Paper 9: Unsteady Flow in Pipes with Gradual or Sudden Area Changes

Abstract

The paper describes a theoretical and experimental investigation into unsteady flows in pipes with cross-sectional area changes. One-dimensional unsteady flow theory using the method of characteristics is used for analysing the wave action in the pipes. Both homentropic and non-homentropic flows are investigated. For gradual area changes (effuser, diffuser) the generalized one-dimensional unsteady flow theories including friction are used. For sudden area changes quasi-steady flow theories at the area change are described to evaluate the boundary conditions. At a contraction the flow is assumed to be isentropic, whilst at an enlargement it is assumed that the flow is adiabatic but not isentropic. In the latter instance, it is assumed that there is a pressure recovery according to the conservation equations; this theory is equivalent to the sudden enlargement theory with pressure recovery at the plane of the area change. Steady flow experiments are described to test the validity of the above assumptions. These show excellent agreement with the theory for the contraction. In the case of the enlargement the tests show that the plane of recovery is some distance downstream of the area change, the distance depending on the dimensions of the area change and the pressure ratio. Extensive unsteady flow tests are described. Good agreement between the theoretical diagrams and experimental results is obtained from the gradual area changes and the sudden contraction. For the sudden enlargement the agreement is good at the pipe ends furthermost from the area change. In the region near the enlargement the flow is strongly three-dimensional. The plane of pressure recovery for unsteady flow is about half the distance downstream from the enlargement for steady flow. The results indicate that once one-dimensional flow is formed the agreement between the theoretical and experimental diagram is good. It is therefore concluded that for gradual area changes the generalized one-dimensional unsteady flow theories may be used, for sudden enlargements quasi-steady flow theories may be used for predicting the flow in the regions some distance from the area change (about four diameters). For sudden contractions there is no limit to the region for consistent results to be obtained.