Turbulent flame propagation in premixed gases: Theory and experiment

Abstract

A two eddy theory of turbulent combustion is presented. This rests upon the assumption, supported by a good deal of experimental evidence, that two scales of eddy are particularly important. One is associated with the integral scale of turbulence, the other with the Kolmogorov scale. It is assumed that all the material in the large eddies is used in the formation of the smaller dissipative eddies. Dissipation along vortex tubes, with the associated molecular transport, is necessary for flame propagation. It is assumed that laminar flame propagation occurs through the large eddies and that the dissipative eddies react chemically along the length of vortex tubes. Eddy decay times and chemical lifetimes are ascribed to both sizes of eddy and rate processes are conveniently based upon a common dimensionless time, τ=u′2t/v. It is shown that the rate of burning in small eddies can be many times greater than that in large eddies. Theoretical values are obtained for the ratio of turbulent to laminar burning velocity, in terms of turbulent Reynolds number and the ratio of laminar burning velocity to r.m.s. turbulent velocity. These are in fair agreement with experimental values, but more data are required on the intermittency and chemical lifetimes of small eddies. Experiments are reported on the effect of turbulence upon flammability limits. These are narrowed as turbulence increases, but counter-action may be taken by increasing the spark ignition energy and by establishing the initial flame in a shielded region where the turbulence is reduced. The relevance of the theory to these results is discussed.