Industry Experience With Waterhammer: Topics of Recent Interest in Waterhammer

Abstract

The analysis of transient flow in a piping system containing one or more trapped gas volumes is considerably simplified when the liquid can be treated by bulk flow theory without propagation effects, complicated by moving boundaries. Many cases that have occurred in the power industry, which involve pump operation, valve opening and closure, and even some pipe ruptures, have time intervals and/or piping segments that can be shown to be dominated by bulk flow with negligible propagation effects. Often, propagation effects become important only for short time intervals at the beginning or toward the end of a given transient. This observation can greatly simplify the solution of such problems for maximum pressures and pipe loadings to a relatively simple procedure. Most models which have received attention or undergone development are based on the mass conservation and momentum principles, with gas state equations, and this is the correct approach for tracking liquid motion and gas volume compression. The energy conservation principle is not required to solve for the pressure and velocity of the liquid in the pipe, and to obtain the resulting forces. However, energy considerations are extremely useful in gaining physical insight to the overall problem. The major insight offered by the energy principle is based on the fact that when liquid flow is initiated in a pipe system containing gas pockets, the total mechanical energy added to fluid in the pipe must be distributed between the liquid and the gas in mechanical forms, namely kinetic, gravitational potential, and compressive or “spring” type energy. If one examines the gas and liquid when it has come to rest and neglects the kinetic and gravitational potential energies, the only stored energy forms are compressive. If the liquid is incompressible, or “rigid,” all the energy is stored in the gas and the resulting pressure is PR. If the liquid is elastic, or compressible, the energy will be shared so that both the gas and liquid will be at the same pressure, P. By comparing pressure P with PR, it is possible to determine if the compressible liquid is capable of storing enough energy to reduce the pressure significantly from that which would result if the liquid were incompressible and all the energy were stored in the gas. A procedure and several examples are given for starting with a given system, predicting the pressure with a rigid or incompressible liquid model, and then determining if a modified analysis is justified, incorporating liquid compressibility and propagation effects.