The present status of the theory of laminar flame propagation

Abstract

Summary Summarizing our considerations concerning the present status of the theory of laminar flame propagation, I wish to state: o (1) That it appears in cases in which the reaction-scheme and the corresponding chemical kinetics are well-defined, a semianalytical method, as presented in this paper, makes a relatively easy determination of the flame velocity possible. There is no necessity for radical simplifying assumptions such as are introduced, for example, in the pure diffusion theories. (2) There is no necessity to take recourse to laborious numerical integration of the differential equations, although the use of digital computers may facilitate such methods. (3) It appears that in the cases dealt with until now, the steady-state assumption facilitates a rather quick determination of the flame velocity of a chain reaction, even in those cases where it does not furnish an exact picture for the distribution of the radicals through the flame zone. (4) It is believed that in order to make further progress in the theory, the most urgent need is a better knowledge of the reaction schemes and the chemical kinetics of the important chain reactions. Especially more exact data are necessary concerning the presence and distribution of the radicals involved. A paper by K. A. Wilde [J. Chem. Phys. 22 , 1788. (1954)] has recently come to our attention. The procedure used by this author for the integration of the simple one-step flame reaction is the same as that used in our first approximation except that ∈ is assumed to vary as ([ϱ=ϱ o )/(1-ϱ o )] n+1 . Here the exponent n is determined by equating the limiting slope of [(ϱ-ϱ o )/(1-ϱ o )] n to the limiting slope of [exp [-ϱ a (1-ϱ)/ϱ }. This procedure leads to the relation 1 Λ = 2 I 1 − θ 0 [ 1 + 2 θ α ( 1 − θ 0 ) ( A − 1 ) which is similar to our Equation (19). For, sufliciently large values of ϱ a , i.e., small values of I, Equations (A-1) and (19) become evidently equivalent. We have evaluated 1 / Λ according to Equation (A-1) and find the results to be less accurate than our second approximation for ϱ a ≥5 but to be better at smaller values of ϱ a . Equation (A-1) gives results which are superior to those determined from Equation (19) for ϱ a Λ about as much too small according to Equation (A-1) as it is too large according to Equation (19) for larger values of ϱ a