Theoretical Analysis of the Unsteady Gas Flow in the Exhaust System of an Engine

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Abstract
The problem studied is that of unsteady gas motion in ducts of both constant and slowly varying cross-sectional area with the effects of wall friction and heat transfer taken into account. The values of the specific heats used in the analysis are those applicable to the instantaneous gas temperature at the instant under consideration, i.e. thermal lags are ignored. To solve the unsteady flow equations, a method is developed based on the theory of characteristics and in the application of this method a pure graphical approach is used for convenience. The plotting technique adopted is the ‘field method of solution’ in which it is assumed that a region of continually varying fluid properties can be broken into a large number of small regions for calculation purposes. The fluid properties are assumed uniform throughout each of these small regions and changes in the fluid properties can only occur across the boundaries or characteristics separating the small regions. With a firing engine, temperature discontinuities will be established at the interface of the hot gases being discharged from the cylinder and the cooler residuals from the previous cycle. Owing to the interaction of successive points of the fundamental pressure pulse with those resulting from the reflection of previous points of the fundamental pulse, sonic velocities can be encountered at the diffuser entry section. The formation of a steep front at the diffuser entry section as a result of these rarefaction waves can produce a shock wave. A method of solution for the existence in the flow of such discontinuities as temperature and shock is included. The general conclusions to be drawn are: (1) true application of the irreversible flow theory gives a good solution of the wave patterns occurring in both the cylinder and exhaust pipe of the engine; (2) the air mass flow can be predicted with good accuracy by application of the irreversible flow theory developed; (3) the poor correlation resulting from application of the isentropic flow theory shows caution should be exercised in the use of this simplified theory.

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