One-Dimensional Transient Flow in Pipelines Modelling and Simulation

This chapter presents a review of the literature related to fluid transients involving column separation and vaporous and gaseous cavitation in pipelines. Basic concepts are clarified, and the classification of water hammer and cavitation models is presented. The historical development of fluid transients is described. The concept of propagation of pressure pulses at sonic velocity through a straight pipeline is presented. 

This chapter gives a detailed description of the mathematical development proposed for the study. The elasticity theory and the general theory of beams are strongly present whereas some assumptions are adopted to simplify the analysis. 

In this chapter, the Method of Characteristics (MOC) is detailed and used to solve the mathematical models defined in the second chapter, where the reservoirpipe-valve-system is considered. The wave-speed adjustment (WSA) scheme is preferred for the MOC. The numerical method is applied to the elastic pipelines on onehand and to the viscoelastic pipelines on the other hand.

The modelling of transient cavitation is described in this chapter by considering column separation modelling where FSI and gas release are taken into account. As detailed for water hammer modelling, transient in straight pipeline is caused by fast closure of shut-off valve. Both vaporous and gaseous cavitation are considered in the numerical models. 

This chapter deals with the numerical results obtained from the simulation of fluid transients in elastic pipes. The MOC with WSA scheme is used and the numerical results are validated against experimental records. The comparison shows good agreement between the two results which validate the earlier proposed models. 

This chapter deals with the numerical results obtained from simulation of fluid transients in viscoelastic pipes. For the non-cavitating flow case, the simulation shows that the pressure fluctuations are rapidly attenuated, and the overall transient pressure wave is delayed in time due to the retarded deformation of the pipe-wall. In addition, the simulation of the cavitating flow gives reasonable results compared to experimental data.