The Theory of Flame Propagation

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Abstract
The characteristics of steady-state one-dimensional flames are expressed in terms of a set of first-order ordinary differential equations suitable for solution by differential analyzers or high speed digital computing devices. Arbitrary systems of chemical kinetics and reaction rates can be investigated. The effect of ambient temperature, pressure, heat transfer from the flame to the flame holder, diffusion of free radicals, thermal conductivity, etc., are easily estimated. The equations which we use are the ordinary hydrodynamic equations of change generalized to include the effect of the chemical reactions. In these the usual expressions for reaction rates are introduced, that is, the rate at which the composition would change in a closed vessel under the local conditions of temperature and density. Equations expressing the diffusion velocities in terms of the composition gradients are given. The flame holder has been idealized in the form of a porous plug through which the fuel can pass freely from left to right, but a semipermeable membrane prevents the product gases moving in the opposite direction. It is found that heat transfer to this flame holder is required to stabilize the position of the flame. The conditions obtained at the hot boundary are expressed parametrically in terms of the roots of a secular equation.

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