Flamelet Crossing Frequencies and Mean Reaction Rates in Premixed Turbulent Combustion

The one-point, one-time description contained in the Bray-Moss-Libby model of pre-mixed turbulent combustion is first generalized to a two-point, two-time formulation which includes information on the time and length scales of the scalar field within turbulent flames. This formulation is then specialized to a one-point, two-time description which is treated in detail so as to yield expressions for the autocorrelation of the progress variable, for the time scale of the scalar field, for the mean crossing frequency of the flamelets and, finally, for the mean rate of chemical reaction. Although the latter expression closely resembles results developed earlier on an intuitive basis, its derivation in the present study permits an assessment of various assumptions and intermediate results by comparison with experimental measurements. Such comparisons as are currently possible are shown to lend support to the analysis and to enhance the prospects of future exploitation of the general formulation.