Mean reaction rates and flamelet statistics for reaction rate modelling in premixed turbulent flames

Abstract

An experimental technique for determining the mean rate of chemical reaction, w >, is developed and applied to turbulent V-shaped flames. Two components of fluid velocity and flamelet position along a line are measured simultaneously. Estimates of w > are obtained by using the experimental data to evaluate gradients of conditional mass fluxes and I >, where I is an indicator function analogous to the reaction progress variable, in two-dimensional conservation equations derived from the continuity equation. The measurement of flamelet position along a line enables corrections for finite flamelet thickness to be incorporated in the estimates of w >. Also obtained are temporal flamelet statistics which arise in the Bray-Champion-Libby (BCL) model for w >: the scalar integral time scale, the flamelet crossing frequency, and the model coefficient g . From w > and the flamelet crossing frequency, Σ and V n |> are inferred, where Σ is the flamelet surface-to-volume ratio and | V n | is the magnitude of the normal component of the flamelet velocity. The scalar integral time scale exhibits a near linear decrease with increasing 〈 I 〉 within the central region of the flame brush. The variation of crossing frequency with 〈 I 〉 is in good agreement with previous studies, and the coefficient g shows a systematic variation, reaching a minimum near 〈 c 〉=0.6. Estimates of 〈 w 〉 and Σ decrease with increasing distance from the flame stabilizer and with increasing turbulent intensity, behavior which is consistent with the observed thickening of the turbulent flame brush. 〈1/| V n |〉 is found to decrease with increasing 〈 I 〉 and with increasing turbulent intensity, but remains within a factor of three of one over the magnitude of the reactant fluid velocity under the experimental conditions studied here.