Modeling of Fluid Interaction Produced by Water Hammer

Introduction

Water hammer as a fluid dynamics phenomenon is an important case study for designer engineers. The majority of transients in water and wastewater systems are the result of changes at system boundaries. It happen typically at the upstream and downstream ends of the system or at local high points (Asli, Nagiyev & Haghi, 2009). Consequently, the results of the present work can reduce the risk of water system damage or failure. The study of hydraulic transients is generally considered to have begun with the works of (Joukowski, 1898) and (Allievi, 1902). The historical development of this subject makes for good reading. A number of pioneers have made breakthrough contributions to the field, including Angus and (Parmakian, 1963) and (Wood & Jones, 1973) who popularized and refined the graphical calculation method. (Wylie & Streeter, 1993) combined the method of characteristics with computer modeling. The field of fluid transients is still rapidly evolving worldwide by (Brunone, Karney, Mecarelli, & Ferrante, 2000; Koelle, Luvizotto, & Andrade, 1995; Filion & Karney, 2002; Hamam & McCorquodale, 1982; Savic & Walters, 1995; Walski & Lutes, 1994; Wu & Simpson, 2002). Various methods have been developed to solve transient flow in pipes. These ranges have been formed from approximate equations to numerical solutions of the non-linear Navier–Stokes equations. Hydraulic transient flow is also known as unsteady fluid flow. During a transient analysis, the fluid and system boundaries can be either elastic or inelastic: (a) elastic theory describes the unsteady flow of a compressible liquid in an elastic system (e.g., where pipes can expand and contract); (b) 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. The continuity equation and the momentum equation are needed to determine V (velocity) and P (surge pressure) in a one-dimensional flow system. Solving these two equations produces a theoretical result that usually corresponds quite closely to actual system measurements. It will be valid based on the validity of the data and assumptions which used for building the numerical model. Transient analysis results that are not comparable with actual system measurements are generally caused by inappropriate system data (especially boundary conditions) and inappropriate assumptions. 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 (Leon, 2007).