Paper 10: Unsteady Flow in Simple Branch Systems

Abstract

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.

A unified method for estimating pressure losses at vascular junctions

“…The quasi‐steady flow assumption was also supported by data of Benson et al . and Bingham and Blair . Nevertheless, in future studies, we plan to evaluate the Unified0D method under pulsatile flow conditions with high fidelity in vivo pressure recordings.…”

An Improved Branched Pipe Model for Multi-Cylinder Automotive Engine Calculations

“…The simplest approach, described by Benson et al (8) and by Blair and Goulburn (3), is to assume that at each time step in the characteristics calculation the pressures in the ends of all the pipes next to the junction are equal. This procedure neglects pressure changes which may occur as flow passes through the junction and in particular it cannot allow for the pressure losses which are associated with flow through branches in the inlet manifold and which can adversely affect delivery ratio.…”

“…Another method proposed by Benson (8) was based on an empirical form of the momentum equation incorporating experimental loss coefficients which were obtained from steady flow tests (9). Coefficients were only obtained for 90" bends and T-junctions and the calculation procedure was limited to junctions with three pipes, but the results of unsteady flow tests showed the momentum model to be superior to the constant pressure theory.…”

“…Furthermore, Benson's work (8) has shown that for good correlation between measured and predicted pressure-time histories, losses must be allowed for in the junction calculation. This paper describes the development of such a model, (16), suitable for use in an automotive engine simulation computer program utilizing the method of characteristics.…”

“…This was similar to the homentropic analysis proposed by Benson (8), although the empirical momentum equations were used in the form indicated by MacLaren (10). It was assumed that in the case where flow in two of the pipes was towards the junction, the pressures in those pipes were equal at the point of branching (8). Referring to Fig.…”