The theory of flame motion

Abstract

The motion of flame has been extensively investigated by experimental methods. The theoretical aspect of one mode of propagation has been studied by D. L. Chapman and by Jouguet. Their observations are limited to the phenomenon known as detonation. For the slower and more usual propagation of flame there is a well-known formula due to Mallard and Le Chatelier. It refers to the horizontal propagation of flame through a still mixture under such circumstances that the pressure produced by the combustion is freely vented into the atmosphere. That is to say, the explosive mixture is ignited at the open end of a horizontal tube, the tube being closed at the other end to shield the mixture from any external currents. This formula was intended as a tentative and general description, without detailed analysis, of the initial, uniform motion of the flame. It is based on the assumption that the trans­mission of flame depends on a balance between the conduction of heat from layer to layer and the cooling. In Mallard's original formula|| the velocity of the flame was held to be inversely proportional to the square root of the cooling due to the wall of the tube; but this relation disappears in the final, joint result of these authors, who wrote their formula V = K T - t / t -θƒ(T. t ), or, tentatively, V=K.L/ c .T - t / t -θ, which becomes V = K . L .Q/ c 2 ( t -θ),