The Influence of Pipe Motion on Acoustic Wave Propagation

Abstract

It is well known that the magnitude of the acoustic wavespeed in piping is influenced by properties of the fluid and the pipe material. Traditionally, derivations have been based on a quasi-static control volume model, where the pipe deformation takes place in the time the liquid acoustic wave travels a known distance along the pipe. In actuality, dilation of the piping causes axial stress waves to propagate along the pipe wall at speeds greater than that of the acoustic wave. Such axial coupling between the liquid and piping has been reported by several investigators, including Walker and Phillips [4], who developed a six-equation model with a three-wave family—radial and axial stress, and axial liquid. In the present study Walker and Phillips’ model is simplified to a four-equation one by neglecting radial inertia, a valid assumption for many practical piping system transients. An eigenvalue analysis of the hyperbolic relations reveals two axial waves—in the liquid and in the pipe wall—which are modified by the coupling action. The traditional wave speed formulations with varied coupling constraints are reviewed in light of the present development. Numerical examples are presented which show the effects of such interaction for various combinations of liquid and piping.