Structure of laminar flames

Abstract

The one-dimensional formulation of the opposed flow strained flame problem, starting from the cylindrical Navier-Stokes equations, is described and compared with the older, Hiemenz potential flow formulation. The eigenvalue in the newer formulation is shown to be a stress on the fluid, and it is shown that the Navier-Stokes equations reduce to expressions for (i) the pressure gradient profile normal to the flame, and (ii) the strain rate profile in the variable density system. The basic features of hydrogen and hydrocarbon flame chemistry are reviewed, and the importance of the temperature T_i at which the system becomes effectively chain branching is demonstrated in the context of flame extinction. It is suggested that in a sense T_i fulfils the function of an ignition temperature. The responses of flames to applied stresses are discussed for diffusion flames, and for premixed flames in both the symmetric back-to-back and the asymmetric unburnt-to-burnt configurations. It is shown that, in opposed flow systems of fixed geometry and finite dimensions, the behaviour of the symmetric back-to-back flames which are not too close to the inlet nozzles are for practical purposes characterized entirely by the applied stress. However, because of viscous effects, particularly near the nozzles, this applied stress cannot be measured directly with precision. Repercussions on extinction limit measurements, and on indirect determinations of one-dimensional burning velocities, are indicated. The use of measurements on expanding spherical flames for the determination of burning velocity is briefly discussed, as also are the effects of flow configuration on the stress and strain rate profiles at extinction.