A unified statistical model of the premixed turbulent flame

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A unified statistical model of the premixed turbulent flame

Bray, K.N.C. / Moss, J.B.

AbstractA unified statistical analysis of the premixed turbulent flame supported by a single-step global reaction is presented. A set of time-averaged balance equations derived from the exact equations of reacting turbulent flow under a thin shear layer, fast chemistry approximation are employed. These equations are closed at the level of turbulence kinetic energy and mean square fluctuation in reaction product concentration, and closure is effected by postulating that the probability density function for product concentration can be specified. The equations which emerge are capable of spanning the range from chemistry- to mixing-limited combustion. An approximate description of turbulent mixing-limited combustion is shown to lead to an explicit time-averaged reaction rate expression similar to Spalding's eddy break-up model. In restricted circumstances the concentration of a trace species which does not contribute significantly to the heat release can be incorporated into the model. Some alternative forms of the probability density function encompassing wrinkled laminar flames and distributed reaction are suggested. Their impact on both the model proposed and the statistical behaviour of experimental observables is investigated—the latter with a view to identifying those experiments which might provide the insight necessary to permit the specification of the probability density function fundamental to the present approach.