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Abstract
A formalism for a flamelet's evolution of its spatial distribution is derived from a field equation which is slightly more general than Williams' field equation. Unlike Williams' field equation, the field equation used here, though non-linear, has the property that an arbitrary linear combination of interface solutions (Heavyside type of functions) is also a solution. We therefore can describe the location of the flamelet with two interfaces rather than one, both moving relative to the flow in the same direction. The volume between these two interfaces is on average conserved; this makes it possible to define a probability density for the spatial distribution of the flamelet, and thereby derive equations describing the evolution of the spatial distribution of folds and wrinkles of the flame front.
Three main conclusions are reached in this paper using this formalism, through the exact analytical study of a flamelet in an arbitrary l-d velocity field, and through the numerical study of a flamelet in a simulated 2-d turbulent velocity field.
(1)The rate of advancement uM of the average location of the flame front can be smaller than the turbulent flame speed uT at short times, and sometimes even smaller than the laminar flame speed uL (at short times). It is shown, in the case of an arbitrary l-d velocity field, that uM = uT ronly after cusps have formed on the flamelet, and uM < uL < uT before.
(2)If the turbulence is too weak or too strong compared with the laminar flame speed, the dispersion of the flame is, at short times, increased by the turbulence and reduced by the laminar flame speed.
(3)The dispersion of the flame is skewed towards the direction of the flame's propagation at all times, even before cusp formation.