Paper 10: Unsteady Flow in Simple Branch Systems

The paper describes a theoretical and experimental investigation into unsteady flows in simple branch systems. In order to simplify the analysis one-dimensional unsteady flow theory is used to analyse the wave action in the pipes. The method of characteristics is used for this purpose, and both homentropic and non-homentropic flows are investigated. The boundary conditions at the branch are represented by quasi-steady flow theories. Two such theories are examined, the first called the constant pressure theory assumed no pressure change across the branch at the junction. A full graphical treatment is given elsewhere (4). In the paper the assumptions and the formulation of the equations for an electronic computer are briefly discussed. The second method assumes a pressure drop across the branch at the junction. An approximate theoretical method of estimating the pressure drop with certain types of flow is given. Using experimentally determined steady flow loss coefficients at the junction the expressions used in the second method are formulated for direct computation using a digital computer. The results are given of an extensive experimental investigation to test the validity and limits of the theories described above. Steady flow experiments to evaluate the loss coefficients at the junction over the range of pressure and flow directions covered by the unsteady tests are described. The unsteady flow tests on a special multi-cylinder pulse generator are discussed in detail. The results show that under certain conditions the calculated pressure diagrams using constant pressure theory do not agree with the experimental diagrams, both the pulse shape and amplitude being incorrect. Using the pressure drop theory together with experimentally determined steady flow loss coefficients there is considerable improvement in the theoretical diagrams. Agreement is obtained over a wide range of flows.