The theory of flame phenomena with a chain reaction

Abstract

For single-step reactions there is a unique relation between reaction rate and reactedness for a given combustible mixture at a specified pressure and initial temperature. This paper examines whether the relation is still unique when chain reactions are present, by considering three types of flame—spontaneous ignition, laminar-flame propagation, and the homogeneous steady-flow reaction zone—with a chain-reaction scheme proposed by Adams & Stocks for the decomposition of hydrazine. It is found that the relation is not unique but that similarities exist between the relation for laminar-flame propagation and the relation for the homogeneous reaction zone. Incidentally, a general method of calculating laminar-flame speeds with reaction schemes of arbitrary complexity is presented. When applied to the hydrazine decomposition flame the predictions of the theory are in fair agreement with experimental results. In particular, the variation of flame speed with temperature is correctly predicted. It is shown that the use of the Karman-Penner 'steady-state assumption' would lead to an overestimate of the flame speed. Consideration of the changes which would result if the chain reaction should branch shows that there would once again tend to be a unique reaction rate versus reactedness relation, and that the laminar-flame speed would be increased by a factor of about three for the hottest flame considered but by larger factors for cooler flames.