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.

Topics
Thermal conductivity, Von Neumann spike, Fluid dynamics, Shock waves
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In region III, for a reasonable gas detonation with κ = 1, γ = 1.25, and υ0/υ∞ = 1.72, it follows that cW/c∞ = 0.91, ρW/ρinfin; = 0.43, TW/T∞ = 0.83, and pW/p∞ = 0.35.
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See MTGL, ref. 9, p. 774. It is easy to show that to a first approximation, G behaves like the x of Eq. (11.7–49). Flames with large kinetic energy have also been discussed by Hirschfelder, Curtiss, and Campbell, Fourth Symposium (International) on Combustion (Williams and Wilkins, Baltimore, 1953).
We are grateful to William W. Wood for pointing out to us errors in the analysis of the solutions near the von Neumann spike in the University of Wisconsin Naval Research Laboratory Report CM‐911 (August, 1957) by J. O. Hirschfelder and C. F. Curtiss.
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© 1958 American Institute of Physics.
1958
American Institute of Physics
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