TRANSIENT ANALYSIS IN PIPE NETWORKS SEMINAR REPORT
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Abstract
Power failure of pumps, sudden valve actions, and the operation of automatic control systems are all capable of generating high pressure waves in domestic water supply systems. These transient conditions resulting in high pressures can cause pipe failures by damaging valves and fittings. In this study, basic equations for solving transient analysis problems are derived using method of characteristics. Two example problems are presented. One, a single pipe system which is solved by developing an excel spreadsheet. Second, a pipe network problem is solved using transient analysis program called TRANSNET. A transient analysis program is developed in Java. This program can handle suddenly-closing valves, gradually-closing valves, pump power failures and sudden demand changes at junctions. A maximum of four pipes can be present at a junction. A pipe network problem is solved using this java program and the results were found to be similar to that obtained from TRANSNET program. The code can be further extended, for example by developing java applets and graphical user interphase to make it more user friendly.
Introduction
Devices such as valves, pumps and surge protection equipment exist in a pipe network. Power failure of pumps, sudden valve actions, and the operation of automatic control systems are all capable of generating high pressure waves in domestic water supply systems. These high pressures can cause pipe failures by damaging valves and fittings. Study of pressure and velocity variations under such circumstances is significant for placement of valves and other protection devices. In this study, the role of each of these devices in triggering transient conditions is studied. Analysis is performed on single and multiple pipe systems. Transient analysis is also important to draw guidelines for future pipeline design standards. These will use true maximum loads (pressure and velocity) to select the appropriate components, rather than a notional factor of the mean operating pressure. This will lead to safer designs with less over-design, guaranteeing better system control and allowing unconventional solutions such as the omission of expensive protection devices. It will also reveal potential problems in the operation of the system at the design stage, at a much lower cost than during commissioning.
Organization
This thesis is divided into five chapters. Chapter 1 includes a brief introduction to transients, review of literature, and objectives of the study. Basic equations of transient flow analysis in pipe networks are 3 discussed in Chapter 2. Two example problems are solved using excel spreadsheet to demonstrate the method of characteristics. Chapter 3 is devoted to use of object oriented technology for analyzing transient problems in a pipe network. Comparison is drawn between procedural language and object oriented approach of analyzing transients in a pipe network. Chapter 4 is about gaseous cavitation in pipes where energy dissipation due to gas release and solution process is studied. Here, thermal exchange between gas bubbles and surrounding liquid is also considered. A comprehensive model to obtain the amount of gas release is developed. Chapter 5 presents the summary of work presented in this thesis, and also discusses its potential application.
Basic Equations of Transient Flow Analysis in Closed Conduits
Introduction
Initial studies on water hammer are done assuming single phase flow of fluid (Wylie et al., 1993). The method of characteristics is most widely used for modeling water hammer. First, the fundamental equations involved in water hammer analysis are discussed, following which two example problems are solved to highlight the analytical technique.
Single pipe with reservoir upstream and valve downstream
From above plots, it is evident that just upstream of the valve (i.e., at the end of the pipe), high pressures are maintained for a longer duration as compared to the middle of the pipe. Hence, pressure surge devices should be placed at pipe joints to avoid failures because they are more susceptible to high pressures
Network Distribution
Consider the network given below (Larock et al., 2000). The Hazen-Williams roughness
coefficient is 120 for all pipes. This network experiences a transient that is caused by the sudden closure of a valve at the downstream end of pipe 5. Wave speed is 2850 ft/s for all the pipes. Transient analysis is obtained for this network.
An Object Oriented Approach for Transient Analysis in
Water Distribution Systems using JAVA programming
Introduction
Most of the algorithms in computational hydraulics discipline are written in procedural
language (FORTRAN, Pascal and C). Procedural programming was found to be adequate for coding moderately extensive programs until 90’s (Madan, 2004). In procedural programming, the strategy is based on dividing the computational task into smaller groups termed as functions, procedures or subroutines which perform well-defined operations on their input arguments and have well defined interfaces to other subprograms in the main program. However, procedural programming approach can get challenging when the code needs to be extended for enhancing the scope of the program. A detailed knowledge of the program is required to work on a small part of the code and poor equivalence between program variables and physical entities further makes it difficult. Integrity of data is another area of concern in procedural programs because, the emphasis is on functions and data is considered secondary.
All the functions of a program have access to data and as a result data is highly susceptible to get corrupted when dealing with complex programs. In addition, there are difficulties related to reusability and maintenance of code as procedural programs are platform and version dependent.
Object-oriented programming in Java
A Java program describes a community of objects arranged to interact in well-defined ways for a common purpose. None of the objects is sufficient on its own. Each object provides specific services required by other objects in the community to fulfill the program’s promise. When an object requires a specific service, it sends a request (called a message) to another object capable of providing that service. The object that receives the message responds by performing actions that often involve additional messages being sent to other objects. This results in a vibrant cascade of messages among a network of objects.
Modeling Transient Gaseous Cavitation in Pipes
Introduction
During transient flow of liquid in pipelines, pressures sufficiently less than the saturation pressure of dissolved gas can be reached. As a result, gas bubbles are formed due to diffusion of cavitation nuclei. In this process of gas release, free gas volume increases. Consequently, the mixture celerity is reduced due to added compressibility of the gas, which in turn may give rise to significant pressure wave dispersion. The decision to account for gas release (Wiggert and Sundquist, 1979) during a pressure transient in a pipe depends upon the system dimensions, type of fluid mixture being transported, extent of saturation of the gas, and low pressure residence times. In long pipelines where big elevation difference exists at different sections of pipe, transient pressures below gas saturation pressure is possible. Also, in highly soluble solutions such as water and carbon dioxide or hydraulic oil and air, significant gas release can take place and should be considered to correctly simulate the transient. Examples of gaseous cavitation are found in large-scale cooling water units, aviation fuel lines, and hydraulic control systems.
Evaluating Thickness of Viscous Sub layer
Thickness of viscous sub layer δ is distance from wall to the intersection between the velocity profiles in the viscous sub layer and the turbulent zone. Linear velocity profile is assumed in the viscous sub layer and in the turbulent zone the profile is locally logarithmic.
Finite Difference Scheme
The pipe is divided into cylindrical grid elements of constant length ∆x in longitudinal
direction and constant area ∆A in radial direction. Velocities are defined at center of each radial mesh, and shear stresses on internal and external sides. Other parameters such as pressure head H, mass m, Temperature T, φ and s vary along longitudinal direction only and are defined at each grid point.
Application of the model
The above model is applied to the single pipe system setup as shown in Figure 6 in Chapter 2. Reservoir is at upstream of the pipe and the valve present downstream is closed suddenly. An initial amount of free gas (air) is assumed in the pipe along with water. Below is the set of values used in the problem
Mass of released gas vs time plot near the valve
As shown above, the results representing head and temperature near the valve, and total mass of gas release are plotted for 2500 time steps (i.e., 5 s). As shown in figure 16, a maximum pressure head of 52 m is reached near the valve during the first 5 s. Also from figure17, a peak temperature of 140 (deg c) is attained during the first 5 s resulting in vaporization of liquid near the valve. As shown in figure 18, the total amount of free gas is reduced during this time. These results can be verified by conducting an experiment with similar conditions. The peak value for head near the valve is attained only once, and further oscillation in pressure head cannot be plotted. This may be due to stability and concurrency issues which are part of
numerical schemes. By using a smaller time step, one can increase the stability of the
numerical computations. But, as McCormack method is an explicit finite difference method, time steps cannot be smaller than a certain value decided by the stability criteria or else, the resulting solution will not be accurate. It can be observed that high values of temperature can be reached during cavitation process.
The combination of high values of pressure and temperature in a pipeline may give rise to disastrous consequences. Accidents arisen from operation errors in pumping plants of combustible liquids are mentioned in literature.
Conclusion
In this study, an excel spreadsheet is developed to critically analyses transients that can occur in closed conduits. The Java program developed as part of this work is an attempt to introduce object oriented technology for analyzing problems in hydraulic engineering field. The code can be further extended, for example by developing java applets and graphical user interphase to make it more user friendly. A MATLAB program was developed to analyses gaseous cavitation using standard equations proposed by Cannizzaro and Pezzinga (2005). Though the gaseous cavitation program seemed stable, there are issues with accuracy and concurrency of the code.Based on author’s experience in this work, it is recommended to use separate models for gas release and for thermic exchange so that parameters can be better estimated.
This thesis is divided into five chapters. Chapter 1 includes a brief introduction to transients, review of literature, and objectives of the study. Basic equations of transient flow analysis in pipe networks are 3 discussed in Chapter 2. Two example problems are solved using excel spreadsheet to demonstrate the method of characteristics. Chapter 3 is devoted to use of object oriented technology for analyzing transient problems in a pipe network. Comparison is drawn between procedural language and object oriented approach of analyzing transients in a pipe network. Chapter 4 is about gaseous cavitation in pipes where energy dissipation due to gas release and solution process is studied. Here, thermal exchange between gas bubbles and surrounding liquid is also considered. A comprehensive model to obtain the amount of gas release is developed. Chapter 5 presents the summary of work presented in this thesis, and also discusses its potential application.
Basic Equations of Transient Flow Analysis in Closed Conduits
Introduction
Initial studies on water hammer are done assuming single phase flow of fluid (Wylie et al., 1993). The method of characteristics is most widely used for modeling water hammer. First, the fundamental equations involved in water hammer analysis are discussed, following which two example problems are solved to highlight the analytical technique.
Single pipe with reservoir upstream and valve downstream
From above plots, it is evident that just upstream of the valve (i.e., at the end of the pipe), high pressures are maintained for a longer duration as compared to the middle of the pipe. Hence, pressure surge devices should be placed at pipe joints to avoid failures because they are more susceptible to high pressures
Network Distribution
Consider the network given below (Larock et al., 2000). The Hazen-Williams roughness
coefficient is 120 for all pipes. This network experiences a transient that is caused by the sudden closure of a valve at the downstream end of pipe 5. Wave speed is 2850 ft/s for all the pipes. Transient analysis is obtained for this network.
An Object Oriented Approach for Transient Analysis in
Water Distribution Systems using JAVA programming
Introduction
Most of the algorithms in computational hydraulics discipline are written in procedural
language (FORTRAN, Pascal and C). Procedural programming was found to be adequate for coding moderately extensive programs until 90’s (Madan, 2004). In procedural programming, the strategy is based on dividing the computational task into smaller groups termed as functions, procedures or subroutines which perform well-defined operations on their input arguments and have well defined interfaces to other subprograms in the main program. However, procedural programming approach can get challenging when the code needs to be extended for enhancing the scope of the program. A detailed knowledge of the program is required to work on a small part of the code and poor equivalence between program variables and physical entities further makes it difficult. Integrity of data is another area of concern in procedural programs because, the emphasis is on functions and data is considered secondary.
All the functions of a program have access to data and as a result data is highly susceptible to get corrupted when dealing with complex programs. In addition, there are difficulties related to reusability and maintenance of code as procedural programs are platform and version dependent.
Object-oriented programming in Java
A Java program describes a community of objects arranged to interact in well-defined ways for a common purpose. None of the objects is sufficient on its own. Each object provides specific services required by other objects in the community to fulfill the program’s promise. When an object requires a specific service, it sends a request (called a message) to another object capable of providing that service. The object that receives the message responds by performing actions that often involve additional messages being sent to other objects. This results in a vibrant cascade of messages among a network of objects.
Modeling Transient Gaseous Cavitation in Pipes
Introduction
During transient flow of liquid in pipelines, pressures sufficiently less than the saturation pressure of dissolved gas can be reached. As a result, gas bubbles are formed due to diffusion of cavitation nuclei. In this process of gas release, free gas volume increases. Consequently, the mixture celerity is reduced due to added compressibility of the gas, which in turn may give rise to significant pressure wave dispersion. The decision to account for gas release (Wiggert and Sundquist, 1979) during a pressure transient in a pipe depends upon the system dimensions, type of fluid mixture being transported, extent of saturation of the gas, and low pressure residence times. In long pipelines where big elevation difference exists at different sections of pipe, transient pressures below gas saturation pressure is possible. Also, in highly soluble solutions such as water and carbon dioxide or hydraulic oil and air, significant gas release can take place and should be considered to correctly simulate the transient. Examples of gaseous cavitation are found in large-scale cooling water units, aviation fuel lines, and hydraulic control systems.
Evaluating Thickness of Viscous Sub layer
Thickness of viscous sub layer δ is distance from wall to the intersection between the velocity profiles in the viscous sub layer and the turbulent zone. Linear velocity profile is assumed in the viscous sub layer and in the turbulent zone the profile is locally logarithmic.
Finite Difference Scheme
The pipe is divided into cylindrical grid elements of constant length ∆x in longitudinal
direction and constant area ∆A in radial direction. Velocities are defined at center of each radial mesh, and shear stresses on internal and external sides. Other parameters such as pressure head H, mass m, Temperature T, φ and s vary along longitudinal direction only and are defined at each grid point.
Application of the model
The above model is applied to the single pipe system setup as shown in Figure 6 in Chapter 2. Reservoir is at upstream of the pipe and the valve present downstream is closed suddenly. An initial amount of free gas (air) is assumed in the pipe along with water. Below is the set of values used in the problem
Mass of released gas vs time plot near the valve
As shown above, the results representing head and temperature near the valve, and total mass of gas release are plotted for 2500 time steps (i.e., 5 s). As shown in figure 16, a maximum pressure head of 52 m is reached near the valve during the first 5 s. Also from figure17, a peak temperature of 140 (deg c) is attained during the first 5 s resulting in vaporization of liquid near the valve. As shown in figure 18, the total amount of free gas is reduced during this time. These results can be verified by conducting an experiment with similar conditions. The peak value for head near the valve is attained only once, and further oscillation in pressure head cannot be plotted. This may be due to stability and concurrency issues which are part of
numerical schemes. By using a smaller time step, one can increase the stability of the
numerical computations. But, as McCormack method is an explicit finite difference method, time steps cannot be smaller than a certain value decided by the stability criteria or else, the resulting solution will not be accurate. It can be observed that high values of temperature can be reached during cavitation process.
The combination of high values of pressure and temperature in a pipeline may give rise to disastrous consequences. Accidents arisen from operation errors in pumping plants of combustible liquids are mentioned in literature.
Conclusion
In this study, an excel spreadsheet is developed to critically analyses transients that can occur in closed conduits. The Java program developed as part of this work is an attempt to introduce object oriented technology for analyzing problems in hydraulic engineering field. The code can be further extended, for example by developing java applets and graphical user interphase to make it more user friendly. A MATLAB program was developed to analyses gaseous cavitation using standard equations proposed by Cannizzaro and Pezzinga (2005). Though the gaseous cavitation program seemed stable, there are issues with accuracy and concurrency of the code.Based on author’s experience in this work, it is recommended to use separate models for gas release and for thermic exchange so that parameters can be better estimated.
TRANSIENT ANALYSIS IN PIPE NETWORKS SEMINAR REPORT
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