Transient Flow in Pressurized Pipes: A Comparative Study of Five Resolution Methods

Abstract This article solves, models, and simulates, by five different methods, the system of partial differential equations of hyperbolic type governing the transient flow in the case of a gravity pipe supplied from a reservoir and equipped with a valve at its extremity. To make this work smoother and more attractive when calculating hydraulic parameters in transient flow, we took into consideration the two valve closing laws most commonly used in practice and in case of fast and slow closing. The reliability and safety of operation of the pressure pipeline system (PPS) depends on protection systems against the harmful effects of transient flow. To be able to place the most suitable protection device where it is needed, we must use numerical methods to model and simulate such processes. To this end, we applied five methods to solve the transient flow equations and subsequently search for the method giving results with practical credibility. The results obtained show that the methods of MarcCormak and Alternative lead, in fast and slow closures, to very close values by giving more logical graphic representations to the phenomenon generated. The Lax-Friedrichs method can join them but with another appearance of the representation of pressures, and the method of characteristics neglects certain parameters such as the inclination of the pipe while the Richtmayer method should be avoided in its current form because of the error gap between it and the other methods, and the graphical representation of the results obtained, like the pressure over time, which does not give a logical interpretation of the phenomenon produced.