 119910

0 10 20 30 40 50 60 70 80 90 100 110 120 130

minus9minus10

minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

z

Figure 17 Acceleration in 119911

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

S(m

m)

z

t (s)

Figure 18 Amplitude in 119911

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

Figure 19 Pressure in pipeline

020406080

100120140160180200220240260280

S(m

m)

0 10 20 30 40 50 60 70 80 90 100 110t (s)

Figure 20 Displacement of HCV

can control starting and stopping of pumps automatically andcan monitor the signals in system running process timely

For the total stroke of valve 119878 the experimental conditionsare as follows In the front 23 of the stroke the velocitywas constant and its value was 001ms In the later 13the velocity is variable (the deceleration is constant) andthe initial value was 001ms The full valve-closing timeswere 44 s Measured values of water hammer parameters inmultistage are shown in Table 3

10 Shock and Vibration

sensor

sensor

Pressuresensor

Pressuregauge

Negativepressure sensor

Jet valves Hydrostatic pipe

Flow sensor Pressure sensor

Drain pipe

Drain pipe

Drain pipe

A-A

X vibration

Z vibration

Y vibration sensor

Figure 21 Arrangement diagram of sensors

Data collection isbeginning

Pump start

Valve start

Full valve opening

Normal drainage

Valve-closing start

Valve closed

Pump stop

Water hammer is finishedData collection is finished

Phase 1

Pump start

Phase 2Pump running

Phase 3Pump stopping

Figure 22 The flow chart of test for pumps

Shock and Vibration 11

HCVs PLC unit

Acceleration sensor

Pressure sensor

PC

Other sensors and execution system

Opticalfiber

Closed-loop control of waterhammer protection

Figure 23 Composition of HCVs control system

Table 3 Measured values of water hammer parameters

Measured parameters Acceleration (ms2) Displacement (mm) Pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Valve-closing times (s)22 48308 64582 54457 157662 285192 153051 4586525 48207 64581 54453 157515 285139 153012 4556428 47986 63215 54394 157495 284632 152036 4495231 45689 61265 52563 136938 268576 130369 4467833 45389 61063 51935 135963 246985 126325 4461236 43236 59638 50632 126985 238965 117652 4267539 17231 11023 16352 92514 63656 113251 3561542 17016 10363 15426 90356 61563 109968 3542344 16987 08692 14112 89482 59354 106432 3500648 16886 08629 14003 89235 59139 106365 35006

5 Results and Discussion

The reliability and effectiveness are illustrated through thecomparison between the results of simulation and experi-ment

(1) Results of Valve-Closing in Single-Stage with a ConstantVelocity and in Multistage with a Variable Velocity AreCompared Pipeline pressures and displacements of valve-opening under these two conditions are shown in Figures 24and 25 respectively The red curves represent the variationsin single-stage with a constant velocity while the black curvesrepresent the variations formultistagewith a variable velocity

Figures 24 and 25 show a significant water hammer effectin single-stage valve-closing with a constant velocity andthe valve-closing time is shorter (22 s) On the other handwater hammer phenomenon was found to be considerablyimproved for multistage valve-closing condition with a vari-able velocity and the valve-closing timewas extended (44 s) Itshows that valve-closing inmultistage with a variable velocitycan control the water hammer phenomenon effective inminedrainage system

(2) Results of the Simulation and Experiment Are Also Com-pared Results for valve-closing with a variable velocity areshown in Table 4

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

PZCPZD

Figure 24 Pressure in pipeline

It can be seen from Table 4 that the simulation forvalve-closing with a variable velocity shows good agreementwith the experiment The errors between simulation andexperiment are less than 5 Therefore the valve-closing in

12 Shock and Vibration

Table 4 Results comparison of simulation and experiment

Parameters Max acceleration (ms2) Max displacement (mm) Max pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Simulation 45830 62672 52341 165122 273335 148726 45798Experiment 48308 64582 54457 157660 285192 153051 45867Errors 46 29 39 47 42 28 02Simulation 16876 08446 13651 86395 56689 104653 34901Experiment 16987 08692 14112 89482 59354 106432 35006Errors 07 28 33 34 44 17 03

0 10 20 30 40 50 60 70 80 90 1000

20406080

100120140160180200220240

t (s)

S(m

m)

S1(FM)S2(FM)

Figure 25 Displacement of HCV

multistagewith a variable velocity can reduce the impact fromwater hammer in mine drainage system

6 Conclusions and Future Work

Limited space and high cost of equipment changing arethe main characteristics for mine drainage system For theproblem of valve-closing water hammer protection in minedrainage system this paper proposed a protection methodbased on velocity adjustment of HCVs The mathematicmodel of valve-closing water hammer is established basedon fundamental equations The strategy of valve-closing inmultistage with a variable velocity is obtained by velocityadjustment strategy of HCVs and it is effective in protect-ing the valve-closing water hammer without change pipingarrangement or addition equipment The results of simula-tions and experiments in different adjustment velocity arecomparedWe obtained that the water hammer phenomenonis not obvious with valve-closing velocity in the front 23 of itsstroke and it is very seriously within the later 13 Thereforewe take a two-stage valve-closing strategy In the first stagethe velocity is constant and its value is 001ms In the secondstage the velocity is variable (the deceleration is constant) andthe initial value is 001ms

Extending errors in the theoretical wave speed havean important influence on prediction of the closure rate

before a water hammer occurs in the actual pipeline A verychallenging mathematical task is variable This is beyond thescope of this paper and may be considered as a future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National 125 Tech-nology Support Program of China under Grant noSQ2012BAJY3504

References

[1] M Sun X-R Ru and L-F Zhai ldquoIn-situ fabrication ofsupported iron oxides from synthetic acid mine drainage highcatalytic activities and good stabilities towards electro-Fentonreactionrdquo Applied Catalysis B Environmental vol 165 pp 103ndash110 2015

[2] A Kaliatka M Vaisnoras and M Valincius ldquoModelling ofvalve induced water hammer phenomena in a district heatingsystemrdquo Computers amp Fluids vol 94 pp 30ndash36 2014

[3] N Jeong D Chi and J Yoon ldquoAnalytic estimation of the impactpressure in a beam-tube due to water-hammer effectrdquo Journalof Nuclear Science and Technology vol 50 no 12 pp 1139ndash11492013

[4] W S Yi J Jiang D D Li G Lan and Z Zhao ldquoPump-stoppingwater hammer simulation based on RELAP5rdquo IOP ConferenceSeries Materials Science and Engineering vol 52 no 7 ArticleID 072009 2013

[5] Q W Yong M Jiang and Y Tang ldquoStudy on liquid pipelinewater hammer and protective device with gas concentrationrdquoAdvanced Materials Research vol 616ndash618 pp 774ndash777 2013

[6] J Zhang J Gao M Diao W Wu T Wang and S Qi ldquoA casestudy on risk assessment of long distance water supply systemrdquoProcedia Engineering vol 70 pp 1762ndash1771 2014

[7] K I M Sang-Gyun L E E Kye-Bock and K I M Kyung-YupldquoWater hammer in the pump-rising pipeline system with an airchamberrdquo Journal of Hydrodynamics Series B vol 26 no 6 pp960ndash964 2015

[8] M A Bouaziz M A Guidara C Schmitt E Hadj-Taıeb and ZAzari ldquoWater hammer effects on a gray cast iron water networkafter adding pumpsrdquo Engineering Failure Analysis vol 44 pp1ndash16 2014

Shock and Vibration 13

[9] M S Ghidaoui M Zhao D A McInnis and D H AxworthyldquoA review of water hammer theory and practicerdquo AppliedMechanics Reviews vol 58 no 1ndash6 pp 49ndash76 2005

[10] A F Colombo P Lee and B W Karney ldquoA selective literaturereview of transient-based leak detection methodsrdquo Journal ofHydro-Environment Research vol 2 no 4 pp 212ndash227 2009

[11] P J Lee M F Lambert A R Simpson J P Vıtkovsky andD Misiunas ldquoLeak location in single pipelines using transientreflectionsrdquo Australian Journal of Water Resources vol 11 no 1pp 53ndash65 2007

[12] N S Arbon M F Lambert A R Simpson andM L StephensldquoField test investigations into distributed fault modeling inwater distribution systems using transient testingrdquo in Proceed-ings of the World Environmental and Water Resources CongressTampa Fla USA May 2007

[13] J Gong A R SimpsonM F Lambert A C Zecchin Y-I Kimand A S Tijsseling ldquoDetection of distributed deteriorationin single pipes using transient reflectionsrdquo Journal of PipelineSystems Engineering and Practice vol 4 no 1 pp 32ndash40 2013

[14] M Ferrante B Brunone and S Meniconi ldquoLeak detectionin branched pipe systems coupling wavelet analysis and aLagrangian modelrdquo Journal of Water Supply Research andTechnology vol 58 no 2 pp 95ndash106 2009

[15] S Meniconi B Brunone and M Ferrante ldquoWater-hammerpressure waves interaction at cross-section changes in series inviscoelastic pipesrdquo Journal of Fluids and Structures vol 33 pp44ndash58 2012

[16] W H Hager ldquoSwiss contributions to water hammer theoryrdquoJournal of Hydraulic Research vol 39 no 1 pp 3ndash7 2001

[17] M S Ghidaoui and B W Karney ldquoModified transformationand integration of 1D wave equationsrdquo Journal of HydraulicEngineering vol 121 no 10 pp 758ndash760 1995

[18] A Adamkowski and M Lewandowski ldquoCavitation character-istics of shutoff valves in numerical modeling of transientsin pipelines with column separationrdquo Journal of HydraulicEngineering vol 141 no 2 2015

[19] E Yao G Kember and D Hansen ldquoAnalysis of water hammerattenuation in applications with varying valve closure timesrdquoJournal of Engineering Mechanics vol 141 no 1 Article ID04014107 2014

[20] R Korbar Z Virag and M Savar ldquoTruncated method of char-acteristics for quasi-two-dimensional water hammer modelrdquoJournal of Hydraulic Engineering vol 140 no 6 Article ID04014013 2014

[21] M Rohani and M H Afshar ldquoSimulation of transient flowcaused by pump failure point-implicit method of characteris-ticsrdquo Annals of Nuclear Energy vol 37 no 12 pp 1742ndash17502010

[22] A Triki ldquoMultiple-grid finite element solution of the shallowwater equations water hammer phenomenonrdquo Computers ampFluids vol 90 pp 65ndash71 2014

[23] A Keramat A S Tijsseling Q Hou and A Ahmadi ldquoFluid-structure interactionwith pipe-wall viscoelasticity during waterhammerrdquo Journal of Fluids and Structures vol 28 pp 434ndash4552012

[24] S-G Kim K-B Lee and K-Y Kim ldquoWater hammer in thepump-rising pipeline system with an air chamberrdquo Journal ofHydrodynamics vol 26 no 6 pp 960ndash964 2014

[25] E B Wylie and V L Streeter Fluid Transients McGraw-HillNew York NY USA 1978

[26] W Wan W Huang and C Li ldquoSensitivity analysis for theresistance on the performance of a pressure vessel for waterhammer protectionrdquo Journal of Pressure Vessel TechnologymdashTransactions of the ASME vol 136 no 1 Article ID 011303 2014

[27] G De Martino F De Paola N Fontana and M GiugnildquoDiscussion of lsquosimple guide for design of air vessels forwater hammer protection of pumping linesrsquo by D StephensonrdquoJournal of Hydraulic Engineering vol 130 no 3 pp 273ndash2752004

[28] T S Lee ldquoAir influence on hydraulic transients on fluid systemwith air valvesrdquo Journal of Fluids Engineering vol 121 no 3 pp646ndash650 1999

[29] D Stephenson ldquoEffects of air valves and pipework on waterhammer pressuresrdquo Journal of Transportation Engineering vol123 no 2 pp 101ndash106 1997

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Shock and Vibration 3

equations Then the foundation equations can be simplifiedas

120597119867

120597119909+1

119892

120597119881

120597119905= 0

120597119867

120597119905+1198862

119892

120597119881

120597119909= 0

(3)

The second-order partial differential equations about119867(119909 119905) and119881(119909 119905) are obtained through the partial derivativeand are taken for variables 119909 and 119905 in (3) Therefore themomentum equations for water hammer wave in pipelinedrainage system are expressed as

1205971198672

1205971199092=1

1198862

1205971198672

1205971199052

1205971198812

1205971199092=1

1198862

1205971198812

1205971199052

(4)

The functions 119865(119909 119905) and 119891(119909 119905) are introduced alongwith characteristic lines 119889119909 = plusmn119889119905 Then the general solutionof (4) can be described as

119867 minus1198670= 119865(119905 minus

119909

119886) + 119891(119905 +

119909

119886)

119881 minus 1198810= minus

119892

119886[119865(119905 minus

119909

119886) minus 119891(119905 +

119909

119886)]

(5)

where 1198670is the initial pressure head 119881

0is the initial flow

velocity and 119865(119909 119905) and 119891(119909 119905) are direct and reflectionfluctuation functions

22 Propagation and Superposition Model of Water HammerWave Based on Characteristic Line Method Pumps andvalves are the generating sources of water hammer wavein hydraulic transition process of pipeline fluid deliverysystem These two kinds of water hammer wave start at thesame time and propagation directions are superimposedThesuperposition leads to strengthening of fluctuations for waterhammer In order to control the water hammer pressureeffectively the superposition effects of water hammer waveneed to be weakened as much as possible

The fundamental equations of water hammer can berewritten as

1198711= 119892

120597119867

120597119905+ 119881

120597119881

120597119909+120597119881

120597119905+119891119881 |119881|

2119863= 0

1198712=120597119867

120597119905+ 119881

120597119881

120597119909+1198862

119892

120597119881

120597119909minus 119881 sin 120579 = 0

(6)

These equations are combined linearly using an unknownmultiplier 120582 Let 119871 = 119871

1+1205821198712be the linear combinationThe

coefficient 120582 can be determined by

120582 = plusmn119892

119886 (7)

t

2Δt

Δt

t = 0

1 Δx i minus 1 i i + 1 N + 1 x

P

C+ Cminus

A B

Figure 1 Characteristic line grid for water hammer calculation

In the constraint of characteristic line equation 119889119909119889119905 =119881plusmn119886 (6) converts to ordinary differential equation as follows

119862+

119889119867

119889119905+119886

119892

119889119881

119889119905minus 119881 sin 120579 +

119891119886119881 |119881|

2119892119863= 0

119889119909

119889119905= 119881 + 119886

119862minus

119889119867

119889119905minus119886

119892

119889119881

119889119905minus 119881 sin 120579 minus

119891119886119881 |119881|

2119892119863= 0

119889119909

119889119905= 119881 minus 119886

(8)

119881 and119881sin120579 are negligible when119881 ≪ 119886 and the tilt angleof pipeline is less than 25∘ The average flow velocity 119881 isreplaced by flow 119876 The characteristic equations are changedinto

119862+

119889119867

119889119905+

119886

119892119860

119889119876

119889119905+119891119886119876 |119876|

21198921198631198602= 0

119889119909

119889119905= +119886

119862minus

minus119889119867

119889119905+

119886

119892119860

119889119876

119889119905+119891119886119876 |119876|

21198921198631198602= 0

119889119909

119889119905= minus119886

(9)

where 119862+ is the characteristic line of forward wave in 119909-axis119862minus is the characteristic line of reflected wave in 119909-axis and119860

is cross-sectional area of pipeThe integral operation and differential conversion are

introduced to (9) The discrete characteristic equations ofwater hammer are obtained as follows Equation (10) and thecharacteristic line grid are shown in Figure 1

119867119875minus 119867119860+

119886

119892119860(119876119875minus 119876119860) +

119891Δ119909119876119860

10038161003816100381610038161198761198601003816100381610038161003816

21198921198631198602= 0

119867119875minus 119867119861+

119886

119892119860(119876119875minus 119876119861) +

119891Δ119909119876119861

10038161003816100381610038161198761198611003816100381610038161003816

21198921198631198602= 0

(10)

4 Shock and Vibration

By solving the above equations transient variables 119867119875

and119876119875in the node 119894 of the pipe over the timeΔ119905 are expressed

as

119867119875=(119862119875+ 119862119872)

2

119876119875=(119862119875minus 119867119875)

119861

(11)

where 119861 = 119886119892119860Consider

119862119875= 119867119860+ 119861119876119860minus

119891Δ119909

21198921198631198602119876119860

10038161003816100381610038161198761198601003816100381610038161003816

119862119872= 119867119861minus 119861119876119860minus

119891Δ119909

21198921198631198602119876119861

10038161003816100381610038161198761198611003816100381610038161003816

(12)

The initial condition of water hammer is that of a steadyflow 119862

119875and 119862

119872in (11) are known and the parameters on

each time step can be solvedHydraulic characteristics of HCV can be described

through loss coefficient 120585 and capacity coefficient119862 Consider

119876119891=119860

radic120585

radic2119892Δ119867119891

119876119891= 119862radicΔ119867119891

(13)

where 119860 is cross-sectional area of the upstream of HCV andΔ119867119891is the pressure difference of HCV in upper and lower

Let 120591 = (1198621198620)(120591 = radic120585

0120585) be the relative opening

displacement of HCVThe dimensionless flow through HCVcan be described as

119902119891=

119876119891

1198761198910

= 120591radicΔℎ119891 (14)

where Δℎ119891is pressure difference on HCV It can be solved

as Δ119867119891Δ1198671198910 The subscript ldquo0rdquo represents HCV being open

completely

3 Optimization Method for VelocityAdjustment of HCV

31 Boundary Conditions Boundary conditions for pumpof outlet are shown in Figure 2 If the inlet loss of pumpis ignored the inlet of pool pump and HCV can becombined and dealt with as a boundary of characteristic linein foundational equations of water hammer

The equilibrium condition for water head is established inthis boundary It can be described as

119867119891+ 119867 minus119867

119897= 119867119901 (15)

where 119867119891is the depth of pool inlet 119867 is the work lift of the

pump 119867119897is the transient resistance loss of HCV and 119867

119901is

the pressure head of HCV outletWe take the balance equations of water head which in

the characteristic line 119862minusand inertia equations of pump unit

Pump Valve

Q1

B

Cminus

P

Figure 2 Boundary conditions of pump outlet

together And then the boundary conditions can be expressedas follows based on the characteristic lines of pumps

119909 = 120587 + arctan119902

120572

119882119867 (119909) =ℎ

1205722 + 1199022

119882119861 (119909) =120573

1205722 + 1199022

(16)

where the pump-lift is ℎ = 119867119867119877 The flow of pump is

119902 = 119876119876119877 The rotational speed is 120572 = 119899119899

119877 The torque is

120573 = 119879119879119877The subscript represents ratedworking conditions

Then (16) is generated as follows

1198651= 119867119895minus 119862119872minus 119861119876119877119902 + 119867

119877(1205722+ 1199022)119882119867(119909)

minus

119867119891011990210038161003816100381610038161199021003816100381610038161003816

1205912= 0

1198652= (1205722+ 1199022)119882119861 (119909) + 120573

0minus 1198701(1205720minus 120572) = 0

(17)

where 1198701= 2119870119899

119877119879119877 119870 = 120587119866119863

2120119892 and 119866119863

2 isrotational inertia 120572

0and 120573

0are rotational speed and torque

in the initial stateThen (17) can be rewritten as follows whenvariables 120572 and 119902 are introduced

1198651+ 1198651119902Δ119902 + 119865

1120572Δ120572 = 0

1198652+ 1198652119902Δ119902 + 119865

2120572Δ120572 = 0

(18)

The problem is solved as follows

120572(119896+1)

= 120572(119896)+ Δ120572

119902(119896+1)

= 119902(119896)+ Δ119902

(19)

in which Δ120572 and Δ119902 are solved through (18)The iterative errors should meet (19) Consider

|Δ120572| +1003816100381610038161003816Δ119902

1003816100381610038161003816 le 120576 (120576 = 00002) (20)

32 OptimizationMethod ofHCVAdjustment Theboundaryconditions of multistage valve-closing are introduced in thecharacteristic line calculation of water hammer for which

Shock and Vibration 5

the best procedure for multistage valve-closing is consideredThe displacement of valve-closing at any time can be deter-mined through linear procedure in multistage valve closure

Through a large number of practical tests the valveclosure with a uniform or uniform variable speed is foundto have a small influence on the water hammer in the front23 of valve-closing stroke while there is a large influenceon the later 13 of valve-closing stroke Therefore the valveclosure process is divided into multistage By doing so the

uniform and uniform variable speeds are both introduced tovalve closure process In the following section we will discussuniform or uniform variable speed calculation method invalve closure process

Assuming that the times of valve-closing in multi-stageare 1198791 1198792 119879

119894 119879

119899 the corresponding displacements of

valve-closing are 1199041 1199042 119904

119894 119904

119899 Then the displacements

of valve-closing at any time 119905 are determined as follows

119904119894

=

1199041

1198791

119905 le 1198791 The 1st stage of valve-closing

1199041+1199042

1198792

(119905 minus 1198791) 119879

1le 119905 le 119879

1+ 1198792 The 2nd stage of valve-closing

1199041+ 1199042+ sdot sdot sdot + 119904

119894minus1+119904119894

119879119894

(119905 minus 119879119894minus1) 119879

1+ 1198792+ sdot sdot sdot + 119879

119894minus1le 119905 le 119879

1+ 1198792+ sdot sdot sdot + 119879

119894 The 119894 stage of valve-closing

1199041+ 1199042+ sdot sdot sdot + 119904

119894+ sdot sdot sdot +

119904119899

119879119899

(119905 minus 119879119899minus1) 1198791+ 1198792+ sdot sdot sdot + 119879

119894+ sdot sdot sdot + 119879

119899minus1le 119905 le 119879

1+ 1198792+ sdot sdot sdot + 119879

119894+ sdot sdot sdot + 119879

119899 The 119899 stage of valve-closing

1199041+ 1199042+ sdot sdot sdot + 119904

119894+ 119904119899= 119878 119905 gt 119879

1+ 1198792+ sdot sdot sdot + 119879

119894+ 119879119899 valve-closing is completed

(21)

where 119904119894is displacement of valve-closing at 119905 and 119878 is the total

stroke of valve-closingFor the valve-closing displacement 119904

119894at any time 119905 we

can calculate the dimensionless opening degree 120591 using (21)through linear interpolation according to equidistantΔ119904

119894and

its input value

120591 = 120591 (119894) +119906(119896)

2[120591 (119894 + 1) minus 119896120591 (119894)] 120591 (119894)

+119906(119896minus1)

2[120591 (119894 + 1) minus (119896 minus 1) 120591 (119894)] + sdot sdot sdot

+1199062

2[120591 (119894 + 1) minus 2120591 (119894)]

+119906

2[120591 (119894 + 1) minus 120591 (119894)]

119906 =119904119894minus 1199040

Δ119904119894

minus 1

(22)

In the scope of velocity adjustment for HCV the velocitydisplacement and time of valve-closing have various combi-nations This paper adopts a multistage adjustment strategyaccording to simulation results of water hammer

The valve closure time for the first stage is equal or closeto the time of the flow of pump that is zero The valve closuretime for the following stages is one in four of the previousstage Consequently the initial valve closure procedure isdetermined Then search computing is taken to determinethe optimization valve closure procedure

4 Case Study and Experiment

41Working Conditions Themine with normal water qualitywas consideredThewater normal inflowwas 50m3h and themaximum inflow was 250m3h Water was discharged into

ground by two drain pipes of which the specifications wereD273times 12 respectively (one was used and another was spare)The pipes in this existing and antiquated mine drainagesystem were seamless steel pipe The allowed pressure was aslower at 64MPa The wellhead elevation was 997991m andthe borehole inclination was 20∘ There were three multistagecentrifugal pumps and two HCVs were used in Figure 3And the specification of pumps was MD280-65 times 6 (119876 =

280m3h119867 = 390m) One pump was used and others weremaintenance when themine was with a normal inflow or twopumps were used and one was spare when the mine was witha maximum inflow

The automatic drainage system was chosen in this mineCheck valves were installed in pump outlet There are HCVsin pipeline shown in Figure 3(a)where the strokewas 220mmwith the structure of HCV shown in Figure 4 During normalpump stoppingHCVswere closed first and then pumpswerestopped The water hammer phenomenon was significant indrains pipeline during this processTherefore we should takesome measures to prevent the water hammer phenomenon

42 Simulations An algorithm was developed using com-mercial simulation software Fluent63 based on the waterhammer theory described in Section 2 The accelerationamplitude pipeline pressure and valve closure displacementwere obtained in the cases of uniform and uniform variablespeed through transient simulation for water hammer Thecorrectness of simulation and the proposed theory werethen verified against experimental results We simulated thevalve-closing in single-stage with a constant velocity and inmultistage with a variable velocity based on the proposedtheory

(1) The Simulation of Valve-Closing in Single-Stage with aConstant Velocity The velocity V = 001ms of valve-closingin single-stage was determined through repeated simulation

6 Shock and Vibration

HCVs

Pump

(a) (b)

Figure 3 Diagram of drain pipes

(1)

(1) Hydraulic system

(2)

(2) Explosion-proof motors

(3)

(3) Valve body

Figure 4 Structure diagram of HCV

Then times of equipment in this situation were obtainedusing (20) to (21) as shown in Table 1

The simulation results of valve-closing parameters insingle-stage with 001ms are shown in Figures 5ndash12

For Figures 5ndash12 the static pressure of pipeline wasat 306MPa for pump stopping After the vacuum wascompleted the pump was started and HCV was open witha constant velocity At this moment pipeline pressure wasincreased alongwith the valve-opening displacement ofHCVThen pressure fluctuations appearedThe valve-opening dis-placement of HCV was 426mm and the maximum pressurewas 384MPa when 119905 = 12148 s After this momentthe pressure was steady The valve-opening displacement ofHCV was 702mm and the maximum pressure was 325MPawhen 119905 = 15244 s The drainage system pressure reacheda steady state along with the increasing of valve-openingdisplacement The pressure of pipeline began to drop when119905 = 62436 s and valve-closing displacement was 534mmWater hammer phenomenon appeared when 119905 = 67211 sWhen 119905 = 706 s the maximum boost of water hammer wasΔ119867 = 152m and the pressure of pipeline at this moment

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

x

Figure 5 Acceleration in 119909

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

x

S(m

m)

Figure 6 Amplitude in 119909

was 477Mpa It is 147 times the normal discharge pressure(325MPa) and the pressure increased by 50 suddenly Theacceleration and amplitude of pipeline in directions of 119909119910 and 119911 were changed significantly when water hammeroccurred Maximum acceleration in directions of 119909 119910 and119911 was 483ms2 646ms2 and 545ms2 and the maximumamplitude was 158mm 258mm and 153mm respectivelyAdditionally the total stroke of HCV was assumed to be 119878Valve-closing with rapid and constant velocity were taken

Shock and Vibration 7

Table 1 Times of equipment in single-stage valve-closing

Equipment actions Pump start Valve-opening Full open Valve-closing Valve closed Water hammer finished Total timesTimes 119905 (s) 4128 7883 31590 46007 67934 110500 21927

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

y

Figure 7 Acceleration in 119910

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

y

S(m

m)

Figure 8 Amplitude in 119910

z

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

Figure 9 Acceleration in 119911

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

z

S(m

m)

Figure 10 Amplitude in 119911

0 10 20 30 40 50 60 70 80 90 100 11010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

Figure 11 Pressure in pipeline

0 10 20 30 40 50 60 70 80 90 100t (s)

020406080

100120140160180200220240260

S(m

m)

Figure 12 Amplitude of HCV

8 Shock and Vibration

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus10minus9minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

x

Figure 13 Acceleration in 119909

in the former 21198783 and a variable velocity was taken in thelatter 1198783 according to the simulation results of valve-closingwater hammer Due to the velocity of valve-closing that hasa large impact on water hammer parameters it is an effectiveapproach to protect water hammer by choosing a reasonablevelocity for valve-closing

The allowed pressure of pipe is lower and its value was64MPa However the pressure of pipeline reached 48MPain the case of 22 s valve-closing from the above analysis Thisvalue is near to the allowed pressure of pipe with the pressurebeing not high and the water hammer phenomenon was notsignificant compared with other mine drainage systems Inorder to reduce the pressure of pipeline to protection pipelineit is necessary to develop water hammer protection

(2) The Simulation of Valve-Closing in Multistage with aVariable Velocity The optimization strategy of valve-closingadjustment for HCV is generated using boundary condi-tions according to optimization method of valve-closingadjustment that is proposed in this paper It is a multistagevalve-closing with a variable velocity In the front 23 ofvalve-closing stroke the velocity is constant and its value is001ms In the later 13 of valve-closing stroke the velocity isa variable (the deceleration is constant) and the initial value is001ms The total time of valve-closing is 43823 s Times ofequipment in multistage valve-closing are shown in Table 2

The simulation results of valve-closing parameters inmultistage are shown in Figures 13ndash20

The pipeline pressuring acceleration and amplitude inthe directions of 119909 119910 and 119911 are significantly reducedin multistage valve-closing with a variable velocity Valve-closing with a constant velocity is started at 46007 s andvalve-closing with a variable velocity is started at 606 s TheHCVs are closed and pumps are stopped at 8983 s In thisprocess themaximumpressure ofwater hammer is 349MPaNo effect of water hammer occurred under this situation

43 Experiments The experimental devices include multi-function data acquisition instrument vibration sensor pres-sure sensors and cable displacement encoder Multifunction

x

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

S(m

m)

Figure 14 Amplitude in 119909

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus10minus9minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

y

Figure 15 Acceleration in 119910

data acquisition instrument has 16 channels and its acqui-sition frequency is 1024 kHz Data of acceleration ampli-tude flow pressure and displacement of valve-closing wereacquired by this multifunction data acquisition instrumentVibration sensor was used to measure piping vibration underthe influence of water hammer It was disposed along withthe 119909 119910 and 119911 direction of the pipe Pressure sensors wereused to measure pipeline pressure Its measurement accuracyand range are 0ndash10MPa and plusmn05 FS Cable displacementencoder was used to posit the displacement of valve-closingThe arrangement diagram of sensors and flow chart of pumpsare shown in Figures 21 and 22

HCVs control system was designed in this experimentwhich is shown in Figure 23 Sensors were used to collectsignals of pressure and acceleration in pipeline PLC unitwas used to analyze pipeline pressure and vibration for waterhammer on the basis of pressure and acceleration signalsAn expected running speed was given to HCVs And thenvoltage current power and fault protection informationof pumps pressure flow temperature vacuum and HCVsstatus information were monitored at real time These multi-parameter data were integrated using of fuzzy control theorywith calculus and control strategy The HCVs control system

Shock and Vibration 9

Table 2 Times of equipment in multistage valve-closing

Equipment actions Pump start Valve-opening Full open Valve-closing Valve closed Water hammer finished Total timesTimes 119905 (s) 4128 85 39504 46007 89830 128816 43823

y

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20minus15minus10minus5

05

1015202530

t (s)

S(m

m)

Figure 16 Amplitude in 119910

0 10 20 30 40 50 60 70 80 90 100 110 120 130

minus9minus10

minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

z

Figure 17 Acceleration in 119911

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

S(m

m)

z

t (s)

Figure 18 Amplitude in 119911

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

Figure 19 Pressure in pipeline

020406080

100120140160180200220240260280

S(m

m)

0 10 20 30 40 50 60 70 80 90 100 110t (s)

Figure 20 Displacement of HCV

can control starting and stopping of pumps automatically andcan monitor the signals in system running process timely

For the total stroke of valve 119878 the experimental conditionsare as follows In the front 23 of the stroke the velocitywas constant and its value was 001ms In the later 13the velocity is variable (the deceleration is constant) andthe initial value was 001ms The full valve-closing timeswere 44 s Measured values of water hammer parameters inmultistage are shown in Table 3

10 Shock and Vibration

sensor

sensor

Pressuresensor

Pressuregauge

Negativepressure sensor

Jet valves Hydrostatic pipe

Flow sensor Pressure sensor

Drain pipe

Drain pipe

Drain pipe

A-A

X vibration

Z vibration

Y vibration sensor

Figure 21 Arrangement diagram of sensors

Data collection isbeginning

Pump start

Valve start

Full valve opening

Normal drainage

Valve-closing start

Valve closed

Pump stop

Water hammer is finishedData collection is finished

Phase 1

Pump start

Phase 2Pump running

Phase 3Pump stopping

Figure 22 The flow chart of test for pumps

Shock and Vibration 11

HCVs PLC unit

Acceleration sensor

Pressure sensor

PC

Other sensors and execution system

Opticalfiber

Closed-loop control of waterhammer protection

Figure 23 Composition of HCVs control system

Table 3 Measured values of water hammer parameters

Measured parameters Acceleration (ms2) Displacement (mm) Pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Valve-closing times (s)22 48308 64582 54457 157662 285192 153051 4586525 48207 64581 54453 157515 285139 153012 4556428 47986 63215 54394 157495 284632 152036 4495231 45689 61265 52563 136938 268576 130369 4467833 45389 61063 51935 135963 246985 126325 4461236 43236 59638 50632 126985 238965 117652 4267539 17231 11023 16352 92514 63656 113251 3561542 17016 10363 15426 90356 61563 109968 3542344 16987 08692 14112 89482 59354 106432 3500648 16886 08629 14003 89235 59139 106365 35006

5 Results and Discussion

The reliability and effectiveness are illustrated through thecomparison between the results of simulation and experi-ment

(1) Results of Valve-Closing in Single-Stage with a ConstantVelocity and in Multistage with a Variable Velocity AreCompared Pipeline pressures and displacements of valve-opening under these two conditions are shown in Figures 24and 25 respectively The red curves represent the variationsin single-stage with a constant velocity while the black curvesrepresent the variations formultistagewith a variable velocity

Figures 24 and 25 show a significant water hammer effectin single-stage valve-closing with a constant velocity andthe valve-closing time is shorter (22 s) On the other handwater hammer phenomenon was found to be considerablyimproved for multistage valve-closing condition with a vari-able velocity and the valve-closing timewas extended (44 s) Itshows that valve-closing inmultistage with a variable velocitycan control the water hammer phenomenon effective inminedrainage system

(2) Results of the Simulation and Experiment Are Also Com-pared Results for valve-closing with a variable velocity areshown in Table 4

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

PZCPZD

Figure 24 Pressure in pipeline

It can be seen from Table 4 that the simulation forvalve-closing with a variable velocity shows good agreementwith the experiment The errors between simulation andexperiment are less than 5 Therefore the valve-closing in

12 Shock and Vibration

Table 4 Results comparison of simulation and experiment

Parameters Max acceleration (ms2) Max displacement (mm) Max pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Simulation 45830 62672 52341 165122 273335 148726 45798Experiment 48308 64582 54457 157660 285192 153051 45867Errors 46 29 39 47 42 28 02Simulation 16876 08446 13651 86395 56689 104653 34901Experiment 16987 08692 14112 89482 59354 106432 35006Errors 07 28 33 34 44 17 03

0 10 20 30 40 50 60 70 80 90 1000

20406080

100120140160180200220240

t (s)

S(m

m)

S1(FM)S2(FM)

Figure 25 Displacement of HCV

multistagewith a variable velocity can reduce the impact fromwater hammer in mine drainage system

6 Conclusions and Future Work

Limited space and high cost of equipment changing arethe main characteristics for mine drainage system For theproblem of valve-closing water hammer protection in minedrainage system this paper proposed a protection methodbased on velocity adjustment of HCVs The mathematicmodel of valve-closing water hammer is established basedon fundamental equations The strategy of valve-closing inmultistage with a variable velocity is obtained by velocityadjustment strategy of HCVs and it is effective in protect-ing the valve-closing water hammer without change pipingarrangement or addition equipment The results of simula-tions and experiments in different adjustment velocity arecomparedWe obtained that the water hammer phenomenonis not obvious with valve-closing velocity in the front 23 of itsstroke and it is very seriously within the later 13 Thereforewe take a two-stage valve-closing strategy In the first stagethe velocity is constant and its value is 001ms In the secondstage the velocity is variable (the deceleration is constant) andthe initial value is 001ms

Extending errors in the theoretical wave speed havean important influence on prediction of the closure rate

before a water hammer occurs in the actual pipeline A verychallenging mathematical task is variable This is beyond thescope of this paper and may be considered as a future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National 125 Tech-nology Support Program of China under Grant noSQ2012BAJY3504

References

[1] M Sun X-R Ru and L-F Zhai ldquoIn-situ fabrication ofsupported iron oxides from synthetic acid mine drainage highcatalytic activities and good stabilities towards electro-Fentonreactionrdquo Applied Catalysis B Environmental vol 165 pp 103ndash110 2015

[2] A Kaliatka M Vaisnoras and M Valincius ldquoModelling ofvalve induced water hammer phenomena in a district heatingsystemrdquo Computers amp Fluids vol 94 pp 30ndash36 2014

[3] N Jeong D Chi and J Yoon ldquoAnalytic estimation of the impactpressure in a beam-tube due to water-hammer effectrdquo Journalof Nuclear Science and Technology vol 50 no 12 pp 1139ndash11492013

[4] W S Yi J Jiang D D Li G Lan and Z Zhao ldquoPump-stoppingwater hammer simulation based on RELAP5rdquo IOP ConferenceSeries Materials Science and Engineering vol 52 no 7 ArticleID 072009 2013

[5] Q W Yong M Jiang and Y Tang ldquoStudy on liquid pipelinewater hammer and protective device with gas concentrationrdquoAdvanced Materials Research vol 616ndash618 pp 774ndash777 2013

[6] J Zhang J Gao M Diao W Wu T Wang and S Qi ldquoA casestudy on risk assessment of long distance water supply systemrdquoProcedia Engineering vol 70 pp 1762ndash1771 2014

[7] K I M Sang-Gyun L E E Kye-Bock and K I M Kyung-YupldquoWater hammer in the pump-rising pipeline system with an airchamberrdquo Journal of Hydrodynamics Series B vol 26 no 6 pp960ndash964 2015

[8] M A Bouaziz M A Guidara C Schmitt E Hadj-Taıeb and ZAzari ldquoWater hammer effects on a gray cast iron water networkafter adding pumpsrdquo Engineering Failure Analysis vol 44 pp1ndash16 2014

Shock and Vibration 13

[9] M S Ghidaoui M Zhao D A McInnis and D H AxworthyldquoA review of water hammer theory and practicerdquo AppliedMechanics Reviews vol 58 no 1ndash6 pp 49ndash76 2005

[10] A F Colombo P Lee and B W Karney ldquoA selective literaturereview of transient-based leak detection methodsrdquo Journal ofHydro-Environment Research vol 2 no 4 pp 212ndash227 2009

[11] P J Lee M F Lambert A R Simpson J P Vıtkovsky andD Misiunas ldquoLeak location in single pipelines using transientreflectionsrdquo Australian Journal of Water Resources vol 11 no 1pp 53ndash65 2007

[12] N S Arbon M F Lambert A R Simpson andM L StephensldquoField test investigations into distributed fault modeling inwater distribution systems using transient testingrdquo in Proceed-ings of the World Environmental and Water Resources CongressTampa Fla USA May 2007

[13] J Gong A R SimpsonM F Lambert A C Zecchin Y-I Kimand A S Tijsseling ldquoDetection of distributed deteriorationin single pipes using transient reflectionsrdquo Journal of PipelineSystems Engineering and Practice vol 4 no 1 pp 32ndash40 2013

[14] M Ferrante B Brunone and S Meniconi ldquoLeak detectionin branched pipe systems coupling wavelet analysis and aLagrangian modelrdquo Journal of Water Supply Research andTechnology vol 58 no 2 pp 95ndash106 2009

[15] S Meniconi B Brunone and M Ferrante ldquoWater-hammerpressure waves interaction at cross-section changes in series inviscoelastic pipesrdquo Journal of Fluids and Structures vol 33 pp44ndash58 2012

[16] W H Hager ldquoSwiss contributions to water hammer theoryrdquoJournal of Hydraulic Research vol 39 no 1 pp 3ndash7 2001

[17] M S Ghidaoui and B W Karney ldquoModified transformationand integration of 1D wave equationsrdquo Journal of HydraulicEngineering vol 121 no 10 pp 758ndash760 1995

[18] A Adamkowski and M Lewandowski ldquoCavitation character-istics of shutoff valves in numerical modeling of transientsin pipelines with column separationrdquo Journal of HydraulicEngineering vol 141 no 2 2015

[19] E Yao G Kember and D Hansen ldquoAnalysis of water hammerattenuation in applications with varying valve closure timesrdquoJournal of Engineering Mechanics vol 141 no 1 Article ID04014107 2014

[20] R Korbar Z Virag and M Savar ldquoTruncated method of char-acteristics for quasi-two-dimensional water hammer modelrdquoJournal of Hydraulic Engineering vol 140 no 6 Article ID04014013 2014

[21] M Rohani and M H Afshar ldquoSimulation of transient flowcaused by pump failure point-implicit method of characteris-ticsrdquo Annals of Nuclear Energy vol 37 no 12 pp 1742ndash17502010

[22] A Triki ldquoMultiple-grid finite element solution of the shallowwater equations water hammer phenomenonrdquo Computers ampFluids vol 90 pp 65ndash71 2014

[23] A Keramat A S Tijsseling Q Hou and A Ahmadi ldquoFluid-structure interactionwith pipe-wall viscoelasticity during waterhammerrdquo Journal of Fluids and Structures vol 28 pp 434ndash4552012

[24] S-G Kim K-B Lee and K-Y Kim ldquoWater hammer in thepump-rising pipeline system with an air chamberrdquo Journal ofHydrodynamics vol 26 no 6 pp 960ndash964 2014

[25] E B Wylie and V L Streeter Fluid Transients McGraw-HillNew York NY USA 1978

[26] W Wan W Huang and C Li ldquoSensitivity analysis for theresistance on the performance of a pressure vessel for waterhammer protectionrdquo Journal of Pressure Vessel TechnologymdashTransactions of the ASME vol 136 no 1 Article ID 011303 2014

[27] G De Martino F De Paola N Fontana and M GiugnildquoDiscussion of lsquosimple guide for design of air vessels forwater hammer protection of pumping linesrsquo by D StephensonrdquoJournal of Hydraulic Engineering vol 130 no 3 pp 273ndash2752004

[28] T S Lee ldquoAir influence on hydraulic transients on fluid systemwith air valvesrdquo Journal of Fluids Engineering vol 121 no 3 pp646ndash650 1999

[29] D Stephenson ldquoEffects of air valves and pipework on waterhammer pressuresrdquo Journal of Transportation Engineering vol123 no 2 pp 101ndash106 1997

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4 Shock and Vibration

By solving the above equations transient variables 119867119875

and119876119875in the node 119894 of the pipe over the timeΔ119905 are expressed

as

119867119875=(119862119875+ 119862119872)

2

119876119875=(119862119875minus 119867119875)

119861

(11)

where 119861 = 119886119892119860Consider

119862119875= 119867119860+ 119861119876119860minus

119891Δ119909

21198921198631198602119876119860

10038161003816100381610038161198761198601003816100381610038161003816

119862119872= 119867119861minus 119861119876119860minus

119891Δ119909

21198921198631198602119876119861

10038161003816100381610038161198761198611003816100381610038161003816

(12)

The initial condition of water hammer is that of a steadyflow 119862

119875and 119862

119872in (11) are known and the parameters on

each time step can be solvedHydraulic characteristics of HCV can be described

through loss coefficient 120585 and capacity coefficient119862 Consider

119876119891=119860

radic120585

radic2119892Δ119867119891

119876119891= 119862radicΔ119867119891

(13)

where 119860 is cross-sectional area of the upstream of HCV andΔ119867119891is the pressure difference of HCV in upper and lower

Let 120591 = (1198621198620)(120591 = radic120585

0120585) be the relative opening

displacement of HCVThe dimensionless flow through HCVcan be described as

119902119891=

119876119891

1198761198910

= 120591radicΔℎ119891 (14)

where Δℎ119891is pressure difference on HCV It can be solved

as Δ119867119891Δ1198671198910 The subscript ldquo0rdquo represents HCV being open

completely

3 Optimization Method for VelocityAdjustment of HCV

31 Boundary Conditions Boundary conditions for pumpof outlet are shown in Figure 2 If the inlet loss of pumpis ignored the inlet of pool pump and HCV can becombined and dealt with as a boundary of characteristic linein foundational equations of water hammer

The equilibrium condition for water head is established inthis boundary It can be described as

119867119891+ 119867 minus119867

119897= 119867119901 (15)

where 119867119891is the depth of pool inlet 119867 is the work lift of the

pump 119867119897is the transient resistance loss of HCV and 119867

119901is

the pressure head of HCV outletWe take the balance equations of water head which in

the characteristic line 119862minusand inertia equations of pump unit

Pump Valve

Q1

B

Cminus

P

Figure 2 Boundary conditions of pump outlet

together And then the boundary conditions can be expressedas follows based on the characteristic lines of pumps

119909 = 120587 + arctan119902

120572

119882119867 (119909) =ℎ

1205722 + 1199022

119882119861 (119909) =120573

1205722 + 1199022

(16)

where the pump-lift is ℎ = 119867119867119877 The flow of pump is

119902 = 119876119876119877 The rotational speed is 120572 = 119899119899

119877 The torque is

120573 = 119879119879119877The subscript represents ratedworking conditions

Then (16) is generated as follows

1198651= 119867119895minus 119862119872minus 119861119876119877119902 + 119867

119877(1205722+ 1199022)119882119867(119909)

minus

119867119891011990210038161003816100381610038161199021003816100381610038161003816

1205912= 0

1198652= (1205722+ 1199022)119882119861 (119909) + 120573

0minus 1198701(1205720minus 120572) = 0

(17)

where 1198701= 2119870119899

119877119879119877 119870 = 120587119866119863

2120119892 and 119866119863

2 isrotational inertia 120572

0and 120573

0are rotational speed and torque

in the initial stateThen (17) can be rewritten as follows whenvariables 120572 and 119902 are introduced

1198651+ 1198651119902Δ119902 + 119865

1120572Δ120572 = 0

1198652+ 1198652119902Δ119902 + 119865

2120572Δ120572 = 0

(18)

The problem is solved as follows

120572(119896+1)

= 120572(119896)+ Δ120572

119902(119896+1)

= 119902(119896)+ Δ119902

(19)

in which Δ120572 and Δ119902 are solved through (18)The iterative errors should meet (19) Consider

|Δ120572| +1003816100381610038161003816Δ119902

1003816100381610038161003816 le 120576 (120576 = 00002) (20)

32 OptimizationMethod ofHCVAdjustment Theboundaryconditions of multistage valve-closing are introduced in thecharacteristic line calculation of water hammer for which

Shock and Vibration 5

the best procedure for multistage valve-closing is consideredThe displacement of valve-closing at any time can be deter-mined through linear procedure in multistage valve closure

Through a large number of practical tests the valveclosure with a uniform or uniform variable speed is foundto have a small influence on the water hammer in the front23 of valve-closing stroke while there is a large influenceon the later 13 of valve-closing stroke Therefore the valveclosure process is divided into multistage By doing so the

uniform and uniform variable speeds are both introduced tovalve closure process In the following section we will discussuniform or uniform variable speed calculation method invalve closure process

Assuming that the times of valve-closing in multi-stageare 1198791 1198792 119879

119894 119879

119899 the corresponding displacements of

valve-closing are 1199041 1199042 119904

119894 119904

119899 Then the displacements

of valve-closing at any time 119905 are determined as follows

119904119894

=

1199041

1198791

119905 le 1198791 The 1st stage of valve-closing

1199041+1199042

1198792

(119905 minus 1198791) 119879

1le 119905 le 119879

1+ 1198792 The 2nd stage of valve-closing

1199041+ 1199042+ sdot sdot sdot + 119904

119894minus1+119904119894

119879119894

(119905 minus 119879119894minus1) 119879

1+ 1198792+ sdot sdot sdot + 119879

119894minus1le 119905 le 119879

1+ 1198792+ sdot sdot sdot + 119879

119894 The 119894 stage of valve-closing

1199041+ 1199042+ sdot sdot sdot + 119904

119894+ sdot sdot sdot +

119904119899

119879119899

(119905 minus 119879119899minus1) 1198791+ 1198792+ sdot sdot sdot + 119879

119894+ sdot sdot sdot + 119879

119899minus1le 119905 le 119879

1+ 1198792+ sdot sdot sdot + 119879

119894+ sdot sdot sdot + 119879

119899 The 119899 stage of valve-closing

1199041+ 1199042+ sdot sdot sdot + 119904

119894+ 119904119899= 119878 119905 gt 119879

1+ 1198792+ sdot sdot sdot + 119879

119894+ 119879119899 valve-closing is completed

(21)

where 119904119894is displacement of valve-closing at 119905 and 119878 is the total

stroke of valve-closingFor the valve-closing displacement 119904

119894at any time 119905 we

can calculate the dimensionless opening degree 120591 using (21)through linear interpolation according to equidistantΔ119904

119894and

its input value

120591 = 120591 (119894) +119906(119896)

2[120591 (119894 + 1) minus 119896120591 (119894)] 120591 (119894)

+119906(119896minus1)

2[120591 (119894 + 1) minus (119896 minus 1) 120591 (119894)] + sdot sdot sdot

+1199062

2[120591 (119894 + 1) minus 2120591 (119894)]

+119906

2[120591 (119894 + 1) minus 120591 (119894)]

119906 =119904119894minus 1199040

Δ119904119894

minus 1

(22)

In the scope of velocity adjustment for HCV the velocitydisplacement and time of valve-closing have various combi-nations This paper adopts a multistage adjustment strategyaccording to simulation results of water hammer

The valve closure time for the first stage is equal or closeto the time of the flow of pump that is zero The valve closuretime for the following stages is one in four of the previousstage Consequently the initial valve closure procedure isdetermined Then search computing is taken to determinethe optimization valve closure procedure

4 Case Study and Experiment

41Working Conditions Themine with normal water qualitywas consideredThewater normal inflowwas 50m3h and themaximum inflow was 250m3h Water was discharged into

ground by two drain pipes of which the specifications wereD273times 12 respectively (one was used and another was spare)The pipes in this existing and antiquated mine drainagesystem were seamless steel pipe The allowed pressure was aslower at 64MPa The wellhead elevation was 997991m andthe borehole inclination was 20∘ There were three multistagecentrifugal pumps and two HCVs were used in Figure 3And the specification of pumps was MD280-65 times 6 (119876 =

280m3h119867 = 390m) One pump was used and others weremaintenance when themine was with a normal inflow or twopumps were used and one was spare when the mine was witha maximum inflow

The automatic drainage system was chosen in this mineCheck valves were installed in pump outlet There are HCVsin pipeline shown in Figure 3(a)where the strokewas 220mmwith the structure of HCV shown in Figure 4 During normalpump stoppingHCVswere closed first and then pumpswerestopped The water hammer phenomenon was significant indrains pipeline during this processTherefore we should takesome measures to prevent the water hammer phenomenon

42 Simulations An algorithm was developed using com-mercial simulation software Fluent63 based on the waterhammer theory described in Section 2 The accelerationamplitude pipeline pressure and valve closure displacementwere obtained in the cases of uniform and uniform variablespeed through transient simulation for water hammer Thecorrectness of simulation and the proposed theory werethen verified against experimental results We simulated thevalve-closing in single-stage with a constant velocity and inmultistage with a variable velocity based on the proposedtheory

(1) The Simulation of Valve-Closing in Single-Stage with aConstant Velocity The velocity V = 001ms of valve-closingin single-stage was determined through repeated simulation

6 Shock and Vibration

HCVs

Pump

(a) (b)

Figure 3 Diagram of drain pipes

(1)

(1) Hydraulic system

(2)

(2) Explosion-proof motors

(3)

(3) Valve body

Figure 4 Structure diagram of HCV

Then times of equipment in this situation were obtainedusing (20) to (21) as shown in Table 1

The simulation results of valve-closing parameters insingle-stage with 001ms are shown in Figures 5ndash12

For Figures 5ndash12 the static pressure of pipeline wasat 306MPa for pump stopping After the vacuum wascompleted the pump was started and HCV was open witha constant velocity At this moment pipeline pressure wasincreased alongwith the valve-opening displacement ofHCVThen pressure fluctuations appearedThe valve-opening dis-placement of HCV was 426mm and the maximum pressurewas 384MPa when 119905 = 12148 s After this momentthe pressure was steady The valve-opening displacement ofHCV was 702mm and the maximum pressure was 325MPawhen 119905 = 15244 s The drainage system pressure reacheda steady state along with the increasing of valve-openingdisplacement The pressure of pipeline began to drop when119905 = 62436 s and valve-closing displacement was 534mmWater hammer phenomenon appeared when 119905 = 67211 sWhen 119905 = 706 s the maximum boost of water hammer wasΔ119867 = 152m and the pressure of pipeline at this moment

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

x

Figure 5 Acceleration in 119909

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

x

S(m

m)

Figure 6 Amplitude in 119909

was 477Mpa It is 147 times the normal discharge pressure(325MPa) and the pressure increased by 50 suddenly Theacceleration and amplitude of pipeline in directions of 119909119910 and 119911 were changed significantly when water hammeroccurred Maximum acceleration in directions of 119909 119910 and119911 was 483ms2 646ms2 and 545ms2 and the maximumamplitude was 158mm 258mm and 153mm respectivelyAdditionally the total stroke of HCV was assumed to be 119878Valve-closing with rapid and constant velocity were taken

Shock and Vibration 7

Table 1 Times of equipment in single-stage valve-closing

Equipment actions Pump start Valve-opening Full open Valve-closing Valve closed Water hammer finished Total timesTimes 119905 (s) 4128 7883 31590 46007 67934 110500 21927

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

y

Figure 7 Acceleration in 119910

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

y

S(m

m)

Figure 8 Amplitude in 119910

z

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

Figure 9 Acceleration in 119911

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

z

S(m

m)

Figure 10 Amplitude in 119911

0 10 20 30 40 50 60 70 80 90 100 11010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

Figure 11 Pressure in pipeline

0 10 20 30 40 50 60 70 80 90 100t (s)

020406080

100120140160180200220240260

S(m

m)

Figure 12 Amplitude of HCV

8 Shock and Vibration

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus10minus9minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

x

Figure 13 Acceleration in 119909

in the former 21198783 and a variable velocity was taken in thelatter 1198783 according to the simulation results of valve-closingwater hammer Due to the velocity of valve-closing that hasa large impact on water hammer parameters it is an effectiveapproach to protect water hammer by choosing a reasonablevelocity for valve-closing

The allowed pressure of pipe is lower and its value was64MPa However the pressure of pipeline reached 48MPain the case of 22 s valve-closing from the above analysis Thisvalue is near to the allowed pressure of pipe with the pressurebeing not high and the water hammer phenomenon was notsignificant compared with other mine drainage systems Inorder to reduce the pressure of pipeline to protection pipelineit is necessary to develop water hammer protection

(2) The Simulation of Valve-Closing in Multistage with aVariable Velocity The optimization strategy of valve-closingadjustment for HCV is generated using boundary condi-tions according to optimization method of valve-closingadjustment that is proposed in this paper It is a multistagevalve-closing with a variable velocity In the front 23 ofvalve-closing stroke the velocity is constant and its value is001ms In the later 13 of valve-closing stroke the velocity isa variable (the deceleration is constant) and the initial value is001ms The total time of valve-closing is 43823 s Times ofequipment in multistage valve-closing are shown in Table 2

The simulation results of valve-closing parameters inmultistage are shown in Figures 13ndash20

The pipeline pressuring acceleration and amplitude inthe directions of 119909 119910 and 119911 are significantly reducedin multistage valve-closing with a variable velocity Valve-closing with a constant velocity is started at 46007 s andvalve-closing with a variable velocity is started at 606 s TheHCVs are closed and pumps are stopped at 8983 s In thisprocess themaximumpressure ofwater hammer is 349MPaNo effect of water hammer occurred under this situation

43 Experiments The experimental devices include multi-function data acquisition instrument vibration sensor pres-sure sensors and cable displacement encoder Multifunction

x

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

S(m

m)

Figure 14 Amplitude in 119909

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus10minus9minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

y

Figure 15 Acceleration in 119910

data acquisition instrument has 16 channels and its acqui-sition frequency is 1024 kHz Data of acceleration ampli-tude flow pressure and displacement of valve-closing wereacquired by this multifunction data acquisition instrumentVibration sensor was used to measure piping vibration underthe influence of water hammer It was disposed along withthe 119909 119910 and 119911 direction of the pipe Pressure sensors wereused to measure pipeline pressure Its measurement accuracyand range are 0ndash10MPa and plusmn05 FS Cable displacementencoder was used to posit the displacement of valve-closingThe arrangement diagram of sensors and flow chart of pumpsare shown in Figures 21 and 22

HCVs control system was designed in this experimentwhich is shown in Figure 23 Sensors were used to collectsignals of pressure and acceleration in pipeline PLC unitwas used to analyze pipeline pressure and vibration for waterhammer on the basis of pressure and acceleration signalsAn expected running speed was given to HCVs And thenvoltage current power and fault protection informationof pumps pressure flow temperature vacuum and HCVsstatus information were monitored at real time These multi-parameter data were integrated using of fuzzy control theorywith calculus and control strategy The HCVs control system

Shock and Vibration 9

Table 2 Times of equipment in multistage valve-closing

Equipment actions Pump start Valve-opening Full open Valve-closing Valve closed Water hammer finished Total timesTimes 119905 (s) 4128 85 39504 46007 89830 128816 43823

y

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20minus15minus10minus5

05

1015202530

t (s)

S(m

m)

Figure 16 Amplitude in 119910

0 10 20 30 40 50 60 70 80 90 100 110 120 130

minus9minus10

minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

z

Figure 17 Acceleration in 119911

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

S(m

m)

z

t (s)

Figure 18 Amplitude in 119911

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

Figure 19 Pressure in pipeline

020406080

100120140160180200220240260280

S(m

m)

0 10 20 30 40 50 60 70 80 90 100 110t (s)

Figure 20 Displacement of HCV

can control starting and stopping of pumps automatically andcan monitor the signals in system running process timely

For the total stroke of valve 119878 the experimental conditionsare as follows In the front 23 of the stroke the velocitywas constant and its value was 001ms In the later 13the velocity is variable (the deceleration is constant) andthe initial value was 001ms The full valve-closing timeswere 44 s Measured values of water hammer parameters inmultistage are shown in Table 3

10 Shock and Vibration

sensor

sensor

Pressuresensor

Pressuregauge

Negativepressure sensor

Jet valves Hydrostatic pipe

Flow sensor Pressure sensor

Drain pipe

Drain pipe

Drain pipe

A-A

X vibration

Z vibration

Y vibration sensor

Figure 21 Arrangement diagram of sensors

Data collection isbeginning

Pump start

Valve start

Full valve opening

Normal drainage

Valve-closing start

Valve closed

Pump stop

Water hammer is finishedData collection is finished

Phase 1

Pump start

Phase 2Pump running

Phase 3Pump stopping

Figure 22 The flow chart of test for pumps

Shock and Vibration 11

HCVs PLC unit

Acceleration sensor

Pressure sensor

PC

Other sensors and execution system

Opticalfiber

Closed-loop control of waterhammer protection

Figure 23 Composition of HCVs control system

Table 3 Measured values of water hammer parameters

Measured parameters Acceleration (ms2) Displacement (mm) Pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Valve-closing times (s)22 48308 64582 54457 157662 285192 153051 4586525 48207 64581 54453 157515 285139 153012 4556428 47986 63215 54394 157495 284632 152036 4495231 45689 61265 52563 136938 268576 130369 4467833 45389 61063 51935 135963 246985 126325 4461236 43236 59638 50632 126985 238965 117652 4267539 17231 11023 16352 92514 63656 113251 3561542 17016 10363 15426 90356 61563 109968 3542344 16987 08692 14112 89482 59354 106432 3500648 16886 08629 14003 89235 59139 106365 35006

5 Results and Discussion

The reliability and effectiveness are illustrated through thecomparison between the results of simulation and experi-ment

(1) Results of Valve-Closing in Single-Stage with a ConstantVelocity and in Multistage with a Variable Velocity AreCompared Pipeline pressures and displacements of valve-opening under these two conditions are shown in Figures 24and 25 respectively The red curves represent the variationsin single-stage with a constant velocity while the black curvesrepresent the variations formultistagewith a variable velocity

Figures 24 and 25 show a significant water hammer effectin single-stage valve-closing with a constant velocity andthe valve-closing time is shorter (22 s) On the other handwater hammer phenomenon was found to be considerablyimproved for multistage valve-closing condition with a vari-able velocity and the valve-closing timewas extended (44 s) Itshows that valve-closing inmultistage with a variable velocitycan control the water hammer phenomenon effective inminedrainage system

(2) Results of the Simulation and Experiment Are Also Com-pared Results for valve-closing with a variable velocity areshown in Table 4

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

PZCPZD

Figure 24 Pressure in pipeline

It can be seen from Table 4 that the simulation forvalve-closing with a variable velocity shows good agreementwith the experiment The errors between simulation andexperiment are less than 5 Therefore the valve-closing in

12 Shock and Vibration

Table 4 Results comparison of simulation and experiment

Parameters Max acceleration (ms2) Max displacement (mm) Max pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Simulation 45830 62672 52341 165122 273335 148726 45798Experiment 48308 64582 54457 157660 285192 153051 45867Errors 46 29 39 47 42 28 02Simulation 16876 08446 13651 86395 56689 104653 34901Experiment 16987 08692 14112 89482 59354 106432 35006Errors 07 28 33 34 44 17 03

0 10 20 30 40 50 60 70 80 90 1000

20406080

100120140160180200220240

t (s)

S(m

m)

S1(FM)S2(FM)

Figure 25 Displacement of HCV

multistagewith a variable velocity can reduce the impact fromwater hammer in mine drainage system

6 Conclusions and Future Work

Limited space and high cost of equipment changing arethe main characteristics for mine drainage system For theproblem of valve-closing water hammer protection in minedrainage system this paper proposed a protection methodbased on velocity adjustment of HCVs The mathematicmodel of valve-closing water hammer is established basedon fundamental equations The strategy of valve-closing inmultistage with a variable velocity is obtained by velocityadjustment strategy of HCVs and it is effective in protect-ing the valve-closing water hammer without change pipingarrangement or addition equipment The results of simula-tions and experiments in different adjustment velocity arecomparedWe obtained that the water hammer phenomenonis not obvious with valve-closing velocity in the front 23 of itsstroke and it is very seriously within the later 13 Thereforewe take a two-stage valve-closing strategy In the first stagethe velocity is constant and its value is 001ms In the secondstage the velocity is variable (the deceleration is constant) andthe initial value is 001ms

Extending errors in the theoretical wave speed havean important influence on prediction of the closure rate

before a water hammer occurs in the actual pipeline A verychallenging mathematical task is variable This is beyond thescope of this paper and may be considered as a future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National 125 Tech-nology Support Program of China under Grant noSQ2012BAJY3504

References

[1] M Sun X-R Ru and L-F Zhai ldquoIn-situ fabrication ofsupported iron oxides from synthetic acid mine drainage highcatalytic activities and good stabilities towards electro-Fentonreactionrdquo Applied Catalysis B Environmental vol 165 pp 103ndash110 2015

[2] A Kaliatka M Vaisnoras and M Valincius ldquoModelling ofvalve induced water hammer phenomena in a district heatingsystemrdquo Computers amp Fluids vol 94 pp 30ndash36 2014

[3] N Jeong D Chi and J Yoon ldquoAnalytic estimation of the impactpressure in a beam-tube due to water-hammer effectrdquo Journalof Nuclear Science and Technology vol 50 no 12 pp 1139ndash11492013

[4] W S Yi J Jiang D D Li G Lan and Z Zhao ldquoPump-stoppingwater hammer simulation based on RELAP5rdquo IOP ConferenceSeries Materials Science and Engineering vol 52 no 7 ArticleID 072009 2013

[5] Q W Yong M Jiang and Y Tang ldquoStudy on liquid pipelinewater hammer and protective device with gas concentrationrdquoAdvanced Materials Research vol 616ndash618 pp 774ndash777 2013

[6] J Zhang J Gao M Diao W Wu T Wang and S Qi ldquoA casestudy on risk assessment of long distance water supply systemrdquoProcedia Engineering vol 70 pp 1762ndash1771 2014

[7] K I M Sang-Gyun L E E Kye-Bock and K I M Kyung-YupldquoWater hammer in the pump-rising pipeline system with an airchamberrdquo Journal of Hydrodynamics Series B vol 26 no 6 pp960ndash964 2015

[8] M A Bouaziz M A Guidara C Schmitt E Hadj-Taıeb and ZAzari ldquoWater hammer effects on a gray cast iron water networkafter adding pumpsrdquo Engineering Failure Analysis vol 44 pp1ndash16 2014

Shock and Vibration 13

[9] M S Ghidaoui M Zhao D A McInnis and D H AxworthyldquoA review of water hammer theory and practicerdquo AppliedMechanics Reviews vol 58 no 1ndash6 pp 49ndash76 2005

[10] A F Colombo P Lee and B W Karney ldquoA selective literaturereview of transient-based leak detection methodsrdquo Journal ofHydro-Environment Research vol 2 no 4 pp 212ndash227 2009

[11] P J Lee M F Lambert A R Simpson J P Vıtkovsky andD Misiunas ldquoLeak location in single pipelines using transientreflectionsrdquo Australian Journal of Water Resources vol 11 no 1pp 53ndash65 2007

[12] N S Arbon M F Lambert A R Simpson andM L StephensldquoField test investigations into distributed fault modeling inwater distribution systems using transient testingrdquo in Proceed-ings of the World Environmental and Water Resources CongressTampa Fla USA May 2007

[13] J Gong A R SimpsonM F Lambert A C Zecchin Y-I Kimand A S Tijsseling ldquoDetection of distributed deteriorationin single pipes using transient reflectionsrdquo Journal of PipelineSystems Engineering and Practice vol 4 no 1 pp 32ndash40 2013

[14] M Ferrante B Brunone and S Meniconi ldquoLeak detectionin branched pipe systems coupling wavelet analysis and aLagrangian modelrdquo Journal of Water Supply Research andTechnology vol 58 no 2 pp 95ndash106 2009

[15] S Meniconi B Brunone and M Ferrante ldquoWater-hammerpressure waves interaction at cross-section changes in series inviscoelastic pipesrdquo Journal of Fluids and Structures vol 33 pp44ndash58 2012

[16] W H Hager ldquoSwiss contributions to water hammer theoryrdquoJournal of Hydraulic Research vol 39 no 1 pp 3ndash7 2001

[17] M S Ghidaoui and B W Karney ldquoModified transformationand integration of 1D wave equationsrdquo Journal of HydraulicEngineering vol 121 no 10 pp 758ndash760 1995

[18] A Adamkowski and M Lewandowski ldquoCavitation character-istics of shutoff valves in numerical modeling of transientsin pipelines with column separationrdquo Journal of HydraulicEngineering vol 141 no 2 2015

[19] E Yao G Kember and D Hansen ldquoAnalysis of water hammerattenuation in applications with varying valve closure timesrdquoJournal of Engineering Mechanics vol 141 no 1 Article ID04014107 2014

[20] R Korbar Z Virag and M Savar ldquoTruncated method of char-acteristics for quasi-two-dimensional water hammer modelrdquoJournal of Hydraulic Engineering vol 140 no 6 Article ID04014013 2014

[21] M Rohani and M H Afshar ldquoSimulation of transient flowcaused by pump failure point-implicit method of characteris-ticsrdquo Annals of Nuclear Energy vol 37 no 12 pp 1742ndash17502010

[22] A Triki ldquoMultiple-grid finite element solution of the shallowwater equations water hammer phenomenonrdquo Computers ampFluids vol 90 pp 65ndash71 2014

[23] A Keramat A S Tijsseling Q Hou and A Ahmadi ldquoFluid-structure interactionwith pipe-wall viscoelasticity during waterhammerrdquo Journal of Fluids and Structures vol 28 pp 434ndash4552012

[24] S-G Kim K-B Lee and K-Y Kim ldquoWater hammer in thepump-rising pipeline system with an air chamberrdquo Journal ofHydrodynamics vol 26 no 6 pp 960ndash964 2014

[25] E B Wylie and V L Streeter Fluid Transients McGraw-HillNew York NY USA 1978

[26] W Wan W Huang and C Li ldquoSensitivity analysis for theresistance on the performance of a pressure vessel for waterhammer protectionrdquo Journal of Pressure Vessel TechnologymdashTransactions of the ASME vol 136 no 1 Article ID 011303 2014

[27] G De Martino F De Paola N Fontana and M GiugnildquoDiscussion of lsquosimple guide for design of air vessels forwater hammer protection of pumping linesrsquo by D StephensonrdquoJournal of Hydraulic Engineering vol 130 no 3 pp 273ndash2752004

[28] T S Lee ldquoAir influence on hydraulic transients on fluid systemwith air valvesrdquo Journal of Fluids Engineering vol 121 no 3 pp646ndash650 1999

[29] D Stephenson ldquoEffects of air valves and pipework on waterhammer pressuresrdquo Journal of Transportation Engineering vol123 no 2 pp 101ndash106 1997

International Journal of

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Journal of

Advances inOptoElectronics

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Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

Shock and Vibration 5

the best procedure for multistage valve-closing is consideredThe displacement of valve-closing at any time can be deter-mined through linear procedure in multistage valve closure

Through a large number of practical tests the valveclosure with a uniform or uniform variable speed is foundto have a small influence on the water hammer in the front23 of valve-closing stroke while there is a large influenceon the later 13 of valve-closing stroke Therefore the valveclosure process is divided into multistage By doing so the

uniform and uniform variable speeds are both introduced tovalve closure process In the following section we will discussuniform or uniform variable speed calculation method invalve closure process

Assuming that the times of valve-closing in multi-stageare 1198791 1198792 119879

119894 119879

119899 the corresponding displacements of

valve-closing are 1199041 1199042 119904

119894 119904

119899 Then the displacements

of valve-closing at any time 119905 are determined as follows

119904119894

=

1199041

1198791

119905 le 1198791 The 1st stage of valve-closing

1199041+1199042

1198792

(119905 minus 1198791) 119879

1le 119905 le 119879

1+ 1198792 The 2nd stage of valve-closing

1199041+ 1199042+ sdot sdot sdot + 119904

119894minus1+119904119894

119879119894

(119905 minus 119879119894minus1) 119879

1+ 1198792+ sdot sdot sdot + 119879

119894minus1le 119905 le 119879

1+ 1198792+ sdot sdot sdot + 119879

119894 The 119894 stage of valve-closing

1199041+ 1199042+ sdot sdot sdot + 119904

119894+ sdot sdot sdot +

119904119899

119879119899

(119905 minus 119879119899minus1) 1198791+ 1198792+ sdot sdot sdot + 119879

119894+ sdot sdot sdot + 119879

119899minus1le 119905 le 119879

1+ 1198792+ sdot sdot sdot + 119879

119894+ sdot sdot sdot + 119879

119899 The 119899 stage of valve-closing

1199041+ 1199042+ sdot sdot sdot + 119904

119894+ 119904119899= 119878 119905 gt 119879

1+ 1198792+ sdot sdot sdot + 119879

119894+ 119879119899 valve-closing is completed

(21)

where 119904119894is displacement of valve-closing at 119905 and 119878 is the total

stroke of valve-closingFor the valve-closing displacement 119904

119894at any time 119905 we

can calculate the dimensionless opening degree 120591 using (21)through linear interpolation according to equidistantΔ119904

119894and

its input value

120591 = 120591 (119894) +119906(119896)

2[120591 (119894 + 1) minus 119896120591 (119894)] 120591 (119894)

+119906(119896minus1)

2[120591 (119894 + 1) minus (119896 minus 1) 120591 (119894)] + sdot sdot sdot

+1199062

2[120591 (119894 + 1) minus 2120591 (119894)]

+119906

2[120591 (119894 + 1) minus 120591 (119894)]

119906 =119904119894minus 1199040

Δ119904119894

minus 1

(22)

In the scope of velocity adjustment for HCV the velocitydisplacement and time of valve-closing have various combi-nations This paper adopts a multistage adjustment strategyaccording to simulation results of water hammer

The valve closure time for the first stage is equal or closeto the time of the flow of pump that is zero The valve closuretime for the following stages is one in four of the previousstage Consequently the initial valve closure procedure isdetermined Then search computing is taken to determinethe optimization valve closure procedure

4 Case Study and Experiment

41Working Conditions Themine with normal water qualitywas consideredThewater normal inflowwas 50m3h and themaximum inflow was 250m3h Water was discharged into

ground by two drain pipes of which the specifications wereD273times 12 respectively (one was used and another was spare)The pipes in this existing and antiquated mine drainagesystem were seamless steel pipe The allowed pressure was aslower at 64MPa The wellhead elevation was 997991m andthe borehole inclination was 20∘ There were three multistagecentrifugal pumps and two HCVs were used in Figure 3And the specification of pumps was MD280-65 times 6 (119876 =

280m3h119867 = 390m) One pump was used and others weremaintenance when themine was with a normal inflow or twopumps were used and one was spare when the mine was witha maximum inflow

The automatic drainage system was chosen in this mineCheck valves were installed in pump outlet There are HCVsin pipeline shown in Figure 3(a)where the strokewas 220mmwith the structure of HCV shown in Figure 4 During normalpump stoppingHCVswere closed first and then pumpswerestopped The water hammer phenomenon was significant indrains pipeline during this processTherefore we should takesome measures to prevent the water hammer phenomenon

42 Simulations An algorithm was developed using com-mercial simulation software Fluent63 based on the waterhammer theory described in Section 2 The accelerationamplitude pipeline pressure and valve closure displacementwere obtained in the cases of uniform and uniform variablespeed through transient simulation for water hammer Thecorrectness of simulation and the proposed theory werethen verified against experimental results We simulated thevalve-closing in single-stage with a constant velocity and inmultistage with a variable velocity based on the proposedtheory

(1) The Simulation of Valve-Closing in Single-Stage with aConstant Velocity The velocity V = 001ms of valve-closingin single-stage was determined through repeated simulation

6 Shock and Vibration

HCVs

Pump

(a) (b)

Figure 3 Diagram of drain pipes

(1)

(1) Hydraulic system

(2)

(2) Explosion-proof motors

(3)

(3) Valve body

Figure 4 Structure diagram of HCV

Then times of equipment in this situation were obtainedusing (20) to (21) as shown in Table 1

The simulation results of valve-closing parameters insingle-stage with 001ms are shown in Figures 5ndash12

For Figures 5ndash12 the static pressure of pipeline wasat 306MPa for pump stopping After the vacuum wascompleted the pump was started and HCV was open witha constant velocity At this moment pipeline pressure wasincreased alongwith the valve-opening displacement ofHCVThen pressure fluctuations appearedThe valve-opening dis-placement of HCV was 426mm and the maximum pressurewas 384MPa when 119905 = 12148 s After this momentthe pressure was steady The valve-opening displacement ofHCV was 702mm and the maximum pressure was 325MPawhen 119905 = 15244 s The drainage system pressure reacheda steady state along with the increasing of valve-openingdisplacement The pressure of pipeline began to drop when119905 = 62436 s and valve-closing displacement was 534mmWater hammer phenomenon appeared when 119905 = 67211 sWhen 119905 = 706 s the maximum boost of water hammer wasΔ119867 = 152m and the pressure of pipeline at this moment

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

x

Figure 5 Acceleration in 119909

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

x

S(m

m)

Figure 6 Amplitude in 119909

was 477Mpa It is 147 times the normal discharge pressure(325MPa) and the pressure increased by 50 suddenly Theacceleration and amplitude of pipeline in directions of 119909119910 and 119911 were changed significantly when water hammeroccurred Maximum acceleration in directions of 119909 119910 and119911 was 483ms2 646ms2 and 545ms2 and the maximumamplitude was 158mm 258mm and 153mm respectivelyAdditionally the total stroke of HCV was assumed to be 119878Valve-closing with rapid and constant velocity were taken

Shock and Vibration 7

Table 1 Times of equipment in single-stage valve-closing

Equipment actions Pump start Valve-opening Full open Valve-closing Valve closed Water hammer finished Total timesTimes 119905 (s) 4128 7883 31590 46007 67934 110500 21927

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

y

Figure 7 Acceleration in 119910

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

y

S(m

m)

Figure 8 Amplitude in 119910

z

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

Figure 9 Acceleration in 119911

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

z

S(m

m)

Figure 10 Amplitude in 119911

0 10 20 30 40 50 60 70 80 90 100 11010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

Figure 11 Pressure in pipeline

0 10 20 30 40 50 60 70 80 90 100t (s)

020406080

100120140160180200220240260

S(m

m)

Figure 12 Amplitude of HCV

8 Shock and Vibration

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus10minus9minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

x

Figure 13 Acceleration in 119909

in the former 21198783 and a variable velocity was taken in thelatter 1198783 according to the simulation results of valve-closingwater hammer Due to the velocity of valve-closing that hasa large impact on water hammer parameters it is an effectiveapproach to protect water hammer by choosing a reasonablevelocity for valve-closing

The allowed pressure of pipe is lower and its value was64MPa However the pressure of pipeline reached 48MPain the case of 22 s valve-closing from the above analysis Thisvalue is near to the allowed pressure of pipe with the pressurebeing not high and the water hammer phenomenon was notsignificant compared with other mine drainage systems Inorder to reduce the pressure of pipeline to protection pipelineit is necessary to develop water hammer protection

(2) The Simulation of Valve-Closing in Multistage with aVariable Velocity The optimization strategy of valve-closingadjustment for HCV is generated using boundary condi-tions according to optimization method of valve-closingadjustment that is proposed in this paper It is a multistagevalve-closing with a variable velocity In the front 23 ofvalve-closing stroke the velocity is constant and its value is001ms In the later 13 of valve-closing stroke the velocity isa variable (the deceleration is constant) and the initial value is001ms The total time of valve-closing is 43823 s Times ofequipment in multistage valve-closing are shown in Table 2

The simulation results of valve-closing parameters inmultistage are shown in Figures 13ndash20

The pipeline pressuring acceleration and amplitude inthe directions of 119909 119910 and 119911 are significantly reducedin multistage valve-closing with a variable velocity Valve-closing with a constant velocity is started at 46007 s andvalve-closing with a variable velocity is started at 606 s TheHCVs are closed and pumps are stopped at 8983 s In thisprocess themaximumpressure ofwater hammer is 349MPaNo effect of water hammer occurred under this situation

43 Experiments The experimental devices include multi-function data acquisition instrument vibration sensor pres-sure sensors and cable displacement encoder Multifunction

x

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

S(m

m)

Figure 14 Amplitude in 119909

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus10minus9minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

y

Figure 15 Acceleration in 119910

data acquisition instrument has 16 channels and its acqui-sition frequency is 1024 kHz Data of acceleration ampli-tude flow pressure and displacement of valve-closing wereacquired by this multifunction data acquisition instrumentVibration sensor was used to measure piping vibration underthe influence of water hammer It was disposed along withthe 119909 119910 and 119911 direction of the pipe Pressure sensors wereused to measure pipeline pressure Its measurement accuracyand range are 0ndash10MPa and plusmn05 FS Cable displacementencoder was used to posit the displacement of valve-closingThe arrangement diagram of sensors and flow chart of pumpsare shown in Figures 21 and 22

HCVs control system was designed in this experimentwhich is shown in Figure 23 Sensors were used to collectsignals of pressure and acceleration in pipeline PLC unitwas used to analyze pipeline pressure and vibration for waterhammer on the basis of pressure and acceleration signalsAn expected running speed was given to HCVs And thenvoltage current power and fault protection informationof pumps pressure flow temperature vacuum and HCVsstatus information were monitored at real time These multi-parameter data were integrated using of fuzzy control theorywith calculus and control strategy The HCVs control system

Shock and Vibration 9

Table 2 Times of equipment in multistage valve-closing

Equipment actions Pump start Valve-opening Full open Valve-closing Valve closed Water hammer finished Total timesTimes 119905 (s) 4128 85 39504 46007 89830 128816 43823

y

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20minus15minus10minus5

05

1015202530

t (s)

S(m

m)

Figure 16 Amplitude in 119910

0 10 20 30 40 50 60 70 80 90 100 110 120 130

minus9minus10

minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

z

Figure 17 Acceleration in 119911

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

S(m

m)

z

t (s)

Figure 18 Amplitude in 119911

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

Figure 19 Pressure in pipeline

020406080

100120140160180200220240260280

S(m

m)

0 10 20 30 40 50 60 70 80 90 100 110t (s)

Figure 20 Displacement of HCV

can control starting and stopping of pumps automatically andcan monitor the signals in system running process timely

For the total stroke of valve 119878 the experimental conditionsare as follows In the front 23 of the stroke the velocitywas constant and its value was 001ms In the later 13the velocity is variable (the deceleration is constant) andthe initial value was 001ms The full valve-closing timeswere 44 s Measured values of water hammer parameters inmultistage are shown in Table 3

10 Shock and Vibration

sensor

sensor

Pressuresensor

Pressuregauge

Negativepressure sensor

Jet valves Hydrostatic pipe

Flow sensor Pressure sensor

Drain pipe

Drain pipe

Drain pipe

A-A

X vibration

Z vibration

Y vibration sensor

Figure 21 Arrangement diagram of sensors

Data collection isbeginning

Pump start

Valve start

Full valve opening

Normal drainage

Valve-closing start

Valve closed

Pump stop

Water hammer is finishedData collection is finished

Phase 1

Pump start

Phase 2Pump running

Phase 3Pump stopping

Figure 22 The flow chart of test for pumps

Shock and Vibration 11

HCVs PLC unit

Acceleration sensor

Pressure sensor

PC

Other sensors and execution system

Opticalfiber

Closed-loop control of waterhammer protection

Figure 23 Composition of HCVs control system

Table 3 Measured values of water hammer parameters

Measured parameters Acceleration (ms2) Displacement (mm) Pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Valve-closing times (s)22 48308 64582 54457 157662 285192 153051 4586525 48207 64581 54453 157515 285139 153012 4556428 47986 63215 54394 157495 284632 152036 4495231 45689 61265 52563 136938 268576 130369 4467833 45389 61063 51935 135963 246985 126325 4461236 43236 59638 50632 126985 238965 117652 4267539 17231 11023 16352 92514 63656 113251 3561542 17016 10363 15426 90356 61563 109968 3542344 16987 08692 14112 89482 59354 106432 3500648 16886 08629 14003 89235 59139 106365 35006

5 Results and Discussion

The reliability and effectiveness are illustrated through thecomparison between the results of simulation and experi-ment

(1) Results of Valve-Closing in Single-Stage with a ConstantVelocity and in Multistage with a Variable Velocity AreCompared Pipeline pressures and displacements of valve-opening under these two conditions are shown in Figures 24and 25 respectively The red curves represent the variationsin single-stage with a constant velocity while the black curvesrepresent the variations formultistagewith a variable velocity

Figures 24 and 25 show a significant water hammer effectin single-stage valve-closing with a constant velocity andthe valve-closing time is shorter (22 s) On the other handwater hammer phenomenon was found to be considerablyimproved for multistage valve-closing condition with a vari-able velocity and the valve-closing timewas extended (44 s) Itshows that valve-closing inmultistage with a variable velocitycan control the water hammer phenomenon effective inminedrainage system

(2) Results of the Simulation and Experiment Are Also Com-pared Results for valve-closing with a variable velocity areshown in Table 4

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

PZCPZD

Figure 24 Pressure in pipeline

It can be seen from Table 4 that the simulation forvalve-closing with a variable velocity shows good agreementwith the experiment The errors between simulation andexperiment are less than 5 Therefore the valve-closing in

12 Shock and Vibration

Table 4 Results comparison of simulation and experiment

Parameters Max acceleration (ms2) Max displacement (mm) Max pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Simulation 45830 62672 52341 165122 273335 148726 45798Experiment 48308 64582 54457 157660 285192 153051 45867Errors 46 29 39 47 42 28 02Simulation 16876 08446 13651 86395 56689 104653 34901Experiment 16987 08692 14112 89482 59354 106432 35006Errors 07 28 33 34 44 17 03

0 10 20 30 40 50 60 70 80 90 1000

20406080

100120140160180200220240

t (s)

S(m

m)

S1(FM)S2(FM)

Figure 25 Displacement of HCV

multistagewith a variable velocity can reduce the impact fromwater hammer in mine drainage system

6 Conclusions and Future Work

Limited space and high cost of equipment changing arethe main characteristics for mine drainage system For theproblem of valve-closing water hammer protection in minedrainage system this paper proposed a protection methodbased on velocity adjustment of HCVs The mathematicmodel of valve-closing water hammer is established basedon fundamental equations The strategy of valve-closing inmultistage with a variable velocity is obtained by velocityadjustment strategy of HCVs and it is effective in protect-ing the valve-closing water hammer without change pipingarrangement or addition equipment The results of simula-tions and experiments in different adjustment velocity arecomparedWe obtained that the water hammer phenomenonis not obvious with valve-closing velocity in the front 23 of itsstroke and it is very seriously within the later 13 Thereforewe take a two-stage valve-closing strategy In the first stagethe velocity is constant and its value is 001ms In the secondstage the velocity is variable (the deceleration is constant) andthe initial value is 001ms

Extending errors in the theoretical wave speed havean important influence on prediction of the closure rate

before a water hammer occurs in the actual pipeline A verychallenging mathematical task is variable This is beyond thescope of this paper and may be considered as a future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National 125 Tech-nology Support Program of China under Grant noSQ2012BAJY3504

References

[1] M Sun X-R Ru and L-F Zhai ldquoIn-situ fabrication ofsupported iron oxides from synthetic acid mine drainage highcatalytic activities and good stabilities towards electro-Fentonreactionrdquo Applied Catalysis B Environmental vol 165 pp 103ndash110 2015

[2] A Kaliatka M Vaisnoras and M Valincius ldquoModelling ofvalve induced water hammer phenomena in a district heatingsystemrdquo Computers amp Fluids vol 94 pp 30ndash36 2014

[3] N Jeong D Chi and J Yoon ldquoAnalytic estimation of the impactpressure in a beam-tube due to water-hammer effectrdquo Journalof Nuclear Science and Technology vol 50 no 12 pp 1139ndash11492013

[4] W S Yi J Jiang D D Li G Lan and Z Zhao ldquoPump-stoppingwater hammer simulation based on RELAP5rdquo IOP ConferenceSeries Materials Science and Engineering vol 52 no 7 ArticleID 072009 2013

[5] Q W Yong M Jiang and Y Tang ldquoStudy on liquid pipelinewater hammer and protective device with gas concentrationrdquoAdvanced Materials Research vol 616ndash618 pp 774ndash777 2013

[6] J Zhang J Gao M Diao W Wu T Wang and S Qi ldquoA casestudy on risk assessment of long distance water supply systemrdquoProcedia Engineering vol 70 pp 1762ndash1771 2014

[7] K I M Sang-Gyun L E E Kye-Bock and K I M Kyung-YupldquoWater hammer in the pump-rising pipeline system with an airchamberrdquo Journal of Hydrodynamics Series B vol 26 no 6 pp960ndash964 2015

[8] M A Bouaziz M A Guidara C Schmitt E Hadj-Taıeb and ZAzari ldquoWater hammer effects on a gray cast iron water networkafter adding pumpsrdquo Engineering Failure Analysis vol 44 pp1ndash16 2014

Shock and Vibration 13

[9] M S Ghidaoui M Zhao D A McInnis and D H AxworthyldquoA review of water hammer theory and practicerdquo AppliedMechanics Reviews vol 58 no 1ndash6 pp 49ndash76 2005

[10] A F Colombo P Lee and B W Karney ldquoA selective literaturereview of transient-based leak detection methodsrdquo Journal ofHydro-Environment Research vol 2 no 4 pp 212ndash227 2009

[11] P J Lee M F Lambert A R Simpson J P Vıtkovsky andD Misiunas ldquoLeak location in single pipelines using transientreflectionsrdquo Australian Journal of Water Resources vol 11 no 1pp 53ndash65 2007

[12] N S Arbon M F Lambert A R Simpson andM L StephensldquoField test investigations into distributed fault modeling inwater distribution systems using transient testingrdquo in Proceed-ings of the World Environmental and Water Resources CongressTampa Fla USA May 2007

[13] J Gong A R SimpsonM F Lambert A C Zecchin Y-I Kimand A S Tijsseling ldquoDetection of distributed deteriorationin single pipes using transient reflectionsrdquo Journal of PipelineSystems Engineering and Practice vol 4 no 1 pp 32ndash40 2013

[14] M Ferrante B Brunone and S Meniconi ldquoLeak detectionin branched pipe systems coupling wavelet analysis and aLagrangian modelrdquo Journal of Water Supply Research andTechnology vol 58 no 2 pp 95ndash106 2009

[15] S Meniconi B Brunone and M Ferrante ldquoWater-hammerpressure waves interaction at cross-section changes in series inviscoelastic pipesrdquo Journal of Fluids and Structures vol 33 pp44ndash58 2012

[16] W H Hager ldquoSwiss contributions to water hammer theoryrdquoJournal of Hydraulic Research vol 39 no 1 pp 3ndash7 2001

[17] M S Ghidaoui and B W Karney ldquoModified transformationand integration of 1D wave equationsrdquo Journal of HydraulicEngineering vol 121 no 10 pp 758ndash760 1995

[18] A Adamkowski and M Lewandowski ldquoCavitation character-istics of shutoff valves in numerical modeling of transientsin pipelines with column separationrdquo Journal of HydraulicEngineering vol 141 no 2 2015

[19] E Yao G Kember and D Hansen ldquoAnalysis of water hammerattenuation in applications with varying valve closure timesrdquoJournal of Engineering Mechanics vol 141 no 1 Article ID04014107 2014

[20] R Korbar Z Virag and M Savar ldquoTruncated method of char-acteristics for quasi-two-dimensional water hammer modelrdquoJournal of Hydraulic Engineering vol 140 no 6 Article ID04014013 2014

[21] M Rohani and M H Afshar ldquoSimulation of transient flowcaused by pump failure point-implicit method of characteris-ticsrdquo Annals of Nuclear Energy vol 37 no 12 pp 1742ndash17502010

[22] A Triki ldquoMultiple-grid finite element solution of the shallowwater equations water hammer phenomenonrdquo Computers ampFluids vol 90 pp 65ndash71 2014

[23] A Keramat A S Tijsseling Q Hou and A Ahmadi ldquoFluid-structure interactionwith pipe-wall viscoelasticity during waterhammerrdquo Journal of Fluids and Structures vol 28 pp 434ndash4552012

[24] S-G Kim K-B Lee and K-Y Kim ldquoWater hammer in thepump-rising pipeline system with an air chamberrdquo Journal ofHydrodynamics vol 26 no 6 pp 960ndash964 2014

[25] E B Wylie and V L Streeter Fluid Transients McGraw-HillNew York NY USA 1978

[26] W Wan W Huang and C Li ldquoSensitivity analysis for theresistance on the performance of a pressure vessel for waterhammer protectionrdquo Journal of Pressure Vessel TechnologymdashTransactions of the ASME vol 136 no 1 Article ID 011303 2014

[27] G De Martino F De Paola N Fontana and M GiugnildquoDiscussion of lsquosimple guide for design of air vessels forwater hammer protection of pumping linesrsquo by D StephensonrdquoJournal of Hydraulic Engineering vol 130 no 3 pp 273ndash2752004

[28] T S Lee ldquoAir influence on hydraulic transients on fluid systemwith air valvesrdquo Journal of Fluids Engineering vol 121 no 3 pp646ndash650 1999

[29] D Stephenson ldquoEffects of air valves and pipework on waterhammer pressuresrdquo Journal of Transportation Engineering vol123 no 2 pp 101ndash106 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Shock and Vibration

HCVs

Pump

(a) (b)

Figure 3 Diagram of drain pipes

(1)

(1) Hydraulic system

(2)

(2) Explosion-proof motors

(3)

(3) Valve body

Figure 4 Structure diagram of HCV

Then times of equipment in this situation were obtainedusing (20) to (21) as shown in Table 1

The simulation results of valve-closing parameters insingle-stage with 001ms are shown in Figures 5ndash12

For Figures 5ndash12 the static pressure of pipeline wasat 306MPa for pump stopping After the vacuum wascompleted the pump was started and HCV was open witha constant velocity At this moment pipeline pressure wasincreased alongwith the valve-opening displacement ofHCVThen pressure fluctuations appearedThe valve-opening dis-placement of HCV was 426mm and the maximum pressurewas 384MPa when 119905 = 12148 s After this momentthe pressure was steady The valve-opening displacement ofHCV was 702mm and the maximum pressure was 325MPawhen 119905 = 15244 s The drainage system pressure reacheda steady state along with the increasing of valve-openingdisplacement The pressure of pipeline began to drop when119905 = 62436 s and valve-closing displacement was 534mmWater hammer phenomenon appeared when 119905 = 67211 sWhen 119905 = 706 s the maximum boost of water hammer wasΔ119867 = 152m and the pressure of pipeline at this moment

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

x

Figure 5 Acceleration in 119909

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

x

S(m

m)

Figure 6 Amplitude in 119909

was 477Mpa It is 147 times the normal discharge pressure(325MPa) and the pressure increased by 50 suddenly Theacceleration and amplitude of pipeline in directions of 119909119910 and 119911 were changed significantly when water hammeroccurred Maximum acceleration in directions of 119909 119910 and119911 was 483ms2 646ms2 and 545ms2 and the maximumamplitude was 158mm 258mm and 153mm respectivelyAdditionally the total stroke of HCV was assumed to be 119878Valve-closing with rapid and constant velocity were taken

Shock and Vibration 7

Table 1 Times of equipment in single-stage valve-closing

Equipment actions Pump start Valve-opening Full open Valve-closing Valve closed Water hammer finished Total timesTimes 119905 (s) 4128 7883 31590 46007 67934 110500 21927

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

y

Figure 7 Acceleration in 119910

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

y

S(m

m)

Figure 8 Amplitude in 119910

z

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

Figure 9 Acceleration in 119911

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

z

S(m

m)

Figure 10 Amplitude in 119911

0 10 20 30 40 50 60 70 80 90 100 11010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

Figure 11 Pressure in pipeline

0 10 20 30 40 50 60 70 80 90 100t (s)

020406080

100120140160180200220240260

S(m

m)

Figure 12 Amplitude of HCV

8 Shock and Vibration

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus10minus9minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

x

Figure 13 Acceleration in 119909

in the former 21198783 and a variable velocity was taken in thelatter 1198783 according to the simulation results of valve-closingwater hammer Due to the velocity of valve-closing that hasa large impact on water hammer parameters it is an effectiveapproach to protect water hammer by choosing a reasonablevelocity for valve-closing

The allowed pressure of pipe is lower and its value was64MPa However the pressure of pipeline reached 48MPain the case of 22 s valve-closing from the above analysis Thisvalue is near to the allowed pressure of pipe with the pressurebeing not high and the water hammer phenomenon was notsignificant compared with other mine drainage systems Inorder to reduce the pressure of pipeline to protection pipelineit is necessary to develop water hammer protection

(2) The Simulation of Valve-Closing in Multistage with aVariable Velocity The optimization strategy of valve-closingadjustment for HCV is generated using boundary condi-tions according to optimization method of valve-closingadjustment that is proposed in this paper It is a multistagevalve-closing with a variable velocity In the front 23 ofvalve-closing stroke the velocity is constant and its value is001ms In the later 13 of valve-closing stroke the velocity isa variable (the deceleration is constant) and the initial value is001ms The total time of valve-closing is 43823 s Times ofequipment in multistage valve-closing are shown in Table 2

The simulation results of valve-closing parameters inmultistage are shown in Figures 13ndash20

The pipeline pressuring acceleration and amplitude inthe directions of 119909 119910 and 119911 are significantly reducedin multistage valve-closing with a variable velocity Valve-closing with a constant velocity is started at 46007 s andvalve-closing with a variable velocity is started at 606 s TheHCVs are closed and pumps are stopped at 8983 s In thisprocess themaximumpressure ofwater hammer is 349MPaNo effect of water hammer occurred under this situation

43 Experiments The experimental devices include multi-function data acquisition instrument vibration sensor pres-sure sensors and cable displacement encoder Multifunction

x

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

S(m

m)

Figure 14 Amplitude in 119909

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus10minus9minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

y

Figure 15 Acceleration in 119910

data acquisition instrument has 16 channels and its acqui-sition frequency is 1024 kHz Data of acceleration ampli-tude flow pressure and displacement of valve-closing wereacquired by this multifunction data acquisition instrumentVibration sensor was used to measure piping vibration underthe influence of water hammer It was disposed along withthe 119909 119910 and 119911 direction of the pipe Pressure sensors wereused to measure pipeline pressure Its measurement accuracyand range are 0ndash10MPa and plusmn05 FS Cable displacementencoder was used to posit the displacement of valve-closingThe arrangement diagram of sensors and flow chart of pumpsare shown in Figures 21 and 22

HCVs control system was designed in this experimentwhich is shown in Figure 23 Sensors were used to collectsignals of pressure and acceleration in pipeline PLC unitwas used to analyze pipeline pressure and vibration for waterhammer on the basis of pressure and acceleration signalsAn expected running speed was given to HCVs And thenvoltage current power and fault protection informationof pumps pressure flow temperature vacuum and HCVsstatus information were monitored at real time These multi-parameter data were integrated using of fuzzy control theorywith calculus and control strategy The HCVs control system

Shock and Vibration 9

Table 2 Times of equipment in multistage valve-closing

Equipment actions Pump start Valve-opening Full open Valve-closing Valve closed Water hammer finished Total timesTimes 119905 (s) 4128 85 39504 46007 89830 128816 43823

y

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20minus15minus10minus5

05

1015202530

t (s)

S(m

m)

Figure 16 Amplitude in 119910

0 10 20 30 40 50 60 70 80 90 100 110 120 130

minus9minus10

minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

z

Figure 17 Acceleration in 119911

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

S(m

m)

z

t (s)

Figure 18 Amplitude in 119911

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

Figure 19 Pressure in pipeline

020406080

100120140160180200220240260280

S(m

m)

0 10 20 30 40 50 60 70 80 90 100 110t (s)

Figure 20 Displacement of HCV

can control starting and stopping of pumps automatically andcan monitor the signals in system running process timely

For the total stroke of valve 119878 the experimental conditionsare as follows In the front 23 of the stroke the velocitywas constant and its value was 001ms In the later 13the velocity is variable (the deceleration is constant) andthe initial value was 001ms The full valve-closing timeswere 44 s Measured values of water hammer parameters inmultistage are shown in Table 3

10 Shock and Vibration

sensor

sensor

Pressuresensor

Pressuregauge

Negativepressure sensor

Jet valves Hydrostatic pipe

Flow sensor Pressure sensor

Drain pipe

Drain pipe

Drain pipe

A-A

X vibration

Z vibration

Y vibration sensor

Figure 21 Arrangement diagram of sensors

Data collection isbeginning

Pump start

Valve start

Full valve opening

Normal drainage

Valve-closing start

Valve closed

Pump stop

Water hammer is finishedData collection is finished

Phase 1

Pump start

Phase 2Pump running

Phase 3Pump stopping

Figure 22 The flow chart of test for pumps

Shock and Vibration 11

HCVs PLC unit

Acceleration sensor

Pressure sensor

PC

Other sensors and execution system

Opticalfiber

Closed-loop control of waterhammer protection

Figure 23 Composition of HCVs control system

Table 3 Measured values of water hammer parameters

Measured parameters Acceleration (ms2) Displacement (mm) Pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Valve-closing times (s)22 48308 64582 54457 157662 285192 153051 4586525 48207 64581 54453 157515 285139 153012 4556428 47986 63215 54394 157495 284632 152036 4495231 45689 61265 52563 136938 268576 130369 4467833 45389 61063 51935 135963 246985 126325 4461236 43236 59638 50632 126985 238965 117652 4267539 17231 11023 16352 92514 63656 113251 3561542 17016 10363 15426 90356 61563 109968 3542344 16987 08692 14112 89482 59354 106432 3500648 16886 08629 14003 89235 59139 106365 35006

5 Results and Discussion

The reliability and effectiveness are illustrated through thecomparison between the results of simulation and experi-ment

(1) Results of Valve-Closing in Single-Stage with a ConstantVelocity and in Multistage with a Variable Velocity AreCompared Pipeline pressures and displacements of valve-opening under these two conditions are shown in Figures 24and 25 respectively The red curves represent the variationsin single-stage with a constant velocity while the black curvesrepresent the variations formultistagewith a variable velocity

Figures 24 and 25 show a significant water hammer effectin single-stage valve-closing with a constant velocity andthe valve-closing time is shorter (22 s) On the other handwater hammer phenomenon was found to be considerablyimproved for multistage valve-closing condition with a vari-able velocity and the valve-closing timewas extended (44 s) Itshows that valve-closing inmultistage with a variable velocitycan control the water hammer phenomenon effective inminedrainage system

(2) Results of the Simulation and Experiment Are Also Com-pared Results for valve-closing with a variable velocity areshown in Table 4

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

PZCPZD

Figure 24 Pressure in pipeline

It can be seen from Table 4 that the simulation forvalve-closing with a variable velocity shows good agreementwith the experiment The errors between simulation andexperiment are less than 5 Therefore the valve-closing in

12 Shock and Vibration

Table 4 Results comparison of simulation and experiment

Parameters Max acceleration (ms2) Max displacement (mm) Max pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Simulation 45830 62672 52341 165122 273335 148726 45798Experiment 48308 64582 54457 157660 285192 153051 45867Errors 46 29 39 47 42 28 02Simulation 16876 08446 13651 86395 56689 104653 34901Experiment 16987 08692 14112 89482 59354 106432 35006Errors 07 28 33 34 44 17 03

0 10 20 30 40 50 60 70 80 90 1000

20406080

100120140160180200220240

t (s)

S(m

m)

S1(FM)S2(FM)

Figure 25 Displacement of HCV

multistagewith a variable velocity can reduce the impact fromwater hammer in mine drainage system

6 Conclusions and Future Work

Limited space and high cost of equipment changing arethe main characteristics for mine drainage system For theproblem of valve-closing water hammer protection in minedrainage system this paper proposed a protection methodbased on velocity adjustment of HCVs The mathematicmodel of valve-closing water hammer is established basedon fundamental equations The strategy of valve-closing inmultistage with a variable velocity is obtained by velocityadjustment strategy of HCVs and it is effective in protect-ing the valve-closing water hammer without change pipingarrangement or addition equipment The results of simula-tions and experiments in different adjustment velocity arecomparedWe obtained that the water hammer phenomenonis not obvious with valve-closing velocity in the front 23 of itsstroke and it is very seriously within the later 13 Thereforewe take a two-stage valve-closing strategy In the first stagethe velocity is constant and its value is 001ms In the secondstage the velocity is variable (the deceleration is constant) andthe initial value is 001ms

Extending errors in the theoretical wave speed havean important influence on prediction of the closure rate

before a water hammer occurs in the actual pipeline A verychallenging mathematical task is variable This is beyond thescope of this paper and may be considered as a future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National 125 Tech-nology Support Program of China under Grant noSQ2012BAJY3504

References

[1] M Sun X-R Ru and L-F Zhai ldquoIn-situ fabrication ofsupported iron oxides from synthetic acid mine drainage highcatalytic activities and good stabilities towards electro-Fentonreactionrdquo Applied Catalysis B Environmental vol 165 pp 103ndash110 2015

[2] A Kaliatka M Vaisnoras and M Valincius ldquoModelling ofvalve induced water hammer phenomena in a district heatingsystemrdquo Computers amp Fluids vol 94 pp 30ndash36 2014

[3] N Jeong D Chi and J Yoon ldquoAnalytic estimation of the impactpressure in a beam-tube due to water-hammer effectrdquo Journalof Nuclear Science and Technology vol 50 no 12 pp 1139ndash11492013

[4] W S Yi J Jiang D D Li G Lan and Z Zhao ldquoPump-stoppingwater hammer simulation based on RELAP5rdquo IOP ConferenceSeries Materials Science and Engineering vol 52 no 7 ArticleID 072009 2013

[5] Q W Yong M Jiang and Y Tang ldquoStudy on liquid pipelinewater hammer and protective device with gas concentrationrdquoAdvanced Materials Research vol 616ndash618 pp 774ndash777 2013

[6] J Zhang J Gao M Diao W Wu T Wang and S Qi ldquoA casestudy on risk assessment of long distance water supply systemrdquoProcedia Engineering vol 70 pp 1762ndash1771 2014

[7] K I M Sang-Gyun L E E Kye-Bock and K I M Kyung-YupldquoWater hammer in the pump-rising pipeline system with an airchamberrdquo Journal of Hydrodynamics Series B vol 26 no 6 pp960ndash964 2015

[8] M A Bouaziz M A Guidara C Schmitt E Hadj-Taıeb and ZAzari ldquoWater hammer effects on a gray cast iron water networkafter adding pumpsrdquo Engineering Failure Analysis vol 44 pp1ndash16 2014

Shock and Vibration 13

[9] M S Ghidaoui M Zhao D A McInnis and D H AxworthyldquoA review of water hammer theory and practicerdquo AppliedMechanics Reviews vol 58 no 1ndash6 pp 49ndash76 2005

[10] A F Colombo P Lee and B W Karney ldquoA selective literaturereview of transient-based leak detection methodsrdquo Journal ofHydro-Environment Research vol 2 no 4 pp 212ndash227 2009

[11] P J Lee M F Lambert A R Simpson J P Vıtkovsky andD Misiunas ldquoLeak location in single pipelines using transientreflectionsrdquo Australian Journal of Water Resources vol 11 no 1pp 53ndash65 2007

[12] N S Arbon M F Lambert A R Simpson andM L StephensldquoField test investigations into distributed fault modeling inwater distribution systems using transient testingrdquo in Proceed-ings of the World Environmental and Water Resources CongressTampa Fla USA May 2007

[13] J Gong A R SimpsonM F Lambert A C Zecchin Y-I Kimand A S Tijsseling ldquoDetection of distributed deteriorationin single pipes using transient reflectionsrdquo Journal of PipelineSystems Engineering and Practice vol 4 no 1 pp 32ndash40 2013

[14] M Ferrante B Brunone and S Meniconi ldquoLeak detectionin branched pipe systems coupling wavelet analysis and aLagrangian modelrdquo Journal of Water Supply Research andTechnology vol 58 no 2 pp 95ndash106 2009

[15] S Meniconi B Brunone and M Ferrante ldquoWater-hammerpressure waves interaction at cross-section changes in series inviscoelastic pipesrdquo Journal of Fluids and Structures vol 33 pp44ndash58 2012

[16] W H Hager ldquoSwiss contributions to water hammer theoryrdquoJournal of Hydraulic Research vol 39 no 1 pp 3ndash7 2001

[17] M S Ghidaoui and B W Karney ldquoModified transformationand integration of 1D wave equationsrdquo Journal of HydraulicEngineering vol 121 no 10 pp 758ndash760 1995

[18] A Adamkowski and M Lewandowski ldquoCavitation character-istics of shutoff valves in numerical modeling of transientsin pipelines with column separationrdquo Journal of HydraulicEngineering vol 141 no 2 2015

[19] E Yao G Kember and D Hansen ldquoAnalysis of water hammerattenuation in applications with varying valve closure timesrdquoJournal of Engineering Mechanics vol 141 no 1 Article ID04014107 2014

[20] R Korbar Z Virag and M Savar ldquoTruncated method of char-acteristics for quasi-two-dimensional water hammer modelrdquoJournal of Hydraulic Engineering vol 140 no 6 Article ID04014013 2014

[21] M Rohani and M H Afshar ldquoSimulation of transient flowcaused by pump failure point-implicit method of characteris-ticsrdquo Annals of Nuclear Energy vol 37 no 12 pp 1742ndash17502010

[22] A Triki ldquoMultiple-grid finite element solution of the shallowwater equations water hammer phenomenonrdquo Computers ampFluids vol 90 pp 65ndash71 2014

[23] A Keramat A S Tijsseling Q Hou and A Ahmadi ldquoFluid-structure interactionwith pipe-wall viscoelasticity during waterhammerrdquo Journal of Fluids and Structures vol 28 pp 434ndash4552012

[24] S-G Kim K-B Lee and K-Y Kim ldquoWater hammer in thepump-rising pipeline system with an air chamberrdquo Journal ofHydrodynamics vol 26 no 6 pp 960ndash964 2014

[25] E B Wylie and V L Streeter Fluid Transients McGraw-HillNew York NY USA 1978

[26] W Wan W Huang and C Li ldquoSensitivity analysis for theresistance on the performance of a pressure vessel for waterhammer protectionrdquo Journal of Pressure Vessel TechnologymdashTransactions of the ASME vol 136 no 1 Article ID 011303 2014

[27] G De Martino F De Paola N Fontana and M GiugnildquoDiscussion of lsquosimple guide for design of air vessels forwater hammer protection of pumping linesrsquo by D StephensonrdquoJournal of Hydraulic Engineering vol 130 no 3 pp 273ndash2752004

[28] T S Lee ldquoAir influence on hydraulic transients on fluid systemwith air valvesrdquo Journal of Fluids Engineering vol 121 no 3 pp646ndash650 1999

[29] D Stephenson ldquoEffects of air valves and pipework on waterhammer pressuresrdquo Journal of Transportation Engineering vol123 no 2 pp 101ndash106 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 7

Table 1 Times of equipment in single-stage valve-closing

Equipment actions Pump start Valve-opening Full open Valve-closing Valve closed Water hammer finished Total timesTimes 119905 (s) 4128 7883 31590 46007 67934 110500 21927

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

y

Figure 7 Acceleration in 119910

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

y

S(m

m)

Figure 8 Amplitude in 119910

z

0 10 20 30 40 50 60 70 80 90 100 110minus10

minus8

minus6

minus4

minus2

0

2

4

6

a(m

s2)

t (s)

Figure 9 Acceleration in 119911

0 10 20 30 40 50 60 70 80 90 100 110minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

z

S(m

m)

Figure 10 Amplitude in 119911

0 10 20 30 40 50 60 70 80 90 100 11010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

Figure 11 Pressure in pipeline

0 10 20 30 40 50 60 70 80 90 100t (s)

020406080

100120140160180200220240260

S(m

m)

Figure 12 Amplitude of HCV

8 Shock and Vibration

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus10minus9minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

x

Figure 13 Acceleration in 119909

in the former 21198783 and a variable velocity was taken in thelatter 1198783 according to the simulation results of valve-closingwater hammer Due to the velocity of valve-closing that hasa large impact on water hammer parameters it is an effectiveapproach to protect water hammer by choosing a reasonablevelocity for valve-closing

The allowed pressure of pipe is lower and its value was64MPa However the pressure of pipeline reached 48MPain the case of 22 s valve-closing from the above analysis Thisvalue is near to the allowed pressure of pipe with the pressurebeing not high and the water hammer phenomenon was notsignificant compared with other mine drainage systems Inorder to reduce the pressure of pipeline to protection pipelineit is necessary to develop water hammer protection

(2) The Simulation of Valve-Closing in Multistage with aVariable Velocity The optimization strategy of valve-closingadjustment for HCV is generated using boundary condi-tions according to optimization method of valve-closingadjustment that is proposed in this paper It is a multistagevalve-closing with a variable velocity In the front 23 ofvalve-closing stroke the velocity is constant and its value is001ms In the later 13 of valve-closing stroke the velocity isa variable (the deceleration is constant) and the initial value is001ms The total time of valve-closing is 43823 s Times ofequipment in multistage valve-closing are shown in Table 2

The simulation results of valve-closing parameters inmultistage are shown in Figures 13ndash20

The pipeline pressuring acceleration and amplitude inthe directions of 119909 119910 and 119911 are significantly reducedin multistage valve-closing with a variable velocity Valve-closing with a constant velocity is started at 46007 s andvalve-closing with a variable velocity is started at 606 s TheHCVs are closed and pumps are stopped at 8983 s In thisprocess themaximumpressure ofwater hammer is 349MPaNo effect of water hammer occurred under this situation

43 Experiments The experimental devices include multi-function data acquisition instrument vibration sensor pres-sure sensors and cable displacement encoder Multifunction

x

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

S(m

m)

Figure 14 Amplitude in 119909

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus10minus9minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

y

Figure 15 Acceleration in 119910

data acquisition instrument has 16 channels and its acqui-sition frequency is 1024 kHz Data of acceleration ampli-tude flow pressure and displacement of valve-closing wereacquired by this multifunction data acquisition instrumentVibration sensor was used to measure piping vibration underthe influence of water hammer It was disposed along withthe 119909 119910 and 119911 direction of the pipe Pressure sensors wereused to measure pipeline pressure Its measurement accuracyand range are 0ndash10MPa and plusmn05 FS Cable displacementencoder was used to posit the displacement of valve-closingThe arrangement diagram of sensors and flow chart of pumpsare shown in Figures 21 and 22

HCVs control system was designed in this experimentwhich is shown in Figure 23 Sensors were used to collectsignals of pressure and acceleration in pipeline PLC unitwas used to analyze pipeline pressure and vibration for waterhammer on the basis of pressure and acceleration signalsAn expected running speed was given to HCVs And thenvoltage current power and fault protection informationof pumps pressure flow temperature vacuum and HCVsstatus information were monitored at real time These multi-parameter data were integrated using of fuzzy control theorywith calculus and control strategy The HCVs control system

Shock and Vibration 9

Table 2 Times of equipment in multistage valve-closing

Equipment actions Pump start Valve-opening Full open Valve-closing Valve closed Water hammer finished Total timesTimes 119905 (s) 4128 85 39504 46007 89830 128816 43823

y

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20minus15minus10minus5

05

1015202530

t (s)

S(m

m)

Figure 16 Amplitude in 119910

0 10 20 30 40 50 60 70 80 90 100 110 120 130

minus9minus10

minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

z

Figure 17 Acceleration in 119911

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

S(m

m)

z

t (s)

Figure 18 Amplitude in 119911

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

Figure 19 Pressure in pipeline

020406080

100120140160180200220240260280

S(m

m)

0 10 20 30 40 50 60 70 80 90 100 110t (s)

Figure 20 Displacement of HCV

can control starting and stopping of pumps automatically andcan monitor the signals in system running process timely

For the total stroke of valve 119878 the experimental conditionsare as follows In the front 23 of the stroke the velocitywas constant and its value was 001ms In the later 13the velocity is variable (the deceleration is constant) andthe initial value was 001ms The full valve-closing timeswere 44 s Measured values of water hammer parameters inmultistage are shown in Table 3

10 Shock and Vibration

sensor

sensor

Pressuresensor

Pressuregauge

Negativepressure sensor

Jet valves Hydrostatic pipe

Flow sensor Pressure sensor

Drain pipe

Drain pipe

Drain pipe

A-A

X vibration

Z vibration

Y vibration sensor

Figure 21 Arrangement diagram of sensors

Data collection isbeginning

Pump start

Valve start

Full valve opening

Normal drainage

Valve-closing start

Valve closed

Pump stop

Water hammer is finishedData collection is finished

Phase 1

Pump start

Phase 2Pump running

Phase 3Pump stopping

Figure 22 The flow chart of test for pumps

Shock and Vibration 11

HCVs PLC unit

Acceleration sensor

Pressure sensor

PC

Other sensors and execution system

Opticalfiber

Closed-loop control of waterhammer protection

Figure 23 Composition of HCVs control system

Table 3 Measured values of water hammer parameters

Measured parameters Acceleration (ms2) Displacement (mm) Pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Valve-closing times (s)22 48308 64582 54457 157662 285192 153051 4586525 48207 64581 54453 157515 285139 153012 4556428 47986 63215 54394 157495 284632 152036 4495231 45689 61265 52563 136938 268576 130369 4467833 45389 61063 51935 135963 246985 126325 4461236 43236 59638 50632 126985 238965 117652 4267539 17231 11023 16352 92514 63656 113251 3561542 17016 10363 15426 90356 61563 109968 3542344 16987 08692 14112 89482 59354 106432 3500648 16886 08629 14003 89235 59139 106365 35006

5 Results and Discussion

The reliability and effectiveness are illustrated through thecomparison between the results of simulation and experi-ment

(1) Results of Valve-Closing in Single-Stage with a ConstantVelocity and in Multistage with a Variable Velocity AreCompared Pipeline pressures and displacements of valve-opening under these two conditions are shown in Figures 24and 25 respectively The red curves represent the variationsin single-stage with a constant velocity while the black curvesrepresent the variations formultistagewith a variable velocity

Figures 24 and 25 show a significant water hammer effectin single-stage valve-closing with a constant velocity andthe valve-closing time is shorter (22 s) On the other handwater hammer phenomenon was found to be considerablyimproved for multistage valve-closing condition with a vari-able velocity and the valve-closing timewas extended (44 s) Itshows that valve-closing inmultistage with a variable velocitycan control the water hammer phenomenon effective inminedrainage system

(2) Results of the Simulation and Experiment Are Also Com-pared Results for valve-closing with a variable velocity areshown in Table 4

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

PZCPZD

Figure 24 Pressure in pipeline

It can be seen from Table 4 that the simulation forvalve-closing with a variable velocity shows good agreementwith the experiment The errors between simulation andexperiment are less than 5 Therefore the valve-closing in

12 Shock and Vibration

Table 4 Results comparison of simulation and experiment

Parameters Max acceleration (ms2) Max displacement (mm) Max pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Simulation 45830 62672 52341 165122 273335 148726 45798Experiment 48308 64582 54457 157660 285192 153051 45867Errors 46 29 39 47 42 28 02Simulation 16876 08446 13651 86395 56689 104653 34901Experiment 16987 08692 14112 89482 59354 106432 35006Errors 07 28 33 34 44 17 03

0 10 20 30 40 50 60 70 80 90 1000

20406080

100120140160180200220240

t (s)

S(m

m)

S1(FM)S2(FM)

Figure 25 Displacement of HCV

multistagewith a variable velocity can reduce the impact fromwater hammer in mine drainage system

6 Conclusions and Future Work

Limited space and high cost of equipment changing arethe main characteristics for mine drainage system For theproblem of valve-closing water hammer protection in minedrainage system this paper proposed a protection methodbased on velocity adjustment of HCVs The mathematicmodel of valve-closing water hammer is established basedon fundamental equations The strategy of valve-closing inmultistage with a variable velocity is obtained by velocityadjustment strategy of HCVs and it is effective in protect-ing the valve-closing water hammer without change pipingarrangement or addition equipment The results of simula-tions and experiments in different adjustment velocity arecomparedWe obtained that the water hammer phenomenonis not obvious with valve-closing velocity in the front 23 of itsstroke and it is very seriously within the later 13 Thereforewe take a two-stage valve-closing strategy In the first stagethe velocity is constant and its value is 001ms In the secondstage the velocity is variable (the deceleration is constant) andthe initial value is 001ms

Extending errors in the theoretical wave speed havean important influence on prediction of the closure rate

before a water hammer occurs in the actual pipeline A verychallenging mathematical task is variable This is beyond thescope of this paper and may be considered as a future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National 125 Tech-nology Support Program of China under Grant noSQ2012BAJY3504

References

[1] M Sun X-R Ru and L-F Zhai ldquoIn-situ fabrication ofsupported iron oxides from synthetic acid mine drainage highcatalytic activities and good stabilities towards electro-Fentonreactionrdquo Applied Catalysis B Environmental vol 165 pp 103ndash110 2015

[2] A Kaliatka M Vaisnoras and M Valincius ldquoModelling ofvalve induced water hammer phenomena in a district heatingsystemrdquo Computers amp Fluids vol 94 pp 30ndash36 2014

[3] N Jeong D Chi and J Yoon ldquoAnalytic estimation of the impactpressure in a beam-tube due to water-hammer effectrdquo Journalof Nuclear Science and Technology vol 50 no 12 pp 1139ndash11492013

[4] W S Yi J Jiang D D Li G Lan and Z Zhao ldquoPump-stoppingwater hammer simulation based on RELAP5rdquo IOP ConferenceSeries Materials Science and Engineering vol 52 no 7 ArticleID 072009 2013

[5] Q W Yong M Jiang and Y Tang ldquoStudy on liquid pipelinewater hammer and protective device with gas concentrationrdquoAdvanced Materials Research vol 616ndash618 pp 774ndash777 2013

[6] J Zhang J Gao M Diao W Wu T Wang and S Qi ldquoA casestudy on risk assessment of long distance water supply systemrdquoProcedia Engineering vol 70 pp 1762ndash1771 2014

[7] K I M Sang-Gyun L E E Kye-Bock and K I M Kyung-YupldquoWater hammer in the pump-rising pipeline system with an airchamberrdquo Journal of Hydrodynamics Series B vol 26 no 6 pp960ndash964 2015

[8] M A Bouaziz M A Guidara C Schmitt E Hadj-Taıeb and ZAzari ldquoWater hammer effects on a gray cast iron water networkafter adding pumpsrdquo Engineering Failure Analysis vol 44 pp1ndash16 2014

Shock and Vibration 13

[9] M S Ghidaoui M Zhao D A McInnis and D H AxworthyldquoA review of water hammer theory and practicerdquo AppliedMechanics Reviews vol 58 no 1ndash6 pp 49ndash76 2005

[10] A F Colombo P Lee and B W Karney ldquoA selective literaturereview of transient-based leak detection methodsrdquo Journal ofHydro-Environment Research vol 2 no 4 pp 212ndash227 2009

[11] P J Lee M F Lambert A R Simpson J P Vıtkovsky andD Misiunas ldquoLeak location in single pipelines using transientreflectionsrdquo Australian Journal of Water Resources vol 11 no 1pp 53ndash65 2007

[12] N S Arbon M F Lambert A R Simpson andM L StephensldquoField test investigations into distributed fault modeling inwater distribution systems using transient testingrdquo in Proceed-ings of the World Environmental and Water Resources CongressTampa Fla USA May 2007

[13] J Gong A R SimpsonM F Lambert A C Zecchin Y-I Kimand A S Tijsseling ldquoDetection of distributed deteriorationin single pipes using transient reflectionsrdquo Journal of PipelineSystems Engineering and Practice vol 4 no 1 pp 32ndash40 2013

[14] M Ferrante B Brunone and S Meniconi ldquoLeak detectionin branched pipe systems coupling wavelet analysis and aLagrangian modelrdquo Journal of Water Supply Research andTechnology vol 58 no 2 pp 95ndash106 2009

[15] S Meniconi B Brunone and M Ferrante ldquoWater-hammerpressure waves interaction at cross-section changes in series inviscoelastic pipesrdquo Journal of Fluids and Structures vol 33 pp44ndash58 2012

[16] W H Hager ldquoSwiss contributions to water hammer theoryrdquoJournal of Hydraulic Research vol 39 no 1 pp 3ndash7 2001

[17] M S Ghidaoui and B W Karney ldquoModified transformationand integration of 1D wave equationsrdquo Journal of HydraulicEngineering vol 121 no 10 pp 758ndash760 1995

[18] A Adamkowski and M Lewandowski ldquoCavitation character-istics of shutoff valves in numerical modeling of transientsin pipelines with column separationrdquo Journal of HydraulicEngineering vol 141 no 2 2015

[19] E Yao G Kember and D Hansen ldquoAnalysis of water hammerattenuation in applications with varying valve closure timesrdquoJournal of Engineering Mechanics vol 141 no 1 Article ID04014107 2014

[20] R Korbar Z Virag and M Savar ldquoTruncated method of char-acteristics for quasi-two-dimensional water hammer modelrdquoJournal of Hydraulic Engineering vol 140 no 6 Article ID04014013 2014

[21] M Rohani and M H Afshar ldquoSimulation of transient flowcaused by pump failure point-implicit method of characteris-ticsrdquo Annals of Nuclear Energy vol 37 no 12 pp 1742ndash17502010

[22] A Triki ldquoMultiple-grid finite element solution of the shallowwater equations water hammer phenomenonrdquo Computers ampFluids vol 90 pp 65ndash71 2014

[23] A Keramat A S Tijsseling Q Hou and A Ahmadi ldquoFluid-structure interactionwith pipe-wall viscoelasticity during waterhammerrdquo Journal of Fluids and Structures vol 28 pp 434ndash4552012

[24] S-G Kim K-B Lee and K-Y Kim ldquoWater hammer in thepump-rising pipeline system with an air chamberrdquo Journal ofHydrodynamics vol 26 no 6 pp 960ndash964 2014

[25] E B Wylie and V L Streeter Fluid Transients McGraw-HillNew York NY USA 1978

[26] W Wan W Huang and C Li ldquoSensitivity analysis for theresistance on the performance of a pressure vessel for waterhammer protectionrdquo Journal of Pressure Vessel TechnologymdashTransactions of the ASME vol 136 no 1 Article ID 011303 2014

[27] G De Martino F De Paola N Fontana and M GiugnildquoDiscussion of lsquosimple guide for design of air vessels forwater hammer protection of pumping linesrsquo by D StephensonrdquoJournal of Hydraulic Engineering vol 130 no 3 pp 273ndash2752004

[28] T S Lee ldquoAir influence on hydraulic transients on fluid systemwith air valvesrdquo Journal of Fluids Engineering vol 121 no 3 pp646ndash650 1999

[29] D Stephenson ldquoEffects of air valves and pipework on waterhammer pressuresrdquo Journal of Transportation Engineering vol123 no 2 pp 101ndash106 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Active and Passive Electronic Components

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RotatingMachinery

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Advances inOptoElectronics

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

8 Shock and Vibration

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus10minus9minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

x

Figure 13 Acceleration in 119909

in the former 21198783 and a variable velocity was taken in thelatter 1198783 according to the simulation results of valve-closingwater hammer Due to the velocity of valve-closing that hasa large impact on water hammer parameters it is an effectiveapproach to protect water hammer by choosing a reasonablevelocity for valve-closing

The allowed pressure of pipe is lower and its value was64MPa However the pressure of pipeline reached 48MPain the case of 22 s valve-closing from the above analysis Thisvalue is near to the allowed pressure of pipe with the pressurebeing not high and the water hammer phenomenon was notsignificant compared with other mine drainage systems Inorder to reduce the pressure of pipeline to protection pipelineit is necessary to develop water hammer protection

(2) The Simulation of Valve-Closing in Multistage with aVariable Velocity The optimization strategy of valve-closingadjustment for HCV is generated using boundary condi-tions according to optimization method of valve-closingadjustment that is proposed in this paper It is a multistagevalve-closing with a variable velocity In the front 23 ofvalve-closing stroke the velocity is constant and its value is001ms In the later 13 of valve-closing stroke the velocity isa variable (the deceleration is constant) and the initial value is001ms The total time of valve-closing is 43823 s Times ofequipment in multistage valve-closing are shown in Table 2

The simulation results of valve-closing parameters inmultistage are shown in Figures 13ndash20

The pipeline pressuring acceleration and amplitude inthe directions of 119909 119910 and 119911 are significantly reducedin multistage valve-closing with a variable velocity Valve-closing with a constant velocity is started at 46007 s andvalve-closing with a variable velocity is started at 606 s TheHCVs are closed and pumps are stopped at 8983 s In thisprocess themaximumpressure ofwater hammer is 349MPaNo effect of water hammer occurred under this situation

43 Experiments The experimental devices include multi-function data acquisition instrument vibration sensor pres-sure sensors and cable displacement encoder Multifunction

x

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

t (s)

S(m

m)

Figure 14 Amplitude in 119909

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus10minus9minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

y

Figure 15 Acceleration in 119910

data acquisition instrument has 16 channels and its acqui-sition frequency is 1024 kHz Data of acceleration ampli-tude flow pressure and displacement of valve-closing wereacquired by this multifunction data acquisition instrumentVibration sensor was used to measure piping vibration underthe influence of water hammer It was disposed along withthe 119909 119910 and 119911 direction of the pipe Pressure sensors wereused to measure pipeline pressure Its measurement accuracyand range are 0ndash10MPa and plusmn05 FS Cable displacementencoder was used to posit the displacement of valve-closingThe arrangement diagram of sensors and flow chart of pumpsare shown in Figures 21 and 22

HCVs control system was designed in this experimentwhich is shown in Figure 23 Sensors were used to collectsignals of pressure and acceleration in pipeline PLC unitwas used to analyze pipeline pressure and vibration for waterhammer on the basis of pressure and acceleration signalsAn expected running speed was given to HCVs And thenvoltage current power and fault protection informationof pumps pressure flow temperature vacuum and HCVsstatus information were monitored at real time These multi-parameter data were integrated using of fuzzy control theorywith calculus and control strategy The HCVs control system

Shock and Vibration 9

Table 2 Times of equipment in multistage valve-closing

Equipment actions Pump start Valve-opening Full open Valve-closing Valve closed Water hammer finished Total timesTimes 119905 (s) 4128 85 39504 46007 89830 128816 43823

y

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20minus15minus10minus5

05

1015202530

t (s)

S(m

m)

Figure 16 Amplitude in 119910

0 10 20 30 40 50 60 70 80 90 100 110 120 130

minus9minus10

minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

z

Figure 17 Acceleration in 119911

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

S(m

m)

z

t (s)

Figure 18 Amplitude in 119911

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

Figure 19 Pressure in pipeline

020406080

100120140160180200220240260280

S(m

m)

0 10 20 30 40 50 60 70 80 90 100 110t (s)

Figure 20 Displacement of HCV

can control starting and stopping of pumps automatically andcan monitor the signals in system running process timely

For the total stroke of valve 119878 the experimental conditionsare as follows In the front 23 of the stroke the velocitywas constant and its value was 001ms In the later 13the velocity is variable (the deceleration is constant) andthe initial value was 001ms The full valve-closing timeswere 44 s Measured values of water hammer parameters inmultistage are shown in Table 3

10 Shock and Vibration

sensor

sensor

Pressuresensor

Pressuregauge

Negativepressure sensor

Jet valves Hydrostatic pipe

Flow sensor Pressure sensor

Drain pipe

Drain pipe

Drain pipe

A-A

X vibration

Z vibration

Y vibration sensor

Figure 21 Arrangement diagram of sensors

Data collection isbeginning

Pump start

Valve start

Full valve opening

Normal drainage

Valve-closing start

Valve closed

Pump stop

Water hammer is finishedData collection is finished

Phase 1

Pump start

Phase 2Pump running

Phase 3Pump stopping

Figure 22 The flow chart of test for pumps

Shock and Vibration 11

HCVs PLC unit

Acceleration sensor

Pressure sensor

PC

Other sensors and execution system

Opticalfiber

Closed-loop control of waterhammer protection

Figure 23 Composition of HCVs control system

Table 3 Measured values of water hammer parameters

Measured parameters Acceleration (ms2) Displacement (mm) Pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Valve-closing times (s)22 48308 64582 54457 157662 285192 153051 4586525 48207 64581 54453 157515 285139 153012 4556428 47986 63215 54394 157495 284632 152036 4495231 45689 61265 52563 136938 268576 130369 4467833 45389 61063 51935 135963 246985 126325 4461236 43236 59638 50632 126985 238965 117652 4267539 17231 11023 16352 92514 63656 113251 3561542 17016 10363 15426 90356 61563 109968 3542344 16987 08692 14112 89482 59354 106432 3500648 16886 08629 14003 89235 59139 106365 35006

5 Results and Discussion

The reliability and effectiveness are illustrated through thecomparison between the results of simulation and experi-ment

(1) Results of Valve-Closing in Single-Stage with a ConstantVelocity and in Multistage with a Variable Velocity AreCompared Pipeline pressures and displacements of valve-opening under these two conditions are shown in Figures 24and 25 respectively The red curves represent the variationsin single-stage with a constant velocity while the black curvesrepresent the variations formultistagewith a variable velocity

Figures 24 and 25 show a significant water hammer effectin single-stage valve-closing with a constant velocity andthe valve-closing time is shorter (22 s) On the other handwater hammer phenomenon was found to be considerablyimproved for multistage valve-closing condition with a vari-able velocity and the valve-closing timewas extended (44 s) Itshows that valve-closing inmultistage with a variable velocitycan control the water hammer phenomenon effective inminedrainage system

(2) Results of the Simulation and Experiment Are Also Com-pared Results for valve-closing with a variable velocity areshown in Table 4

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

PZCPZD

Figure 24 Pressure in pipeline

It can be seen from Table 4 that the simulation forvalve-closing with a variable velocity shows good agreementwith the experiment The errors between simulation andexperiment are less than 5 Therefore the valve-closing in

12 Shock and Vibration

Table 4 Results comparison of simulation and experiment

Parameters Max acceleration (ms2) Max displacement (mm) Max pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Simulation 45830 62672 52341 165122 273335 148726 45798Experiment 48308 64582 54457 157660 285192 153051 45867Errors 46 29 39 47 42 28 02Simulation 16876 08446 13651 86395 56689 104653 34901Experiment 16987 08692 14112 89482 59354 106432 35006Errors 07 28 33 34 44 17 03

0 10 20 30 40 50 60 70 80 90 1000

20406080

100120140160180200220240

t (s)

S(m

m)

S1(FM)S2(FM)

Figure 25 Displacement of HCV

multistagewith a variable velocity can reduce the impact fromwater hammer in mine drainage system

6 Conclusions and Future Work

Limited space and high cost of equipment changing arethe main characteristics for mine drainage system For theproblem of valve-closing water hammer protection in minedrainage system this paper proposed a protection methodbased on velocity adjustment of HCVs The mathematicmodel of valve-closing water hammer is established basedon fundamental equations The strategy of valve-closing inmultistage with a variable velocity is obtained by velocityadjustment strategy of HCVs and it is effective in protect-ing the valve-closing water hammer without change pipingarrangement or addition equipment The results of simula-tions and experiments in different adjustment velocity arecomparedWe obtained that the water hammer phenomenonis not obvious with valve-closing velocity in the front 23 of itsstroke and it is very seriously within the later 13 Thereforewe take a two-stage valve-closing strategy In the first stagethe velocity is constant and its value is 001ms In the secondstage the velocity is variable (the deceleration is constant) andthe initial value is 001ms

Extending errors in the theoretical wave speed havean important influence on prediction of the closure rate

before a water hammer occurs in the actual pipeline A verychallenging mathematical task is variable This is beyond thescope of this paper and may be considered as a future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National 125 Tech-nology Support Program of China under Grant noSQ2012BAJY3504

References

[1] M Sun X-R Ru and L-F Zhai ldquoIn-situ fabrication ofsupported iron oxides from synthetic acid mine drainage highcatalytic activities and good stabilities towards electro-Fentonreactionrdquo Applied Catalysis B Environmental vol 165 pp 103ndash110 2015

[2] A Kaliatka M Vaisnoras and M Valincius ldquoModelling ofvalve induced water hammer phenomena in a district heatingsystemrdquo Computers amp Fluids vol 94 pp 30ndash36 2014

[3] N Jeong D Chi and J Yoon ldquoAnalytic estimation of the impactpressure in a beam-tube due to water-hammer effectrdquo Journalof Nuclear Science and Technology vol 50 no 12 pp 1139ndash11492013

[4] W S Yi J Jiang D D Li G Lan and Z Zhao ldquoPump-stoppingwater hammer simulation based on RELAP5rdquo IOP ConferenceSeries Materials Science and Engineering vol 52 no 7 ArticleID 072009 2013

[5] Q W Yong M Jiang and Y Tang ldquoStudy on liquid pipelinewater hammer and protective device with gas concentrationrdquoAdvanced Materials Research vol 616ndash618 pp 774ndash777 2013

[6] J Zhang J Gao M Diao W Wu T Wang and S Qi ldquoA casestudy on risk assessment of long distance water supply systemrdquoProcedia Engineering vol 70 pp 1762ndash1771 2014

[7] K I M Sang-Gyun L E E Kye-Bock and K I M Kyung-YupldquoWater hammer in the pump-rising pipeline system with an airchamberrdquo Journal of Hydrodynamics Series B vol 26 no 6 pp960ndash964 2015

[8] M A Bouaziz M A Guidara C Schmitt E Hadj-Taıeb and ZAzari ldquoWater hammer effects on a gray cast iron water networkafter adding pumpsrdquo Engineering Failure Analysis vol 44 pp1ndash16 2014

Shock and Vibration 13

[9] M S Ghidaoui M Zhao D A McInnis and D H AxworthyldquoA review of water hammer theory and practicerdquo AppliedMechanics Reviews vol 58 no 1ndash6 pp 49ndash76 2005

[10] A F Colombo P Lee and B W Karney ldquoA selective literaturereview of transient-based leak detection methodsrdquo Journal ofHydro-Environment Research vol 2 no 4 pp 212ndash227 2009

[11] P J Lee M F Lambert A R Simpson J P Vıtkovsky andD Misiunas ldquoLeak location in single pipelines using transientreflectionsrdquo Australian Journal of Water Resources vol 11 no 1pp 53ndash65 2007

[12] N S Arbon M F Lambert A R Simpson andM L StephensldquoField test investigations into distributed fault modeling inwater distribution systems using transient testingrdquo in Proceed-ings of the World Environmental and Water Resources CongressTampa Fla USA May 2007

[13] J Gong A R SimpsonM F Lambert A C Zecchin Y-I Kimand A S Tijsseling ldquoDetection of distributed deteriorationin single pipes using transient reflectionsrdquo Journal of PipelineSystems Engineering and Practice vol 4 no 1 pp 32ndash40 2013

[14] M Ferrante B Brunone and S Meniconi ldquoLeak detectionin branched pipe systems coupling wavelet analysis and aLagrangian modelrdquo Journal of Water Supply Research andTechnology vol 58 no 2 pp 95ndash106 2009

[15] S Meniconi B Brunone and M Ferrante ldquoWater-hammerpressure waves interaction at cross-section changes in series inviscoelastic pipesrdquo Journal of Fluids and Structures vol 33 pp44ndash58 2012

[16] W H Hager ldquoSwiss contributions to water hammer theoryrdquoJournal of Hydraulic Research vol 39 no 1 pp 3ndash7 2001

[17] M S Ghidaoui and B W Karney ldquoModified transformationand integration of 1D wave equationsrdquo Journal of HydraulicEngineering vol 121 no 10 pp 758ndash760 1995

[18] A Adamkowski and M Lewandowski ldquoCavitation character-istics of shutoff valves in numerical modeling of transientsin pipelines with column separationrdquo Journal of HydraulicEngineering vol 141 no 2 2015

[19] E Yao G Kember and D Hansen ldquoAnalysis of water hammerattenuation in applications with varying valve closure timesrdquoJournal of Engineering Mechanics vol 141 no 1 Article ID04014107 2014

[20] R Korbar Z Virag and M Savar ldquoTruncated method of char-acteristics for quasi-two-dimensional water hammer modelrdquoJournal of Hydraulic Engineering vol 140 no 6 Article ID04014013 2014

[21] M Rohani and M H Afshar ldquoSimulation of transient flowcaused by pump failure point-implicit method of characteris-ticsrdquo Annals of Nuclear Energy vol 37 no 12 pp 1742ndash17502010

[22] A Triki ldquoMultiple-grid finite element solution of the shallowwater equations water hammer phenomenonrdquo Computers ampFluids vol 90 pp 65ndash71 2014

[23] A Keramat A S Tijsseling Q Hou and A Ahmadi ldquoFluid-structure interactionwith pipe-wall viscoelasticity during waterhammerrdquo Journal of Fluids and Structures vol 28 pp 434ndash4552012

[24] S-G Kim K-B Lee and K-Y Kim ldquoWater hammer in thepump-rising pipeline system with an air chamberrdquo Journal ofHydrodynamics vol 26 no 6 pp 960ndash964 2014

[25] E B Wylie and V L Streeter Fluid Transients McGraw-HillNew York NY USA 1978

[26] W Wan W Huang and C Li ldquoSensitivity analysis for theresistance on the performance of a pressure vessel for waterhammer protectionrdquo Journal of Pressure Vessel TechnologymdashTransactions of the ASME vol 136 no 1 Article ID 011303 2014

[27] G De Martino F De Paola N Fontana and M GiugnildquoDiscussion of lsquosimple guide for design of air vessels forwater hammer protection of pumping linesrsquo by D StephensonrdquoJournal of Hydraulic Engineering vol 130 no 3 pp 273ndash2752004

[28] T S Lee ldquoAir influence on hydraulic transients on fluid systemwith air valvesrdquo Journal of Fluids Engineering vol 121 no 3 pp646ndash650 1999

[29] D Stephenson ldquoEffects of air valves and pipework on waterhammer pressuresrdquo Journal of Transportation Engineering vol123 no 2 pp 101ndash106 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 9

Table 2 Times of equipment in multistage valve-closing

Equipment actions Pump start Valve-opening Full open Valve-closing Valve closed Water hammer finished Total timesTimes 119905 (s) 4128 85 39504 46007 89830 128816 43823

y

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20minus15minus10minus5

05

1015202530

t (s)

S(m

m)

Figure 16 Amplitude in 119910

0 10 20 30 40 50 60 70 80 90 100 110 120 130

minus9minus10

minus8minus7minus6minus5minus4minus3minus2minus1

01234567

a(m

s2)

t (s)

z

Figure 17 Acceleration in 119911

0 10 20 30 40 50 60 70 80 90 100 110 120 130minus20

minus15

minus10

minus5

0

5

10

15

20

25

30

S(m

m)

z

t (s)

Figure 18 Amplitude in 119911

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

Figure 19 Pressure in pipeline

020406080

100120140160180200220240260280

S(m

m)

0 10 20 30 40 50 60 70 80 90 100 110t (s)

Figure 20 Displacement of HCV

can control starting and stopping of pumps automatically andcan monitor the signals in system running process timely

For the total stroke of valve 119878 the experimental conditionsare as follows In the front 23 of the stroke the velocitywas constant and its value was 001ms In the later 13the velocity is variable (the deceleration is constant) andthe initial value was 001ms The full valve-closing timeswere 44 s Measured values of water hammer parameters inmultistage are shown in Table 3

10 Shock and Vibration

sensor

sensor

Pressuresensor

Pressuregauge

Negativepressure sensor

Jet valves Hydrostatic pipe

Flow sensor Pressure sensor

Drain pipe

Drain pipe

Drain pipe

A-A

X vibration

Z vibration

Y vibration sensor

Figure 21 Arrangement diagram of sensors

Data collection isbeginning

Pump start

Valve start

Full valve opening

Normal drainage

Valve-closing start

Valve closed

Pump stop

Water hammer is finishedData collection is finished

Phase 1

Pump start

Phase 2Pump running

Phase 3Pump stopping

Figure 22 The flow chart of test for pumps

Shock and Vibration 11

HCVs PLC unit

Acceleration sensor

Pressure sensor

PC

Other sensors and execution system

Opticalfiber

Closed-loop control of waterhammer protection

Figure 23 Composition of HCVs control system

Table 3 Measured values of water hammer parameters

Measured parameters Acceleration (ms2) Displacement (mm) Pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Valve-closing times (s)22 48308 64582 54457 157662 285192 153051 4586525 48207 64581 54453 157515 285139 153012 4556428 47986 63215 54394 157495 284632 152036 4495231 45689 61265 52563 136938 268576 130369 4467833 45389 61063 51935 135963 246985 126325 4461236 43236 59638 50632 126985 238965 117652 4267539 17231 11023 16352 92514 63656 113251 3561542 17016 10363 15426 90356 61563 109968 3542344 16987 08692 14112 89482 59354 106432 3500648 16886 08629 14003 89235 59139 106365 35006

5 Results and Discussion

The reliability and effectiveness are illustrated through thecomparison between the results of simulation and experi-ment

(1) Results of Valve-Closing in Single-Stage with a ConstantVelocity and in Multistage with a Variable Velocity AreCompared Pipeline pressures and displacements of valve-opening under these two conditions are shown in Figures 24and 25 respectively The red curves represent the variationsin single-stage with a constant velocity while the black curvesrepresent the variations formultistagewith a variable velocity

Figures 24 and 25 show a significant water hammer effectin single-stage valve-closing with a constant velocity andthe valve-closing time is shorter (22 s) On the other handwater hammer phenomenon was found to be considerablyimproved for multistage valve-closing condition with a vari-able velocity and the valve-closing timewas extended (44 s) Itshows that valve-closing inmultistage with a variable velocitycan control the water hammer phenomenon effective inminedrainage system

(2) Results of the Simulation and Experiment Are Also Com-pared Results for valve-closing with a variable velocity areshown in Table 4

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

PZCPZD

Figure 24 Pressure in pipeline

It can be seen from Table 4 that the simulation forvalve-closing with a variable velocity shows good agreementwith the experiment The errors between simulation andexperiment are less than 5 Therefore the valve-closing in

12 Shock and Vibration

Table 4 Results comparison of simulation and experiment

Parameters Max acceleration (ms2) Max displacement (mm) Max pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Simulation 45830 62672 52341 165122 273335 148726 45798Experiment 48308 64582 54457 157660 285192 153051 45867Errors 46 29 39 47 42 28 02Simulation 16876 08446 13651 86395 56689 104653 34901Experiment 16987 08692 14112 89482 59354 106432 35006Errors 07 28 33 34 44 17 03

0 10 20 30 40 50 60 70 80 90 1000

20406080

100120140160180200220240

t (s)

S(m

m)

S1(FM)S2(FM)

Figure 25 Displacement of HCV

multistagewith a variable velocity can reduce the impact fromwater hammer in mine drainage system

6 Conclusions and Future Work

Limited space and high cost of equipment changing arethe main characteristics for mine drainage system For theproblem of valve-closing water hammer protection in minedrainage system this paper proposed a protection methodbased on velocity adjustment of HCVs The mathematicmodel of valve-closing water hammer is established basedon fundamental equations The strategy of valve-closing inmultistage with a variable velocity is obtained by velocityadjustment strategy of HCVs and it is effective in protect-ing the valve-closing water hammer without change pipingarrangement or addition equipment The results of simula-tions and experiments in different adjustment velocity arecomparedWe obtained that the water hammer phenomenonis not obvious with valve-closing velocity in the front 23 of itsstroke and it is very seriously within the later 13 Thereforewe take a two-stage valve-closing strategy In the first stagethe velocity is constant and its value is 001ms In the secondstage the velocity is variable (the deceleration is constant) andthe initial value is 001ms

Extending errors in the theoretical wave speed havean important influence on prediction of the closure rate

before a water hammer occurs in the actual pipeline A verychallenging mathematical task is variable This is beyond thescope of this paper and may be considered as a future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National 125 Tech-nology Support Program of China under Grant noSQ2012BAJY3504

References

[1] M Sun X-R Ru and L-F Zhai ldquoIn-situ fabrication ofsupported iron oxides from synthetic acid mine drainage highcatalytic activities and good stabilities towards electro-Fentonreactionrdquo Applied Catalysis B Environmental vol 165 pp 103ndash110 2015

[2] A Kaliatka M Vaisnoras and M Valincius ldquoModelling ofvalve induced water hammer phenomena in a district heatingsystemrdquo Computers amp Fluids vol 94 pp 30ndash36 2014

[3] N Jeong D Chi and J Yoon ldquoAnalytic estimation of the impactpressure in a beam-tube due to water-hammer effectrdquo Journalof Nuclear Science and Technology vol 50 no 12 pp 1139ndash11492013

[4] W S Yi J Jiang D D Li G Lan and Z Zhao ldquoPump-stoppingwater hammer simulation based on RELAP5rdquo IOP ConferenceSeries Materials Science and Engineering vol 52 no 7 ArticleID 072009 2013

[5] Q W Yong M Jiang and Y Tang ldquoStudy on liquid pipelinewater hammer and protective device with gas concentrationrdquoAdvanced Materials Research vol 616ndash618 pp 774ndash777 2013

[6] J Zhang J Gao M Diao W Wu T Wang and S Qi ldquoA casestudy on risk assessment of long distance water supply systemrdquoProcedia Engineering vol 70 pp 1762ndash1771 2014

[7] K I M Sang-Gyun L E E Kye-Bock and K I M Kyung-YupldquoWater hammer in the pump-rising pipeline system with an airchamberrdquo Journal of Hydrodynamics Series B vol 26 no 6 pp960ndash964 2015

[8] M A Bouaziz M A Guidara C Schmitt E Hadj-Taıeb and ZAzari ldquoWater hammer effects on a gray cast iron water networkafter adding pumpsrdquo Engineering Failure Analysis vol 44 pp1ndash16 2014

Shock and Vibration 13

[9] M S Ghidaoui M Zhao D A McInnis and D H AxworthyldquoA review of water hammer theory and practicerdquo AppliedMechanics Reviews vol 58 no 1ndash6 pp 49ndash76 2005

[10] A F Colombo P Lee and B W Karney ldquoA selective literaturereview of transient-based leak detection methodsrdquo Journal ofHydro-Environment Research vol 2 no 4 pp 212ndash227 2009

[11] P J Lee M F Lambert A R Simpson J P Vıtkovsky andD Misiunas ldquoLeak location in single pipelines using transientreflectionsrdquo Australian Journal of Water Resources vol 11 no 1pp 53ndash65 2007

[12] N S Arbon M F Lambert A R Simpson andM L StephensldquoField test investigations into distributed fault modeling inwater distribution systems using transient testingrdquo in Proceed-ings of the World Environmental and Water Resources CongressTampa Fla USA May 2007

[13] J Gong A R SimpsonM F Lambert A C Zecchin Y-I Kimand A S Tijsseling ldquoDetection of distributed deteriorationin single pipes using transient reflectionsrdquo Journal of PipelineSystems Engineering and Practice vol 4 no 1 pp 32ndash40 2013

[14] M Ferrante B Brunone and S Meniconi ldquoLeak detectionin branched pipe systems coupling wavelet analysis and aLagrangian modelrdquo Journal of Water Supply Research andTechnology vol 58 no 2 pp 95ndash106 2009

[15] S Meniconi B Brunone and M Ferrante ldquoWater-hammerpressure waves interaction at cross-section changes in series inviscoelastic pipesrdquo Journal of Fluids and Structures vol 33 pp44ndash58 2012

[16] W H Hager ldquoSwiss contributions to water hammer theoryrdquoJournal of Hydraulic Research vol 39 no 1 pp 3ndash7 2001

[17] M S Ghidaoui and B W Karney ldquoModified transformationand integration of 1D wave equationsrdquo Journal of HydraulicEngineering vol 121 no 10 pp 758ndash760 1995

[18] A Adamkowski and M Lewandowski ldquoCavitation character-istics of shutoff valves in numerical modeling of transientsin pipelines with column separationrdquo Journal of HydraulicEngineering vol 141 no 2 2015

[19] E Yao G Kember and D Hansen ldquoAnalysis of water hammerattenuation in applications with varying valve closure timesrdquoJournal of Engineering Mechanics vol 141 no 1 Article ID04014107 2014

[20] R Korbar Z Virag and M Savar ldquoTruncated method of char-acteristics for quasi-two-dimensional water hammer modelrdquoJournal of Hydraulic Engineering vol 140 no 6 Article ID04014013 2014

[21] M Rohani and M H Afshar ldquoSimulation of transient flowcaused by pump failure point-implicit method of characteris-ticsrdquo Annals of Nuclear Energy vol 37 no 12 pp 1742ndash17502010

[22] A Triki ldquoMultiple-grid finite element solution of the shallowwater equations water hammer phenomenonrdquo Computers ampFluids vol 90 pp 65ndash71 2014

[23] A Keramat A S Tijsseling Q Hou and A Ahmadi ldquoFluid-structure interactionwith pipe-wall viscoelasticity during waterhammerrdquo Journal of Fluids and Structures vol 28 pp 434ndash4552012

[24] S-G Kim K-B Lee and K-Y Kim ldquoWater hammer in thepump-rising pipeline system with an air chamberrdquo Journal ofHydrodynamics vol 26 no 6 pp 960ndash964 2014

[25] E B Wylie and V L Streeter Fluid Transients McGraw-HillNew York NY USA 1978

[26] W Wan W Huang and C Li ldquoSensitivity analysis for theresistance on the performance of a pressure vessel for waterhammer protectionrdquo Journal of Pressure Vessel TechnologymdashTransactions of the ASME vol 136 no 1 Article ID 011303 2014

[27] G De Martino F De Paola N Fontana and M GiugnildquoDiscussion of lsquosimple guide for design of air vessels forwater hammer protection of pumping linesrsquo by D StephensonrdquoJournal of Hydraulic Engineering vol 130 no 3 pp 273ndash2752004

[28] T S Lee ldquoAir influence on hydraulic transients on fluid systemwith air valvesrdquo Journal of Fluids Engineering vol 121 no 3 pp646ndash650 1999

[29] D Stephenson ldquoEffects of air valves and pipework on waterhammer pressuresrdquo Journal of Transportation Engineering vol123 no 2 pp 101ndash106 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Shock and Vibration

sensor

sensor

Pressuresensor

Pressuregauge

Negativepressure sensor

Jet valves Hydrostatic pipe

Flow sensor Pressure sensor

Drain pipe

Drain pipe

Drain pipe

A-A

X vibration

Z vibration

Y vibration sensor

Figure 21 Arrangement diagram of sensors

Data collection isbeginning

Pump start

Valve start

Full valve opening

Normal drainage

Valve-closing start

Valve closed

Pump stop

Water hammer is finishedData collection is finished

Phase 1

Pump start

Phase 2Pump running

Phase 3Pump stopping

Figure 22 The flow chart of test for pumps

Shock and Vibration 11

HCVs PLC unit

Acceleration sensor

Pressure sensor

PC

Other sensors and execution system

Opticalfiber

Closed-loop control of waterhammer protection

Figure 23 Composition of HCVs control system

Table 3 Measured values of water hammer parameters

Measured parameters Acceleration (ms2) Displacement (mm) Pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Valve-closing times (s)22 48308 64582 54457 157662 285192 153051 4586525 48207 64581 54453 157515 285139 153012 4556428 47986 63215 54394 157495 284632 152036 4495231 45689 61265 52563 136938 268576 130369 4467833 45389 61063 51935 135963 246985 126325 4461236 43236 59638 50632 126985 238965 117652 4267539 17231 11023 16352 92514 63656 113251 3561542 17016 10363 15426 90356 61563 109968 3542344 16987 08692 14112 89482 59354 106432 3500648 16886 08629 14003 89235 59139 106365 35006

5 Results and Discussion

The reliability and effectiveness are illustrated through thecomparison between the results of simulation and experi-ment

(1) Results of Valve-Closing in Single-Stage with a ConstantVelocity and in Multistage with a Variable Velocity AreCompared Pipeline pressures and displacements of valve-opening under these two conditions are shown in Figures 24and 25 respectively The red curves represent the variationsin single-stage with a constant velocity while the black curvesrepresent the variations formultistagewith a variable velocity

Figures 24 and 25 show a significant water hammer effectin single-stage valve-closing with a constant velocity andthe valve-closing time is shorter (22 s) On the other handwater hammer phenomenon was found to be considerablyimproved for multistage valve-closing condition with a vari-able velocity and the valve-closing timewas extended (44 s) Itshows that valve-closing inmultistage with a variable velocitycan control the water hammer phenomenon effective inminedrainage system

(2) Results of the Simulation and Experiment Are Also Com-pared Results for valve-closing with a variable velocity areshown in Table 4

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

PZCPZD

Figure 24 Pressure in pipeline

It can be seen from Table 4 that the simulation forvalve-closing with a variable velocity shows good agreementwith the experiment The errors between simulation andexperiment are less than 5 Therefore the valve-closing in

12 Shock and Vibration

Table 4 Results comparison of simulation and experiment

Parameters Max acceleration (ms2) Max displacement (mm) Max pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Simulation 45830 62672 52341 165122 273335 148726 45798Experiment 48308 64582 54457 157660 285192 153051 45867Errors 46 29 39 47 42 28 02Simulation 16876 08446 13651 86395 56689 104653 34901Experiment 16987 08692 14112 89482 59354 106432 35006Errors 07 28 33 34 44 17 03

0 10 20 30 40 50 60 70 80 90 1000

20406080

100120140160180200220240

t (s)

S(m

m)

S1(FM)S2(FM)

Figure 25 Displacement of HCV

multistagewith a variable velocity can reduce the impact fromwater hammer in mine drainage system

6 Conclusions and Future Work

Limited space and high cost of equipment changing arethe main characteristics for mine drainage system For theproblem of valve-closing water hammer protection in minedrainage system this paper proposed a protection methodbased on velocity adjustment of HCVs The mathematicmodel of valve-closing water hammer is established basedon fundamental equations The strategy of valve-closing inmultistage with a variable velocity is obtained by velocityadjustment strategy of HCVs and it is effective in protect-ing the valve-closing water hammer without change pipingarrangement or addition equipment The results of simula-tions and experiments in different adjustment velocity arecomparedWe obtained that the water hammer phenomenonis not obvious with valve-closing velocity in the front 23 of itsstroke and it is very seriously within the later 13 Thereforewe take a two-stage valve-closing strategy In the first stagethe velocity is constant and its value is 001ms In the secondstage the velocity is variable (the deceleration is constant) andthe initial value is 001ms

Extending errors in the theoretical wave speed havean important influence on prediction of the closure rate

before a water hammer occurs in the actual pipeline A verychallenging mathematical task is variable This is beyond thescope of this paper and may be considered as a future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National 125 Tech-nology Support Program of China under Grant noSQ2012BAJY3504

References

[1] M Sun X-R Ru and L-F Zhai ldquoIn-situ fabrication ofsupported iron oxides from synthetic acid mine drainage highcatalytic activities and good stabilities towards electro-Fentonreactionrdquo Applied Catalysis B Environmental vol 165 pp 103ndash110 2015

[2] A Kaliatka M Vaisnoras and M Valincius ldquoModelling ofvalve induced water hammer phenomena in a district heatingsystemrdquo Computers amp Fluids vol 94 pp 30ndash36 2014

[3] N Jeong D Chi and J Yoon ldquoAnalytic estimation of the impactpressure in a beam-tube due to water-hammer effectrdquo Journalof Nuclear Science and Technology vol 50 no 12 pp 1139ndash11492013

[4] W S Yi J Jiang D D Li G Lan and Z Zhao ldquoPump-stoppingwater hammer simulation based on RELAP5rdquo IOP ConferenceSeries Materials Science and Engineering vol 52 no 7 ArticleID 072009 2013

[5] Q W Yong M Jiang and Y Tang ldquoStudy on liquid pipelinewater hammer and protective device with gas concentrationrdquoAdvanced Materials Research vol 616ndash618 pp 774ndash777 2013

[6] J Zhang J Gao M Diao W Wu T Wang and S Qi ldquoA casestudy on risk assessment of long distance water supply systemrdquoProcedia Engineering vol 70 pp 1762ndash1771 2014

[7] K I M Sang-Gyun L E E Kye-Bock and K I M Kyung-YupldquoWater hammer in the pump-rising pipeline system with an airchamberrdquo Journal of Hydrodynamics Series B vol 26 no 6 pp960ndash964 2015

[8] M A Bouaziz M A Guidara C Schmitt E Hadj-Taıeb and ZAzari ldquoWater hammer effects on a gray cast iron water networkafter adding pumpsrdquo Engineering Failure Analysis vol 44 pp1ndash16 2014

Shock and Vibration 13

[9] M S Ghidaoui M Zhao D A McInnis and D H AxworthyldquoA review of water hammer theory and practicerdquo AppliedMechanics Reviews vol 58 no 1ndash6 pp 49ndash76 2005

[10] A F Colombo P Lee and B W Karney ldquoA selective literaturereview of transient-based leak detection methodsrdquo Journal ofHydro-Environment Research vol 2 no 4 pp 212ndash227 2009

[11] P J Lee M F Lambert A R Simpson J P Vıtkovsky andD Misiunas ldquoLeak location in single pipelines using transientreflectionsrdquo Australian Journal of Water Resources vol 11 no 1pp 53ndash65 2007

[12] N S Arbon M F Lambert A R Simpson andM L StephensldquoField test investigations into distributed fault modeling inwater distribution systems using transient testingrdquo in Proceed-ings of the World Environmental and Water Resources CongressTampa Fla USA May 2007

[13] J Gong A R SimpsonM F Lambert A C Zecchin Y-I Kimand A S Tijsseling ldquoDetection of distributed deteriorationin single pipes using transient reflectionsrdquo Journal of PipelineSystems Engineering and Practice vol 4 no 1 pp 32ndash40 2013

[14] M Ferrante B Brunone and S Meniconi ldquoLeak detectionin branched pipe systems coupling wavelet analysis and aLagrangian modelrdquo Journal of Water Supply Research andTechnology vol 58 no 2 pp 95ndash106 2009

[15] S Meniconi B Brunone and M Ferrante ldquoWater-hammerpressure waves interaction at cross-section changes in series inviscoelastic pipesrdquo Journal of Fluids and Structures vol 33 pp44ndash58 2012

[16] W H Hager ldquoSwiss contributions to water hammer theoryrdquoJournal of Hydraulic Research vol 39 no 1 pp 3ndash7 2001

[17] M S Ghidaoui and B W Karney ldquoModified transformationand integration of 1D wave equationsrdquo Journal of HydraulicEngineering vol 121 no 10 pp 758ndash760 1995

[18] A Adamkowski and M Lewandowski ldquoCavitation character-istics of shutoff valves in numerical modeling of transientsin pipelines with column separationrdquo Journal of HydraulicEngineering vol 141 no 2 2015

[19] E Yao G Kember and D Hansen ldquoAnalysis of water hammerattenuation in applications with varying valve closure timesrdquoJournal of Engineering Mechanics vol 141 no 1 Article ID04014107 2014

[20] R Korbar Z Virag and M Savar ldquoTruncated method of char-acteristics for quasi-two-dimensional water hammer modelrdquoJournal of Hydraulic Engineering vol 140 no 6 Article ID04014013 2014

[21] M Rohani and M H Afshar ldquoSimulation of transient flowcaused by pump failure point-implicit method of characteris-ticsrdquo Annals of Nuclear Energy vol 37 no 12 pp 1742ndash17502010

[22] A Triki ldquoMultiple-grid finite element solution of the shallowwater equations water hammer phenomenonrdquo Computers ampFluids vol 90 pp 65ndash71 2014

[23] A Keramat A S Tijsseling Q Hou and A Ahmadi ldquoFluid-structure interactionwith pipe-wall viscoelasticity during waterhammerrdquo Journal of Fluids and Structures vol 28 pp 434ndash4552012

[24] S-G Kim K-B Lee and K-Y Kim ldquoWater hammer in thepump-rising pipeline system with an air chamberrdquo Journal ofHydrodynamics vol 26 no 6 pp 960ndash964 2014

[25] E B Wylie and V L Streeter Fluid Transients McGraw-HillNew York NY USA 1978

[26] W Wan W Huang and C Li ldquoSensitivity analysis for theresistance on the performance of a pressure vessel for waterhammer protectionrdquo Journal of Pressure Vessel TechnologymdashTransactions of the ASME vol 136 no 1 Article ID 011303 2014

[27] G De Martino F De Paola N Fontana and M GiugnildquoDiscussion of lsquosimple guide for design of air vessels forwater hammer protection of pumping linesrsquo by D StephensonrdquoJournal of Hydraulic Engineering vol 130 no 3 pp 273ndash2752004

[28] T S Lee ldquoAir influence on hydraulic transients on fluid systemwith air valvesrdquo Journal of Fluids Engineering vol 121 no 3 pp646ndash650 1999

[29] D Stephenson ldquoEffects of air valves and pipework on waterhammer pressuresrdquo Journal of Transportation Engineering vol123 no 2 pp 101ndash106 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 11

HCVs PLC unit

Acceleration sensor

Pressure sensor

PC

Other sensors and execution system

Opticalfiber

Closed-loop control of waterhammer protection

Figure 23 Composition of HCVs control system

Table 3 Measured values of water hammer parameters

Measured parameters Acceleration (ms2) Displacement (mm) Pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Valve-closing times (s)22 48308 64582 54457 157662 285192 153051 4586525 48207 64581 54453 157515 285139 153012 4556428 47986 63215 54394 157495 284632 152036 4495231 45689 61265 52563 136938 268576 130369 4467833 45389 61063 51935 135963 246985 126325 4461236 43236 59638 50632 126985 238965 117652 4267539 17231 11023 16352 92514 63656 113251 3561542 17016 10363 15426 90356 61563 109968 3542344 16987 08692 14112 89482 59354 106432 3500648 16886 08629 14003 89235 59139 106365 35006

5 Results and Discussion

The reliability and effectiveness are illustrated through thecomparison between the results of simulation and experi-ment

(1) Results of Valve-Closing in Single-Stage with a ConstantVelocity and in Multistage with a Variable Velocity AreCompared Pipeline pressures and displacements of valve-opening under these two conditions are shown in Figures 24and 25 respectively The red curves represent the variationsin single-stage with a constant velocity while the black curvesrepresent the variations formultistagewith a variable velocity

Figures 24 and 25 show a significant water hammer effectin single-stage valve-closing with a constant velocity andthe valve-closing time is shorter (22 s) On the other handwater hammer phenomenon was found to be considerablyimproved for multistage valve-closing condition with a vari-able velocity and the valve-closing timewas extended (44 s) Itshows that valve-closing inmultistage with a variable velocitycan control the water hammer phenomenon effective inminedrainage system

(2) Results of the Simulation and Experiment Are Also Com-pared Results for valve-closing with a variable velocity areshown in Table 4

0 10 20 30 40 50 60 70 80 90 100 110 120 13010

15

20

25

30

35

40

45

50

P(M

Pa)

t (s)

PZCPZD

Figure 24 Pressure in pipeline

It can be seen from Table 4 that the simulation forvalve-closing with a variable velocity shows good agreementwith the experiment The errors between simulation andexperiment are less than 5 Therefore the valve-closing in

12 Shock and Vibration

Table 4 Results comparison of simulation and experiment

Parameters Max acceleration (ms2) Max displacement (mm) Max pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Simulation 45830 62672 52341 165122 273335 148726 45798Experiment 48308 64582 54457 157660 285192 153051 45867Errors 46 29 39 47 42 28 02Simulation 16876 08446 13651 86395 56689 104653 34901Experiment 16987 08692 14112 89482 59354 106432 35006Errors 07 28 33 34 44 17 03

0 10 20 30 40 50 60 70 80 90 1000

20406080

100120140160180200220240

t (s)

S(m

m)

S1(FM)S2(FM)

Figure 25 Displacement of HCV

multistagewith a variable velocity can reduce the impact fromwater hammer in mine drainage system

6 Conclusions and Future Work

Limited space and high cost of equipment changing arethe main characteristics for mine drainage system For theproblem of valve-closing water hammer protection in minedrainage system this paper proposed a protection methodbased on velocity adjustment of HCVs The mathematicmodel of valve-closing water hammer is established basedon fundamental equations The strategy of valve-closing inmultistage with a variable velocity is obtained by velocityadjustment strategy of HCVs and it is effective in protect-ing the valve-closing water hammer without change pipingarrangement or addition equipment The results of simula-tions and experiments in different adjustment velocity arecomparedWe obtained that the water hammer phenomenonis not obvious with valve-closing velocity in the front 23 of itsstroke and it is very seriously within the later 13 Thereforewe take a two-stage valve-closing strategy In the first stagethe velocity is constant and its value is 001ms In the secondstage the velocity is variable (the deceleration is constant) andthe initial value is 001ms

Extending errors in the theoretical wave speed havean important influence on prediction of the closure rate

before a water hammer occurs in the actual pipeline A verychallenging mathematical task is variable This is beyond thescope of this paper and may be considered as a future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National 125 Tech-nology Support Program of China under Grant noSQ2012BAJY3504

References

[1] M Sun X-R Ru and L-F Zhai ldquoIn-situ fabrication ofsupported iron oxides from synthetic acid mine drainage highcatalytic activities and good stabilities towards electro-Fentonreactionrdquo Applied Catalysis B Environmental vol 165 pp 103ndash110 2015

[2] A Kaliatka M Vaisnoras and M Valincius ldquoModelling ofvalve induced water hammer phenomena in a district heatingsystemrdquo Computers amp Fluids vol 94 pp 30ndash36 2014

[3] N Jeong D Chi and J Yoon ldquoAnalytic estimation of the impactpressure in a beam-tube due to water-hammer effectrdquo Journalof Nuclear Science and Technology vol 50 no 12 pp 1139ndash11492013

[4] W S Yi J Jiang D D Li G Lan and Z Zhao ldquoPump-stoppingwater hammer simulation based on RELAP5rdquo IOP ConferenceSeries Materials Science and Engineering vol 52 no 7 ArticleID 072009 2013

[5] Q W Yong M Jiang and Y Tang ldquoStudy on liquid pipelinewater hammer and protective device with gas concentrationrdquoAdvanced Materials Research vol 616ndash618 pp 774ndash777 2013

[6] J Zhang J Gao M Diao W Wu T Wang and S Qi ldquoA casestudy on risk assessment of long distance water supply systemrdquoProcedia Engineering vol 70 pp 1762ndash1771 2014

[7] K I M Sang-Gyun L E E Kye-Bock and K I M Kyung-YupldquoWater hammer in the pump-rising pipeline system with an airchamberrdquo Journal of Hydrodynamics Series B vol 26 no 6 pp960ndash964 2015

[8] M A Bouaziz M A Guidara C Schmitt E Hadj-Taıeb and ZAzari ldquoWater hammer effects on a gray cast iron water networkafter adding pumpsrdquo Engineering Failure Analysis vol 44 pp1ndash16 2014

Shock and Vibration 13

[9] M S Ghidaoui M Zhao D A McInnis and D H AxworthyldquoA review of water hammer theory and practicerdquo AppliedMechanics Reviews vol 58 no 1ndash6 pp 49ndash76 2005

[10] A F Colombo P Lee and B W Karney ldquoA selective literaturereview of transient-based leak detection methodsrdquo Journal ofHydro-Environment Research vol 2 no 4 pp 212ndash227 2009

[11] P J Lee M F Lambert A R Simpson J P Vıtkovsky andD Misiunas ldquoLeak location in single pipelines using transientreflectionsrdquo Australian Journal of Water Resources vol 11 no 1pp 53ndash65 2007

[12] N S Arbon M F Lambert A R Simpson andM L StephensldquoField test investigations into distributed fault modeling inwater distribution systems using transient testingrdquo in Proceed-ings of the World Environmental and Water Resources CongressTampa Fla USA May 2007

[13] J Gong A R SimpsonM F Lambert A C Zecchin Y-I Kimand A S Tijsseling ldquoDetection of distributed deteriorationin single pipes using transient reflectionsrdquo Journal of PipelineSystems Engineering and Practice vol 4 no 1 pp 32ndash40 2013

[14] M Ferrante B Brunone and S Meniconi ldquoLeak detectionin branched pipe systems coupling wavelet analysis and aLagrangian modelrdquo Journal of Water Supply Research andTechnology vol 58 no 2 pp 95ndash106 2009

[15] S Meniconi B Brunone and M Ferrante ldquoWater-hammerpressure waves interaction at cross-section changes in series inviscoelastic pipesrdquo Journal of Fluids and Structures vol 33 pp44ndash58 2012

[16] W H Hager ldquoSwiss contributions to water hammer theoryrdquoJournal of Hydraulic Research vol 39 no 1 pp 3ndash7 2001

[17] M S Ghidaoui and B W Karney ldquoModified transformationand integration of 1D wave equationsrdquo Journal of HydraulicEngineering vol 121 no 10 pp 758ndash760 1995

[18] A Adamkowski and M Lewandowski ldquoCavitation character-istics of shutoff valves in numerical modeling of transientsin pipelines with column separationrdquo Journal of HydraulicEngineering vol 141 no 2 2015

[19] E Yao G Kember and D Hansen ldquoAnalysis of water hammerattenuation in applications with varying valve closure timesrdquoJournal of Engineering Mechanics vol 141 no 1 Article ID04014107 2014

[20] R Korbar Z Virag and M Savar ldquoTruncated method of char-acteristics for quasi-two-dimensional water hammer modelrdquoJournal of Hydraulic Engineering vol 140 no 6 Article ID04014013 2014

[21] M Rohani and M H Afshar ldquoSimulation of transient flowcaused by pump failure point-implicit method of characteris-ticsrdquo Annals of Nuclear Energy vol 37 no 12 pp 1742ndash17502010

[22] A Triki ldquoMultiple-grid finite element solution of the shallowwater equations water hammer phenomenonrdquo Computers ampFluids vol 90 pp 65ndash71 2014

[23] A Keramat A S Tijsseling Q Hou and A Ahmadi ldquoFluid-structure interactionwith pipe-wall viscoelasticity during waterhammerrdquo Journal of Fluids and Structures vol 28 pp 434ndash4552012

[24] S-G Kim K-B Lee and K-Y Kim ldquoWater hammer in thepump-rising pipeline system with an air chamberrdquo Journal ofHydrodynamics vol 26 no 6 pp 960ndash964 2014

[25] E B Wylie and V L Streeter Fluid Transients McGraw-HillNew York NY USA 1978

[26] W Wan W Huang and C Li ldquoSensitivity analysis for theresistance on the performance of a pressure vessel for waterhammer protectionrdquo Journal of Pressure Vessel TechnologymdashTransactions of the ASME vol 136 no 1 Article ID 011303 2014

[27] G De Martino F De Paola N Fontana and M GiugnildquoDiscussion of lsquosimple guide for design of air vessels forwater hammer protection of pumping linesrsquo by D StephensonrdquoJournal of Hydraulic Engineering vol 130 no 3 pp 273ndash2752004

[28] T S Lee ldquoAir influence on hydraulic transients on fluid systemwith air valvesrdquo Journal of Fluids Engineering vol 121 no 3 pp646ndash650 1999

[29] D Stephenson ldquoEffects of air valves and pipework on waterhammer pressuresrdquo Journal of Transportation Engineering vol123 no 2 pp 101ndash106 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Shock and Vibration

Table 4 Results comparison of simulation and experiment

Parameters Max acceleration (ms2) Max displacement (mm) Max pressure119886(119909) 119886(119910) 119886(119911) 119878(119909) 119878(119910) 119878(119911) 119875 (Mpa)

Simulation 45830 62672 52341 165122 273335 148726 45798Experiment 48308 64582 54457 157660 285192 153051 45867Errors 46 29 39 47 42 28 02Simulation 16876 08446 13651 86395 56689 104653 34901Experiment 16987 08692 14112 89482 59354 106432 35006Errors 07 28 33 34 44 17 03

0 10 20 30 40 50 60 70 80 90 1000

20406080

100120140160180200220240

t (s)

S(m

m)

S1(FM)S2(FM)

Figure 25 Displacement of HCV

multistagewith a variable velocity can reduce the impact fromwater hammer in mine drainage system

6 Conclusions and Future Work

Limited space and high cost of equipment changing arethe main characteristics for mine drainage system For theproblem of valve-closing water hammer protection in minedrainage system this paper proposed a protection methodbased on velocity adjustment of HCVs The mathematicmodel of valve-closing water hammer is established basedon fundamental equations The strategy of valve-closing inmultistage with a variable velocity is obtained by velocityadjustment strategy of HCVs and it is effective in protect-ing the valve-closing water hammer without change pipingarrangement or addition equipment The results of simula-tions and experiments in different adjustment velocity arecomparedWe obtained that the water hammer phenomenonis not obvious with valve-closing velocity in the front 23 of itsstroke and it is very seriously within the later 13 Thereforewe take a two-stage valve-closing strategy In the first stagethe velocity is constant and its value is 001ms In the secondstage the velocity is variable (the deceleration is constant) andthe initial value is 001ms

Extending errors in the theoretical wave speed havean important influence on prediction of the closure rate

before a water hammer occurs in the actual pipeline A verychallenging mathematical task is variable This is beyond thescope of this paper and may be considered as a future work

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the National 125 Tech-nology Support Program of China under Grant noSQ2012BAJY3504

References

[1] M Sun X-R Ru and L-F Zhai ldquoIn-situ fabrication ofsupported iron oxides from synthetic acid mine drainage highcatalytic activities and good stabilities towards electro-Fentonreactionrdquo Applied Catalysis B Environmental vol 165 pp 103ndash110 2015

[2] A Kaliatka M Vaisnoras and M Valincius ldquoModelling ofvalve induced water hammer phenomena in a district heatingsystemrdquo Computers amp Fluids vol 94 pp 30ndash36 2014

[3] N Jeong D Chi and J Yoon ldquoAnalytic estimation of the impactpressure in a beam-tube due to water-hammer effectrdquo Journalof Nuclear Science and Technology vol 50 no 12 pp 1139ndash11492013

[4] W S Yi J Jiang D D Li G Lan and Z Zhao ldquoPump-stoppingwater hammer simulation based on RELAP5rdquo IOP ConferenceSeries Materials Science and Engineering vol 52 no 7 ArticleID 072009 2013

[5] Q W Yong M Jiang and Y Tang ldquoStudy on liquid pipelinewater hammer and protective device with gas concentrationrdquoAdvanced Materials Research vol 616ndash618 pp 774ndash777 2013

[6] J Zhang J Gao M Diao W Wu T Wang and S Qi ldquoA casestudy on risk assessment of long distance water supply systemrdquoProcedia Engineering vol 70 pp 1762ndash1771 2014

[7] K I M Sang-Gyun L E E Kye-Bock and K I M Kyung-YupldquoWater hammer in the pump-rising pipeline system with an airchamberrdquo Journal of Hydrodynamics Series B vol 26 no 6 pp960ndash964 2015

[8] M A Bouaziz M A Guidara C Schmitt E Hadj-Taıeb and ZAzari ldquoWater hammer effects on a gray cast iron water networkafter adding pumpsrdquo Engineering Failure Analysis vol 44 pp1ndash16 2014

Shock and Vibration 13

[9] M S Ghidaoui M Zhao D A McInnis and D H AxworthyldquoA review of water hammer theory and practicerdquo AppliedMechanics Reviews vol 58 no 1ndash6 pp 49ndash76 2005

[10] A F Colombo P Lee and B W Karney ldquoA selective literaturereview of transient-based leak detection methodsrdquo Journal ofHydro-Environment Research vol 2 no 4 pp 212ndash227 2009

[11] P J Lee M F Lambert A R Simpson J P Vıtkovsky andD Misiunas ldquoLeak location in single pipelines using transientreflectionsrdquo Australian Journal of Water Resources vol 11 no 1pp 53ndash65 2007

[12] N S Arbon M F Lambert A R Simpson andM L StephensldquoField test investigations into distributed fault modeling inwater distribution systems using transient testingrdquo in Proceed-ings of the World Environmental and Water Resources CongressTampa Fla USA May 2007

[13] J Gong A R SimpsonM F Lambert A C Zecchin Y-I Kimand A S Tijsseling ldquoDetection of distributed deteriorationin single pipes using transient reflectionsrdquo Journal of PipelineSystems Engineering and Practice vol 4 no 1 pp 32ndash40 2013

[14] M Ferrante B Brunone and S Meniconi ldquoLeak detectionin branched pipe systems coupling wavelet analysis and aLagrangian modelrdquo Journal of Water Supply Research andTechnology vol 58 no 2 pp 95ndash106 2009

[15] S Meniconi B Brunone and M Ferrante ldquoWater-hammerpressure waves interaction at cross-section changes in series inviscoelastic pipesrdquo Journal of Fluids and Structures vol 33 pp44ndash58 2012

[16] W H Hager ldquoSwiss contributions to water hammer theoryrdquoJournal of Hydraulic Research vol 39 no 1 pp 3ndash7 2001

[17] M S Ghidaoui and B W Karney ldquoModified transformationand integration of 1D wave equationsrdquo Journal of HydraulicEngineering vol 121 no 10 pp 758ndash760 1995

[18] A Adamkowski and M Lewandowski ldquoCavitation character-istics of shutoff valves in numerical modeling of transientsin pipelines with column separationrdquo Journal of HydraulicEngineering vol 141 no 2 2015

[19] E Yao G Kember and D Hansen ldquoAnalysis of water hammerattenuation in applications with varying valve closure timesrdquoJournal of Engineering Mechanics vol 141 no 1 Article ID04014107 2014

[20] R Korbar Z Virag and M Savar ldquoTruncated method of char-acteristics for quasi-two-dimensional water hammer modelrdquoJournal of Hydraulic Engineering vol 140 no 6 Article ID04014013 2014

[21] M Rohani and M H Afshar ldquoSimulation of transient flowcaused by pump failure point-implicit method of characteris-ticsrdquo Annals of Nuclear Energy vol 37 no 12 pp 1742ndash17502010

[22] A Triki ldquoMultiple-grid finite element solution of the shallowwater equations water hammer phenomenonrdquo Computers ampFluids vol 90 pp 65ndash71 2014

[23] A Keramat A S Tijsseling Q Hou and A Ahmadi ldquoFluid-structure interactionwith pipe-wall viscoelasticity during waterhammerrdquo Journal of Fluids and Structures vol 28 pp 434ndash4552012

[24] S-G Kim K-B Lee and K-Y Kim ldquoWater hammer in thepump-rising pipeline system with an air chamberrdquo Journal ofHydrodynamics vol 26 no 6 pp 960ndash964 2014

[25] E B Wylie and V L Streeter Fluid Transients McGraw-HillNew York NY USA 1978

[26] W Wan W Huang and C Li ldquoSensitivity analysis for theresistance on the performance of a pressure vessel for waterhammer protectionrdquo Journal of Pressure Vessel TechnologymdashTransactions of the ASME vol 136 no 1 Article ID 011303 2014

[27] G De Martino F De Paola N Fontana and M GiugnildquoDiscussion of lsquosimple guide for design of air vessels forwater hammer protection of pumping linesrsquo by D StephensonrdquoJournal of Hydraulic Engineering vol 130 no 3 pp 273ndash2752004

[28] T S Lee ldquoAir influence on hydraulic transients on fluid systemwith air valvesrdquo Journal of Fluids Engineering vol 121 no 3 pp646ndash650 1999

[29] D Stephenson ldquoEffects of air valves and pipework on waterhammer pressuresrdquo Journal of Transportation Engineering vol123 no 2 pp 101ndash106 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 13

[9] M S Ghidaoui M Zhao D A McInnis and D H AxworthyldquoA review of water hammer theory and practicerdquo AppliedMechanics Reviews vol 58 no 1ndash6 pp 49ndash76 2005

[10] A F Colombo P Lee and B W Karney ldquoA selective literaturereview of transient-based leak detection methodsrdquo Journal ofHydro-Environment Research vol 2 no 4 pp 212ndash227 2009

[11] P J Lee M F Lambert A R Simpson J P Vıtkovsky andD Misiunas ldquoLeak location in single pipelines using transientreflectionsrdquo Australian Journal of Water Resources vol 11 no 1pp 53ndash65 2007

[12] N S Arbon M F Lambert A R Simpson andM L StephensldquoField test investigations into distributed fault modeling inwater distribution systems using transient testingrdquo in Proceed-ings of the World Environmental and Water Resources CongressTampa Fla USA May 2007

[13] J Gong A R SimpsonM F Lambert A C Zecchin Y-I Kimand A S Tijsseling ldquoDetection of distributed deteriorationin single pipes using transient reflectionsrdquo Journal of PipelineSystems Engineering and Practice vol 4 no 1 pp 32ndash40 2013

[14] M Ferrante B Brunone and S Meniconi ldquoLeak detectionin branched pipe systems coupling wavelet analysis and aLagrangian modelrdquo Journal of Water Supply Research andTechnology vol 58 no 2 pp 95ndash106 2009

[15] S Meniconi B Brunone and M Ferrante ldquoWater-hammerpressure waves interaction at cross-section changes in series inviscoelastic pipesrdquo Journal of Fluids and Structures vol 33 pp44ndash58 2012

[16] W H Hager ldquoSwiss contributions to water hammer theoryrdquoJournal of Hydraulic Research vol 39 no 1 pp 3ndash7 2001

[17] M S Ghidaoui and B W Karney ldquoModified transformationand integration of 1D wave equationsrdquo Journal of HydraulicEngineering vol 121 no 10 pp 758ndash760 1995

[18] A Adamkowski and M Lewandowski ldquoCavitation character-istics of shutoff valves in numerical modeling of transientsin pipelines with column separationrdquo Journal of HydraulicEngineering vol 141 no 2 2015

[19] E Yao G Kember and D Hansen ldquoAnalysis of water hammerattenuation in applications with varying valve closure timesrdquoJournal of Engineering Mechanics vol 141 no 1 Article ID04014107 2014

[20] R Korbar Z Virag and M Savar ldquoTruncated method of char-acteristics for quasi-two-dimensional water hammer modelrdquoJournal of Hydraulic Engineering vol 140 no 6 Article ID04014013 2014

[21] M Rohani and M H Afshar ldquoSimulation of transient flowcaused by pump failure point-implicit method of characteris-ticsrdquo Annals of Nuclear Energy vol 37 no 12 pp 1742ndash17502010

[22] A Triki ldquoMultiple-grid finite element solution of the shallowwater equations water hammer phenomenonrdquo Computers ampFluids vol 90 pp 65ndash71 2014

[23] A Keramat A S Tijsseling Q Hou and A Ahmadi ldquoFluid-structure interactionwith pipe-wall viscoelasticity during waterhammerrdquo Journal of Fluids and Structures vol 28 pp 434ndash4552012

[24] S-G Kim K-B Lee and K-Y Kim ldquoWater hammer in thepump-rising pipeline system with an air chamberrdquo Journal ofHydrodynamics vol 26 no 6 pp 960ndash964 2014

[25] E B Wylie and V L Streeter Fluid Transients McGraw-HillNew York NY USA 1978

[26] W Wan W Huang and C Li ldquoSensitivity analysis for theresistance on the performance of a pressure vessel for waterhammer protectionrdquo Journal of Pressure Vessel TechnologymdashTransactions of the ASME vol 136 no 1 Article ID 011303 2014

[27] G De Martino F De Paola N Fontana and M GiugnildquoDiscussion of lsquosimple guide for design of air vessels forwater hammer protection of pumping linesrsquo by D StephensonrdquoJournal of Hydraulic Engineering vol 130 no 3 pp 273ndash2752004

[28] T S Lee ldquoAir influence on hydraulic transients on fluid systemwith air valvesrdquo Journal of Fluids Engineering vol 121 no 3 pp646ndash650 1999

[29] D Stephenson ldquoEffects of air valves and pipework on waterhammer pressuresrdquo Journal of Transportation Engineering vol123 no 2 pp 101ndash106 1997

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of