ABSTRACT
The ranges of various methods for analysis of water hammer in pipes are included by approximate equations to numerical solutions of the nonlinear Navier-Stokes equations. In this chapter a case study with experimental and computational approach on hydrodynamics instability for a water pipeline have been presented. This book shows the water hammer effect on flow and pressure variations in surge tank as a surge protection device. Therefore, computational performances of a numerical method have been showed by a dynamic model for water transmission failure condition water hammer and surge-protection needs must be considered in the context of a water utility’s risk management and environmental protection plan. Surge or water hammer, as it is commonly known is the result of a sudden change in liquid velocity. Water hammer usually occurs when a transfer system is quickly started, stopped or is forced to make a rapid change in direction. During a transient analysis, the fluid and system boundaries can be either elastic or inelastic: 1) Elastic theory, describes unsteady flow of a compressible liquid in an elastic system (e.g., where pipes can expand and contract). 2) Rigid-column theory, describes unsteady flow of an incompressible liquid in a rigid system. It is only applicable to slower transient phenomena. Both branches of transient theory stem from the same governing equations. Among the approaches proposed to solve the single-phase (pure liquid) water hammer equations are the Method of Characteristics (MOC), Finite Differences (FD), Wave Characteristic Method (WCM), Finite Elements (FE), and Finite Volume (FV). One difficulty that commonly arises relates to the selection of an appropriate level of time step to use for the analysis. The obvious trade-off is between computational speed and accuracy. In general the smaller the time step, the longer the run time but the greater the numerical accuracy. The challenge of selecting a time step is made difficult in pipeline systems by two conflicting constraints. First, to calculate many boundary conditions, such as obtaining the head and discharge at the junction of two or more pipes, it is necessary that the time step be common to all pipes. The second constraint arises from the nature of the MOC. If the adjective terms in the governing equations are neglected (as is almost always justified), the MOC requires that ratio of the distance ∆x to the time step ∆t be equal to the wave speed in each pipe. In other words, the Courant number should ideally be equal to one and must not exceed one by stability reasons. For most pipeline systems, having as they do a variety of different pipes with a range of wave speeds and lengths, it is impossible to satisfy exactly the Courant requirement in all pipes with a reasonable (and
common) value of ∆t. Faced with this challenge, researchers have sought for ways of relaxing the numerical constraints. Two contrasting strategies present themselves. The method of wave-speed adjustment changes one of the pipeline properties (usually the wave speed, though more rarely the pipe length is altered) so as to satisfy exactly the courant condition [1-55]. In this work an experimental and computational method was used. It applied for prediction of surge tank effects on pressure and flow variation at leakage condition in two cases: 1) pressure and flow variation at surge tank location, 2) pressure and flow variation at leakage location. Therefore, it mentioned to transient flow at water transmission pipeline failure condition.
