Application of the Method of Characteristics to the Transient Flow of Gases

Abstract

Although problems relating to non-uniform flow of a compressible fluid have been tackled by a number of workers, investigations have generally been limited to the study of one-dimensional non-viscous adiabatic flow. This type of flow, however, is associated with so many problems encountered by mechanical engineers that an easy and reliable method of solution is extremely important. The method of characteristics described in this paper provides a comparatively simple method of solving such problems by a graphical process. It consists essentially in the simultaneous construction of two corresponding diagrams:— (a) The state diagram showing the changes in the state of the fluid produced by spreading disturbances. (b) The position diagram depicting the spreading of the disturbances. The graphical construction of these diagrams is based upon certain special mathematical properties of the equations which describe the motion and enable boundary conditions corresponding to any particular problem to be readily taken into account. Applications include the phenomena occurring in internal combustion engine exhaust and intake pipes, in particular, those relating to the Kadenacy system of scavenging. It is also applicable to the type of flow encountered during the emptying of cylinders, in pulsating ram jet engines and, in general, in any engine making use of the intermittent flow of gases. The phenomena occurring in long indicator passages during tests on high-speed engines also come within its scope.