08-09-2014, 01:12 PM
TRANSIENT ANALYSIS IN PIPE NETWORKS
TRANSIENT ANALYSIS.pdf (Size: 560.89 KB / Downloads: 128)
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 are3
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 ptogram. 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 timesteps (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 MacCormack 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 operationg errors in pumping plants of
combustible liquids are mentioned in literature.
Conclusion
In this study, an excel spreadsheet is developed to critically analyse 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 analyse 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.