Thermal Nature of Concentration Limits of Combustion

Abstract

An explanation is proposed for the concentration limits of slow combustion of gas mixtures due to the diffusionalthermal instability of a fl ame and the leading role of the thermal effect of mixture combustion. Basic to this explanation are the following experimental facts obtained for a wide class of mixtures: the concentration limits of slow combustion of a mixture and of its detonation are closely coinciding and depend strongly on the stoichiometric composition of mixture; there is an approximate symmetry relation between the upper and lower combustion limits. It is shown that the fl ame temperature of gas mixtures depends on their stoichiometric composition and that as their stoichiometric relation deviates from unity, the state of mixture combustion approaches the stability threshold beyond which a stationary fl ame cannot exist.Introduction. The concentration limit of combustion of a mixture with stoichiometric composition is manifested as a sudden disappearance of a fl ame when the concentration of a combustible (or of an oxidant) reaches its maximum or minimum value [1]. Despite the great practical importance of this phenomenon, it has not yet found any satisfactory theoretical explanation.At the present time several theories have been advanced that explain the existence of the combustion concentration limit and that can be subdivided into two classes. In the models falling into the fi rst class, the concentration limit is reached through the heat losses from the fl ame zone, with these losses being due to radiation, molecular transfer, and convection. The second class consists of models according to which the mixture combustion concentration limit ensues on violation of the balance between the branching and breaking of the chains of a corresponding chemical reaction and of the balance between heat and mass transfer, as well as at a great difference between the diffusion coeffi cients of the atoms, radicals, and molecules participating in the chemical reaction. Despite the abundance of various explanations for the existence of the combustion limit, none of the theories developed so far has gained wide acceptance. Theory of the Combustion Concentration Limit.The assumption on the occurrence of the mixture combustion concentration limit due to the loss of heat by radiation was made by D. B. Spalding [1], Ya. B. Zel′dovich, and V. V. Voevodskii [2]. Subsequently this idea underwent development in the works of A. I. Rozlovskii [3]. According to the radiative mechanism of the mixture combustion concentration limit, which in many ways is similar to the mechanism underlying the onset of gas combustion limit in narrow tubes [4], the extinction of fl ame in the course of mixture combustion occurs when the fl ame temperature is decreased by a value equal to N. N. Semenov′s interval. The rate of fl ame decreases in this case by a factor of e 1/2 (e ≈ 2.72) compared to the value corresponding to mixture combustion under adiabatic conditions. The theory of the occurrence of the mixture combustion concentration limit d...