5. Finite Amplitude Waves in Combustible Gases

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Abstract
1. Introduction. The generation of pressure waves from the rapid liberation of chemical energy within a gaseous system is one of the most immediately noticeable and practically significant of the consequences of many combustion processes. Apart from anything else the velocity of the signal that carries the message that an energy releasing reaction has taken place somewhere within the system will be that of the local speed of sound or greater if, as is likely, the signal is a shock wave. One usually thinks of these events on a rather large scale, of a laboratory or a building or even perhaps whole building complexes, so that the damaging blast waves have long ago left behind the regions in which actual chemical reactions occur and are travelling through the chemically inert surrounding atmosphere. Important as the study of phenomena of this type obviously is, it must be recognized that pressure waves are born within domains that sustain the combustion reaction, where they will interact in a direct fashion with the reactions themselves and a mutual dependence will exist. This interdependence of combustion reactions and gas dynamics is the theme of the present article. The matter is one of great significance for any transient combustion process and will have applications even in pseudo-steady phenomena such as detonation waves, whose small-scale cellular structure consists of a regular pattern of transversely travelling waves and reaction fronts.

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