Influence of Pipe Friction and Heat Transfer on Pressure Waves in Gases: Effects in a Shock Tube

Abstract

Finite-amplitude pressure waves travelling in gases in pipes are subject to the influence of pipe friction and heat transfer to or from the pipe wall. Where the pipe section is moderate or small these factors cause serious departures from the classical laws governing wave motion under frictionless adiabatic conditions. The paper presents a theoretical analysis of the effects of friction and heat transfer, assuming that at any instant and location the frictional force and heat-transfer rate in a pipe element are those for steady flow at the same Reynolds number. Based on the three-directional method of characteristics, a step-by-step procedure is developed for the solution of practical problems involving wave motion in pipes of moderate diameter, for example, in internal-combustion engine exhaust pipes. The procedure is illustrated by application to the wave motion in a simple shock tube of moderate initial pressure ratio. Experiments using such a shock tube confirm the validity of the theoretical treatment.