Contribution to the theory of the structure of gaseous detonation waves

Abstract

The paper presents exact solutions to the equations governing the distributions of temperature, velocity and pressure in a gaseous detonation wave, for the cases in which the dimensionless volumetric-reaction-rate w: (a) has a concentrated peak near the hot boundary but negligible values elsewhere; (b) obeys the law w=n(τ−τC){(τ−τCτH−τC)n−1−(τ−τCτH−τC)2n−2}, where n is a constant, τ is the dimensionless stagnation temperature, and subscript C denotes upstream conditions. Other exact solutions are also discussed. The methods used are analytical and graphical, requiring no high-speed computing facility. The gas is supposed to have a Lewis Number of unity and a Prandtl Number of 3/4; for convenience its thermodynamic properties are supposed to be those of a perfect gas. It is argued that, although the reaction-rate functions considered do not correspond to the chemical-kinetic properties of any particular detonating gas, studies of the kind presented permit clear perception of most of the important properties of real gaseous detonations.