Theory of Detonations. I. Irreversible Unimolecular Reaction

Abstract

The composition, temperature, and pressure as functions of distance in a steady‐state, plane gaseous detonation wave are studied. The effects of the coefficients of viscosity, diffusion, and thermal conductivity are included. The basic equations are set up for a gas in which the irreversible unimolecular reaction A→B takes place with the release of energy. The topological nature of the solutions is discussed and some detailed numerical solutions are given. The numerical calculations (obtained by a point‐by‐point integration of the detonation equations) indicate a strong probability that there is a highest ambient pressure above which a steady‐state detonation cannot take place, and indicate a possibility that there is an ambient pressure below which a detonation cannot occur. In the examples considered, there is strong coupling between the reaction zone and the shock zone so that the solutions never come close to the von Neumann ``spike.'' If the Mach number is greater than unity, the solutions have an entirely different nature and exist for only a single ambient pressure rather than for a range of pressures. However, from hydrodynamical considerations, a detonation wave initiated from either a point or a fixed wall can become equivalent to the steady‐state solutions only if the Mach number is greater than or equal to unity.