Transient discharge of a pressurised incompressible fluid through a pipe and analytical solution for unsteady turbulent pipe flow

Abstract

The dynamics involved in the process of sudden discharge of a pressurized liquid to the atmosphere is studied, a case of broad interest in fire protection Engineering. The state of the art in the literature regarding such discharge process is presented. A one-dimensional hydraulic model is developed for this flow, which takes the form of ordinary intregro-di ferential equations that are solved numerically. A sensitivity analysis is carried out with respect to all the parameters on which the model depends, with special emphasis on the friction generated by the turbulence. The generic methods of describing turbulence are analysed, including the statistical representation, the filtering of turbulent quantities and the full analytical description. A general analytical solution for the turbulent, incompressible and unsteady flow in a pipe is developed. A three-dimensional computational model for the described flow is elaborated. The modelling of turbulence turns out to be the most important and conflicting point of such model. The results obtained are compared with those predicted by the one-dimensional hydraulic model previously developed. Results are presented regarding the internal structure of the turbulence in strongly accelerated flows. A remarkable increase of said turbulence is anticipated in the proximities of the wall, that could not be explained only with the Reynolds number.