Wave Damping and Smoothing in the Unsteady Pipe Flow

Abstract

A modification of the governing equations for unsteady pipe flow is proposed based on the results of many experiments carried out for steel and HDPE pipes of various lengths. Strong damping and smoothing of the pressure wave observed in the experiments suggest that these effects are caused not only by the liquid viscosity, represented in the governing equations by an algebraic term, but also by some other processes that are not described by these equations. The phenomena observed in physical experiments, such as time-varying pressure wave celerity and smoothing of the wave front, cannot be reproduced by the standard unsteady pipe flow model even if various modifications of the formula for shear stress available in the literature are applied. For this reason, an attempt to take into consideration additional dissipative processes was undertaken. On the basis of an approximate model of the elastic behavior of the liquid and wall pipe material, an approach accounting for the variable pressure wave celerity is proposed. Moreover, a diffusive term reproducing the irreversible processes at the pressure wave front is introduced into the dynamic equations. The numerical tests showed that the proposed approach leads to better agreement between the computational and experimental results.