Fundamental approach to laminar flame propagation

The complete system of equations for a theory of laminar flame equations is presented, taking into account both heat conduction and diffusion, for the case of an arbitrary number of simultaneous reactions. The eigenvalue problem determining the flame velocity is formulated. Two examples are given in order to show that explicit analytical expressions for the flame velocity can be obtained, which are in good agreement with the results obtained by numerical integration of the equations. In the first example (hydrazine decomposition) one reaction is considered as global, i.e., rate-controlling, reaction. In the second example (ozone decomposition) a hypothesis is introduced for the concentration of the free radical O, which corresponds to the steady-state approximation generally used in classical chemical kinetics. In both cases approximate explicit formulae are obtained for the flame velocity using legitimate approximation methods, without making drastic assumptions. The steady-state assumption used for the ozone flame has a bearing on a better understanding of the mechanism of chain reactions in general. The method indicated in the paper gives hope that the more complicated chain reactions, such as the combustion of hydrocarbons, will also be made accessible to theoretical computation.