Paper 2: Behaviour of Rarefaction Waves at the Junction of a Branched Duct

Abstract

The results of an investigation into the behaviour of rarefaction waves at a junction formed by the intersection of two ducts are presented. Pressure measurements have been made in junctions in which the side branch forms an angle of 45°, 90°, and 135° with the main branch. In the 90° junction the effect of the area of the side branch to that of the main branch is examined; the values of the ratios being 1·0, 0·5, and 0·25. The amplitude of the incident rarefaction waves varies from 3 to 20 inHg. The development of the quasi-steady flow pattern has been obtained by Schlieren photography. This information, together with the pressure measurements, has been used to develop a quasi-steady, one-dimensional, semi-empirical analysis of the flow. The results of this analysis are in good agreement with the pressure measurements and can be used as boundary conditions for the examination of pipe networks by the method of characteristics.

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

“…A series of experiments conducted by Deckker with others (13,14,15) on three-pipe junctions with three different configurations has provided a useful insight into pressure wave behaviour within the junction itself but a completely theoretical analysis of the events occurring was found to be impossible. A set of diagrams was therefore produced, based on the experimental results obtained and arranged to be suitable for use in calculations employing the method of characteristics.…”

“…PL -~c = CL(pc U3previous time step (15) As in the supplier type calculation, CL depends on the angle between pipe L and pipe c while p, and u, are again based on I and /3 from the previous time step to avoid an iterative procedure. For other flows towards the junction it is assumed as before that p,, -pL = 0.…”

“…To satisfy the requirements of the generalized junction model the experimental results were replotted to provide loss coefficients suitable for equations (14) and (15). Since equations (1-12) represent the best fit for the data taken, it is evident that some simplification is introduced by using equations of the form shown for the generalized model.…”

“…It is evident that the generalized model takes no cognizance of the pressure rise which can occur in dividing (1-12), (14) and (15) are independent of Reynolds number and so in engine simulation work these coefficients may be considered constant. Fig.…”