Unsteady Flow through a Four-Way Branch in the Exhaust System of a Multi-Cylinder Engine

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Abstract
This paper is concerned with the investigation of unsteady flow through a four-way branch, with particular reference to its application to flow in the exhaust system of a multi-cylinder engine. The only methods of solution hitherto available are for unsteady flow through a three-way branch. The potentially most accurate theory of those reported takes pressure and entropy changes at the junction into account, but cannot be used in practice since the iterative processes employed in this method often become divergent (I)‡. A convergent method of solution has therefore been developed and is utilized to study the unsteady flow through a four-way branch, making the usual assumption of quasi-steady flow at the junction. A general computer programme for multi-cylinder engines combining the programmes for the cylinder boundary, for the nozzle boundary, for unsteady flow in the pipes, and the present method for branched systems has been developed (in Algol code) to compute the flow variables (pressure, velocity, and temperature) in the exhaust system and cylinders. The temperature variations which can arise in an engine are fully taken into account. Experimental data are presented for both steady and unsteady flow conditions. The steady data have been used to supply the pressure coefficients needed for full computation in the non-steady flow case. Simpler theories involving assumed pressure coefficients are also employed in shorter programmes which yield acceptable results of lower accuracy. Consequently, it appears that prediction can now be made to sufficient accuracy, in the range of pressure amplitudes and Mach numbers investigated, without the need for comprehensive steady flow testing.

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