Radial and Axial Variations in Transient Pressure Waves Transmitted Through Liquid Transmission Lines

Abstract

An implicit factorization method has been developed for solving numerically the complete two-dimensional Navier-Stokes and continuity equations for pressure transients in a slightly compressible viscous liquid contained in a rigid pipe. Two problems have been analyzed: (1) The stopping of a steady Poiseuille flow by closure of a valve, and (2), the initiation of a nearly rectangular pressure pulse at the end of the pipe. In problem (1), radial as well as axial pressure variations were found; nearly periodic damped waves exist at the centerline and at the wall, and are approximately 180 deg out of phase. Essentially plane waves are found for problem (2), regardless of whether the fluid is flowing or not, provided that the initial pulse magnitude is not too large; the results show that the viscous effects are concentrated in a thin boundary layer.