Embed Size (px)
Citation preview
NOTE TO USERS
This reproduction is the best copy available.
The Development of a Simulation Mode1 of
Pipeline Network Systems with Check Valve
Tianhe Wen
A Thesis
in the Depamnent of
Mechanical Engineering
Faculty of Engineering and Computer Science
Presented in Partial Fulfiiiment of the Requirements
for the Degree of Master of Applied Science at
Concordia University
Montreal, Quebec, Canada
Q Tianhe Wen, 2001
uisiins and Acquisitions et Bib mgraphii Setvices services bibliographiques "9
The author bas granted a non- L'auteur a accordé une licence non exclusive licence allowing the exclusive pemiettant a la National h i of Canada to Bibiiothéque nationale du Canada de reproduce, Ioau, distribute or seii reproduire, prêter, distri'buer ou copies of this thesis in microform, vendre des copies de cette thèse sous paper or electronic formats. la foxme de microfi&e/film, de
reproduction snr papier ou sur format élec~onique.
The author retains omership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'anîeur qni protège cette thèse. thesis nor substantiai exûacts fiom it Ni la îhèse ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation.
ABSTRACT
The Development of a Simulation Model of Pipeline Network Systems with Check Valve
Tianhe Wen
The objetive of this thesis is to design and implement a software package to
rnodel and simutate pipeline netwark systerns with check valves. The application package
is written under the window's environment to provide the hydraulic engineer a user
friendly interface for case of simulation and anaiysis without requiring to write code.
Discussion of the phenomenon of hydraulic transients, derivation of the
differentiai equations, cornparison of drfferent kinds of anaiysis methods, and
investigation of the method of characteristics solution and basic boundary conditions are
ai1 established. The check vdve dynamic equation is investigated for the analysis of
pipeline transients, and formuIae for flow torque acting on the valve discs are derived by
introducing the orifice sequence model. Dynamic behavior of pumps is considered during
the pipeline transients, and the analysis of this behavior combines the method of
charactenstics with check valve dynarnics, pump characteristic and pump boundary
conditions both for pump failure and pump start up. Numericd solutions to pipeline
transients, check vaive dynamicq and pump characteristic are established. Finally, the
impIementation into a working simulation program of a dynamic model for pipeline
network systerns with check vaives is desaibed, and a user guide for the software
HyrioAmlps and HyrioGruphic is presented.
ACKNOLEDGMENTS
The author wishes to express bis gratitude to his supewisors Dr. J. V. Svoboda
and Dr. H. Hong, for their guidance and inspiration throughout the author's graduate
studies.
The author appreciates îhe cooperation and support given by Mr. D. Barday,
former President of Ritepro Inc. A h , the author would like to express his gratitude to
Mr. P. Major, the Chief Engineer of Ritepro Inc., for his technical assistance throughout
the research.
Table of Contents
Chapter 1 Introduction .................................................................................................... 1
1.1 Summary ...................*~..*..................*..................*.*.*..............~................................. I
7 ..................................................................... 1.2 Classification of Hydrriulic Transients ,
1 3 Classification of Check valves ................................................................................. 3
1.4 Review of Previous Work ..................................................................................... 5
.......................................................................................... 1.4.1 HydrauIic Transients 5
.................................................................................... 1.4.2 Check Valves D ynamics 6
1.4.3 Cornputer Pro-pn Simulation of Transients in Pipelines and
Check Valves ..................................................................................................... 7
.......................................................................................................... 1.5 Thesis OutIine S
Chnpter 2 Transients in Pipelines ............................................................................... 11
............................................................................................................ 2.1 introduction I I
2.2 Basic Equations of Tnnsients in Piperines ...................................................... 13
2.2.1 Continuity Equation ......................................................................................... 13
2.2.2 Equation of motion .................................... .. 15
.................................. 2.3 Cornparison of Method of Transient Andysis in Pipelines 16
............................................................................... 2.4 The Method of Chancreristic 17
2.4.1 Introduction ..................................................................................................... 17 . .
2.4.2 Charactensuc Equations ............................................................................... 18
.................................................................... 2.4.3 Finite Difference FormuIations 20
2.4.4 Basic . Boundary Condiaons ............................................................................. 23
................................................................................................ 2.4.4. I Reservoir 2 4
........................................................................................ 2.4.4.3 Series Ji~nmon 25
..................................................................................... 2.4.4.3 Branch Junmon 26
2.4.4.4 Valve or O+ce ....................................................................................... 29
..................................................................... 2.4.5 Boundary Conditions for Pump 31
2.4.5.1 Introduction ............................................................................................ 31
................................................. 2.4.5.2 Boundary Cundirionsfbr Pwnp Failure 32
................................................ 2.4.5.3 Borurdary Condition for Pwnp Sran Up 37
Chapter 3 Check Valve Dynarnics ................................................................................ 39
3.1 Introduction ........................................................................................................... 39
....................................................................... 3.2 Check Vdve Differentid Equation 40
3.3 Component Torque ................................................................................................ 41
3.3.1 Countenveight Torque ............................................................................... 42
3.3.2 Spring Torque ............................................................................................... 43
3.4 Check Valve Flow Torque ................................................................................... 45
.................................................................................................... 3.4.1 Introduction 45
........................................................................... 3.4.2 Check Vdve Pressure Drop 46
.............. 3.4.2.1 Coefficient ofResistance of a Wafer Swing-Disk Check Valve 47
........................................... 3.4.2.2 Coeftrcient ufResistmce of Fonvard Flow 50
3.4.2.3 Coefficient ofResistance orReverse Flow 53 \ ............................................. 34.3 Swing-Disk Check Vaive Flow Twque .................................................. 54
3.5 Boundq Condition for Check Vdve .................................................................. 57
Chapter 4 Simulation and M d 1 of Pipeline Nework
Transients with Check Vaive System .......................................................... 59
4.1 inuoduction .......................................................................................................... 59
42 Algebraic Solution to a Piping System ................................................................ 60
............................. 4.2.1 Aigbn ic Representation and Continuous Ston- Data 60
........................................................................................................ 4.2.2 Indexing 63
4.2.3 Simulation of Piping System ........................................................ 6 6
............................................. 4 3 Numerical Mode1 and SimuIation for Check Vdve 68
4.3.1 Check Valve Dynamic S ystem Model .......................................................... 68
4.32 The Runge-Kutta Numericd Soiution to
the Check Valve Dynamic Equation ............................................................ 70
4.4 Newton-Raphson Solution m h p Boundvy Condition ................................... 73
Chapter 5 Software Implementation of Tnnsients in
Pipeline Nenkrork and Check Valve S ystem ............................................ 77 ........................................................................................................... 5.1 Introduction 77
5.2 Anaiysis for Hydro-Andysis Software Package .............................................. 78 . * ...................................................................................... 5.2.1 ProbIem Description 78
5.2.2 Input Parameters ............................................................................................ 79
5.2.3 Output Requirement .................................... ............................................... 81
5.3 Software Design .................................... f.. .......................................................... 83
5.3.1 Algorithm for the Hydro-Analysis ................................................................ 83
................................................................................... 5.3.2 Hiemhical Dia-pm 84
5.3.3 Object Oriented Programming Design for Hydro-Analysis .......................... 87
........................... 5.3.3.1 Major Class Description for Grapliic User btreface 87
........................................... 5.3.3.2 Class Description of Transients Simdation 92
.................................................... 5.3.3.3 Class Description of Graphic Oritprrt 97
5.4 Introduction to HydroAnaiysis S o b m ............................................................. 98
................................................................................................... 5.4.1 Overview 98
........................ 5.4.2 User Guide for Software Procm Package Hydrohalysis 100
...................................................................................... 5.4.2. 1 Gening sraned 100
5.4.2.2 Setting Sysrern Parmeren ................................................................... 100
................................................................... 5.4.2.3 Getting Simrilarion Output 112
.................................................................................................. Chapter 6 Conclusion 116
6.1 Summary .......................................................................................................... 116
.............................................................................. 6.2 Suggestions for Future Work 120
REFERENCES ........................................................................................................... 122
....................... APPENDIX A: Reviews of Method of Transient Analysis in Pipelines 127
............................................................................ APPENDK B: himp Characteristics 138
................................................................................ APPENDX C: Simulation ResuIts 143
............................................. APPENDIX D: Head Files for Software Hydro-Anaiysis 155
vii
List of Figures
.................................................. Fig . 2.2.1 Notation for Continuity and Motion Equation 13
Fig . 2.4.1 Chmctenstic Lines in x-t Plane ....................................................................... 20
.................................................. Fig . 2.4.2 The x-t Finite Difference Grid .... .................... 21
......................... Fig . 2.4.3 Reservoir Boundq: (a) Upstream end; (b) Downstream end 24
Fig . 2.4.4 Series Junction .................................................................................................. 26
.......................................................... Fig . 2.4.5 B ranching Junction ...................... .... 27
Fig . 2.4.6 Valve in line ................................. .... .......................................................... 30
Fig . 2.4.7 Pump and Valve in Pipeline Systems ........................................................ 32
........................................... Fig . 2.4.8 Approximation of Pump Curve by a Scraight Line 34
Fig . 2.3.9 Pump Start Up .................................................................................................. 38
Fig . 3.2.1 Schematic of Check Vaive ............................................................................... 40
Fig . 3.3.1 Counterweight .................................................................................................. 42
Fig . 3.3.2 Cylindrical Helical Bending spring ................................................................. 43
.................................................................. Fig . 3.3.3 Cylindrical HelicaI Torsion Spring 44
............................ Fig . 3.4.1 Orifice Mode1 for Wafer-Type Swing-Disc Check Valve -45
Fig . 3.4.2 Orifice Sequence Mode1 ................... .. ........................................................ 31
Fig . 3.4.3 Unsteady Fiow Through an Check Valve ..................................................... 54
Fig . 4.1.1 Block Diamm of Pump. Check Valve and Pipelines ........................ .. ...... 59
......................... Fig . 4.1. I x-t Diagram for Algebraic Representations in Series Sysrrm 61
Fig . 4.2.2 Branching System with Pump and Check Valve ............................................. 64
......................................................................... Fig . 4.2.3 indexing of Branching System 65
Fig. 4-24 Fiowchart of Piping System Simulation .......................................................... 67
Fig . 4.3.1 Fiowchart of Check Vdve Numerical Simulation ........................................... 69.
Fig . 4.4.1 Newton-Raphson Solution for Pump ...................... ... ................................. 75
Fig. 5.3.1.1 Flow Chart of Hydro-AnaIysis ..... ,. .......................................................... 53
Fig . 5.3.2.1 (a) Hienrchical Diagram for Hydro-hdysis ............................................. 85
.................................. Fïg . 5.3.2.1 (b) Hiemhical Diagnm for Grapphic User interface 85
................................... Fig . 5.3.2.1 (c) Hiemhical Diagram for Tmsients Simulation 86
............................................. Fig . 5.3.2.1 (d) Hierarchical Diagnm for Output Graphic 86
Fig . 53.3.1 The operation and attributes oFCM~nFrame ................... ........ ......... 87
Fig . 5.3.3.2 Operation of CChildFme ........................................................................... 88
Fig . 5.33.3 Operation of ChydroAnalysisView .................................. ., ..,., ................. 88
Fig . 5.3.3.4 The operation and mibutes of CFrontPageFonnView ............................. 89
Fig . 53.3.5 Opencion of CHydroAndysisApp ...................................... .. ........ 90
. ...........*.................*..... Fig 5.3.3.6 Operation of Chydro AnaiysisDac .... .................. 90
Fig. 53.3.7 The operation and atiiibutes of PlotPnntoutDlg ................................... 91
................................... Fip . 53.3.8 The operation and attributes of Pipe ... .......... 92
................................................ . Fig 5.3.3.9 Operation of PipeNeQCv & PipeNet2NoCv 93
........................................................... . Fig 5.3.3.10 Opention & Attributes of PumpFail 94
Fig- 5.3.3.1 1 Operation & Attributes of PurnpStrirt ........................................................ 95
...................................................... . Fig 5.3.3.12 Operation & Actributes of CheckVaIve 96
........................................................ . Fig 5.3.3.13 Description of HydroGmphic Classes 99
................................................................ Fig . 5.4.2.1 Main Window of HydroAndysis 101
Fig . 5.41.2 Dialog Box for Connection Panmeters ...................................................... 102
Fig 5.4.2.3 Didog BOX of Indexin: .............................................................................. 103
........................................................................... Fig . 5.4.2.4 Diaiog Box of Simulation 104
......................................................................... . Fig 5.4.2.5 Dialog Box of PLot & Print 105
......................................... Fr g. 5.4.1.6 Didog Box for Pump Check Vdve Panmeters 106
............................................................. . Fig 5.4.2.7 Diaiog Box of Pipeline Pumeters IO7
........................................................ . Fig 5.4.2.8 Didog Box of Reservoir Panmeters 108
................................................... . Fig 5.4.2.9 DiaIog Box of Conml Vdve Panmeters 108
Fig . 5.4.2.10 Didog Box of Junction Panmeters .......................................................... 109
................................................................................... . Fig 5.4.2.1 1 Menu File Window 110
...................................................... . . Fig 5.42.12 Save Mode1 As Window .. 111
................................................................................ Fig- 5.4.2.13 Open Mode1 Widow 112
........................................ . Eg 5.4.2.14 HydroGraphic Main Page (With Check Valve) 113
............................................................................ . Fig 5.4.2.15 Display of the Plot Dam 114
............................................ . Fig A i Circuit Represent of Lumped Parameter Method 130
.................................................................. . Fig A 2 BIock Diagram for Single Pipeline 134
Fig . B 1 Polar Diagram of 8 ......................................... 140
Fig . B 2 Complete Pump Chmcteristics ................................................................... 141
.... Fig . C 1 SimpIe Pump, Check Valve , and Pipe System ....................,.................... 144
.......................................... Fig . C 2 Indexing of Branching Systems ........................ ,. 151
Fig . C 3 Graphic Display of Branching System Wxthout Check Valve .......................... 152
............................... Fig . C 4 Gnphic Display of Branchin; System With Check Valve 152
Nomenclature
Cv, cvm
Area of pipe, Project a m of the disc and disc m.
Pump characteristics parameters, Project m a of the disc and disc a m
nomai to the flow Stream
Pump characteristics parameters
Area of valve opening
Wave speed
Constants to describe pump head-discharge cuve
Pipeline chmcteristics impedance
Known constants in compatibiIity equations
CaIculate prirameter in compatibility equations
Pipeline capacity
Name of characteristic equations
Vdve or orifice discharge coefficient
Known constants in compatibility equations
Nomd dng coefficient
Cdculate parameter in compatibility equations
Valve flow coefficients
Pipe diarneter
Disc forward and reverse flow forces
Friction Factor
Gnvitational acceleration
Pressure head
Rated pressure head of pump
Pump start up shutoff head
S tead state or mean pressure head
DimensionIess pressure head for pump fadure
I Moment of inerùa of rotating parts for pump
J Total moment of inertia for check valve
I I
Q Qin
Qn
Moment of inertia of counter weight for check valve
Moment of inertia of the disc and arm assemble for check vdve
Bulk modulus of elasticity
Valve coefficient of resistance
Vdve coefficient of resistance; Disc fiction constant
Vdve coefficient of resistance
Fourth order Runge-Kutta parameters
Spring constant
Pipe length
Mass
Rotational speed of pump
Rated speed of pump
Number of reach in pipeline
Discharge
hfiow
Junction or nodal flow
Pipeline flow; Pump flow
Check vdve or valve Fiow
Pipeline resistance coefficient
Toque on pump or check vaIve; Time
S tead state torque of pump
Beiuing friction torque of check valve
Counterweight torque
Fiow toque of check valve
Rated toque of pump
Spring torque of check valve; Pump start up shutoff time
Weight torque due to rotating disc
Time
Velocity
DimensionIess velocity
VeIocity ; Weight
xii
DimensionIess pump chriracteristics
Distance along the pipeline; Angular position in pump chamteristic curve
Characteristic impendence
Elevation of pipe above cimm
Dimensionless speed ntio for pump fidure; Torque ratio for pump s u up
Dimensionless toque ratio for pump failure
Specific weight of fiuid
Ange of torssonal sprinz
Pump efficiency
Opening of Check valve
Multiplier in characteristics method
Dimensionless flow ratio for pump faiIure
M a s density
Dimensionless valve opening
Angular velocity
Chapter 1
Introduction
1.1 Summary
A pipeline system is a combination of pipinp components with the objective of canying
incompressibIe or compressible fluid to one or several users. An industrial pipeline
system may be considered, for most of its operatinp time, to be in a steady srate of flow.
But a rapid velocity (or pressure) change, an accident or a non-normal operition in ri
pipeline system will resuit in a hydnulic uansient. This can shonen the life span of
certain pipeline components and even damage them.
Common txamples of the causes of transients in engineering sysrsms include:
1. Opening, closing of valves in a pipeline
2. Starting or stopping the pumps in ri purnpinz system
3. Starting-up a hydraulic turbine, accepting or rejecting load
4. Vibrations of the vanes of a mnner or an inpeller, or of the bIades of a fan.
Check valves are pieces of equipment which were originally developed and fitted
to pipelines in order to prevent the lines dnining backwards when pumps sropped - They
were sometirnes also used to prevent downstrem resetvoirs from empcying, in addition.
they prevent reverse rotation of pumps, thereby avoiding damage to seds and to the gear
of the dnving motor.
The undesired effects of flow reversai vary depending on the application. Some
examples where check valves are used include:
O In tank fiil-up applications, a check valve is instaiIed on a supply pipe which is beIow
the water Iine to prevent draining the tank in the case of flow supply pressure drop.
A check valve installed on the output of a pump would prevent high downstream
pressure from dnving the pump in reverse in the event of a power failure.
in an intermittent pumping application where the ffuid supply level is beIow the
pump, a check valve is instdIed at the foot of rhe inlet suction Iine to prevent draining
of the pipe ruid hence unnecessq priming of the system.
1.2 Classification of Hydra ulic Tra nsien ts
Hydnulic tmnsients may be classified into the foIlowing three categories:
I . Tnnsients in closed conduits
3. Tmsients in open channels
3. Combined free-surface-pressurÏzed tmsient fiows.
The analysis of transients in closed conduib may be further subdivided into two
types:
1. Distributed systems
2. Lumped systems
In distributed systems, the transient phenomenon occurs in the f o m of traveling
waves. Places in which such transients occur include water suppIy pipes. power plmi
conduits, and gas-uansmission lines.
In the analysis of lumped systems, any change in the flow conditions is assurned
to take place instantaneously throughout the system. Le.. the fi uid is considered as LÏ solid
body. Mathematically, transients in the distributed systems are represented by partial
differentid equations, whereas îhe transients in the lumped systerns are described by
ordinary differential equations. If oUa is much Iess than 1, then the system may &e
analyzed as a lumped system; otherwise, the system must be anafyzed as a disrributed
system. In the previous expression. CO= frequenp of oscillation. L = lrnyrh of riir
pipeline, and a = wave velociry.
In this thesis, discussion will focus mainly on transients in closed conduits.
1.3 Classification of Check valves
Some of the most commonly used check valves rire clusified here according ro openimg
principle.
A bal1 check valve consists of a bail insened into the flow to permit essentiaIly
unrestricted flow in the preferred direction. Flow in rhe reverse direction carries the bail
to the seat, immediately blocking the line. The valve may be spring or gravity Ioaded so
chat the minimal flow per opention is controllable. The bal1 check valve is used for hioh
viscositi Iiquids, in smdl size (ma. 2"') tmsport lines, and in hydraulic and pneumatic
power systems.
A piston check valve consists of a piston similar to a globe valve disc, which. in
normal operation, is kept suspended by the flow forces. The piston MIS by ,oravity when
the flow forces become insufficient or negative. This type may also be spring or gravi-
loaded. The piston check valve is widely used for Iiquids and gases and is particularly
effective for high-pressure stearn services.
The swing-disk check valve consists of a disc inserted into the line and rotating
about a pivot shaft. In norrnd operation, the disc is kept open by the flow forces. The disc
closes due to p v i t y when the fluid forces becorne insufficient, Counterweights.
dashpors, or springs may be added to control the disc closing characteristics.
The swing-disc check valve is the rnost commonly used type in industrial
pipelines, in a wide range of pipe dimensions (from 2" to over 48" diameter) and
openting pressures. in the folIowing, the investigation is focused mriinly on the swing-
disc check valve.
The category of Swing-Disc Check Valves can be funher subdivided into the
following types:
1. Conventionai bore or reduced orifice swing check valves
2. Full bore swing check valves
3. Wafer swing check valves, which are essentialIy convenrioncil bore types. with
reduced length and weight and favorable economic and instaflntion characteristics.
The disc of the swing check valve can reach dimensions of over 100 cm diameter
and a weight of over 2 tons, for such I q e disk. counterweights become necessriry to
open the vaive in normal openting conditions and dmpers are required to reduce the
dynamic forces.
1.4 Review of Previous Work
1.4.1 Hydraulic Transients
The smdy of hydraulic transients began with the investigation of the propagation of
sound waves in air, the propagation of waves in shallow water, and the flow of water in
pipes.
In 1897, Joukowski conducted extensive experiments in Moscow on pipes chat
were, respectively, 7620 m long and 50 mm in diameter, 305 m long and 101.5 mm in
diameter, and 305 m long and 151.5 mm in diameter. Based on his experimental and
theoreticat studies. he published his clusic report [ I l on the basic thsory of the writsr
hammer. He developed a formula for wave velocity, ctiking inro consideration the
elasticity of both the water and the pipe walls. He also investigrited the relationship
0 tWO between the reduction of flow velocity and the resulting pressure rise by usin=
methods: the conservation of energy and the continuicy condition. He discusscd the
propagation of a pressure wave along the pipe and the retlection ot the pressure wrivrb
from the open end of a branch, and studied the effects of air chambers, surge tanks. and
spring safety vdves on water hammer pressures. FinalIy, he found that the pressure rise
was a maximum for closing times, Tc 1 2 L l a , in which L= length of the pipeline and a
= ~ v m e speed.
Allievi [ I l published the seneml theory of water hammer in 1902. He obtained an
expression of the pressure nse at the valve and presented charts for the pressure rise and
drop caused by a wi i fody closing or opening vaive. He dso studied the rhythmic
movement of a vdve. He proved that the pressure cannot exceed twice the static head
Based on Joukowski's theory, in 1920, Gibson [ l ] presenced a paper thnt
included, for the first time. nonlinear friction losses in the analysis. He also invented an
appmtus to measure the turbine discharge using the pressure-tirne history foIlowing ri
load rejection.
Schnyderc [ I l includcd complete pump characteristics in his analysis of water
hamrner in pipelines connected to centrifuga1 pumps. He was the t k t to include rhe
friction losses in the graphitai analysis .
Since 1951, sevent books [2-101 have been published on the subject. Several
rnethods of andysis have been developed, such as Method of Characteristics [4.7,33].
Lumped Parameter Method [ 14,151 in tirne domain, Four-Pole Equations Modeling
Method [6] and Transmission Line ModeIing Method r37.38.391 in frequency domain.
1.4.2 Check Valves Dynamics
The investigation of check valve dynamics and check valve related pressure s u r p have
been conducted by Pool. Fonvit and Cariton [ I l ] . Their work focused on modelinp the
check vaIve dynamics more accuntely in order to obtain better surge pressure
predictions. Swing-disc and tiitingdisc check valves were considered.
Csemniczky [12] studied the hydrauiic performance characteristics of pressure
drop and momentum for tiltingdisc check valves. He derived a semi-empiricai formula
describing the momentum acting on the disc shaft-
Hong and Svoboda 113, 141, in 1981, presented the cornputer mode1 of a swin_o
check vdve suitable for use in Iumped parameter pipe network simulation. The vaive is
viewed as a variable resistor with a resistance king the function of the disc angle. The
fluid was treated as incompressible.
Cavazzoni [15], in 1983, used an Orifce Seqiience Mode1 to determine the
coefficients of resistance for check valves. The valve dynamic system was represented by
a second order, non-Iinear differential equation. Additional elements such as
counterweights and springs were exarnined and introduced, as additional ternis. into the
generai differentiai equation.
In 1983, Provoost El61 presented results of the study of the dynamic
characteristics of several types of check valves. he noted the importance of the local
reverse velocity and the decelention of the liquid during closure.
Significant contributions ware made by Thorley [17] in 1987. where valve
characreristics have been studied with a view to defining a boundriry condition for
computer coding and also to establish the 'right' type of check valve to use in a particular
installation.
1.4.3 Cornputer Program Simulation of Transients in Pipelines and Check
Valves
The arrivai of the 1960's and the advent of the high-speed digital computer begrin a new
era in transient anaIysis of pipelines and check valves. In 1967, Streeter and Wylie (41
showed the application of the computer to comptete a comprehensive hydraulic tnnsients
anaiysis. Watters [a] gave a FORTRAN program to soive simple pipe and pipe networks
in 1979, Cavazzoni [15] simulated pipes and check vaIves separacely by a FORTRLY
pro-gram in 1984. Hong [14] cornbined pipes simuIsition and check valves simulation rn
1983. in 1994, Cavazzoni developed a CU program [18] to solve transient flow in
pipeline networks systems using the finite element method. Sadfa designed the
FORTRAN program Cl81 to solve for the transient piping network flow in 1998.
Today the emphasis on pipeline transient analysis is almost entirely concentrated
on cornputer applications and window p m p m . lenkins [L91 developed a window
program HAMMER which simulates the effeccs of the water hammer in a reservoir and
pipeline system in which a valve at the downstream end is opened or closed by the user.
F a t [20] designed software Faast-3 which is an interactive, graphicat fini te-element
progrrirn for anaiyzing fluid flow in piping systems.
The objective of this thesis is to mode1 and sirnulate pipeline network systrms with check
valves. The study focuses on three major ares:
1. Analysis of hydnulic tmsients for pipeline network sytem
2. Analysis of check vdve dpamics, especiaily for swing-disc check valve dynnmics
3. Compter program implementation of combined pipelines and check valves
This study wiII begin by developing the governing equations for the transienc tlow
in closed conduits. In Chapter 2, conùnuiry and momentum equations will be incroduced.
Severai assumptions are made and then condensed into a simplified version. The
chancteristics method will also be discussed in Chapter 2. Finally, basic boundary
conditions including valve and pump will be investigated in this chapter.
Chapter 3 will present the study of pressure drops across the check valve, and
ffow forces acting on the vdve disc. An orifice sequence mode1 will be developed. in
order to predict the pressure drop through a valve as a function of a disc angle, for direct
and reverse flows. Coefficients of resistance for the vdve and for the disc alone will bs
developed. and the disc flow torque will be investigated to determine a relationship
between drag forces and total torque. The check vaive dynamic system will be
represented by a second order, non-linear differential equation.
Chapter 4 wiI1 give the procedure for implementing computer simulation of
pipelines with check valves. This chapter will give consideration to the integrrition of the
pipelines simulation, check valves dynamics. and pump charticteri~tic analpih. Thr
solution to pipeline transient by the characteristic method, to check valve dynamics b)
the Runge-Kutta method, and to pump chancteristic equations by the Newton-Rriphson
method will also be discussed in this chapter. Some algorithms, tlow chart and code will
also be presented.
Chapter 5 will present anaiysis of the pipeline network systrrns Crom the vie\\
point of software engineering; design and implementation will be done using Objecr-
Orïented Pro,oramming techniques. The rinalysis will include some high-level dgorithrns.
hierarchical diagram and detail descriptions of the class and some objects. The user guide
for the software HydroAnnlysis and HvdroGrcrphic will also be given in this chapter.
Finally, Chapter 6 wi11 include results and the conclusion to this study in addition
to suggestions for hrther work.
Appendix A gives Ihc review of seved solution mehods used in hydrauiic
transient analysis. Most of the major methods used in the analysis are introduced. The
lumped parameter, Four-Pole Equacions Modeling, and transmission line methods are
then given in detail. Appendix B is the pump characteristics which wiil be used in rhis
study. Appendix C gives the extra simulation results of pump friilure and srart up.
Appendix D lises the head file for the program package HydrauAnaIysis and
HydnuGraphic.
Chapter 2 -
Transients in Pipelines
2.1 lntroduction
Fiows in pipes are usudly in an unsteady state. Aitering the rate of flow can cause large
pressure fluctuations which can endanger the integrity of the pipe. Such pressure
fluctuations are called pressure transients and the state of flow in which they occur is
called transient Jow.
In solid body mechanics, one may anniye the situation of a m a s when being
acted on by a force. The mass is considered to be concentnted at its center of +pvity and
Newton's second Iaw is applied, taking into account any fnctionai forces present. if the
force is not CO-linear through the center of ~ v i t y , angular momentum and mguIar
acceIentions must be considered, This technique cm be applied to a m a s of water with
equd validity but, if the m a s of water is very long and thin, as occurs in pipelines, such
an approach is unredistic. This is because of the fact that when a force is applied to a
long mass of water, that force is propagated through the water by wave action.
Consequently this process occurs over a finite period of time and so the entire mas
involved does not experieace the force at the same time. An analysis that takes account of
this effect is caüed an elasn*~ mlysis, whei~as the usuai method of andyzing soiid
bodies is said to be a ngid body analysis.
From the above, there are two basic methods for the andysis of unsteady flows:
ci@d column theory and elastic theory. Obviously the elastic theory is more accurate uian
the rigid column theory. Therefore discussion will focus on the elastic theory in this
chapter.
2.2 Basic Eguations of Transients in Pipelines
Two equations are used to solve probIems of unsteady flow in pipes, one being a form of
the continuity equation and the other king a form of the momentum equation (or motion
equation). Since the flow velocity and pressure in transient fiows msiy be functions of
time ris well as distance, these equations are a set of panial differentid equations.
2.2.1 Continuity Equation
To derive the continuity equation, we apply the Reynolds vansport theorem [SI for the
conservation of mas. First, we chose the control surface and control volume as show in
Fig. 2.2.1. where x is the distance, V is the vdocity, and W is the veIocity of section
moving.
Applying Reynolds transport theorem to the above conuol volume gives
The above equation cm be simplifieci:
This equation holds for converging or diverging tubes as weil as for cyiindrical
pipes on ri dope or horizontai. It is also valid for any fluid. and for ri$d or highly
deform;lbk tubes, as no sirnplifying ssurnptions have been required.
XI
2.2.1 isiotation for Continuity and Motion Equation
To write this equntion in terms of the variables of interest, as pressure p and
vclocity V, wwe express the derivatives of p md A in texms of p and V as following. The
first term in (2.2.2) takes into account the compressibility of the fluid. Pressure is
inmduced with the definition of bulk modulus ofelasticity of a fiuid.
This equation cm be wriaen as
The second tenn in (2.2.2) deds with the elasticity of the pipe wdl and its rate of
deformation with pressure. For prismatic tubes, area is a function of pressure only
Substituting (22.4) and (2.2.5) into (2.2.2) yields
Now we define (71: a' = P . . K d 4
where a is the speed with which a pressure wave tnveIs back and forth in an elastic
conduit filled with sli_ohtiy compressible fluid.
From (2.2.7), (2.2.6) becomes
In the above cquation,
The above equation cm be approximated by negecting the spatial variation of V
whenever both spaual and tirne-varying t e m appex in the s m e equation, because in
gened, spatiai variation is much less than time-varyinz variation. Sa that ((3.2.9)
So (2.2.8) is simpIifÎed as:
(23. LI)
It is a common pnctice in hydrauiïc engineering to compte pressures in a
pipeline in t e m of the piezometric head, H, above a specified ciam and use the
dischq-e. Q. as the second vaiabIe instead of the fiow vehcity V
in whizh z = elevcltion of the pipe centeriine.
From (22.12), the dope term is usualIy smdl and mriy be ne~iected,
With the above assumption, (2.2.1 1) becornes
This is the sirnplified continuiry equntion.
2.2.2 Equation of Motion
For the equation of motion, the Reynolds Transport Theorern [SI for the conservation of
mornennim cm be used We c m obeain
'Ihe above equation can be simplifie&
wheref= Darcy-Weisbach friction factor. The above equation is valid for canverging or
divergïng pipe Bow.
dv av Similar rezrson as (2.2.10), (i.e., - = - ), and (3.2-16) reduces tu:
dr at
From (1.2.13 we cm get the foliowing
JP a~ az - = pg(--- ax ) = pg(- - sin 8) a.t a.r a.r a.r
Substitution into (3.217)
Since Q=VA, we findly derive
which is the simptified hydnuIic-grade-line form of the equation of motion. It is
resuicted to less compressible fi uid (such as liquids), ff owin; rit a low veIocity.
2.3 Cornparison of Methods of Analyss
The continuiq and motion equations are the basis of hydnulic ansients anaiysis. They
are quasi-iinear, hyperbolic, partiai differentiai equations. A closed-form solution of these
equations is not available. However, by negiccting or l i n e d n g the noniinear t e m ,
seved methods have been used for nurnencdly inte-dng nonlinear, hyperboiic partiai
differentiai equations, such as method of chancteristics, finite-difference method, finite
eIement method, and linear eelement method.
The method of chancteristics converts the two partiai differentid equations of
motion and continuity into four total differer?tial equations. This method has become
quite popular and is extensively used. For the andysis of systems having complex
boundary conditions, this rnethod has proven to be superior to other methods in severai
aspects, such as its stability, accuracy, easy of programming, and efficiency of
computations.
in the finitedifference method, the partial derivatives are replaced by finite
difference approximations such that the unknown conditions at a point at the end of a
time sep are expresseci in terms of the known conditions at the beginning of the tirne
step. Since the algebraic equations for the entire system are soIved simultaneously, the
anaIysis of complex boundary conditions by iterative procedures may require a large
amount of computing time. The Iinear element method and finite element method even
need 20 times more computation time to solve the same probIem [15]. But for complex
pipelines, the method of characteristics is supenor to the finite difference method, mainly
for its efficient handling of boundary conditions. Therefore, the method of characteristics
is chosen after cornparing with the above methods and with other methods such as the
lump parameter method and the transmission line rnethod, which reviewed in Appendix
A.
2.4 The Mefhod of Charactensfics [7,30,3 1,33 J
2.4.1 Introduction
In section 2.3, it was demonstrated that the method of chmeristics be superior to the
other method. Seved methods used for the solution of hydraulic transients wilI be
discussed and compared in Appendix A The details of the method of characteristics are
presented in this section In this method, the partial differentiai equations will be
transformed into particular total differential equations. These total differential equations
will then be integrated to yield finite difference equations, and fiirthermore algebraic
equations, which can be conveniently handled. Simple, basic boundary conditions are
aiso discussed m this section.
2.4.2 Characteristic Equations
The motion and continuity equations (22.20) and (2.2.14) can be rewn'tten respectiveiy:
Let us consider a linear combination of Eq.(2.4.l) and (2.4.2) using a unknown multiplier
Any two real, distinct values of h will yieId two equations in tenns of the two dependent
variabIes H and Q that will be equivaient to Eq. (2.4.1) and (2.4.2). Appropriate seiection
of two particular values ofh Ieads to a simplification ofEq.(2.43).
if H = H(x, t) and Q = Q(x, t ) , then the total denvatives are
The unknown multiplieril is defined as
The soIution of Eq.(2.4.5) yields two pdcular values of A,
Substitution of these values of A into EqQ.4.3) le& to hvo pairs of equations which are
grouped and identified as C' and C- equations.
and
Thus hvo real values of A have been used to conven the originai two p h d
differentid equations to two totd differentid equations in the independent variable t.
However, a price has been paid for this simplification: Eq.(2.4.1) and (3.42) were vdid
everywhere in the x-t plane: in contrat Eq.(2.4.7) is valid ody dong the saight fine
given by Eq.(1.4.8), and (2.4.9) is vdid only dong the straight Iine given by Eq.(2.4.10).
1 in the x-t plane, Eq.(2.4.8) and (2.4.f 0) represent two stni$t lines having dopes k-.
a
These lines are caiIed the characteristic h e s as show in Fig 2.4.1.
Fig 2.1.1 Characteristic Lines in x-4 Plane
24.3 Finite Difference Formulations
in pncrice. the pipeline is divided iria an even number of reaches, N, each Ar in 1en-h.
as shown in FÎg 2.43. Assuming that the values of Q ztnd Hat point A and B are known,
and we want ro determine their vdues ac point P, this nn be done by solving Eq42.4.7)
and (3.4.9) as foIIows.
By muitiplying the Iefr-hand side of E q . ( X i ) by dt and interping, we obtrirn
in which we use subscripts A and P CO indicrite locations in the x-t plane. For exanipIe,
4 and Qp are the head and discharge at point P.
Fig. 2.42 The x-t Finite Difference Grid
The hrst two inte-oral terms of Eq.(2.4.11) may be evduared erisily. However, this cruinot
be done for the third tem, because the variation of Q with respect to t is not explicidy
known. Thus an approximation must be introduced in this evdtution. A number of
options exist. The objective is to maintain a simpIe f o m that will provide reasoniibie
accuncy in generai unsteady fiow and that will hoId conditions steady during steady
fiow. It is therefore best to use the trapezoidd rule to maintain the l inev fom of the
in tep ted equations. It is of second-order accuracy, and is a satisfactory approximarion
for most problems.
~ Q I Q I ~ ~ = ~ Q ~ ;A I (2.4.12)
By substituting Eq.(2.4.12) into (2.4.11), and noting that Ar = +& , integntion dong the
characteristic iine AP, and simiiarly dong the characteristic Iine BP resuits in
These two cornpatibility equations are algebmic relations that describe the [mien t
propagation of the piezornetric head and flow in a pipeline. By solving for 4, these
equations may be witten
in which B is n function of the physicai properties of the fiuid and the pipeline. often
clled the pipeline chmcteristic impedmce:
and R is the pipeline resistance coefficient:
The fiiction factor f mriy be a constant, or it may be adjusted with the Iocd Reynolds
number in accordance with the Moody dia-oram in each reach at each time sep during
cdculations.
The solution to a problem in Iiquid transients usually begins with steady-state
conditions at time zero, so that H and Q are known initiai vdues at each computing
section (Fi- 2-42), for t = O. The solution consists of finding H and Q for aitemare grid
points dong t = dt, then proceeding to r = 2&, and so on, until the desired time duntion
has been covered. At any interior grid intersection point, point P ac section i , the two
compatibility equations are solved sirnul~eousty for the unknown Qi and Hi .
Eq.(2.4.15) and (2.4.Io) rnay be written in a simple form
C': Hi = C, - B,Qi (2.4.19)
C- : Hi =CM + BMQi (2.4.20)
Where
C p = Hi-[ + BQ,-, Bp = B+RI QI-[ 1 (2.4.2 1)
= Hl+, - BQi+l B M =B+RIQl+, I (1.4.22)
solving for Hi ruid Qi :
CP - c, B ~ + B ~
(1.4.34)
Thus the computation procedure uses the currenc values of H and Q at point i - I and i + 1 to cornpute their values at point i at one time interval Ar later. Usudly, the
startins values are known for a steady flow condition, which is calIed the boundary
condition. The discussion concerning the boundary conditions wiIl be presented in the
next section and in a later chapter.
2.4.4 Basic Boundary Conditions
In the last section, it was indicated that boundary conditions are required to determine the
transient-state head and discharge at the boundaries. Devices such as pump, vaive,
reservoir and junctions fom these boundaties. They may be Iocated at either end of a
pipeline or at some intermediate point. if they are Iocated at the downstrem end (x = L),
fi:. 2.4.3, the C? characteristic equation (2.4.19) can be used, while if it is at the
upsmm en& the C chmeteristic q u h n (2.4.20) can be appIied. The folIowing are
typicai boundary condition equations:
2-4.41 Reservoir
1. Ar the upsrream end of the line: Fig 2.4.3a
Fig. 2.43 Reservoir Boundary: (a) Upstream end; (b) Domistream end
At a large upstream reservoir the elevation of the hydrauIic p d e iine nomdy cm be
assumed constant during a shortdurarion transient This boundary condition is described
as HI = HR, in which HK is the elevarion of the reservoir surface above the reference
&tum. At e x h time step, Hf is known, and QI is determined by a direct solution of
Eq.(2.4.20)
The subscript 1 refers to the upstream section, at point P, Frg. 2.4.3a; Chi and Bbf are
variables in the computationd procedure but are dependent only on known values from
the previous time sep, in this case point B, section 3.
3. At the downstream of the line Fig. 2.436:
The boundq condition is described as: HNS = HR, Sirnilarly. Eq.(2.4.19) is used
where the subscript NS refers to point P. Cp and Bp c m be cdculated by the previous
time step.
This type of junction, althou* shown in fig. 2.4.4 as a diameter change, appIies equaiIy
well to a singie-diameter pipe with a change in roughness, thickness, or constraint
condition, or any combination of these possible variabies. At the junction (Fig. 2.4.4),
Eq.(2.4.19) is avaiIabIe forpipe 1, and Eq. (2.420) is available for pipe 2.
Fig 2.4.4 Series junction
The continuity expression and the condition of a common hydraulic-grade-line
elevation provide nvo equations, as follows:
Q w s = Qz.1 Ht,a = Hii
where the fint subscript refers to the pipe number and the second one refea to the end
condition. By solving these equations simultmeously with Eq.(3.4,19) and (1.4.20). the
folIowing is obcriined:
2.4.4.3 Brancli Junction
A junction is visuahed as a point connection of elements in a system, at whic h there are
two variables: a nodal fiow, a, wbch may be zero, with inflow being positive, and a
no&[ pressure or hyhuIic-pde-iine elevation. Fîg 2-45 shows a branching junction of
pipeline with a potential nodal flow Q,t.
Fie. 2.45 Brrinching Junction
There are two types of junctions or nodes:
1. A constant pressure
2. A constant ff ow
Referring to FI^. 2.4.5, a continuity equation is written at the junction summing
the inff ow,
in which the ZQ, is the summation of al1 instuitaneous pipeline flows. When minor
Iosses are negiected, we have
The compritibility equritions ;ire also avaiIabIe in erich pipe: Eq. (2.4.19) for pipe 1 and 2,
Eq. (24.20) for pipe 3 and 4.
For a junction with a known pressure head (unknown nodal flow), such as rit a
reservoir or pressure tank, the pipeline flows are determined directiy from appropriate
application of Eq(2.4.19) and (2.4.20), and the no& flow Q,, is then determined directly
from Eq.(2.4,29).
For a junction with known (may be zero), the compatibility equations are
writren in the following form:
The sumrnrition of these equations &es
and indudes ai1 the pipelines connected to the junction. Substitution into Eq.(2.439)
yieIds an equation form simiIar to the compatibiiity equations to compute the pressure
head:
in which C, =- 1 Sc and B, = -. The compatibility equations then yield the tiow in each s 8 S B
pipe. This method mrty be applied to any number of pipes and c m be extended to non-
pipe elernents such as valves and pumps.
2.4.4.4 Valve or Orifice 132,361
Valves or orifices may be located within a given pipeline, between two different Iines, at
the reservoir, aat pipeline terminations, or in my number of other positions in systems.
Fig.2.4.6a shows a valve between two pipelines, and Fig. 2.4.6b shows a schematic
representation of the vdve with nodes a and b as the inrerconnectin_o junctions on both
sides of the valve.
Use of the steady state orifice equation negects my inertia effects from
accelerating or decelerating flow througJi the vdve opening and also implies that there is
no opportunity for a change in the volume of fluid stored in the valve body. For positive
flow, Fig 2,4.6b, with HI, NS = & and HtVi = 6, the orifice equation is
Q, =au =a. = ~ , & , / ~ (2.4.33)
in which AG is the area of vaive opening and Cd is the dischq-e coefficient.
For steady state flow, the simiiar equation is
in which the subscript zero refers to steady conditions for each variable. A dimensionless
--t I l --tg! - Valve
Valve
Fig. 2.4.6 Valve in line
valve opening is useful in specifjklg valve motions as rt function of time and is defined ris
For the steady flow of Qo and the corresponding energ loss of &, t = 1, and for no flow
with the vaive closed, t = O. By dividing the unstendy Eq. (2.4.33) by the stendy strtte
flow Eq,(2.4.34), we obtain
a,, = a,, = Q" = - JH.-H, JH,
Applying Eq. (2.4.19) in pipe 1 and (3.420) in pipe 2, combined with Eq.(1.4.36), we
g=t
in which
For flow in the negative direction the orifice equation is
and when combined with Eq(2.4.19) and (2.4.20), ive c m get
Once the flow is known, Eq.(2.4.19) and (24.20) cm be used to find the pressure head.
The above describes onIy the rnost basic b o u n d q conditions used in anaiyzing
pipelineîheck valve trmsients. The check vaIve boundq condition wilI be discussed
specificaiIy in cietail in Chapter 3.
2.4.5 Boundary Conditions for Pump
2.4.5.1 Introduction
The method of characteristic may be used to a n d s e the hydrauIic transients during
pump M u r e or s m Since the purnping head and discharge depend upon the pump
speed, transieni-state speed changes must be taken into consideration in the analysis. For
this purpose, specid boundary conditions for the pump end of a pipeline must be
deveIoped In this section, the dynamic behavior of pumps is considered. A method for
the determination of the boundary conditions for the pump end is developed. This is
followed by discussions of pump failure and pump startup for single. series and prir~llel
pump connections.
2.4.5.2 Boundary Conditions for Pump FaiIure [7,8.25]
The dynamic behavior of a pump faiIure depends on the instantaneous pressure-tlow
response in the piping system, the rnomennim equation for the rotating masses. and the
pump characteristic curves as described in Appendix B. The primary element equations
are the torque-angular decelention equation describing the speed change in response to
the resisting torque, and an equation that describes head balance across the pump.
Purnp Vat ve
Fig.2.47 Pump and Valve in Pipeline Systems
Refemng to Fig 2.4.7, a pump with discharge valve in a pipeline system will be
used to iliustrate the handling of a pump faiIure. If h e nodai flows are zero and there is
no change in Iiquid stonge between nodes a and c, the instantaneous flow, Q, is the same
at the pipe ends and thmu,@ the pump and valve.
With one pipe only at node a the nodd equation is the d cornpatibility equation
for pipe 1:
Fa =Ha-Cp+BpQ=O (2.4.4 1)
The comparable equation 3t node c is :
F, = He-Ch( -B,Q=O (2.4.42)
AC node b the equntion is: Q = Ql = Q3.
The element equation for the vaive is:
F , = H , - H , - A H , = O
w here
Q;?' For a conuol discharge valve, C, = - , as discussed in Sec. 3.1.4.4 (Eq. 2-4-38),
*Mo
wirh the head loss acmss the valve equal ro ma when the flow is Q, and r = 1. The
vdve position, 7 , is given as a function of t h e during the transient calculation.
1. Head Balance Eparion
The head balance reIritionship across the pump at any instant is
H a + H = H, (1.4.45)
in which H is the total dynamic head amss the pump. This total dynamic head is @en
by Eq(B.8) and (B.5)
H = H& = ~ ~ ( 2 +v2)w,
Fig 2-48 Approximation of Pump Curve by a Straight Line
To use the cuve of WH in Eq.(2A.16), a suai@t line is used to replace the curve
of IVH for the proper vicinity of of .r. In Fg. 2.4.8 where x is the approximate location of
V ~c + tan-' - , obtained by extrapoiating v and u from previous cdcuIations, a süaight
cf
X line is defined through the two adjoining data points. as: i = - i 1.
Ar
ïkis is a integer arithmetic expression that 1oc;itss the subscript for the datrt point
to the left. Then (i - l)Ar, WH (i) and iAr? WH (i + 1) are the Cartesian coordinates of the
nvo data poines. B y substitution into WH = 4 + 41,
Now, we know the vdues of AI and A~J by the pump characteristics curve (or
tabuIar data). The Eq.(2.4.46) becornes
H = H ~ ( $ + +)[4 +4(lr+m41)~ a
and the Eq,(2.4.45) becomes
The above equation reIatss the head on each side of the pump to the vanables a and v.
When cornbined with Eq. (2.4.41-2.4-43). noticing that Q = LQ,, the following
is obtained:
(2.4.50)
This equation contains unknown u and v only, ruid it is valid for convoi valves.
2. Speed Change Equation
The change in rotational speed of the pump depends on the unbdanced toque applied:
2
WRg : FV is the weight of mtating parts plus entrained ticpici, R, is the in which I=- g
dw radius of gyration of the rotating mas, o is the anguia. v e l o c i ~ in radians, and - is
di
the angular acceIeration. On the basis of Eq.(B.5), EqQ.4.51) may be wrinen as
In this equation,
y = specific wei@ of liquid
IR = pump efficiency at rated conditions.
N a=- T0 T
a. =- Po =- p z - N , NR TR TR
Eq.(Z4.53) is solved over two Ume step, by using an average vdue of $ during the time
step, and so ic become:
This cm be simplified to:
Referring to Fig. B.2, the characteristics toque equation is
in which Bo and B, are found in the same rnanner as A. and Al, thrit is
v Fr = (aL +v')[B, + B,(Z + tan'' -)]+Bo -Cr& -a) =O a
This is the speed chanse equation in v and a
To develop the boundary conditions for a single pump, Eq.(1.4.41) to (2.4.44)
and (2.4.49) must be solved simultaneousIy , or Eq.(2.4.50) and (2.4.59) must be solved
directiy and simuit;ineously for v and u using the Newton-Raphson method [7].
2.3.5.3 Borindury CondihOn for Pump Start Up
Centrifugai pump stmup is usuaIly accomplished with the discharge vdve ctosed; as the
pump approaches operating speed, the valve is opened siowly.
Andysis for pump startup is generaily based on the assumption that the speed
rises from zero to NR IinearIy. Mer a reasonabIe Ts is selected, u is known:
Thus the pump speed is known during the transient conditions, and we do not
have to use the torque characteristics and the polar moment of inertia CO determine u
at different time. This simpIifies the necessary compuntions considerably.
Fig. 2.42 Pump Shrt Up
in homologous form, the curve for the pump in Fig. 2-48 takes the form
in which Hs is the shutoff head, and a! and a2 are constant, normdly neytive, to descnbe
the pump chancteristic curve.
M e n Eq.(2.4.60) is combined with Eq.(2.4.19) and (2,420), the discharse may
If a check valve is put near a pump, one must consider the valve head Ioss and
simuleaneously solve EqQ.4.60) and (3.4.3)-
Chapter 3
Check Valve Dynamics
Check valves are placed in pipelines to prevent back flow. They are usually located at
pumping stations, but may ais0 be used at other locations in systems. Ideaily, when the
flow reverses at the location of the check valve, it closes, thus preventing back fiow.
More realistically, since the vaive position is controlled by the flow and valve dynamics,
closure occurs after some degree of back flow is established. This causes an
instantaneous stoppage of the reverse flow with the corresponding pressure rise. The
Iaqe pressure rises associated with the reduction of this reverse velocity accelerate the
ciosure, resuiting in hi_pher pressure which ultimately dams the moving element ont0 its
seat,
It is important to know the dynamic behavior of the check valve in the analysis of
pipeline transients. Dynamic torque or force equation is therefore required in the anaIysis
together with an energy equation to describe the losses across the valve which are
accrued by back flow pnor to its seaiing.
A swingdisk check val& typidly contains a relatively fieely moving part nich
as a disk, whose motion is dictated by severa! eIements including the movement of the
fluid, its weight, external forces such as a spring or counter weight, friction, and possibly
a damping device.
In this chapter, the check valve differential equation of motion wiH be introduced,
foliowed by a detailed discussion of various toque and forces such as ffow force and
pressure drop. An orifice sequence mode1 will be introduced for predicting the pressure
drop through a valve as a function of disk angIe. The disk flow torque will be
investigated and an equivaIent torque arm and a torque arm coefficient will be introduced
to derennine the disk torque thrit depends on coefficient of resistance and flow conditions.
3.2 Check Valve Diferenfial Equation [t 2, I 6, i 7 ]
For a s w i q check vaive, Fig. 3-21 provides a schematic in which 6 is the open angle of
the valve disk.
Fig. 3.2.1 Schematic of Check Valve
The clochvise moments about the pivot point are considered positive. The toque
equation becornes:
where J , is the moment of inertia of the disk and arrn zissembiy and J , is the moment
of inertia about the hinge for an atrached counter weight.
The torque due to the weight Wr of the rotating disk is given by T,,
Tw =W,L, cos8 (3.2.2)
& is the bearing friction torque. It may be a consrrint relsted to a frictional
coefficient, the pivot pin radius, and the submerged weizht of the gate, but is ais0 likely
to depend on at Ieast the angular velocity [21]. The friction toque would be of the fom
in which K, and K1 are constants ruid n an arbirnry but constant power.
T, is the countenrreight torque, TF is the flow torque, and Ts is the spring
toque. Some of the above torque cm be obtained by theoreticai denvation, some of it
c m only be abtained by expenment. h the next section, the toque components are
separately discussed.
3.3 Component Toque
The toque component 1151 includes the countL:rweiCht, extemal s p ~ g and others such
as dash-pot. They cause the toques which cm be easiIy determined h m vdve structure,
dimension and material properties. In this section, only the normal components such as
counterweight and extemai spring are discussed.
Fig 33.1 Counterweight
33.1 Counterweight Torque
A counterweight is an auxiiiary, extema1 device, used to modiQ the static and dynamic
characteristics of a cIapper-hinge system. IL may be used:
1. to reduce the weight torque in the open position
2. to modify the weight torque in the closed position
3. to increase system inertia
The counterweight dynamic equation (referring Fig 3.3.1) is:
d '6 rt t , L,' *(-?.) = WC Lc * sin(y +O)
di-
Referring to Eq.(3.2.1), the countenvei~ht inertial and countenveight torque m:
5 J , =m,L, (3.3 2)
T,, = WC L, * sin(y + 8) (3.3.3)
3.3.2 Spring Torque
Adding springs is the most common way of reducing the check valve closing time.
Springs are also used to increase, or to genente, a closing torque, when the disk is in a
near-closed position.
Fig 3 3 2 Cylindrical HeIicai Bending spring
There are two types of springs (Fig 3.3 -2 and Fig. 3 33):
1. CylindricaI heIical spring subject to bending
2. Cylindrical helical springs subject to torsion
(a) Torsional Sprin,o (b) Kinematic of Torsional Spring
Fi:. 3.3.3 Cylindrical Helical Torsion Spring
HeIical springs subject to bending (Frg. 3.3.2) do not require rigid pivot connections, or
extemal devices, yet they cannot be changed without removing the disk. The bending
spring contribution to the valve differentid equation is
T' = KI *(@-a,) (3.3.4)
in which
Ks is the spring constant
8, is the spring angu1a.r pre-Ioad
T, is the spring toque
HeIicaI springs subject to torsion (Fig 3.3.3) require a rigid connection, but they
c m be easily inspected and chmged
The torsion spring torque is
TS = KS *ELS - L,,,)*L, +sinS,
in which, Ks is the spring constant and Lso is the sprins free length.
3.4 Check Valve Flow Torque
3.4.1 Introduction
With a pipethe in normal operating conditions, flow forces act on the disk surface,
keeping it in the open position. These flow forces are a combination of lift and d r g
effects. The magnitude and point of application of lift forces depend on the fluid-dynamic
characteristics of the disk and hinge and on the angle of anack u. The Mt forces increase
with the opening angle and reach a maximum for opening angies to 70'. Magnitude,
direction and point of appkation of iïfi forces depend on the pressure distribution on the
upper and [ower surfaces of the disk-hinge systems.
The magnitude of the drig forces my be detennined when the valve's total
pressure losses are known. There are two ways by which to detemhe h g forces: one is
the experimentai coefficient representation; the other is by which the orifice sequence
model, in which the drag forces cm be seen as the sum of five elementary components
comsponding to the five contractions and expansions of pipe.
In this section, the orifice sequence mode1 is introduced and used to determine the
pressure drop for fonvard and reverse flow. Aftenvard, the tlow toque for forward and
reverse flow cm be deterrnined.
3.4.2 Check Valve Pressure Drop
A wafer check valve (Fig.3.4.1) mny be modeied as a sequence of orifices in which the
valve's coefficient of resistance cm be assumed as a combination of the coefficient of
resistance of the elernentary conuactions and expansions.
Pressure drop and tiow through an elemenrxy contraction or expansion are
related by the following Darcy Formula:
We can substitute
into Eq(3.4.1) to obtain:
The flow rate c m be rewritten as:
Eq.(3 -4.4) becomes:
4": Refemng to (Eq.2.3.38): cV = - 2M
Complue Eq. 3-46 and Eq. 3.4.7:
In Eq. 3.4.5, the K is the coefficient of cesistance, and represents an equivalent
length, in pipe diarnerer of straight pipe:
1 K=-= L c*v2 /,=&
3.4.2.1 Coeflcient of Resistance o j a Wafer Swing-Disk Check Valve
Hong [14] studied the pressure losses tfirough a wafer vdve, using water as the fluid. The
check vdve was modeled as two restrictions in series. The upstream restriction was due
to the orifice and the downstrem restriction was due Co the wide-open disc. Each
restriction was composed of an enmnce contraction fotIowed by an exit expansion (Fig.
3.4.1).
Resmcnon Resuicuon
(6) Orifice Mode1 for Wafm-type (a) Vdve georneuy Swingdisc Check Vdve
Fg. 3.1.1 Orifice Model for CVrifer-Type Swing-Disc Check Valve
The coefficients of resistance for the orifice and disc can be assumed as independe~t. The
overd1 nomdized resistmce coefficient is @en by:
where & is the projected area of the disc and disc arm nomd to the flow srrem. Its
vaiue c m be cdculated as [14]:
- 2 L, X, (1 - COS 8) + 2do X, sin 0
where & and i, are the haIf widrh and cotai length of the disc ami and is the disc s h d t
displricement with respect to the seat plane, and Ki, and Kj are @en as:
AIso, we cm wrire Kz and & as:
Refemng to Eq. (3.4.9), another expression m3y be used to represent the resistmce
coefficient wben disc angIe greater thm 19.
where & is the equivalent length of the valve.
The vdue of the equivaient length for wder disk check valves depends on vaive
sizes and disc openins angles. For a widely open valve, the equivaient Iength of a wafer
check valve can be approximated as:
3.42.2 Coeficient of Resistance of Fomard Flow
Cavazzoni [15] had improved the above orifice mode1 with the following assurnptions
(Fig.3.4.2):
The valve's intemal geometry may be idedized as an orifice, the seat ma, and a
circuIar disc, and the verticd projection of disc and hinge (the disc am) area Four
characteristic surfaces can be identified and their area assumed to be the surface area of
four orifices in sequence. Ushg Fig. 3.4.2 notations:
f do + (a) Valve Geometry (b) Disc Ideaikation (c) Sequence of Orifices
Fig 3.42 Orfice Sequence Mode1
= 0.7 (form coefficient)
The coefficient of resistance for each eIementary contraction and expansion can be
caIculated as foI1ows:
and
the above formula is valid for :
For disc ange less than 19, the coefficient of resistrince m3y be considered as
3.4.2.3 Coeflcient of Resistance of Reverse Flow
Using the s m e notations as Fig. 3.42, the elementq coefficients of resistance for a
reversed flow are:
The above formuIa is vdid for:
loO c e < 70°
For disc ange less than IO0 the coefficient of resistance may tx: considered as:
Now that the coefficient of resisnnce for forward and reverse flow has been
obtriined, Eq. (3.4.3) cm be used to detemirie the pressure drop for the forward and
reverse flow condition.
3.4.3 Swing-Disk Check Vaive Flow Torque
Fig3.43 shows the important panmeters for the unsteady flow condition through a
check valve. Due to the fluid forces acting qainst the valve disc, a [orque To is created
which acts on the disc shaft forcing the disc to swing with the angular veIocity w.
Fig 3.43 Unsteady Flow Tbrougti a Check ~ d v e
The reIative uniform fluid velocity VR with respect to the anguIar veIocity of the
disc forward flow is given by:
where La is the hinge am length and Bis the disc opening angle.
w h m Qv is the flow thmugh the vdve and A2 is the orifice area. And v,* = - - 4
For reverse flow,
V, = V,' - Law cos 8
Qv and V,- = - . Where AI is the pipe area. 4
The flow force is acting normal to the disc center and is expressed in t e m of the
normal cimg coefficient CND:
F, = + pC,VDA,VR I VR I (3.4.37)
where AJ is the disc area and p is the density of water.
This may ais0 be written in the fom of Qv :
QZ FD = ~ ~ u x a l -
4
where is the total coefficient of mistance.
The fiow torque acting on the disc shaft for a wafer swing-disc check vaIve is
given as:
Tm = FD La (3.4.39)
For compIete description of the fiuid torque actin~ on the valve disc, the normal h g
coefficient musc be determined as a function of disc ange and pipe flow Reynoids
number. This may be obtained through experimentation.
If the orifice sequence mode1 is introduced, the h g force cm be seen as the sum
of five elementary components corresponding to the five contractions and expansions.
Now, the Toque Arm Coefficient (TAC) is introduced. It cm be obtained throua
experimentation [19J, or represented by the foliowing approximation:
0' <8<20" TAC = 0.74
20' < 6 < 70" TAC = 0,0209 * 8 + 0.322
The disc shaft toque cm be modified as:
T;,=TACL,*F,
For reverse flow, the flow force cm be written as:
and
FRC = FRI + FR? + FRj + FRI
The algebnic expression of TAC is:
o Y < e ~ 2 o = TAC = 0.65
20' c 8 < 4Y TAC= 0.01 l7*8 iO.416
45' < 8 < 70' TAC = 0.0583 * 8 - 1.6820 The reverse flow toque is:
Tm =TAC*LA * FK
3.5 Boundary Condition for Check Valve [21,24]
If the check valve is Iocated iniine, refem'ng to section 2.4.4 and section 3.4.2, using
Eq. (3 .4.8), Eq. (2.4.40) becomes:
(3.5.2)
Once the flow is known, Eq.(2.4.19) and (2.4.20) can be used to find the pressure head.
If the check valve is Iocated near a pump, refemng to section 2.4.5.2, using
Eq43.4.8). Eq.(2.4.50) becomes:
(3.5.4)
K or is the coefficient of resistance, and may be obtained by using the
equation discussed in Sec. 3.4.2.1-3.4.2.3.
It h s been demonstnted that a11 the toque represented in section 3 3 and
Eq.(3.2.1) are available for calculation and nuinericiil representation. Therefore, it is
possible to represent check valve dynmics by using a set of ordinxy differential
equations, which cm be solved using numericd techniques.
Chapter 4
Simulation and Mode1 of Pipeline Network
Transients with Check Valve System
4.1 Introduction
Experimentai investigation of pipeiine transients with n check vdve system would be
very expensive. In a large pipe and valve system, it also wouId be very difficuIt and time
consuming. As an alternative, an adequate cornputer simulation would be a valuable
substitution as a design aid and for system performance evaluation.
The complete numericd mode1 consists of the pipeline system model, rhe check
valve dpmics motel, and the pump characteristic model. me relation of these three
mode1 parts is shown in Fig. 4.1.1.
i Valve simulation i
Fig. 4.1 .l Block Diagram of Pump, Check Valve and Pipeline
The simulation of the pipeline, check valve and pump system mdces use of the
nuterid presented from chapters 1 and 3. In this Chapter, discussion focuses on the
solution of tLe proceeding chapters. The detailed soiution of the characteristic method for
o pipeline transient will be studied in section 4.7. The check vdve dynarnic equation wiI1
be solved by the Runge-Kutta method in section 43. The pump characteristic equation
will be solved by the Newton-Rdph method in section 4.4. In this chapter, an example of
a network pipeIine system will be presented, and the detailed flow chart and an d~orithm
for the system simulation will be discussed.
4.2 Algebraic Solution to a Piping System [33,34]
4.2.1 Algebraic Representation and Continuous Storage Data
The Ci and C' chmcteristic equations may be msformed into other f o m in which
time is a subscript, and in which the chmcteristic Iines extend to more than one reach,
eenemlly the full pipe len-gh. The equations are caiied Algebraic Eqrulrions. These C
equations may be used to solve most problems handled by the method of chanceeristics,
bur they have a form which is particuIarIy convenient for transient caiculations in piping
systems and networks.
The algebnic forms of the equations have the foIlowing properties:
t. They are compatibiiity equations appüed over one or more reaches of a pipe.
2. Tirne is indicated by an integer subsaïp~
in which the first subscript indicaies section number and the second indicates the tirne
counter K = t / At. The pipeline characteristic impedance and resistance coefficient may
a be applied to the total pipe Iength, so that 3 = - fL and R = -
gA 2 g ~ ~ ' -
Refemng to Fig. 4.2.1, each of the variables H and Q is dimensioned to the size of
the maximum value KM in the entire system, K,tI = L/(a At) + 1. The integer K is used as
a counter for each time step, and Kp is used as a pointer to identify the position in vector
H or Q at which current values of the variables are stored. At each iteration when K is
incremented, so is Kp, the vaiue of the pointer. When Kp exceeds KW, the value is set
back to zero, so that it points ro the first position in the vector. In this example,
information must be retained in pipe 2 for N2 + 1 = 5 computationai steps. Since, for this
system, the characteristic Iines of pipe 2 extend bac k the farthest. KM = 5. B y starting the
.n diagram KLW -1 computational increments before the transient stms (Fig. 4.2.1), and
storing the steady state values, the equations miiy be solved at each pipe end with the
incorporation of boundaries and nodal conditions.
The advantages of these algebnic reprtsentations over the normal chancteristic
equations are:
1. They are normally appIied over several reaches, with no need to calculate the
transient at the intewening sections.
2. They are computationaUy efficient for solution of multipipe systems such as
networks, because intenor point caicdations are avoided-
3. They use a mal1 Ar = U(Na), so ttiat the boundary condition detail is preserved.
But there are some disadvantages inherent in this method, because the characteristic lines
are generally extended over more thzin one reach, the friction term may be less ziccume
for hi@-friction systems. AIso, since the information must be retained h m time steps
extending bacbard in time more thm one time step, more computer storage is needed to
compIete the cdcuIntion. However, because of the sophistication of modem cornputers
which are used in these simulations, memory storage is not a cruciai issue. It therefore is
sensible to choose the algebraic equzitions to cdculate for the pipeline-check vdve
urinsient simulation.
4.2.2 lndexing [18]
If the alsebraic fom of the equations in multi-pipe systems is to be used, first the rnethod
for storing the system topology must be esnblished. This is cdIed the Utde-ring method.
An index vector is provided which offers one form of bookkeeping to describe the system
connection. It is oriented around the nodes of the system and, for each node, die
following information is aven: the node number, the number of elements attached to the
node, and an element number with a sign to indicate whether it is the upstream or
downstrearn end of the element, and the nurnber of the eIement section adjacent to the
node for each eIement attached.
The form of the index vector is:
1. node number (a node represents a connection point, such as a pump, vaive,
accumulator, resemoir, and pipe junction)
2, nurnber of elements (number of pipes connected to the node)
3. element number (pipe number - sign for flow out h m the node
+ sign for flow into the node.)
4. element section nurnber adjacent ta the node
5. secund eIement number
6. element section number adjacent to the node
7. if there 3 or more elements connected to the node, then steps 5 and 6 are
repeated as needed
Fig. 4.2.2 Branching System with Pump and Cbeck Vaive
@ -Node numba 1 -Section number 4
*lement nurnber
9e
Fig. 4.2.3 Indexhg of Branching Sgstem
Refemng to Fig. 4.2.2 and 4.2.3, for a check valve represented by node number 1;
there are two pipe elements connected to this node. The first is pipe number 1, in which
flow is out from the node by this eIemenr, so its sign is minus (-1) and the section number
for this pipe adjacent to the node is 1. Enement number 5 is the smdl length of pipe that
connects the pump to the check vaIve. Hoiv is inro the node by element 5 and the section
number adjacent to the node is 10.
The index for node 1 is:
1,2, -1, 1,5, 10
The above index describes that at node number 1 we have 2 elements. The first
element is -1, section nurnber 1; the second eIernent is 5, section number 10.
For the pipe branch represented by node 2, the index is:
2,3, 1,2 , -2,3, -3,s
The above index means that at node 2, thete are 3 eIements (pipes), pipe 1 is flow
into the node, the sign is positive, and the section number is 2. The other two pipes iire
flow out of the node, so they are -2 and -3, and the section numbers are 3 and 5
respectively.
For the reservoir represented by end node 4, the index is:
4,1,3,6
The index indicates that node number 4 has 1 pipe element number 3 connected to
it, and the adjacent section is number 6.
The index vector does not provide ai1 of the information needed for transient
anrilysis, but it does give the necessary data to enable caiculations at junctions and
boundaries, especially in connection relationship. The physicd panmeters that describe
each element are needed, in addition to nodal information such as the nodal flow,
pressure, and elevation.
4.2.3 Simulation of Piping Systern
To compte ansient-state conditions in a pipins system, the shortest pipe in the system
is divided into a number of reaches so that a desired computationai time intervd, At. is
obtained [25,26] b y
The remaining pipes in the system are divided into reaches having equal lengths by usin_o
Eq. (42.3). If necessary, the wave velocities are adjusted to satisfy Eq. (423) so that
chrtncterîstics p a s through the grid points- Tbe steady-state discharge and pressure head
at al1 the sections are then cornputed, and tfieir vdues are saved or printed
The time is then incrernented, and the mnsient conditions are computed at dI the
interior points and at the bound;iries. This process is continued until transient conditions
for the required time rue computed. Fig. 4.2.4 show the ffowchiut of this procedure.
l 7 Save or Rint flow and Head
1 I~tore 4 as Q H for the systeml
Fig. 4.2.4 FIowchart of Piping System Simulation
4.3 Numerical Model and Simulation for Check Valve
4.3.1 Check Valve Dynamic System Model
The complete numerical mode1 consists of the combination of a valve dynamics mode!
with a mode1 of the piping system in unsteady flow conditions. While the piping system
mode1 has been investigated in the last section, in this section the check valve numericd
mode1 is deveioped. The Runge-Kutta method is used to soIve the second order
differential equation, representing a gened valve systern operating under unsteady
conditions.
The check valve dynamic system is represented by a second order, nonlineu,
di fferential equntion, described in Section 3.3, Eq. (3.3.1). Before this dynmic equation
is solved, the relationships between the purnp and check valve, and the piping sysrem and
check valve. must be considered.
Fig. 4.1.1 shows these relations. The check vaIve dynamics requires information
for torque To and fiow m e QV initiai conditions. After simulation, the check valve disc
opening angle 8 and disc angular veIocity w can be obtained. men, h m the disc angie
information, the check valve coefficients of resistance K are calculated, Given the check
valve pressure drop Ap and the Eiow coefficient, the fi ow rate Qv through the check valve
is caiculated The fi ow torque To created at the disc arm is then calculated using the check
vdve Aow and coefficients of resistance. The total toque must indude the approprixe
components of the disc wei@t toque, counterwei@t torque, spring torque, b p e r
weight toque and the inertia. As described above, the flowchart for numericd simulation
of the check valve is shown in Fig. 43.1.
- --
Cal1 from Piping or Pump simul I
Initiai Condition "--'
1 F o r w d Row 1 1 Reverse Flow 1 Coefficient of Resistance ~oeficienient of resistance 1
I
Flow Torque
Toool Torque 1 1 Totd Toque
Runge-Kutta Solution c
Fig 1.3.1 FIowchart of Check VaIve Numerid Simutation
4.3.2 The RungeKutta Numerical Solution ta the Check Valve Dynamic
Equation
Tn section 32, the check valve differentid equation was described as a second order
ord inq differential equation. Refening to Eq. (3.2.1), it may be wrinen in the gened
form as a nonlinex function of torgue:
Therefore Eq. (4.3.1) cm be rewritten as:
where I is system total moment of inertia, and T is system total torque as a funcrion of
disc angiar velocity o, dise opening angle 19, and Ume t.
8 is disc opening angIe
w is disc mgular velocity
The system total moment of inertia are the sum of the moments of inertia of ai1
moving parts, incIuding dix, counterweight, darnper, and so forth. The system total
torque term T is represented by a set of relations describing:
Coefficient of resistance
Fiow toque
Countentrei@t effect
8 S pring effect
8 Damper effect
Valve geometric and dynamic parameters
The Runge-Kutta fourth order dgorithm [37,38] cm be applied to Eq. (4.3.2 and
4.33) simultaneousty.
Consider a first ordinary differentid equation with initial condition y(O),
We cm calculate y ,+, at the next time inmement r,,, = t, + h , with a known
value of y, at the previous time step r , . The founh order Runge-Kutta formula is written
as:
For Eq. (4.3.2), the fmt derivative vruiabies are:
h=hr y = 8 f ( Y J ) = WU)
and at the same time for Eq.(4.3.3), the second derivative variables are:
and the known initial condition are:
W ( I =O) =w, e(t = O) = e,
According to Eq. (4.3.5), the foIIowing is the C" code for the Runge-Kutta method:
double KI. K. K3:M LI. U. U. L4. Tr, rhem rlreraR, 011regaR:
KI = ToJ * Dc //for coeficieiu of Eq. (4.3.3) LI=011lega WC //for coe@ien of Eq- (4.32) Tr=T+0.5*Dc tirera = itlrera * Pi /1 JO; 18th radimatr, û,,isatt+Dt rIietaR = rltera + 0.5 *LI; theraD = rheraR * 180/ Pi; // B ui degree 01negaR = Onrega + 0.5 * KI; // mis the angular velociry ar r. @ is ar r+Dr
Qcv = GerVult.eFlow ( Tr, rIretaD); ToJ = GerToraiïorque(Qcv, tlieraD, OmegaR);
K1= ToJ W r ; i2 =01negaR * DC
Tr = T + 0.5 *Dr; rlieraR = rhera + 0.5 *U; rIreraD = rlreraR *I8O/ Pi; OinegaR = Oniega + 0.5 * K2;
Qcv = GerValreFloiv ( Tr, r1tetaD); ToJ = GetTora~orque(Qcv, rlietaü, OmegaR):
K3 = ToJ * Dr; U =OmegaR -Dr:
T r = T + D c rhetaR = theta + LI; tIreraD = rhetaR ' l8O/ Pi; OmegaR = Oniega + K.3;
Qcv = Ger VaiveFlow ( Tr, tIteraD); ToJ = GerToraiïorque(Qcv, tiietaD. OmegaR);
KI = ToJ * Dc Li( = OmegaR * Dr;
/DisulngularVeloc@ = Omega + (KI + 2 * KI + 2 W + KJ) / 6; fdic.4ngieRad = rheta + (LI + 2 *LZ + 2 W + L.1) /6; Irhese nvo ~uriables will be rtored
in Sysrems
The above p r o c m can be cdled at a pump junction or a piping junction according to the
valve placement.
4.4 Newton-Raphson Solution to Pump Boundary Condition m
in chapter 2, the head balance equation and speed change equation for the pump
conditions were derived as:
These equations can be solved simultaneously for a and v as following by using the
Newton-Raphson method:
As a first step in the solution a and v are approximated at the new time step by an
extrapolation of the previously computed values, two time stepq a, vo, and four tirne
steps, W. voo, eariier.
v=2v0 -Y, a=2ao -a, (4.4.2)
aF, aF, aF, aFr , ,Fr, -, - are waluated for this a. and v. Next the coefficients F, , - -
av aa a~ aa
The derivatives are:
a4 v - =2afB0 +4[lr+tan4-)J-~,v+C, a ~ r a
Eq. (4.4.1) can be solved for ha and Av :
Lec a''' and v"' be the initiai estimated values, and cr"' and v"' be the d u e s
after first itention. Then, the foliowing equations yieId improved values of a and v :
= +
y") = y") +Av (4.4.9)
This procedure is repeated either a fned number of times or until the surn of the
absolute values of the corrections ba and Av is less than an acceptable tolerance (e-g.,
0.0002). The flowchart of Fig. 4.4.1 iIlustntes the above procedure.
Cal1 from Piping Systern G
4
Compute X, i, A,, 4, B,, Bo
I Compute FH, FT, and their
Derivauon Usine Eq.(4.4.3-6)
1 Compute AG Av Using Eq.( 4.4.7), (4.4.8) kk=kk+l
t
Compute Qp HP- C;= Fig. 4.4.1 Newton-Raphson Solution for Pwnp
In this chripter, the numerical aspect of algebnic representation for the chmcteristic
method, check valve dynlimics equrition, and pump boundary conditions has been
discussed An ekgant soIution for pipeline transient andysis wris shown to be achieved in
the use of algebnic sdution, continuous data stonge, and indexing for system topology.
A fiowchart and C++ code were given for ciex and direct illustration to the check valve
and pump dynmic simulation. The software des@ which irnplements this andysis will
be given in the foilowing chapter.
Chapter 5
Software lmplement of Transients in
Pipeline Network and Check Valve System
In the previous chapters, the main focus was on the theory and methods for dealing with
hydraulic transients. The basic equations, the methods of anaiysis, die specific solution,
and specific bound;iry conditions were investiszited. As well, pipeline configuration, the
pump charactenstics, and the check vdve dynamics were discussed. Hydnulic transients
in the pipeline network system are implemented by, and interacted with the pump and
check valve dynamic behavior and software progrm. Therefore, the following chapter
wiI1 focus on the andysis of the pipeline network system with a view of softwre
engineering and desi9 and coding for the Hydro-Andysis program package using
Object-Oriented Progmnming techniques.
The andysis, which inchdes the problem specification and requirement anaiysis,
simulation analysis, input and output analysis, and the user interface analysis wiIl be
performed in Section 5.3. The design will inciude hi$ Ievel dgorithm and hierarctiical
diagrans chat wiII be given in Section 5.3. Aiso in this section, C" pror- Ianguage
wiIl be used to perfom transient andysis. As weII. visual C? wüI be used to design the
user interfaces for user-friendIy input and pphics output. The introduction to a i l classes
used in this package wi11 be given in this section as well, and Section 5.4 wiii simulate a
pipeline network system. What follows is an indepth step-by-step description of how to
use this sofnvare package.
5.2 Anaiysis for Hydru-Analysis Software Package
5.2.1 Problem Description
The application should input the pipeline connection information, the individual pipes,
pump, and vdve geometricd and characteristic data, and then simulate the system for a
period of time. Next it shouId determine the pressure at certain nodes and fiow nte at
certain sections dunng the occurrence of tmsients. After finishing the simulation, the
application should Save the output data, such as the Head (pressure) and Row nre with
respect to time, and aIso produce a -pphic output for the Head and Flow rate.
The pipeIine network transients anaiysis and simulation should combine the
pipeline tnnsients, pump and check valve dynamic simulation. This simulation should be
performed at different situations, such as in pump stm-up, pump failure, and cases in
which the convol valve is closed and when it is opened. The application can also handIe
different network connections: the senes system, the paraIlel system, the branch system,
and network system. It c m ded with diKerent pump anangements, including sinde
pump, senes pumps, the panlIeI pumps, and cornplex pumps. Findly, it c m simulate the
system for different sizes and types o i check valves.
5.2.2 Input Parameters
As described in Section 4.2.2, the connect relationship for a nenvork pipeiine system is
&en by an index vectot. The flow direction for a pipe and the type of junctions should
be specified The input data for the connection, pipe, junction, pump, check valve, vdve
and reservoir is as follows:
The connection parmeters include:
1. Index data
2. Nurnber of index
3. Nurnber of pipes
4. Number of junctions
5. Nurnber of pumps
6. Upstream junction numbers of a pipe
7. Downstream junction numbers of a pipe
The junction parametes include:
1. Type of a junction
3. Junction hend
3. Junction fiow n te
4. Junction elevation
The pipeIine panmeters include:
1. Pipe
2. Pipe diameter
3. Pipe friction factorf
The pump parameters include:
1. Pump start up
3. Pump failure
3. Pump normal run
4. Pump stop
For the pump s tm up, the foIIowing musc be laiown:
Pump coefficient Ao, Ai, and A:
i Time to gain speed Ts
Pump shut off Head &
For the pump failure:
8 Rated pump flow rate
8 Rated pump head
Rated pump torque
- 8 Rated pump speed
Pump specific speed
. Pump chmcteristic data
For the pump normal opention:
Pump coefficient Ao, Ar, and Az
The check valve parameters inchde:
1. Check valve size
2. Pipe diameter
3. Disc weight
4. Hinge len,gh
5. Auxi l iq device p m e r e r s such as counterweight, extension spring,
dash pot and so on
The control vdve parameters indude:
Vdve performance chmte r t
8 Valve closure time T,
The reservoir parameter is:
* Elevation of the reservoir
The simulation parameters are:
8 Sm time of simulation
Stop time of simulation
The output pumeters are:
Plot location
8 Pnnting or swing data location
For the pIot locations, the FolIowing must be known:
Junction number for head vs time
8 Pipe section nurnber for flow rate vs time
Findly, for the print out and save location, the foI1owing must be known:
Junction number for head vs. time (Maximum 3)
Pipe section number for flow rate vs. time (Ma.xhum 3)
5.2.3 Output Requirement
The output of the application incIudes the ۔le output and the p p h i c output
The file output gives the following &tx
1. Time
2. Flow rate at the pump element
3. Row rate at certain pipe locations (the pipe number are indicated by the user,
maximum 3)
4. Head at certain junctions (the junction numbers are in6icated by the user,
maximum 3)
5. Check vdve disc opening angle (il there are check vdves in this system)
The _mphic output should have the foIlowing Features:
1. Plot the Head vs. Time and Flow nre vs. Time simultmeousiy on the screen.
2. Display the following information:
pump start-up, pump failure, or pump normal nin
with or without the check valve
the pipe nurnber for the flow rate plot, the junction number for the head
ptot
3. A plot from which h e user my erisily obtain the data
4. Easy convol of pphic output display such as Iine type, color, and styIe
5.3.1 Algorithm for the Hydro-Analysis
The high level dgonthm c m be summarised as following
begin the application
read data (infornrarion for rhe nenvork connection, pipe, junmon, pump, check valve, valve, reservoir) read infonnarion on saving resulrs mdplonUlg resrilts
consrnrcr the nenvork system derennine the initialjlow rare for each pipe and head for each junction srne and print the initial fiow rate, head and check valve disc angle
Wtile the tirne is less tlimt tirne marùnwn (the fime of simulation)
if the element is check valve do check valve dynamic malysis get check valve disc angle
end if
calcrilare the pipe elementjlow rare and head calctrlare the pump elementflow rate and head
srore theflow rate, Itead and check valve disc angle for next time srep use Save andprint rhejlow rate, head of indicared [ocarion and check valve disc
angle time increment for the na t xsrp
end while
graphic displq the resrdt offlow rare Vs. time and head Vx. time
end the application
Fig 5.3.1.1 shows the flow chart of the above algorithm:
1 SW. save ni prim the initiai pmmm - --1
, S m savc and @nt KQ. 0
Fig 53.1.1 Flow Chart of Hydro-Analysis
5.3.2 Hierarchical Diagram
Before outIining the object-oriented-programming design, the hierarchicd d i a _ m for
the Hydra-Anaiysis (Fig. 5.3.2.1) is presented below:
* I
t
T ransients G r a p h i c S irn u Iatio n O u t p u t
i b
G r a p h ic LJ ser I n terface
FigS.33.1 (a) Hierarchid Diagram for Hydro-Analysis
Fig. 53.2.1 (b) Hierarchical Diagram for Graphic User Interface
Fig. 53.2.1 (c) Hierarchical Diagram for Tmnsients Simulation
Fig. 532.1 (d) Hierarchical Diagram for Output Graphic
5.3.3 Object-Oriented Programming Design for HydrctAnalysis
In this project, the Object Oriented Programming (OOP) [29] technique is used to design
the Graphic User Interface, Transént Anaiysis and Graphic output.
5.3.3.1 Major CIass Description for Graphic User Interface
This class provides an enclosed space on the desktop within which al1 application
interactions take place. This M e window is the frame to which the menu and
are attached.
Fig 5.3.3.1 The operation and attributes of CMainFrame
CChÎIdFrame is the frame bat hoIds the CHy&oAna£ysisyiew class and passes messages
and events to the CHyriiomZysisView class for processing or display.
Fig. 5.3.3.2 Operation of CChildFrame
This is the c i ss that displqs the visual representation of the document for the user. This
c lss passes input information to the CHydraAnalysisDoc clss and receives display
information from the CHydroAnuZysisDoc.
Fig 5.3.3.3 Operation of ChydroAnalysisView
The CFrontPageFomView cIss is the fom f m e . It holds visible objects attached to the
form. It is the base chss for views containhg conuols. It is used to provide form-based
documents in applications. It coordinates and intencts with the transient andysis (such as
PipeNet, Checkvalve, PrrmpFail, PrirnpSfan) clriss and p p h i c output application.
Fig 5.33.4 The operation and attributes of CFrontPageFormView
The CHydroAnafysisApp class mates dl of the other components in the application. It is
ais0 the class chat receives a11 event messages and then passes the messages to the
CFrontPageFomView and CHydroAndysisView classes.
Fig 533.5 Operation of CHydroAnalysisApp
6. CHydroAnalysisDoc
The CHydroAnalysisDoc class houses the document. This is the location of al1 the data
structures necessary to house and manipulate the data that maices up the document. This
class receives input from the CHydroAnalysisVinv class and passes dis play information
to the CHydraAnalysisView class. Finally, this class is also responsibte for savins
and retrieving the document data from files.
Fig 53.3.6 Operation of CHydroAnalysisDoc
CInputParameterDlg indudes the following classes:
CIndcrPara-Dlg
Fig 5.33.7 The operation and attributes of PlotPrintoutDlg
Ail of these classes receive data which is inpuned via the diaiog box, and then
transfer the data to the CFronrPageFonnView cIass. Fry 5.33.7 is the operation and
attributes of one of these cIasses. Other cIasses perform simiIar operations but with
different attributes.
' 5.3.3.2 C k s Description of Tratlsienb S i m u ~ o n
1. Pipe
The Pipe class is the base class for pipe simufation. It anaiyzes one element only. It cm
calculate flow rate Q md head H for each reach of pipe or pump. It aiso caiculates A, B,
and R, where A is the adjusted sound wave, B is the pipeline characteristic impedance,
and R is the pipeline resistance coefficient (referring to Eq. 2.4.17 and 2.4.18). Other
attribute such as Ndn, Nreach, and Nrip record number of down junctions. reach and up
junctions for this pipe.
Fïg. 5.3.3.8 shows the operation and amibures of the class Pipe. Pipelnitl ...)
obtains the data from the CFronrpageFormView class and transfers i c to PipeNeQCv.
VulveDoivnF-Hf) then proceeds to anaiyze the syscem if there is a control valve i n rhis
pipe.
Fig 533.8 The operation and attriiutes of Pipe
2. PipeNet2Cv and PïpeNer2NoCv
* GetHNFt] - + GctO(iit.nt)
-T P p N a b l b v
f- + GctONri] - @ Inih'alF-Hri]
- + InitiaIFnitiaIFHri) !- * Pi~ipaluncF-Hkt. nt]
:- + P+iuncF-H~i. nt] i- * PipeNcUNOc<ait int [ J,. int. a. nt. kt*
:- + PipeNdZC<it. int [ L int. nt. nt. flcat.M[Lbat[LW[l.int[Lint[t
Fig5.3.3.9 Operation of PipeNet2Cv & PipeSeQNoCv
PipeNetXv class inheritance the class Pipe, PumpStart, PrimpFail and CheckVuIve. This
is the class that connects a11 pipes, pumps and check valves tosether, forming a whole
pipeline network system. PipeNerXv clas simuIates the system that includes check
valves, whiIe the cIass Pi'eNet2NoCv does not inchde the check vdve. The opemion of
these two classes is shown is Fig. 5.3.3.9.
PrimpFail ciass is another base ciass for pipeline network simuIation. It simply
concentrates the hydraulic transient mdysis during pump failure, interacting with the
class Pipe if there is no check vaive Iocated after pump, and clriss Checkvolve when there
is a check vaIve Iocated after h e pump. Referring to Fig.5.3.3.10, the operation is:
Fig. 53310 Operation & Attributes of PumpFhil
PwnpFailO and -PumpFail() are respectively, the construccor and destructor of
the PumpFail clus. PumpFail (int) ovedoads the consuuctor. Therefon. only when there
is a check valve dter the pump. PumpValveBC(int) wiil Anaiyze the sytem. Otherwix,
PipeIHQ(inr) will suffice.
The anributes:
A--the wave speed
M O , AL00 - dimesionless pump speeds 4 at successive tirne step
AR, XL-pipeline ma, len-gh
B-pipeiine impedance, referring to Eq. (2.3.17)
BEïûJ3ETA-p~vîous and currmr dimensionless toque
CK-valve Iuss coefficient in velocity head
DT- time step
DX-dimensionless purnp data spacing, rad
EL4evaéon of the pump node
F-Darcy-Weisbach fiction factor
G-gravitational acceletation
K, Hp, Q, Qp, N-head and flow m e and speed during the transients
HR, QR, TR, RN-pump rated herid, ffow rate, torque and speed
KIT, KhrtAX-number and maximum number of Newton's method
TM-duration of transients
TOL-tolemce in Newton's method
V, VO, V00-dimensionless discharges at successive time steps
WB, WH-homoIogous torque and head data
WRR-rotational moment of pump
PrtmpSran class is a base class, it gets the data from CFrontpageFonnVierv clriss, and
then initializes the pump chmcteristic curve, so that the pump flow rate or head can be
determined by using this chmctenstic curve.
Referring to Eq. (3.3.60), the atmbutes A I and A2 are constants for the
chanctenstic curve, Hs is the pump shutoff Head, and Ts is the time for the pump to gain
speed. Jprmp is the initial element number for pump.
Fig. 5.33.11 Operation & Attributes of PumpStart
5. CheckValve
The base class CheckValve performs the check vdve dynarnic anaiysis. The check valve
dynamic analysis considers opention of added cornponents, such as:
DiscTorqrteIfzoclt). Using the specifics discussed in Section 3.3, other appropriate
components cm be added.
Fig. 5.3.3.12 shows the opention of the Checkvaive class. CheckVdve(), and
-ClreckValve() are, respectively, the constmctor and desuuctor of this class.
CheckValvelnirCfzoar,inr) mates the check vdve with different vdve size and maximum
disc opening mgIe.
Fig. 53.3.12 Operation & Attributes of Checkvaive
Refemng to Eq. 32.1, before perfoming the check valve dynarnic anriIysis, the
flow torque TF, and the bearing friction torque Tb mut both be known. In this analysis,
the bearing friction torque will not be considered, becriuse it is a very small term
cornpared with other component terms such as the counterweight and spring.
The operation DirectFZu~v~uat), DirectTorqudrm(irtr), ReverseFlow(),
ReverseTorqneAm(inr), and FlorvTorqrie~oatJToarfroar) are al1 for the analysis of the
fiow torque TF in Section 3.4.3. GeomericParamerer(fioat) and
GetCoeficientsOjResistance() are used to determine the coefficients of resistance for the
check valve dynamic analysis, as discussed in Section 3.4.2. GetTotalTorqtreCJIoarJIoat),
GerJoverT~oatJloar), GerDischtgie() and ValveDynamicsCflUat,float,jloat$oat) are
invoked in the final srrise of the check vdvt dynlunics amiysis. Rk4(......) is used to
sohe the dynlimic equation by Runge-Kutm method. The attributes of this c l a s are
shown in Fig. 5.3.3.12, The meanines are clex and wiII not be discussed.
The p p h i c output application is separated from the HydroAnaiysis sofnvm package.
During a fun, the HydroAnalysis starts the HydroGnphic probpm and then sen& the
andysis results to it. HydroGtaphic receives the data and disptays the Head and FIow
Rate pIot.
In the Hydro-Graphic application, the classes CHydroGraphicApp,
CHydroGruphicDoc, CHydroGraphicView, and ChfainFrame have the same
functionality as the CHydroAnalysisApp, CHydroAnu1ysisDoc, CHydroAnalysisVim, and
CMainFranre in the Hydro-Andysis.
QCBaseGraplz and QCBasePuge are two base classes for p p h i c output.
BuildGraph(PGRAPH-DEF,HDC) is used for initidizing the base p p h , and
BtrildPage(PPAGE-DEF) is used for initiaiizing the base page.
Class Graplrs is inherited h m the ciass QCBaseGraph.
BtrildGraph(PGRAPH-DEFJDC Mc) implements the plot. It gets the data from
HydroAnalysis application, and then plots two p p h s on the same page. The attributes of
this class are as ioI1ows: m-nGraplzNrrmber is the =ph number on the page;
nrgDynGrDesc is the pointer to p p h descriptions for dyamic p p h i c plotting, and
mqSraGrDesc is the pointer to p p h desaiprions for static p p h i c plotting.
CIass Pagel is inherited from class QCBasePage. BrrildPage(PPAGE-DEF)
impIements the page setting, indicating the page size, color, and position. The attributes
of this c I s s are as folIows: mqGraphl and mpGraplr2 are the p p h i c identity in this
same page. Fig 5.3.3.13 shows the description of HydroGraphic Class.
5.4 Introduction to HydroAnaiysis Software
5.4.1 Overview
HydroAnalysis is a pro- which simulates the hydraulic ansient in pipehe networks
with a check valve system. The program cm soIve the ansient fIow prob1em.s in simple,
branch and compIex pipetine systems.
B-@ HydroGtaphic claset 5- CAboud)lg &-y CHydroGraphWQp @--y CHydroGraphidim El-V CHydroGraphkMi &-y CMainframe @-2 . . Graphs 1 . . -%+ . . BuikiGraph(PGRAPH-DEF, HDC hdc] . . i . . - . . + G r H i nNm] . . i . ;- . Q m-nGraphNumber . . i . . - . . QmgDynGrDesc . . . . i :- 9 mgÇtaGrDesc 6-Y Pagel i . &g+ . BuüdPagefPPffiE-DE0 . . i . I-- . + Pagel0 i . . - . . 0 "Pagel0 r . - . Q mgGtaphl i i- $ mgGraph2 E-Y . . QCBaseGraph
i - + BMldGraph$GWHgEF.HDCl E -y QCBasePage . . : - 0 BuadPage(PPAGEgEF] @a Globalt
Fig. 5.3.3.13 Description of HydroGraphic Classes
The pro-pn HydroAnalysis is cornpletely interactive using the hlicrosoft
WINDOW Gnphicd User Interface. ïhe user can set and change a11 of the parameters
which describe the pipeline network and check vaive system. The simulation of the
hydraulic üansients caused by pump start up, pump failure, or valve operation cm only
be undenaken once a11 of the parameters describing the pipeline, pump, check valve,
vdve and reservoir have been defined
M e n nmning the simulation, the pressure head at indicated junctions (node) and
flow rate at indicated pipe are both written to a text Ne at each time step. The He is
saved to the working directory, and the user can read and print it at any time later. The
results of simulation crin be visualized as a -mph plotting the pressure head versus cime at
an indicated junction, and flow nte versus time for an indicated pipe.
The solution procedure adopted in the proe- does not make any allowance for
water column sepantion, which occurs when the pressure in the pipeline reaches the
saturated vapor pressure of the fluid, Therefore, c m should be taken when dedinz with
negative pressures produced by the pro-m. It should be noted that this procoram is to be
used strictly for liquid simulation, because the compressibility of the fluid was not
considered.
To run the Hydrohalysis probonm. the user will require a compueer sprem
running eirher Pvlicrosoft WNDOWS 95 or Iater, or WNDOWS NT 4.0 or later.
5.4.2 User Guide for Software Program Package HydraAnalysis
To simulate a pipeline network with an check vdve system, one needs only need to run
the appiication Hydrohalysis. The KydroGrapltic will be executed automaticdly during
the mnning of HydroAnaiysis. M e r starcing the application HydroAnaiysis, the main
window appem (see Fig.5.4.2.1).
5. A22 Seüing System Paranteters
1. Semng the Connection Parameters
Under the main window, one must set the connection parameter 6rst Pressing the button
Connecrion Pmameters, the foilowhg dialog box is displayai (Fig. 54-22):
-elemtnt number
Fig. 5.4.2.1 Main Window of HydroAnaiysis
Fig. 5.4.2.2 Diilog Box for Connection Parameten
The pipeIine network and check valve systern is displayed as shown in the main window
(Fig. 5.4.2.1). One may set the number of pipes, junctions, pumps index, and up and
down junction numbers of pipe and purnps as show in Dialog Box (Fig.S.4.22)- One
also must indicate the minimum reach number and sound speed. Normaîiy, the rninirnum
reach number is set to 2 or 3, and the somd speed is set between 1400 to 1550 mis for
water.
2. Setîing Index, Plot, Print and SinricIaflon Parameters
R e f h g to Section 4.2.2, the index for this system is shown in Fig. 5.4. 2.3. It should be
noted that the non-pipe eIements should be numbered 1st. Any others pipe elements may
be numbered by the user.
Fig. 5.4.23 Diaiog Box of indering
The user must also choose the duation of simulation. Fig. 5.4.2.4 shows the Dialog Box
of Sidation Parameters. ïhe user must define the duration of the simulation before the
program will begin that simulation. It s h d d be noted the solution procedure used
is based on the method of characteristics, and the computational tirne step is set at
the time it takes for an sound wave to traveI h m one reach to the next dong the pipe.
The program will save three pressure head records and three flow rate records at each
time step into file. The time duration cannot be set too large, because the size of the file
depends on the duration of the simulation which is selected by the user.
Fig. 5.4.2.4 Dialog Bor of Simulation
Fig 5.4.2.5 shows the Didog Box of Plot Print parameters. ïhe print and plot locations
are to be set by the user. The program will plot only one junction location for head and
one pipe location for flow rate, but will print (or save) a maximum of three Iocations for
head and three pipe locations for tlow rate.
After print out or display, if the user needs to print or display more locations, they
can do so by re&g to the main window and resetting the Plot and Print dialog box to
the desired parameter.
Fig. 5.4.25 Diaiog Box of Plot & Print
3. Setting Pump and Check Vaive Parameters
The pump-check valve parameter dialog box is show in Fig. 5.4.2.6. The user m u t set
the following data:
Check vaIve diameter: the user can set it by cboosing from a Iist box. if the user
checks the check box of WithOtctCheckVuIve, this list box will be greyed.
Set pump operation status: the user can choose h m the four radio buttons in the box.
1) If the user chooses pump start up, the fîrst group edit box d l appear, in which
the user cm set the pamp start up data such as Ts, Hs, AO, AI, and A2. The otfier
two boxes wüi be greyed See Fig. 5.4.2.6 in the Ieft coIumn.
if the user chooses pump failure, the second group edit box will appear, and the
other two wiii be greyed. The user can set Rated pump flow, head, torque, and
speed. See the middle column of Fig. 5.4.2.6.
if the user chooses pump normal m, the 1st group edit box will appear, the user
will oaly need to set AO, AI, and A2 for this operation status. See the right column
of Fig. 542.6.
[f the user chooses the last radio button Pump Sbp, al1 of these three groups are
grayed, and the user is not required to set any data at al.
Fig. 5.4.2.6 Dirilog Box for P m p Check Vaive Parameters
4. Setîing Pipe, Junction (Uode), Reservoir, and Control Valve Parmeters
The effect of transients in the pipeline will be different dqmding on the phpical
properties of the pipe, junctian, reservoir, and valve. It is assumeci at the staa of the
simuiation that steady state conditions exist in the pipeline network system, Fig. 5.4.2.7,
5.4.2.8, and 5.4.2.9 show the pipeline, reservok and junction parameters dialog box.
Fig. 5.4.2.7 Dialog Box of Pipeline Parameters
107
Fig. 5.4.2.8 Dialog Box of Resewok Parameters
if the transient5 in the pipeline are caused by the control valve closure or opening, the
valve opening and valve closure or open tirne can be defined by the user. The control
valve parmeters Dialog box is shown in Fig. 5.4.2.9,
Pig. 5.4.2.9 Dlaiog Box of Control Vaive Parameters
The steady state of flow will be controNed by the reservoir head, the diameter, length and
fiction factor of the pipeline, the junction type, the head, flow, and elevation of juuction,
and the initial vaive settings as showing in Fig. 5.4.2.10 .
Fig. 5.4.2.10 Dirilog Box of Junction Parameters
5. Save Model to afile, open a modelfrom previousfiIe
After aii of the parameters are set by the user, it is recommended that the model be saved
to a file for later r e p d use. At the main window menu, under File, Save Model As. ..,
the Save As window appears, allowing the user to save the model at any directory
indicated by the user, by entering the file name and then swing. îhe user is not
required to give the file extension, because the systm will add the mod
extension automatically. PIease refer to Fig. 5.42.1 1 - 5.4.2.12.
Fig. 5.4.2.11 Mena File Wlndow
Fig. 5.4.2.12 Save Mode1 As Window
AAer the user saves the made1 as a model file, pressin ie main
window begins the simulation. Next tirne, if the user wishes to nui a simulation, he or she
can start with a New or Open the model file. Refening ta Fig. 5.4.2. t 1, under the File
menu, Open Model, the foliowing Open widow will display (Fig. 5.4.2.13).
It should be remembered that initial data must be set by the user before a
simulation can be started Therefore, the save fiuiction of this program is very usefid for
users who intend to do multiple simulations of the same system, and the user is only
required to open the exiting model.
Fig. 5.42.13 Open Model Wiadow
After the user finishes inputting al1 of the data settings and presses the START button
under the main window of HydroAnalysis, the HydroGraphic page will display. There are
two plots displayed in this page (Fig. 5.4.2.14). One graphs the Head (Pmme) versus
T ie , and the other graphs Flow Rate (Discharge) versus Tirne.
In the Head (Pressure) Vs Tirne Plot for this case, it is shown that this plot is for
Pump start, with check valve at the location of junction (Node) number 5. The Flow Rate
(Discharge) Vs ïime plot shows that the curve is at the location of Pipe Number 4, pump
staa, and with the check valve. The simulation results of simple pipe with pump faiiure
wili be shown in Appendix C. Sùnulation resuits of other example pipeline network
systems will aiso be illustrateci in this Appendix.
Fig. 5.4.2.14 EydroCraphic Main Page (With Check Vaive)
The user cm change display characteristics of the plot such as the line me or line
attributes by doubleclicking the plot field under the main page. The plot parameters
window will appear. The plot data can also be displayed on the screen by clicking the
Dota Button h m the plot parameters window, a list of data wiii display on the scmn.
The user can then copy the resuiting plot &ta to an Excel, Word or Text file, for further
anaIysis. (Fig. 5-4.2.15).
Fig. 5.42.15 Display of the Plot Data
The system saves Head (Pressure) and Flow Rate (Discharge) of a maximum of
three Iocations wtomaticaiiy. The user can open the fie containiag this data under the
defauit directory by using NotePaci or WordPad. The user can also plot other locations of
this system by closing the Main Page, retuming back to the Main Window, changing the
Plot Parameters, and restarting the sixdation.
In this chapter, analyses of the pcoblem, input, and output were fmt introduced;
next, the Hydro-Analysis and Hydro-Graphic software were implemented by us iq
dgorithms, hierrurhicd diagram, and description of major classes. A users guide was
provided, giving detailed demonsmtions for this software. This software mates an
effective simulation for hydraulic transients in pipelines with check vaIve systems. It h a
a user-fnendly graphie interface and aIlows a user plenty of choices for convenient
simulation and andysis of pipeline systerns.
Chapter 6
Conciusion
6.1 Summary
The purpose of this thesis was CO design and implement a software package to mode1 and
simulate pipeline networks including check valve systerns. This objective was achieved
by analyzing hydnulic transients for pipeline network systems, analyzing check valve
dynamics, and implementing rhe software package which combines the pipelines with
check valves.
After introducing the continuity and motion equations. Chapcer 2 obrriined the
= some Hÿdraulic-Grade-Line form of the equations of motion and continuity by usin,
assumptions and simplifications. The equations are most suitable to the hydrriuIic
transients analysis for pipeline network systems, but are restricted to less compressible
fluids flowing at a low velocity.
The method of analysis of hydrauiic trisient tlow in pipeline sysrcrnh tartec ci
with the equations of motion, continuity and other physical property relationships. From
these basic equations, different methods employing different restrictive assumptions have
evolved. The charzicteristics method was andyzed and compared to the lumped panmeter
method in the time domain, the four-pole equations and the tmsmission line modelins
method in the frequency domah
The method of characterisllcs h a severai advantages over ocher rnethods thrit m
particulady relevant for hydrautic transients problems. These include an explicit solution
' and a procedure that is relatively simple with approximations. Therefore, it is par tic^ lrirly
suitable for the anaiysis of systems with complex boundary conditions.
Besides using the basic method of characteristics in this study, some improvement
has been added to this method. The Finire Difference Formulations and AIgebnic
Representation were combined to the rnethod of charactenstics. During the
implementation of the integrating chancreristic equation (2.4.7) and (24.9). the
trapezoidal rule was introduced for maintaining the linear form of the intsgrated
equations, at the same time keeping the second-order accuracy.At end of this chapter. the
introduction of the pump characteristic md the derivations of the boundary conditions for
pump faiiure and pump start up were inchded,
in Chapter 3, the check valve dynarnic equation was investigated for the analysis
of pipeline transiencs. The torque due to the weight of the rotliting Jisk. TV,, . the bearing
friction torque, Tb , the counterweight torque. T,.,, . the tlow torquc. TF . ancf the . ~p r ing
torque TI, were included in the dynarnical equation. The tlow torqus wris included in the
valve analysis, in which the orifice sequence mode1 was introduced. then determincd the
pressure drop for fotward and reverse now.
An important issue was CO determine the coeficient of resistance of a check valve.
The coefficient of resistance of the check valve is a function of the valve geornrrp and
disc opening angle. During the occurrence of uansient, the coefficient of resistance is
cdculated at each time step. Finaily. the check vaive boundary condition was introduced.
Chapter 4 presented the numericd model used to simulate pipeline network
transients including the check valve. This included the pipeline system model. check
valve dynamics model, and the pump characteristic model.
The pipeline system mode1 was developed based on the method of characteristics
which was investigated in Chapter 2. The solution was dgebraic. The use of continuous
data storage, connection index vector, and a fiowchart of the simulated procedure were
introduced.
The advantages of algebnic representations over the normal characreris~ic
equations can be summarized as:
They are norrnally applied over several reaches, with no need to cdculate the
transients at the intervening section; they are therefore a cornpucationrtlly
efficient solution for mukipipe systems such as networks.
0 They use a small Ar = LI(Na), so chat the boundary condition drtail is
presewed.
The variables H and Q of each time step are continuaily stored by using KM
(K,\,=U(a Ar) +/) which is the maximum size in the system, K which is used as a counter
for each time step, and Kp which is used as a pointer to identify the position in the veçror
H or Q at which current values of the variables are stored. At eüch iteration whrn k' is
incremented, so is Kp, the vaiue of the pointer. When Kp exceeds KM, the value Kp is set
back to O, so that it points to the first position in the vector. This procedure wiH save
much tonge space during computation.
The system topology musc be stored before starting the simulation. An indexing
method was introduced which offers one form of bookkeeping CO describe the system
connection. Ir was orïented around the nodes of the systern and, for each node. the
following information was given: the node number, the element number (sign) attached
to the node, and the eIement section number adjacent to node.
The check valve dynamic syscem rnodel was represented by a second order.
nonlinex, differentid equation. This equation c m be sulved using the fourth arder
Runge-Kutta algorithm. It must be solved simuitaneously with the pipeline sirnufation or
pump dynamic simulation. Check valve dyriamics need toque To and flow rate QV as
initiai conditions. At the end of each tirne step of simulation. the check valve d i x q i e 0
and disc angular veIocity o is obtained. Then, from the disc information. the check valve
coefficient of resistmce EL check valve pressure drop hP, and flow rate Qv are
calculated The flow toque To is caIcuIated by Qv and K. The above procedure is
illustmed by a flowchart in Fig.4.3.1.
The pump characteristic mode1 includes the head balance and speed change
equations. These equations crin be solved simuItaneously for u and v using 'itwton-
Raphson method. The flowchan of this solution was illustnted in Fig.4.4.I.
Chapter 5 described the irnplementation of the dynamic modei of pipeline
network systems with check valves into a working simulation pmsnm. This progrtim
inciudes three parts: Hydro-Analysis. User Graphic input. and User Gr~phic Output.
which were involved in two application. One wris the H~droAn~rlv.sï.s application {H>ctio-
Analysis and User Gnphic Input), and ttie other was the HydroGrciphic (User Gnphic
Output).
An overview of the prograrn was given including the andysis and the design of
the Hydro-Analysis and Hydro-Graphic applications. The analysis application consistsd
of probIem description. input and output requiremenc. The design wxs focusecf on rhr
dgorithrn, the hienrchicd diagram, major class descriptions, and their inter-relationship.
The user interface is essential in achieving the goals of this work. The Microsoft
Windows Graphic User Interface was used. The user could easiiy set and change dl of
the panmeters describing the pipeline network and check vaive system through a window
dialog box, button conuol, edit box, and other standard interface methods. This
application simulates hydraulic transients caused by pump failure, pump start up. or
control valve operation (closing, opening). It cm also be used in the system wirh or
without the check valve. The results of simulation can be visudized ris ri plot in whish
pressure (head) Vs. time at indicated junction and flow rate Vs. time rit indicated pipe.
The indicated pressure and flow rate can also be stored in text file which can be princed
or read at any time later.
In conclusion. the contributions of this thesis are:
Provided a hydnulic transient simulation package under the windon'b
environment with gnphics user interface for eue of use.
inchded pump dynamics. and check valve dynamics in the pipeline
transient analysis.
Improved algebraic representation and continuous data srorage to ihc
method of characteristics.
6.2 Suggestions for Future Work
The program HydroAnalysis is only the first step t o w d s the simulation of pipeline
systems with check valves. The solution procedure adopted in the p r o p m did not
consider the problem of water column separation. Although this only occurs when the
. pressure in the pipeline reaches the saturated vapor pressure of the fluid, it should be
considered in the rnethod of characteristics. Streeter and Wylie ['il introduced a procedure
in which the development, growth. and collapse of a cavity were considered as an internai
boundary condition. The pressure of column separation computed by using this approxh
was, however, found to be higher chan those measisured on a prototype. Therefcre. there
remains more work on this topic, especidIy in pro- irnplementation.
An expenmentiil aniilysis of the Orifice Sequence Mode1 for the check valve
dynarnic analysis is required. Experimentd nining is also necessary for progrrim
HvdroAnalysLr. Since al1 concepts and most dgorithms rire oniy considered for the
incompressible flows, compressibility will need to be inregrrited into the dynamic and
tmsients fl ow mode1 in the funire.
The user interfaces in this appIication onIy meet the basic requirement for thib
project, Throughout this thesis. great effort was made to fulfiII basic usable requiremrntb.
but thrre remains room for a grerit d r d more work in this area. .At pressnt. an indes
vector hris to be input through the window interface point by point. The complrxity u i the
pipeline networks system is lirnited by the size of mays which were used for panmeters
input of pipes. junctions, pumps, and valves. A well defined database shoutd be created to
store the pipe parmeters, pump chmcteristic data, and check valve panmerers. X
,srapphic user input should be introduced for the pipeline topoIogy data. so thac the user
would need onIy to dng in, and connect each elernent. and input parrimeters gnphicrilly.
Finaily. the gnphic output should be irnproved to display and store more plots as freely
chosen by the user.
REFERENCES
1. Wood, F. M., "History of Water Hammef', Report No. 65, Department of Civil
Engineering, Queen's University a i Kingston, Ontario, Canada, April 1970.
2. Rich, G., 'Hydrauiic Transients*, McGraw-Hill Book Co., New York, 1951
3. Parmakian, J., 'Water Hammer Anaiysjs: Prentice-Hall, Inc,, Englewood
Cliffs, N.J., 1955.
4. Street, V.L., and Wylie, E. B., "Hydraulic Transientsn, McGraw-Hill Book Co.,
New York, 1967.
5. Fox, J. A., "Hydraulic Anaiysis of Unsteady Flow in P@e Networks", John
Wiley & Sons,lnc., New York, 19ï ï .
6. Watters, G. Z., "Modern Analys& and mntroi of Unsteady Flow in P@elines:
Ann Arbor Science Publications, Ann Arbor, Ml, 1979; 2"d ed., Butterworth,
Boston, London, 1983
7. Wylie, E. B and Streeter, V. L., Wuid Transients",cGraw-Hill Book Co.,
New York, 1983.
8. Chaudhry, M. H., 'Appiied Hydrauiic Analysis: 2nd ed., Van Nostrand
Reinhold Co., Princeton, N. J., 1987.
9. Fox, J. A., "Transient Flow in Paes, Open Channeis and Sewersny John Wiley
& Sons, Inc., New York, 1989.
1 0. Sharp, B. B. and Sharp D.B., " Water Hammer: pracfial solutions", Arnold
Publishers, London, 1996.
1 1. Pool, E. B., Polwit, A. J. and Catiton, J. L., 'Prediction of Surge Pressure from
Check Valve for Nuclear Loops" Paper 62-WA-219, Amer. Soc. of Mech.
Engrs, October 1962.
12,Csemniczky, J., 'Hydraulic Investigations of the Check Valves and Bufferfiy
Valves: Proceedings of the Fourth Conference on Fluid Machinery,
AKADEMIA, 1 972,PP. 293-305.
1 3. Hong, H. and Svoboda, J., "Modei of Swing-disc Check Valve Suitable for
Lumped Parameter P@ing Network Simulation", Report, Concordia University,
Montreal, Quebec, Canada, 1981.
14.Hong, H., "The Design of Wafer Swing-Disc Check Valves for OptLmal
Performance: Thesis of Master of Engineering in the Faculty of Engineering,
Concordia University, Montreal, Canada, 1983.
15.Cavazoni E. M, "Design Optimitation and Performance Evaluation of a
Gravity Check Valve for Gas Service", Thesis of Master of Engineering In the
Department of Mechanical Engineering, Concordia University, Montreal,
Quebec, Canada, 1 984.
16. Provoost,G.A., Cn'tical Analyss to Determine Dynamic Characteristics of
Non-Retum Valve: 4m Int. Conf. On Pressure Surges, Bath, 275-286,1983.
17.Thorley, A.R.D. 'Check Valves Beha~or under Transient Flow Conditions, a
State-of-Art Review", Tram A.S.M.E. J Fluids Engineering 11 1 178-183,
1987.
18. Sidi Ould Sadfa, "Simulation for the Dynamic Response of a Transient
Hydraulic System: Project report. Dept. of Mechanical Engineering,
Aerospace Engineering, Concordia University, 1998
19. "Simulation of Water Hammer in Pipes with HAMMER",ersion 2.0
http~//www.civl.bee.qut.edu.au/projects/hamrner.htmI
20. "Faast Software for fluid transients: httpY/www.faast.com/
21. Thoriey, A.R.D., 'Dynamic Response of Check valves",-rn international
Conference On Pressure Surges, Bath, 231-242, 1983.
22.V. L. Streeter, and E. B. Wylie, "Fluid Mechanics: 8" ed., McGraw-Hill, New
York, 1985.
23.A. R. D. Thorley, "Fluid Transients in pbeline Systems: O. & L. George,
Herts, England, 199 1.
24.A. R. O. Thotley, and J. H. Oei, "Dynamic Behavior of a Swing Check Valve:
ProcSm int. Symp. Water Column Separation, IAHR, Obemach, Germany, Sept, 1 981
25. M. Suda, "Simulation of Valve CIosure aiter Pump Failure in PQeline", Journal
of Hydraulic Engineering, Vol. 117, No. 3, March 1991
26.Krasimir P. lvanov and Emil G. Boumaski, "Combhed Distributed and
Lumped Pôrametets Mode1 for Transient Flow Analysis in Complex Pîpe
Networks", Comput. Methods in Appl. Mech. Engrg. Vol. 130, 1996
27. B. Carnahan, H. A. Luther, and J. O. Wilkes, "Applied Numencai Methods",
John Wiley & Sons. Inc., New York, 1969.
28. Shoichiro Nakamura, "Applied Numefical Methods wilh Soffware", prentice
Hall, lnc. New Jersey, 1991.
29. David Budgen, 'Software Design: Addison-Wesley, 1 994
30. B. W. Kamey and D. Mclnnis, "Efficient Calculation of transient Row in
Simple P@e Networks",ournal of Hydraulic Engineering, Vol. 118, No. 7,
Juiy 1992
31. M. S. Ghidaoui and B. W. Kamey, "Equivalent Diferential Equatiuns in
Fked-Gnd CharactenStics Method: JoumaI of Hydraulic Engineering, Vol.
120, No. 10, October 1994
32. 0. A. Mclnnis, B. W. Kamey and D. H. Axworîhy, "Efficient vaive
Representation in Fixed-Grid Characteristics Method: Journal of Hydraulic
Engineering, Vol. 123, No. 8, August 1997
33. B. W. Kamey and M. S. Ghidoui, "Flexible Discretization Algorithm for Fixed-
Gnd MOC in P@elines",ournal of Hydraulic Engineering, Vol. 123, No. I l ,
November 1997
34. P. Krus, K. Weddfelt and J. O. Palmberg, 'Fast pipeline Mudels for
Simulation of Hydraulic Systems",ournal of Dynarnic S ystems,
Measurement, and Control, Vol. 116, March 1994
35. T. Chen and R. F. Boucher, "Junction CharactenSfrCs of Energy Wave
Methods: Proc Instn. Mech. Engrs, Vol. 21 1 Part C, 1997
36.A. S. Elansary, W. Silva and M. H. Chaudhry, "Numerical and Expenmental
Investigation of Transient P@e Row", Journal of Hydraulic Research, Vol. 32,
No* 5,1994
37. E. E Kitsios and R. F. Boucher, "Transmission Line Modeling of a Hydraulic
Position Control System", Proc Instn. Mech. Engrs, Vol. 200 No. 84, 1986
38. R. F. Boucher and E. E. Kiisios, "Simulation of Ruid Network Dynamics by
Transmisson Ene Modeling", Proc Instn. Mech. Engrs, Vol. 200 No. Cl, 1986
39. S. M. Beck , H. Haider and R. F. Boucher, "Transmission Lhe Modehg of
Simulated Drill Strings Undergoing Water hammef, Proc Instn. Mech. Engrs,
Vol. 209, Part C: Journal of Mechanical Engineering Science, 1995
Appendix A Review of Methods of Transients
Analysis in Pipelines
A 1. Introduction
There are two kinds of unsteady flow in pipes. One is the tr-ent msi flow that
represents the intermediate-flow condition when flow is changed corn one steady state to
another. The other is the osciIIatotyjlow that rnay be devetoped into a rtsonancr which
depends on the characteristics of the piping system and of the excitation,
A 2 Methods for Andyzing the Oscillatory Ftow
OsciIIatory flow may be andyzed either in the tirne domain or in the frequency bain.
In the tirne domain, one can use the Method of Characteristics. Using this method,
the partial diflerentiai equations describing the unsteady flow are converteci into ordinary
differential equations a d then solved. Analysis of the osciIIatory fiow by this method
assumes that the initial steady-state discharge and pressure head in the piping system are
equd to their mean values or equd to zero-flow condibons. The specified forcing
hnction is then imposed as a boundary condition, and the system is andyzed by
considering one fiequency at a hme. The disadvantage of this method is that it requires a
considerable amount of cornputer time. The main advantage is that the nodinear
relationships cm be inctuded in the analyses.
In the frequency domain, there are two methods of malysis availabie:
1. Impedance Merhod
in this method, the Terminal Impedance, &, which is the ratio of the oscillatory
pressure head to the discharge, is computed by using the known boundary conditions. An
impedance d i a c m between @ and is plotteci. The frequencies at which lZtf is
m~ximum are the resonant frequencies of the system.
Because of the lengthy a1;ebraic equations involved, the method is suitable for
di@d computer analysis only.
2. Transfer Marrir Merhod
The second method for doing frequency andysis is the urinsfer matrix method. It
h a been used for analyzing stnrctud, mechanical vibrations and eIectrical systems. The
method is brtsed on the linearized equations and on sinusoidal fiow and pressure
fluctuations.
The m s f e r mauix method is simpler and more systematic thm the impedmce
method. This method is suitable for both hmd and di@mI computations.
A 3 Method for Anaiyzing Transient State Fiow
NI methods of analysis of transient flow in pipes stm with the equation of motion,
continuity, or energy and equations of state and other physical property relationships.
From these basic equations seved different rnethods, each employing different
restrictive assumptions, have evoIved-
1. Method of characteristics [7,3 1,32,33] -
The characteristic rnethod of analysis tmforrns the partial differencial equations
of motion and continuity into ordinary differentiaI equations. It has several advantases
over other methods that are particuliiriy relevant in water hammer type pcoblems. These
inchde a f i n l y established stability criterion, an explicit solution so that different
elernents physicdly removed from one anothet in systems are handIed independently. and
a procedure that is relacively simple for approximations. Therefore. the method is
particuIarly suitable for the analysis of systems havins cornplex boundiiry conditions.
Its prirnary disadvantage is the requiremenc of strict adherencr CO chs tirne step-
distance interval reiationship. The method of characreristics has been discussed in detriil
in Section 2.4.
1. Lrimped Parameter Method 114,261
In the lumped-paramecer method, the pipe is divided into n-sections of equaI
Iength, where the fluid inertia, fluid capacirance and pipe elasticity and shear stress
becween the fluid and pipe wails are Iumped. Fig A 3.1 is a circuit represenrrttion of one
section of a pipeline. Between each consecutive node a Iumped mistance R and tluid
inertmce 1 represent, respectively, the friction losses and the fluid inertia in the
correspondin3 sections, At each interior node a capacitmce C connects the node to
zround. C represents the sum of hdf the capcitance of adjacent lumps. t
With reference to Fig. A 1, the coupled non-Iinear differentid equiitions retating
pressure head H at each interior node to the Flow rate Q thmu* each section, are @ven
dQ 1 '- = -(Hi - H,,, - RP,?) i = 123, ..., n dt I
In which 1143
Section i-I Section i
Eig. A 1 Circuit Represent of Lumped parameter method
where, f is the Darcy-Vieisbach friction factor, L is the length of the pipe, d, is the pipe
dimeter, A, is the pipe are& n is the section amount, a is the pressure wave propagation
speed for the fluid.
The lumped-panmeter method describes the system pressures and fiows by
coupled non-linear differential equations. This method may be satisfactory at very tow
frequencies and with a large enough n, but it requires excessive amounts of computer
time.
Frequency Domain
In order to derive the four-pole equations, the continuity and motion equations
cm be solved by using hplace transformation [22,23]. One cm obtain
In which E is the bulk ModuIus for the fluid and
Where, J,,($) is cdied BesseI functions of order n.
And
where, v is the viscosity.
where. a is cailed "viscosity factor".
An approximation over the whole frequency m g e is made, especinlly for the
We introduce the characterisric impedance 2, and the sonic velociry a
The equation (A?) and (A.3) cm be rewrinen as the following:
(A.9)
(A. 10)
Elimination of the pressure P h m the above
The solution of this second-order differentiril equlition
when .FU, at the input end of the pipe, P = PI and Q = QI, so:
(A. 12)
(A. 13)
Lettins P= Po and Q = Q, at .x = L, the output end of the pipe and inuaducing the wave
propa_oation time along the pipe Iine
Thefutir-pole eqrtarions are obtained as folIows:
We cm write above equation in the form of matrix
(A. 13)
(A. 15)
The block dia- shown in Fig. A2 cm be used to represent the dyamic behavior of
one single pipeline.
The four-pole equntion provides a pmctical solution in the frequency domriin. It is
very usehl for the andysis, synthesis and design of hydmutic pipelines.
Solutions in the time domain cm be found theoretically. By inverse Laplxe
msformation, the frequency domain c m be transformed into the time domain. However,
this procedure turns out to be exuemeIy complicated. The main difficulty cornes from the
frequency dependent friction factor N.
Fig A2 BIock Diaboram for Single Pipeline
n e use of four-poIe equritions may be considered for simulation. Using SimuIink
toolbox in Marlab, one m3y buiId black d i a c m for the single simple pipeIine; however,
for large and cornplex pipeline systems, ic remriins difficuit.
Transmission Line Modeling is essentidiy a hme-deIay rnethod, borrowing its
main concepts and fundamenuls of its cornputsitionai solution scheme h m the field of
electricaI power lines. In its eIemenrary fonn, a fhid nework is treated as a set of pipes
(OC pipe secment) where waves travel wirh a pure time delay. Connecting the pipes are
junctions of various types at which the waves are scattered (transmitted, reflected and /or
attenuated).
Sirnilar to the four-pole equation system andysis, The transmission line equation
are obtained as fo1Iows:
(A. 16)
where P and m are pressure and mas Elow at stations 1 (upstream) and 2 (downstream),
T is the acoustic tirne delay between stations, 2, is the characteristic impehce and D is
the D opentor i.e., eTD ~ ( t ) = F(r + T) .
Equation (A.16) is remnged as:
(A. 17)
(A. 18)
The first and second bncketed terms of buth equations (A.17) and (A.18) represent
ri&tward (u) and IeftwYd (v) travelling waves respec tively,
(A. 19)
Equation (A.19) defines IL and v, che decolrpIed wave variabIes. The pressure and fiow are
thus simply determined from hem as
The relationship between u and v at each end of a transmission Iine may be confirmed
now by substituting for P and m in equation (A.16). giving
Since the e'TD is the delay opentor
Thus, ti and v waves are linexly related to right and teft going p and m waves. and
therefore underso onIy a time delay in the line.
To use TLiM method in network modeling, al[ lines are divided into a number of
identical time delay lengths (Ar) along which u ruid v waves travel unaltered. Each line is
modeled computationally by a pair of software resisters, one each for the left- and right-
going waves. A feature of the method is that al1 dyamic elernents are modeIed as
distributed elernents-nrimely as losstess tnnsmission lines. Inenance and capaciunce
are modeled by equivaient opened- or ciosed-end transmission Iine snibs of delay At.
Resistance (simpty, although not essentiaiIy, linear) is Iumped at the junctions where a11
wave transformation (via scattering or attenuation) is thus concenated. Thus the mode1
consists onIy of resistive junctions and transmission lines (using both actuai lines and
short stubs representing dynamic eiements). The system can be represented by a general
scarzeriitg tnatrîr which acts on the incident wave vector to pmduce the reffected wave
vector.
If 4 represents incident waves and vi emergent waves from a junction, a matrïx S
c m be consmcted which contains a11 the junction scattering coefficients. This matrix
operates on the P vector of incident waves to produce a v vector of emergent waves. One
time step Iater this emergent vector of waves becomes the incident vector at the junction,
A forcing term F may be included as following:
[ v L = s[1dt+ F[P] (A.24)
where S is scanering matrix, F is the linear amy of forcing coefficients and [pl is the
forcing vector. Thus, the major concern is to find the scattering matrix S by studying
different pipe connections and different elements.
From the above anaiysis, this kind of method combines the lumped panmeter and
distributed p m e r e r modeIs, frequency domain analysis, and the time domain
impiement. It cm therefore be used to solve the problem of simple pipeline network. and
possible be extend for use in analyzing more complex systems.
There are other methods which may be used in hydraulic vansient malysis, such
as the graphical rvarer Irammer method in which friction is neglected in its theoreticai
development, but taken into account by correction.
Appendix B
Pump Characteristics
The reintionship between the pump discharge, Q, and the pumping head, H, must be
specified in a mathematical modet. The dischmge, Q, of a centrifuga1 pump is a function
of the rotationai speed, N, and the pumping herid, H, whereas transient-state speed
chanses depend upon the net toque, T, and the combined moment of inertia of the pump,
motor, ûnd liquid entnined in the pump impeller. Thus, four variables are involved in the
c h ~ t e ~ s t i c s , tiie pump dynamic head H, the discharge Q, toque ï, and the rotritional
speed N. Two of these variables may be considered independent (Le., for a given Q and
N, H and Tare determined from the characterisrics).
Since ffow conditions may be described for a turbine in the same manner as a
pump, we can use turbine chmctenstics to pump. For a @en geometricdly simitar
senes of turbine, with D representing the linex dimension, the homologous equation [8]
becomes:
where the subscripts L and 2 refer to two different-shed units of the homologous senes.
m e n resuicted to a parùcular unit, with the subscripts referrïng to two homologous
operating situations, Eq.(B. 1) reduces to
The homologous theory assumes that efficiency does not change with the size of unit, so
that
Combination of Eq.(B.2) and (B.3) obtain:
Various variables at the point of best efficiency are referred to as rared conditions. By
using these vdues as a reference, the following nondimensional variables may be
de fined:
where the subscript R indicates the nted conditions.
On the bais of Eq.(B.5), the dimensionless-homologous relations may now be
expressed as
h - VS. - - VS. - v / 3 v h a P c r - vs. - - VS. - a' a a' u V' v v 2 v
h v According to the homologous theory, - vs. - is the head-discharge relation
a' Q!
B v for any speed a! of chat unit, and similarly - vs. - is the representation of the torque- a = ar
discharge relations for any speed a of that unit.
During normal pump opecation, h, j7, v, and u are aU positive. However, during
the transient-state conditions, they may become negative individualIy or in p u p s .
Becriuse the above relations m difficutt to handle, the following method may be used to
overcome this di fficulty.
12 v B v vs. tan-'- vs. tan-' -
a' + v' a a2+v= U
v It is noted that for a given - one clin deveIop h ti
from a pIot of - vs. U a' + v' a'
v - , so that homoIo_oous relacionships are preserved in Eq.p.7). a
/ &arc tan
Fig B.1 Polar Diagnm of 0
If one had complete pump ditta for dl zones of opention, referring to Fig(8.1). a polar
v Ir diqmm of 8 =tan" - VS. r = and VS. r = ' would repmsenr the
U Q' + V' &Y' + V*
complete characteristics of the pump by two cIosed curves [7].
Pump Charactristics
Fig B.2 Cornpiete Pump Characteristics
v=O a=O v=O CGcO v=O
Turbine
Zone
vso ac0
O n/2 7r 3n/2 2R
Reversed Speed
Dissipation
Zone
v > O
uc0
Dissipation
Zone
v < o
a20
Normal
Zone
v 2 0
u20
-1 v The angle 1 = + un - may also be plotred as an abscissa against WH(.r) or a
v To obtain the rectan_ouIar coordinate plot (Fig B.?), the 0 =tan-L- is an angle between
a!
- X and f 15 . It holds for al1 red vaiues of v andu except v=O and a=û at the same
time. The p m e t e r x varies from O to 3jr . We cm determine sets of vdues of H, Q, T,
and N, or K. Q, El, and efficiency q for various openting points throughout the zone.
Since To =- 'Hi for a purnp. and To = Q H y q for a turbine, T rnay be rl
deremined. Thus the four values II. 8, v, and ucan bs obtained, when nted values UR,
Th QR and NR are given. From Eq. (BA), .r, WH* and W,', may be determined for each
openting point.
Appendix C
Simulation Results
1. Simple pump, check valve andpbe system simulation dvroig pump folure
Valve
Fig. C 1 Simple Pump, Check Valve, Pipe Systems
The results of the simulation are as foiiowing:
. US.54 145.286 145.O
147 147.397 ld?. 347 148.048 149 m 242 149.799 149.973 150.819 152 lll 114 es48 1S6.971 lS8.13
160.369 164.151 167.569 170.942 175.068 180.259 185.96
191.997 203.676 223.513 220.174 231.304 248.R1 2 6 7 . U 287.8% 356.854 495.251 7 71.036 lStQ.l6 3532.24 2472.14
-2O5, 948 -933,314 -2896.37 -1867 .O4
738.973 1448.46 3364.94 2365.86
-173.017 -865.447 -21 37.61 -1766.61 707.994 1384.13 3214.08 2269.69
-143.829 -004.385 -2594.07 -1614.95 680.452 1326.1
3077.33
2. Branching system with check value and wiîhout check vabe simulation
Hg. C 3 Graphic Display of Branching System Without Check Valve
Fig C 4 Gnphic Display of Braacbing System With Check Valve
152
Simulation Result of Branchine Svstem without Check Valve: Tian Qnup 9 1 Q 2 4 3 Bn 1 Iin 2 Bn 3
0 1.14192~-007 1.14192~-007 1.56917 73 73 70
79.0731 79.0731 79 -0731 85.3492 85.3492 87.8811 103.604 10s. 11
120.606 l25.194 124.38 124.71
124 -721 118.672 118.168 121.235 lO6.Ol6 98.9lD9 84.4173 80 .a203 80.2193 86.2624 85.9322 87.8399 102.343 103.696 117.487 121.51
120. R 9 119.965 lZO.049 114.375 113.79
116.751 lOI.OSl 96.4724 0 4 0282 80 1446 80.7188 86.346 85.4775 86.649 99.3088 100.43 112.066 U S . 476 113.737 113.013 113.234 108.138 107.759 110.741 99.1493 93 .I417 83.3456 80.072 81.0431 86.1359 84.6693 85.1227 F5.7004 96 -6234 106. OX! lO8.851 lO6.567 lOS.8U6 lO6.213 LOl.8lI 101.72 lO4.7U
SimuIation R d t s of Branchin~ Svstem With Check Valve: Tira
-Po 9 1 Q 2 4 3 Ba 1 Bn 2 9, 3 Theta
O 0-0.0007 1.56917 73 73 70 O O. 275 O 0-0.0935833 1.60888 73 79 -0731 70 O
Appedix D
Head File for HydrauAnalysis And HydrauGraphic
/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / I / / / / / / / / / / / l / / / / / / / / / / / / / / / / / / / / / / / / / / / O ProntPageFormview.h : interface of class / / @ author: Tianhe Wea, 1999 / / @ Version:Z.O / / O Copyright: nitepro Inc. / / fi! Concordia University
#if -Ise-VER >= 1000 #praqma once #endif / / -MSC,VER >= 1000 / / FrontPageFormView.h : header file / 1 llinclude "DefineOData.hm / / l / / / / / / / / / / / / / / / / / I / / / / / / I / / / / / / / / / / / / / / / l / l / / / / / / l / l l l / / / / / / l / / / l l / / ~ l l / l / / / CFrontPageFonnView f a m view
/ / Farn Data public:
/ / f (2SXJiAT.i ( CFrontPaçef crrnView) enum ( IDE = IDD-FXONT-PAGE } :
/ / NOTE: the CTassWi=ard will adà data nenOers herp l / } 1 A"r x-DATA
/ / Attributes public :
RESEJZVIOR-DATA CONTROL-VALVE-DATA S ïXUiATION-DATA PIPE-LINE-DATA i m c ~ ION-MTA ~-cEECKCKVACVF~DATA PLOT-WINTOUT-DATA CONECTION-D&TA mEX-DATA / / Operations public :
ReserviorDaca; Contro llIalvData ;
SimulationData; pipeLineData [li] ; / / you have 17 pipes
JunctianData [16] ; / 1 sixteen naw Pump~eckValvData[3I; / / 3 now
?lotPrintout!lata; ConectionData; IndexData[ZOOI ;
/ / Ovezrides // ClassWizard generated virtual function overrides / / { ( A P X , V I K ~ (CFrontPageFormViewl protected: v i r t u a l void DoDataExchange(CDataEXchdnge~ pDX); / / DDX/DCV support v i r tua l BOOL PreCreateWhdow[CRUTESTRM:TL C S ) ;
/ / 1 ~AP]CVIRTOAL
/ / Imglementation protected:
virtual -CLrantPageFormView ( ) ; #ifdef -DEBUG
v i r t u a l void AssertValid t l const ; virtual void Dmp (CDumgCantexth dcl COU%;
#endi f
/ / m e r a t e c i message mag functians / / ( (AFX,MSG (CFrontPageForrnView) afxgisg void OnPipeLineParamLO; abcmg void onPipeLineParam2 [ 1 ; a-g void O ~ ~ e s e m x P a r a m l l ; afx_rnsg void OnSimulationParam( i ; a fx-mg vo id 0nJunc t i a n ~ a r d ( ) : a f x m g void afx_plsg void a f x m g void a f x m g void afx-msg void afx_rnsg void afx-mg void a fx-msg v~oid afx-nug void a f x m g voici ah-mg void
//({AFXJNSEXT,LOCA?IGN}} / / Microsoft Devela~er Szudio vil1 irsex ac!C:ional declaraticas L=&iatel.~ before the previous line.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / / / B CheckVa1ve.h: interface for the Checkvalve class. / / O author: Tianhe Wer, 1909 / / @ Version:2.O / / O Copyright: Ritepro Inc. / / @ Concordia University
tif JSC-VER >= 1000 tpragma once tendif / / JSC-VER >= 1000
#define KDIFECTTOT 1 #define KDIRECTSEAT 2 $define KDLRECTLNTERM 3 tdefine KDIRECTUZIT 4 #define DIRECTAW 5 tdefine KREVTOT 6 tdef ine KREVSEAT 7 #define KREVZNTERM 8 #define KREVEXIT 9 tdefine REVERSEAnM 10
tdef ine HAXWGLE 70
class Checkvalve
public: Checkvalve ( l ; vircual -CheckValve l ) ;
flaat fFLowTorcpe: float fDiscTorque; float fCTinPPorciue; float £TotalTorque; flcat fDiscAngularveiaci:y: float fDensity:
float fPipeDiameter;//Dt float f PipeAirea; floac fSeatDiameter; //D2 f loat f SeatArea; float EDiscDiamecer; / /DCL float fDiscArea: float fShaftOffSet;//DIs float fHingeLength;//ALA float ftiingeWidth;//2 . XD f loat fDis&iomentOf Inertia; 1 INN float EDiscWeight;//WV f loat EDiscCenterOfGravity; / / A X int iDiscMaxAngle;//TFIIAF float fDiscOfESetAnqle;//AETAV f loat fPipeFriction; flaat frxitinqûrif icei)iameter: f loat f IntermediateCrif iceDianecer; f loat EPipeToSeatR; floaç fIntarmediacËorificelK; float fEbùtingOrif icek;
float fVa1veTocal.K; f loat fC'IWWeight; f loat ECTWLever ; float fCTWgle; f loat f c m 0 m ~ t O f Inertia; float f~pringkllUnitialAagie; f loat fSpringAnnlength; float fSpringPivot~hafaistance; float f~pringExtension; float fSpringExtensionFactor; float fRestedSpringLength; float fmtensionSpringTorque; float fCoilSpringFactor; / / Nm/o float fCoilSprFngInitia1Angle;//0 Cloat fCoilSpringTorque; //Filn
f loat f~oef f i c i e n t s ~ f R e s i s t a n c e [ ~ l [IO 1 ; f laat GeomeCricParameters ( f l0at) ; flaat DirectPlow(f1oat); f loat ReverseFlow ( ) ; f loat PTowTorque ( f loat, float , f loat l ; float DirectTorqueAm(int); float ~everseTorqueA.nn(int) ; f loat DiscTorque ( f loac) ; f loat CFrPTorqLte ( f loat ; float TorqueFromExtensionSgring(tioa:i; f loat TosqueFromCoilSpring ( f loat l ; float ValveDynamics ( f lca:, float, flcaci ; f loat ValveDynamics ( flcat, floac, Lloac, flaac) ; f laat GetDiscAngle ( 1 ; vcid checkValve1nic ( ftoat. int) ;
f loat GetCaeff iciencsCflesist~~ce ( ;
floac GecTotalTorque 1 float, f loati ; f loat GetValreFlow ( f loat, f laac, flcati ; n i d rkl(flcat *. floar,float,fioac -,floa:,Elcac ( * ) (flca:i,flca:[], flcz:
El, i n d ; f h a t R 3 4 (Eloac. f laac, f loat, float, f Ioat, f Ica:) ;
private: float mlscilnglelub;
/ / / / / / / / / / / / l / / / / l / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / l / / / / / / / / / / / / B Chi1dFrm.h : interface of the CChiIdFrame class / / @ author: T i e W e n , 1909 / / B Versi0a:P.O / / B Copyright: Ritepro Inc. / / @ Coacordia University
#praqma once #e?.dif / / JSCCVEK >= 1000
class CChiLdFrame : public (mDIChildWnd C
DECyLflE-DYNCFEATE ( CChi ldFrame 1 public :
CChildPrame ( 1 ;
/ I Attributes pub1 ic :
I / Operations public :
/ I fmpleneataticn public :
virtual -CChil&-rane ( ; iCifdef ,DESUG
virtual void irsser:Valid ( 1 co~s:: virtual voi5 C w (CZmpCanc&xth ec) cer,sr:
#endif
/ / Generated message map 2mccions protected:
/ I I IAFX-EG (CChildFrame) / / NOTE - he ClassUizazd wi l l a& and remove member functions
here. / / DO NOT EDIT what you see in these blacks of generat& code!
/ / 1 IAFX-KG DECLARE-MESSGEEMAP ( I
1 :
/ / E IAE'X-INSERT-WCATIONI 1 / / kficrosoft ~eve lopez Studio wi l l k e r z a&cional declarations immedia:ely before the previaus line.
/ / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / / / Q C0nectionPara.h : interface o f class / / Q author: Tianhe Wen, 1999 / / B Versioa:Z.O / / @ Copyxight: Ritepro fnc. / / @ Concordia University / / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
%if -MSC,VER >= 1000 tpragma once #endif / / -E(-jC-VER >= 1000 / / Canecti0nPara.h : header file
/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / i / / / / / / / / / / / / / / / CConectionPara dialog
class CConectionPara : public CDialog t / / Construction public :
CConectionPara(C:JndT pParent = NULL); / / starrdard constlructo:
/ / Dialog Data / / ( (&.Y-DATA (CCcneccionPara) enum ( U3D = IDC,DLG,CONETCTION } : UTNT m-fNm*ige; UINT m,f NunJuc t ; UINT m-fNcmPumi~; UIm m-f Sumlzdex ; UINT m,nDowj?ipipe02 ; UïNT m-nDowJXpipe0 1 ; üINT m-nDowJNpipe0 3 ; UINT m-nDawZNpipeO4 ; UDJT m-nDowJXpipeOS; U Z m m~iDowJNpigeO6 ; üINT m-nDowJNpipe07 ; U m m-nDowJXpipe0 8 ; UINT m-nDowJNpipe0 9 ; U m m-nDowJNpipe1i.l; VINT m-nDowJNpipeL1; UIN'r m-nDowJNpipei2 ; UINT nl,nDowJNpipel3 ; UINT m~~DmJNpipe24 ;
DïNT m-nDowJNpipeT5 ; DINT m,aDawJNpipel6 ;
m-nDowJNpipei7 ; DINT m-nDowYNpipe18; U m iQnDowJNpipeT9 ; UrNT m-nDawJNpipe20 ; MNT m~DowJNpipe21; ûiîül? m_riDowJNpipe22 ; UINT m-nDawJNpipe23 ; DINT m-nDowJNpipe24 ; UINT III-nDowJNpipe25 ; D m m-rDowJNpipe26; tlZNT m-nDowJNpipe27 ;
WINT m,nDowJNpipeZB; UINT m,nDoiJiJNpipeZ9: UINT m-oDowJNpipe30;
UINT f loat UINT UINT - UINT UINT UINT UINT UINT UINT OINT UINT UIN'r u m UINT OINT VINT UINT UIN'r UINT UINT UINT UINT UINT u m ri UZNT UINT u m OINT UINT //llAE
m-nlChReach; m-fSoundSpeed; m,nUpJNpipeOl; mm_nUpMpipeOl;nUpMpipe02; m-nUpJNpipe03; m-nUpJNpipe04; m-nUp3Np ipeO 5 ; in-nUpJNpipe06; 1~nUpJNpipeO7 ; m~nUpïNpipe08; mm,nUpJNpipeaS;nUpINpipe09 ; m-nUpJiUpipel0; mm,aUpJNgipelL;nUpJNBipelL; m-nUp&Vp igelt ; mm_nUp3Npiper3;nUpüNpipel 3 ; m-nUpJNpipel4 ; ~nUp3Npipel S ; m-nUpJNpipel6; ~nUplNpipel7; m-nUpTNpipel8 ; m-nUplNpipel9; m-nUpJNpipe20; m-nUpJNpipe21; m-nUpJNpipe22; m-nUpJNpipe23 ; m-nUpTNpipe24 ; m-nUpJXp ipe2 5 ; m-nUpJNp ipe2 6 ; m-nUpJNe ipe2 7 ; m-nUpJNp ipet E ; m-nUpJNpipet9; rn-nUpuI ipe3 O ;
x-DATA
/ / Overrides / / Classiiizazà generateë virrial fünction overrides / / { (AFX,VZRWAL ( CConectianParz~ protected: virtual void DoDataExchange{CDztaE;tchange* pDX); / / DDX/DDV supparl, / / 1 1 AEFX~mmArd
/ / lmplementation protected:
/ / Generated message nap Eunccions / / ( ( AE'X-MSG (~~onectiarr~aral'
/ / afx-msg void OnSutIn6exT ( 1 ; / / 1 1AE'X-EG DECZARECZAREMSsAG2-KAP ( 1
1;
/ / E CAl?X,INSERT~LOCXTIO~ 1 / / Microsof t Developez Studio will insert additional declarations imediately before the previous line.
/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / l / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / @ Cts1ValveDlg.h : interface oE class / / @ author: Tianhe Wen, 1999 / / @ Version:2.0 / / @ Copyright: Ritepro Tnc. / / @ Concordia University
#if JSC-VER >= LOO0 #pragma once #endif / / ,MçC-VER >= LOO0 / / CtrIValveD1g.h : header file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / CCtrlValveDlg dialog
class CCtrlValveDlg : public CDialaç E / / Construction public :
CCtrlValveDlg(CNndg parent = NCTLL); / / standard const,uctar
/ / Dialog Data / / [ [SX-DATA(CCtr1ValveDlgl enum ( IDD = IDD,DLG-CTIZL,V.~<vZ 1 ; f laac ~ E T a u l ; f loat m-fTau2 ; float m-fTau3 ; f loat m-fTauC : f loac m-fTau5 : float m-fTau6; f laat m-Eau7 ; long m-nTime; / / 1 I LFX-DATA
/ / Overrides / / ClassWizard qeneraced v i r c s l 5-xccicc cvetti&es / / f [AEX-VIXT'üX ( CCtzlValveDlc) protected: vittuaï void DoDataExchl~e (Ca:a3&ac~er pDX1; / / DDX/D!W support 1 / I ?AEX-VIXrn
/ / fmplementation pro tected:
/ / i iAF;CINSERTTLOCArrON} 1 / / Kicrosoft Developer Studia will insert additiollal declarations immediarely before the previaus line. #endif // !defined(AFXAFXCTRI;VALVED~G-E-76576583,COBD-llD2~B4E44OOAOC974979AA~WEDED1
/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / B D e f i n m a t a - h : interface of class / / Q author: Ti- WC?, 1999 / / B V e r s i o n : 2 . 0 / / @ C o p y r i g h t : R i t e p r o Inc. / / B C o n c o r d i a U n i v e r s i t y / / / / 1 / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / ~ / / / / / ' / / ~ / / / /
# ifndef DEFINEDDAT9.H # d e f i n e DEFINEI3DATA-H
typedef struct I Élaat fKeadR1; f Lou t fïieaadRS ; f l o a t fEeadR3; float faeadR4;
1 RESERVIOR-DATA ;
typedef struct ( float fTau[7] ; in t nTime:
1 CONTROL-VALVE-DATA;
typedef s t ruc t ( f l o a t fStartTime; f loat f S t o p T i m e ;
) SïXJïATICN-DATA ;
UINT E P r i n t o u t ? i p e t ; DINT EPrintoutPipe7; USNT f Printout3ipe3 ; U ï N T fPrintcut3unl; UINT f P r i n c o u c J u n 2 ; VINT fPrlntaucJun3 :
) PLOT-PRINTOUT-DATA;
typedef srruct ( UINT nNimiP i p e ;
UINT n N W ~ ? c t ; UINT mrmipump; UINT nNtmmdex; UINT nMih5each; f l a a t f Saunàçpeeü;
/ / int f I n d e u 1 2 0 0 I ; UZNT niJpJNPipe[QOl; UïNT nDwJNPipe [ 40 1 ;
} CONECTION-DATA;
typedef strict [
typedef strucr ( f l o a t flliaxueter; f l o a t f t r i c t i o a ; f l a a t flenqth;
1 PIPE-LIUS,DATA;
typedef struct ( int nJunayyie; Eloat fElevacion; float fFlow; f l o a t fHead;
typedef s t r u c t ( int nPumpStatus; int ruliameter;
/ / s t a r tup , f a i l , noraal, stop / / always e f fec t ive , it is O hased index, it is noc
the r e a l diameter value //you se lec ted , bu t it is the posi t ion, s t a r t i n g £rom O , t h i s i s
t rue / / f o r the specified speecï a l sa
int nCheckvalve; f l o a t EAO; / / e f f ec t ive on s t a r tup f l o a t W; / / .............. f l o a t fA2; 1 1 . ............... f l o a t fEs; / / .............. f l o a t fTs; / / .................. f l o a t ff low; / / e f f ec t ive CR f a i l f l o a t fsead; / / ..................... f l o a t fTcrq; / / .................. f l o a t fspeed;
.............. i n t nSpecifiedSpeed; / / f l o a t fNo-malil0 ; / / e f f e r z k e c?, nornal floa: fNonialAl; f l o a t LirlcmalXZ;
1 m ~ c ~ ~ c K - ~ A L v E - ~ A T A ;
/ / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / / / Q Cr0ntWnd.h : interface cf cLass / / B author: Tianhe Wen, 1999 / / 4 Version:S.O / / Q Copyright: Ritepro Inc. / / @ Concordia University / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / l / / / / / / / / l / / / / / / ~ / / / / / / / / / / / / / /
#if JSC-VER >= 1000 #pragma ance #endif / / ,WC-VER >= LOOO / / Fr0ntWnd.h : header file / /
class CFroncWnd : public CWnd i / / Cons tructian public:
CFrontWnd ( ) ;
/ / Attributes pcblic :
/ / Operations public:
/ / Imglemeïtation public:
virtual -CFrcncWnâ ( 1 ;
/ / Generated message nap fuccions protected:
/ / ( iAFXXMSG (CFrontWndl afxmsg void OnPaFnt i ; / / 1 1AFX-MSG
1 / ( (&~-INSE3iTTLOCATION1 I / / Microsaf t Developer Stuc?ic w i l l inser t aocitianal 6eclaratians imediateLy before the previous line.
/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /~ / / / / / / / / / / / B HydroAnaiysis.h: main header f i l e for the HYDRûiWXYSIS application / / 4 author: Tianhe W e n , 1999 / / B Version:2.0 / / B Capyriqht: Ritepro ïnc. / / 4 Concordia University / / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
# i fnde f -AFXWINX- terror include 'scdafx.hl before ZDcluding this f i l e for PCI!
fiendi f
#inchde 'resource.hR / / main syaibols
/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / CHydroAnalysisApp: 11 See HydroAnalysis.qp fcr the Mlenentaticn of tk i s class / /
//EEAFX-MSG(CE.:yCrcilnalysisApp) a f x s g void d~ppithout i ) ; / / NOTE - the ClassWiaard w i l l aOd. anà remove nember functions here. / / üû NOT EDIT w h t you seo in these blocks of generated ccde !
/ / ) l r n - M S G DECLARE~SSAGE-MaP ( 1
1;
/ / ( (ilFXilFXINSERTTLOCA?raM) 1 / / Microsoft Developcr Studio w i l l inser: a w t i o n a l &darations imte6iately before the previous l ine .
/ / // @ HydroAnalysisDoc,h : interface of the CRydroAnalysisDac class / / B author: Tianhe W e n , 1999 / / B Version:2.0 / / B Copyright: Ritepro Inc. / / 8 Concordia University / / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . #if !de fin& (AFX,h~RO~YSIÇDOCÇDOCHHB66D4D61I49D1~1TD33BD3IIOOEO291l2S677LNCLUD~ -1 #define APX-~ROANALYsIÇWCÇWCEE366D4D61-49Dl-11D3,BD3I-OOEO2911S567-IN~ISD~
#if _MSC,VER >= 1000 Cpragma once #endif / / -MSC-VER >= 1000
elass ~~ydroiînalysisCoc : public CDocument C protected: / / create f r o m sezialization only
CIiydrodnalysisDacO; DECLAflZ-DYNGEATE (CEyàroanalysisDcc)
/ / Attributes pub1 ic :
/ / Operations public :
/ / Implementation public:
virtual -CEyeoAialy s isDx i 1 ; #ifdef -DEBUG
viztual void AssertValid() const; virtual void Dump (CuumpConcext& dc) cccsc:
#endi f
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / / / B KydroAnalysisView-h : in te r face of the CEIydraAnalysisView c l a s s / / @ auchor: Tianhe Wen, 1999 / / @ Venion:2.0 / / B Copyright : Ritepro Inc. / / O Concordia University 1 / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / I / / / / / l / / / / / / / ~ / / f / / / / / / / / / / / / / / / /
t i f -FISC-VEX >= 1000 ltpragma once #endif / / JSC-VER >= 1000
class CtiydrohnalysisView : public CView c protected: / / a e a t e Eram ser ia l izac ion oaly
CHydroAnalysisView i ; DECLARE-DYNCRZATE ( CEydroAnalysisView)
/ / Att r ibutes publ ic :
CIiydroAnalysisCocr GetTroCun@IItO;
/ 1 Opera t ions publ ic :
/ / Overrides / / Class!.lizard gerieraced vir t r ta l fucc-icn averr ides / / ( (~Fx-nnTuX (C5:rCroiinalysisVlew) public : v i r t u a l vc io CrSraw(C.C' p K ) ; I l ove-~i66er? :G &aw :Lis viod v i r t u a l =COL ?reCreateWindcwiWTES~ECT& CS) ; protected: v i r tuaf =COL ~n~repare?rinting(CPri~:I?.fc* pIn fe ) ; v i r t u a l voLd OrSegin?rinting(C=C' p K , ClrintIafo ' pf?fc) ; v i r t u a l void OrSndFrintinq (CD? PCC, Clr intInf or pxnfo) ; / / 1 1 A F L r n T d
/ / ïmplemenration public:
v i r t u a l ayc?roAnalysis~iewO; # i fdef -DESOG
v i r cua l voici as se r tVa l id0 const; vf rtual void Ctmg (CIXrmpC~nt~th dc) cars t ;
àendi f
/ / Generateci message map funccians procecced: .
/ / E CkLCJfSG iCSy&aAnalysisView) / / NOlZ - the ClassWizard w i l l a& axà remove member functioas h=e. / I DO NOT EDST w h t you see in these blocks of generated code ! / / 1 )AEX-EiG D E C L À R E C L À R E ~ ~ G E ~ ~ ( )
1;
#i£ndef JEBUG / / debug version in EydroAnalysisView.cpp inl ina MydroAnalysisD4c8 CEydroAnalysisView: :GetDocument (
( seturn (CHydroAnalysisDac*lmqDacument; 1 #euclif
/ / ( {Am,INSERT,LOCXTXON) 1 / / Wcrosoft Developer Studio will insert additional declarations immediately before the previous line.
/ / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / / / @ ïndexPazaJ1g.h : header file / / Q aa tbr : Tlanhe Werr, 1999 / / O Version:2.0 / / B Copyright: Ritepro fnc. / / @ concordia University / / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#if ! def in&(APX,f?IDEX,~ARAARADLGARABB3OEFC8E22~C66L1D2~986A~4445~354OOOOOLYC5~~~~ èdefine AFX,~EXP~~DLGBOEFCBU,E3C6~?lD2,9~6L4445535400OO,LWLVC~~
#if ,üSC-VER s= 1000 #pragma once Rendif / / 3 C - V E R .= 1000
class C1adwara-DTg : public CDiaLog I / / constructicn public :
CIndexoara-Dlg [ mad* pParent = KXL) ; / I s t a n u d conçrructor
i n t i n t int int int int i n t int int int int i n t blt int int int int
/ / ûuerrides / / Classwizard çenerateù virtual f u ~ c r i o n averrides / / ( (UX-VIITUAL (CIndexPara-Dlg 1 procected : virtual VOL& DaDataExcbge(CE)at&ck~qe* pDX); I l DDX/DDV support I l 1 } L=X_VTn?uAL
/ / Implementatian protecced:
before fie previous IFae.
/ / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / / / B Junction1Dlq.h : header f i l e / / @ author : Tianiïe \ien. 1999 / / I Versi0n:l.O / / @ Copyright: Ritapro Inc. / / @ - Ccncordia Univers i ty / / / / / / / / / / / / / / / / / / / / / l / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / f / / / / / / / / / / / / / /
# i f ,MSCCVER >= 1000 #pragma once #endif / / -MSC,VZ3 >= 1000 / / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / CJunctioniDlg d ia log
class CJunctionlDlc : p u b l i c W i a l o g f / 1 Const-qction pub1 i c :
CJunctioni31ciCnlndo pParent = NOLL); / / s tandard ccns:zuc:or
/ / Dialog Data / / ( (AFX,D;iT: (CJunctionlDlg) equm f IDD = IDD-DLG-JlJNCTIONI }; EOOL m-Kbeckl : BQOL m-Kkeck2 ; EOOL m-Kkeck3 ; EOOL m-tCkeck4; ECOL m-tCheck5 ; EQOL ut-kCkeck6 ; BOOL m-kCkeck7 ; EOGL m-kCkeck8 ;
f loar m-fZlcr2 ; f l o a t m-fEle7r4; f l o a t m-fELevrS ; f l o a t m-fZe~r6; f l o a t m-fsf ov7 ; f l o a t m,f-rov% ; f l o a c m,f?lctrt: f l o a t m-fllcut ; f l o a t m-fFlcsr3 : f l o a t m-fFlcr4; f l o a t m-fr'lcu5 : f l o a t m-fFlor6; f l o a t m,f?lcr7; f l o a t m,f?lcr8 ; f l o a t rn,&*esci,l; f l o a t rn_Leac;3; f l o a t rn-fEez3 ; f l o a t s_LXeac',4 ; f l o a t m-EeaCJ ; f l o a t m-fEea56 ; f l o a t m-fuea57 7;
f l o a t m-fueaE2 ; //}}AFX,DATA
/ / Overrides / / ClçssWizard genezated virtua!. fwction cver-rides / / ( (MX-VIRTüAL (CJunctionlDlg) protected: virtual void DaDataExchangeiCDataExchaaqe* pDX1; / / DDX/DDV support / / 1 JAFX-rnTlJilL
/ / lmplementation protected:
/ / Geaerateü message map funccions / / t C~X,~G(CJunctianlDlgl
/ / NOTE: the ClassWizard will add m e m b e r functions here / / 1 Irn-MSG DECr;;\RE-KESSXGEEP139 [
1;
/ / ( (Li%-INSERT-LOCATION) 1 / / Mierosoft Developer Studio will insert additional declaracians intmediarely before tke previous line.
c l a s s CMainFrame : public ~IPraxieWnd C
DECURE-DYNXMC ( WinFrane) public:
CHainFrame ( 1 ;
/ / Atvihu tes public: / / Operations public: / / Ove- ides
/ / ClassWizarc! ~ezeraced vi r tual cCwcticn cverrides / / [ (LFX-VIR?'UX IC2~ir,fr~v I v i r t u a l EOOL P:oCreateWinEow[~TFSTaUCT& CS) ;
/ / ) 1 &Y-VIBTUX / / Impleztencation public:
v i r t u a l -Ch(!infrane ( 1 : #Ffdef -DESUG
v i r t u a l voic! &ser:ValidO cocsc; v i r t u a l voie Gmp (CDurpconceut& dc) cons:;
#endif
protected: / / conczo~ bar &edCed m e e r s CStatusBar mJmdStatusEar: CToolSar m-wiaTocl9ar;
/ / Generated message map functions protected:
I I ( {~MSG(îXai r~Frane) ah-msg i n t OnCreate iL2CEATESTXTICT lpCreateSlxxt ) ;
/ / NOTE - the ClassWizazà w i l i add acld r m v e member functians heze. / / Dû NOT D I T w h t you see in these blocks of geceraced code! / / 1 1X'LFSG
DEaARE-MESSAG"s"sMX~ ( 1 private:
CFrontWnd* mgFrontWnd; 1; / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / I I f / I / / I / / / / / / / / / / / ~ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / ( ~ k o X _ r n ~ T T L O W T I O N I 1 / / Kicrosoft Developer Studio w i L L iasert additional declara t ims imme&iateLy before the previous l ine.
/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / B Pipe-b: i n t e r f ace f o r the Pipe c lass . / / B author: Tianhe Wen, 1999 / / @ Version:Z.O / / @ Copyright: Ritepro Inc. / / @ Concordia University / / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#define P I 3.1415427 Wdef ine DEGTOEWD 0 .Ol74533 Wdefine Ri\I3TODEG S7.2957?
class Pipe [ public:
Pipe(}; virrual -?ipe I ) ;
v o i s PipeInit(inc, inc , inc , f loac , f l o a t [ I , floa'c[I, floatil , int[l. i n t [ I ) ;
void PipoTuncF-Ei inci ; fLoat PipaluncEead ( 1 ;
vaid ValveDownF-a( f l o a t , i n t , const f l oa t [ l , f loat . Elaatl ; vair2 ValveTauDowEf( f l o a t , f l o a t , i n t , const f k a t (1, floac. f l o a t . f loac. f loa t l ;
f k a t PrmrpJunc ( 1 ; void ResvLQF-iiI: f l o a t ) ; f Loat ~eNo~EZead( f l o a t l ; f l c a t GetPlawliat) ; f l o a t GecEeadlintl ; void Refniriaiize( iati ; f l o a t TimeStep i 1 ;
priva te : fLoat Q [NumRea&+l1: f loat H[NmReach+ll: f loat QpCNumRea~h+ll; float Hp[NumReach+ll:
/ / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / / / @ PipelD1g.h : header f i l e / / B author: Tianhe Wen, 1999 / / B Versioa:2.0 / / B Copyright: Ritepro Lnc. / / B Concordia University / / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
t i f -M!àC,VER >= 1000 tpraçma once lendi f II ,MÇc-m >= 1000 / / / /
class CPipeLDLg : public CDialag t / / Construction publ ic :
CPipelDlg(C:Jno* pParent = NCiLL) ; / / star.&rd canst,ruc:or
/ / Dialog Data / / ( (AEC-DATA (CPipelDlg) enum ( I 3 D = TDD,DLG,PIPI-LINEI 1: f l o a t m-EDianecerl : f l o a t m-fDiameter2 ; f l o a t m-fDiametez3 ; f l o a t ~n-fDianeter4; f l a a t m-fDiuecer5; f l o a t m-fDiamecer6: f l o a t m-fDiameter7 ; f l o a t m-fDiameter8 ; f l o a t m-fDianeter9 ; f l a a t n-fCr Lc=ienl; f l o a t ~ f i r i c c i o n 2 ; f l o a t m-fFriccion3 : f l o a t m,ffrFction4 ; f l o a t m-fFriccion5 ; f l o a t m-fYrfctian6; f l o a t m-ffrictionf ; f l a a t mJFricCion8 ; f l o a t xi-fFriction9 : f l o a t m-f L=çthl; f l o a t m-fLer,gthS; f l o a t m-fLerrgbch3 ; f l o a t ILI-ELegth4; f l o a t m-f Length5 ; f l o a t ntflengdr6; f l o a t m-ELezgth7; f l o a t m-Uezgth8 ; f l o a t m-flagth9 ; / / 1 )ilFX-DATA
;/ Overrides / / Classiiizazd generated v i r t u a l function overr ides
/ / [ f A t X I V f R ~ (CPipelDlgi pratected: virtual void DoData~xchange(CDataExdiaage* pDX1; / / DDX/DOV support / / 1 } .L%-VIRrn
/ / ïmplementation pro tected:
/ / Gaerated message map functions / / ( (.L=X-KSG (CPipelDlg) / / NOTE: the ClassWizard will add m e r n b e r functions here / / 1 l m - M Ç G DECLx_HEçSÀGEEW ( 1
1 :
/ / { (AFXJNSZ3T-LûCATION) ) / / Kicrasofc Develo~er Studio will insert addicional dechrations ixmtediately before the ~reviaus lhe.
/ / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / / / @ PigeNet2Cv.h: i n t e r f a c e f o r t he PipeNet2Cv class. / / @ author: Tianhe Wen, 1999 / / @ Version:2.0 / / @ Copyright: Ritepro fnc. / / @ Concordia Universi ty / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / l / / / / / / / / / / / / / / / / / f
# i f -MSC-VER >= 1000 lpragma once liendif / / ,kf!iC-VER >= 1000
Wdefine NtmiJ 20 Wdefine NirmP 20 Wdefine NZND 200 Wdefine KM 11
t inc lude *PmpStart . hg t inc lude 'CheckVa1ve.h"
c l a s s P i p e V e t X v : publ ie Pipe, publ ic PumpStarr, publ ic CheckValve
i public:
PipeXetXvi ; v i r t u a i -PipeNetXv ( ;
PipeNetetlCv(int, i n t [ ] . inc, i n t , i n t , i z t , Éloat, f l o a t [ ] . Éloat[J ,flcat [ ] , i n t [ I , i n t [ I , f l o a t l l , f l oac [ I , E ioa t [ J , i n t [ I , f l o a t , i n t , f 1aa t , f k a t , floa:, f l o a t ) ;
void Initial?-E ( i n t 1 ; void PipeJuncP-H(int,int); void PrrmpJuncF-H( flaat, int) ; void PumpfuncF-H(float, i n c , f l o a t ) ;
f l a a t Ge=(int) : f l a a t GetQN(int1; f l o a t -=t int , i n t ) ; f l o a t GetQiint , in t ) ; f l o a t Z[NrmtJI,CN[NdI .BN[N&] ,QE[N&+L],m[NIM)]; f l o a t CC[NWI [10] , E C [ W ] [ l a ] ; i n t Ntype[NumJI IF^ [NumJI ;
/ / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / / / @ PipeNet2NoCv.h: interface for the PipeNet2NoCv class. / / @ author: Tianhe Wen, 1999 / / 8 Version:2.0 / / 8 Copyright: Ritepro Inc. / / 8 Concordia University 11 / / / / / / / / / / / / / / / / / l / / I / / / / / / / / / / / / / / / I / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / /
#if -SC-VER >= 1000 tpragma once #endif / / JSC-VER >= 1000 ldefine NumJ 20 ldefine N W 20 #define NIND 200 ldefine EM 11
class PipeVet2NoCv : public Pipe , public PumpSta:: { public :
PipeNecZNcCv i ;
/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / @ PlotPrincoutDlg.h : header file / / @ author: Tinnhe Wen, 1999 / / e Version:2.0 / / @ Copyright: Ritepro Inc. / / @ Concordia University / / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . #if !deEined(AFXAFXPMTPRINTOUTDLGPKBS~SL888EO97711D2~986A,44455354OOOOOIMUUDEDED 1
#if ,MX-VER >= 1000 #pragma once Rendif / / -üSC,VER >= 1000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / PLo tPrintoutDlg dialog
class PlotPrintoutDlg : public CDialog ( / / Construction public :
PTotPrintoutDlg(CWnd* pParenc = NILLI; / / standard constructor
/ / Dialog Data / / ( (m-MTA(PlotPr i r r toutD1g) enum ( IDD = IDD-DLG-PLOTDLG 1; UINT m-fPlotJunNum; UINT m-fPiotPipeNum; UINT m-f PrintoutPigel; UINT m-fPrincoutPipe?; UXNT m-fPrintauc~ipe3 ; U f m m-f PrintaurJun2 : üîNT m-fPrintoucjun1; UINT nt-f PrintaucJun3 : / / ) }=-DATA
/ / Ove-rides / / ClassWizard generatd virtual fuocciao averrides / / ( (AFLVIRlWAL iPlotPrintoutDlg1 protecred: v;Lrtual void DoDataZxchançe (CData%ckattgeW pDX) ; / / DDX/DDV support / / l I A E ' X ~ v I a m
/ / ïm?lementation protected:
/ / Generaced message map furicticns / / ( (AFX-ESG(PlotPrintoutOLgl / / NOTE: the C l a s s W i ~ a ~ will add nesker functions here / / 1 lAFXAFXMsG DECLiLPEPEEESSAGEGEW { )
1 :
/ / I CLFXXIN!5ERTTLOCATION) } / / Kicosoft Developer Studio wFLl inset a&tional declarations immediately before the previous line.
/ / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / / / @ himpCheckValveD1g.h : header file / / @ author: Tianhe Wen. L999 / / B Version:2.0 / / B Copyright: Ritepra Inc. / / B Concardia University / / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#if -MSCCVER >= 1000 lgragma once #endif / / -MSC-VER >= LOO0 / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / ! / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / ChrmpCheckValveIllg d ia log
class CmÿapCheckValveDlq : public CDialoç ( 11 Cons cruet ion pub1 ic :
CPunqCheckVaLve9lg (Cd~d* pPkrerit = NüLL) ; / f staxiar6 c c n s t v c t o r
/ / Dialog Data / / { [AFX-DATA (CFunpCheckValve9lg) enum { IDD = IDD-DLG-PUYS-CEiECK-~nLVZ > : CComboBax n-Lis t S p e M ; CComboBox m-ListSpeeë?; CComùoBox p-ListSpeedl; CComboBox nJistDianeter3 ;
f l o a t m,f!!sPrnip3 ; Eloat m-fFlawPumpL ; f l o a t ~~fFlowPmrtp2 ;
f l o a t ri-fTlowPlmtp3 ; f l o a t m - f a e a d h n p l ; f l o a t m-fgeadPimrp2 ; f l o a t m-fgeadhrmp3 ; f l o a t m - f S p e e d 2 t m p l ; f l o a t m-fSpeecfPrmip2 : f l o a t m-fSpeeaPtmp3 ; f l u a t ~fTorqPimrgt ; f l o a t m-fTorq-Srmp2; f l o a t m-fTorqPuaip3 ; Eloat m-fTsPtrmp1; f l o a t mJTsPurnp2 ; f l o a t m-ETsPimrpi ; f l a a t m-fEump2AO ; f l o a t m-fEump3AO;
f l o a t m-fPumpZAt: f l o a t ~ f P u m p 3 A l ; f l o a t 1q_f?mp2A2 ; f l o a t m,f3ump3XZ ; f l o a t m-fhÿnp2NorXO ; f l o a t m-fhmrp3NorAO ; f l o a t ~q_fPumpZNorAl; f l o a t nt-fh~ip3NorAl: f l o a t m-fPump2NorA2 ; f l o a t m-fFump3NorA2 ; i n t ~ n m t m p l s t a t u s ; iac ~nPMip2Sta tus ; inc m-nPump3Status; BOOL mJNoCheckValve ; / / 1 1 AFX-MTA
/ / Ovezides / / ClassWizard generated v i r t u a l fmc t ion overrides //{(m-WRTn;lL(CPumpcheckValveDlg1 protected: v k t u a l void DoDacaExchange(çDataExchange* pDX1; / / DDXIDDV support / / } }AFX-VIRTtTAL
public:
/ / i n d ~ ~ fo r the diameter, and speed i n t m-nS~eed3 ; inc m-nSpeed2 ; in t m-nspeedl ; i n t m-nDimeter3 ; Lac n-rLiianecer2 ; i r r t m-nDimecerl;
void void void void void void vo id VQ i d
1;
ShovFaiiWndPl( BOdL bShow = TRDE); çbouÇtartupWndP2 ( BOOL bShow = TRUE) ; ShawNormalWndP2 ( B W L bShow = TRUE) ; ShowPailWndPZ( BoOL bShow = TRUE) ; ShowStaxtupWndP3( BOOL bShow = TRUE); ShowNormalWndP3 ( BWL bShow = l'RUE) ; ShowFailWndP3( BOOL bShow = TRUE); ShowCZieckvalvelWnd(5WL bShow ='l!RUE);
/ / { {AFX,INÇERTTLûCATION) 1 / / Piicrosoft Developer Studio will insert additional declarations ixnmediatefy befare the previous line.
llendif / / !&fined(~-~~C~VEDLGGHH76S765B44COBDBDIID2J4Z44OOAOC974979AALNCLm3E
D-1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / / / Q PrrnrpPail-h: in ter face for the P q F a i l elass- / / Q author: Tiaahe W e n , 1999 / / @ Varsian:Z.O / / @ Copyright: Ritepro Inc. / / B Concardia University / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / f / / / / / / / / / / / / / / / / / / / / / / / / / / /
class PlrmpFail I public :
PumpFail(1; h m i p f a i l ( intl ; virtual -PmpFailO;
public:
float A, XL, EL. D. F, CB.EZ(,TR.LV.HiL3, G.T.I.T3L.VZ.R.B,A~,~://V float DX,VO,VOO,i150,ZOO.DT,BETA,B~TO; float WHi891,WB[B91 .Q[SI , I ! [SI ,F!ptSI,PF~SI; i n t N,KIT, KMAX;
void PipeJHQ (int ; void PrmrpValve3C ( int i : vaid ~owcstzeanResoiv( f h a c , int ) ; void ReInitialize(Fnt1;
double Intezpclacec~falue (double, Fnc. h t ) ;
/ / / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / / / @ hmigStk-t-D: interface f c r t k e PmpStart class. / / @ author: Tianhe W e n , 1999 / / e Version:2.0 / / B Copyright: Ritepro Inc. / / @ Concordia University / / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
# i f ,M!àC-VER >= LOO0 Bpragma once Bendif / / ,MSc_VEEC >= 1000
class PumpStart { public:
PumgStart Il ;
virtual -PumpStartO; void PumpStartInit ( Eloat, f laat, float, f lcat . i n t , int) ;
int Jpumg; f loat XS,AI,AZ.Ts;
/ / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / / / Q ReserviorD1q.h : header f i l e / / @ autior: Tiarihe Wen. 1999 / / @ Version:2-0 / / @ Copyright: Ritepro ïnc. / / e Concordia University / / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . # i f !defined(AFX_KEç~~ORDLG~RR765765822COBDDlID2~4E4QOOAOC974979Ai\INCLUDWED) #define Anr,REç~~ORDLG-Kn76576582~CO9D9D1~22A4E4QOOAOC974979AAINCLUDED~
# i f -MSC,ïEX >= 1000 #pragma once lendif / / ,MSCCtZX >= 1000 / / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / CRese-tviorDlq d ia lag
c l a s s CReservior3lg : public CDialog C / / Cons:,uction publie:
CXese,-vicrXg (C!Jndm pParenz = NULLI ; // s:ar.&xd consc-mcccr
/ / Dialcg Data / / ( (A=XJATX ICRese-~l0rDlg1 erium ( IDD = IDD-DLG,RES"aVOIR 1; Éloac m-fEieadi ; f l o a t rn-fSead2 ; f l o a t m-fSead3 ; f l a a c m-fEfead4 : / / ) 1 MX-EXX
/ / Overrides / / Class:iFzarC çezezatecf v i r t u a l functicr, overrides //((ÀFX,E-?~(CReserviorDlg) ~roree tec i : virtua' vcid DoDataExchange (CDataExùlancer pDX) ; / / DDX/DDV sugpcrr / / 1 1 &-x-mmAL
/ / Iatplenentaticn pro tected:
/ / Gerieraze4 message map functions / / ( ( k i - X S G (CReserviorDlgi / / NOTE: cke ClassWizard w i l l a& meaber functions here / / 1 ) iLfXJEG DEU;AREU;AREESSAGEGEKAP ( 1
1;
/ / ( (xC-INSEi(TTLCCATION1 1 / / K i c o s o f t Developer Studio w i l l inser: a d f i t i c m l declaracions inmieciiately before cke prevLous Une .
/ / / / / / r / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / P SimulatiouD1g.h : header file / / @ author: Tianhe Wen, 1999 / / Q Versi0n:Z.O / / @ Copyright: Ritepro Inc. / / B coacor&ia University / / / / / / / / / / j / l / / / / / ~ / / / / / / / / / / / / / r / / / / r / / / / / r / / r / / / / / / / / / ~ / / / / / / / / / / / / / / / #if !defiaed(~S~TIONtiLGLGRRDC9H7C92~CODl,llD2~4E4~OOAOC974979A~WctIJD~~) #&fine APX_S~TIONDT;GT;GRRDC9B7C921CODlIllD2-A4E4-OOAOC97499A,~NCL~~-
class CSimularionDlg : public COialoç i / / Consuuctian public:
CSimuLacicnDlg(Cdndl pParenc = NCTLLI; / / standardconstructor
/ / Ove--riees / / Classwi=azd generated virtital funceion a v ~ z i d e s / ( [MX-VInTUAL (CSimulacianDlql
protected: vircual voiü DoDataExcharrge(CDataExchango* pDX); / / DDXfCDV support / / 1 I MX-ViXTüAL
/ / Implenentatian protected:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / / / B HyàrcGraphic.h : main header f i l e for the BYflRM;IIAPHIC application / / @ Author: Tianhe Wen, 1999 / / @ Version: 1 . 5 // @ Copyright: Ritepro Ine. / / @ Concordian University / / . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
# i fnde f -AFXWïN-R- #error include ' sc2iifx.h' becore including this f i l e f c r E
tendif
/ / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / f / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / MydraGraphicApp : / / See Hydr-oGraphic .cpp for the implene3cacion of t h i s c l a s s
class (JiybtoGraphicApp : ~uhlic Cdi~App I p&l ic :
EydroGraahFcApp ( I ; public : - EDATA m-hhtai ; / / &ta sec bmxiles
D A T A ~ h D a t a 2 ; real type rXeWa1s [ 8 1 ;
/ / Ovezzides / / ClassWFzard gezeracecl virtual f n c t i c n cverrides / / ( CAFX-VI,?TETIU; (CSydroGraghicApp 1 public: v i r t w l BOOL InitInst=ce ( ;
/ / } ) A E L v n r n
/ / Implernencation / / [ [AFX-Hsu ((ItfydraGraphicApp) a f x ~ g void OnAppAbout i ; / / NOTE - the ClassWizkrd w i l l a&? and remve m m b e z furrctions here. / / DO NOT EDIT w h t ycu s e e i?? these blockç o f generated cc6e !
/ I l lmAFX= DECLAREECLAREMESSAGEMESKAP ( )
1 : / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / i / / / / / / ~ / l / / / l / / /
before the previous l ine ,
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / / / t3 Hy&oGraphicDoc.h : in te r face of the CHydroGraphicDoc c l a s s / / e Author: Tianhe Wen, 1999 / / B Version: 1.5 / / Q Copyright: Ritepro Inc. / / @ Concordian University
# i f ,MSC,VER >= 1000 Ypragma once #endif / / -USC,VER >= 1000
c l a s s CHy6roGraphicDoc : public Cilocinnent I protected: / / creace from se r i a l i za t i on only
CHydroGraphicDoc i 1 ; DECLARE-DYNGEATE (CE*ydroGraphicDoc 1
/ / Att r ibutes public :
/ / Operations pub1 ic :
/ / Overrides / / Class%i:ard ger.erated v i r m a l functicn o v ~ z z i 0 e s / / ( (X~lt2VInTTJiJ; (CuyckcGraphic9cci public: v i r t u a l void S e r i a l i ~ e ( C ~ c 3 i v e Ç a r ) : / / 1 1 xx-vrnma
/ / Implene!,?tacion gublic:
v i r t u r l -Cs:yùzoGraphic9ac ( ) ; t i f de f -DESUC
v i r t u a l void Assertval id0 cor.st; v i r t u a l vcid Durm(cDumpContextL dc) cons:;
B-dif
/ / / / i3 HydroGraphicView.h : i n t e r f ace of the CHydraGraphicView c l a s s / / @ Author: Tianhe Wen, 1999 / / @ Version: 1.5 / / e Copyright: Ritepro Inc. / / 0 Concordian University / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / f / / / / / / / /
/ / def ine graph c l a s s based on BaseGraph ...........................................................................
c l a s s Graphs : public QCBaseGraph I public: / / construccor
Graphs (int nNun) ; PGnXPE-DEF m-~DynGrDesc; / / pointer to pragk descrlgcor
PGRXPfiDEF msStaGrDesc ;
i nc rn-nGraphNurnber; / / graph n&er i n Fage
c l a s s Pape1 : ~iYlic CCsaseFaçe r praceere&:
vistual vaid Buildoage (??XEJE); / / user f-r.c=ion i n i t i a l i z i n ç Faqe p u h l i c :
Gra~hs. mçGraphl; Grapns* m-pGrap'r.2;
c l a s s EydroGraphicView r pub l ic CView I pratecced: / / creace f t c m s e r i a l i z a t i o n only
CEiydraGzaphicView ( ) ; DEFI-CYXXATE (CnydroGraphicView)
procected: Pagel *m-pgl; / / poin ter t o the pace objecc Pagel ' rn~Pg2; PFAGE-DEI mgEaq&esc;
PFPGE-DEF m~PageDesc2 ;
/ / Attributes public:
CEIyüroGraphicDoc* GetDocument [ ) ; \
/ / Operations public :
/ / Overrides / / ClassWizard gezzeraced virtual function overrides //((Am-VIRTOXLi(3iyaZroGraphicView) public : virtual void OaDraw(CDCT pK); 11 overridderi CO draw this view virtual void OnInicialüpdate[void); virtual BWL PretreateWindow(CREXTfSTflUCT& CS); protected: virtual BWL OnPreparePrintiq(CPrintInfo* pInfo); virtual void OnBeginPriating(CDC1 pDC, CPrincInfo* pInfo); virtual void OnEndPrincing(CDC1 pK, CFrinrInfo* phfoi; virtual void GnPrinc (CD? p K , CPrintInfo* pInfa) ; / / ) ) ~ V I R T O A L
/ / fmplenentation public :
virtual -CIiydroGraphicView~ ) ; #ifdef ,DEBUG
virtual void AssercValidi) consc; vircual voic? Dm? (COumpConce-~cs cic) const:
Xendi f
protected:
/ / Generated messaçe nat: fÿr.c:ions prctecceà:
/ / ( (XEII,MSG (C9icizcGraphicVFer) afx-msg vcid CnSire(U1XT nFGe. i / /afx-msç vcil OnFileSat-e i) ; 11 1 ) ~ , M E G DECLÀR,t-MESSAGE - w (
private : Oiecc m,rc?riz',5ec::
l ;
#ifndef ,DrSUG / 1 Cehg vers i c n iri EydrcGrapBicr~iew. cw inline OiydroGraphic3oc* CydroGraphicView::CeflocmntO
{ r e c m (wcGrapilicDoc*) m-oEacmenc; 1 #endif
/ / / / / / / / / / / / / / / / / / / : / 1 / / 1 / / / / / / / / / 1 / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / : / / / / 1 / ( (Ans_INSzRT,LOCATION) } / / Micrasoft Devetoper Studio will fnserc additional declaracions iamiediately before the previous lke.
#endif / / !def ined (i\FX,RYDR~rrRPfrI:CV12fJJBBFE3025~-4682211D3~HD 1,00E029T12567-IXLiTDD -)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / / / 4 HainPnn-h : interface of the CXainFrauie class / / @ Author: Tianhe W e n , 1409 I l B Version: 1.5 / / @ Copyright: Ritepro Inc. / / @ Concordian University I I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . #if !deEined(AFX,mINmM-nnf 63337SE9,46a2,1lD3,BD3 1-00E029112567,ITIC~u~m-) #def ine AFXAFX~-HHF63D25EI_46822L~~33BD31,00E029112SB7,INCLUDD- #if -MÇCCVEK >= 1000 ltpragma once Oendif / / JfSC-W >= 1000
class CMainFrame : cublic CmZFrameWnd ( protected: / / czeace from serializacion cnly
DECZARE-DYNCAEXTE I CEain?:ame 1 / / Attributes public : CMainFrameO ; / / Operations public:
procecteù: / / c m t r o l ka= &&ded s e e r s CStacusEar m_wndS:acüs8ar; CToolSar m-wnt2Taal9ar;
/ / Gezeraced message m g functicns protected:
/ / A ALEX-FSG(CMain="ranei afx-mâq Lit O n C r e a t e ( L P I ~ T E S ~ ~ lpCreateStrucr) ; afx-mg void OnDes'=tay( 1 ; ah-msg void OnTimer (m?F nIDEt-ertt) ;
/ / NOTE - the ClassWiza-+ uili a 2 ami ratme m&ez Fxictiocs here. / / W NOT EDIT w h t yau sep ic these Dlo=Ics of çeserated ccde! / / 1 1 XéT-VSG DECLARE-MSSXGZ-m i 1
1 : / 1 / / / / / / / / / / / / / / / / / / / / / I / / / / I I I / / I I I / / / / f / / / / / / / / / / / / ~ / / / / / ; / / / / / / l / l l / l / / l / / / / ( (&?XJNSERTTLOCATION~ I / / Kicosoft Develcper Studio w',ll inserr additional declaracians iaonediately hefare the previous iine. #eacEf / / !def~&(~-~~HHF63D2S~-46a24LlD3-BO3l-OOED29LI2S677ZL1I(J;UD~-)
