A Priori Model for the Effective Lewis Numbers in Premixed Turbulent Flames

Abstract

A simple a priori model for the effective Lewis numbers in a premixed turbulent flame is presented. This a priori analysis is performed using data from a series of direct numerical simulations (DNS) of lean (φ = 0:4) premixed turbulent hydrogen flames, with Karlovitz number ranging from 10 to 1562. Those simulations were chosen such that the transition from the thin reaction zone to the broken reaction zone is captured. The conditional mean of various species mass fraction (< Y_i | T >) vs temperature profiles are evaluated from the DNS and compared to equivalent unstretched laminar premixed flame profiles. The turbulent flame structure is found to be different from the laminar flame structure. However, the turbulent flame can still be mapped onto a laminar flame with an appropriate change in Lewis numbers. Those effective Lewis numbers were obtained by minimizing the error between the DNS results and predictions from unstretched laminar premixed flames. A transition from "laminar" Lewis numbers to unity Lewis numbers as the Karlovitz number increases is clearly captured - equivalently, as the turbulent Reynolds number increases, given that the ratio of the integral length scale to the laminar flame thickness is fixed throughout the series of DNS. Those results suggest the importance of using effective Lewis numbers that are neither the "laminar" Lewis numbers nor unity in tabulated chemistry models without considering the impact of the turbulent Reynolds number or Karlovitz number. A model for those effective Lewis numbers with respect to the turbulent Reynolds number was also developed. The model is derived from a Reynolds Averaged Navier-Stokes formulation of the reactive scalar balance equations. The dependency of the effective Lewis numbers to the Karlovitz number instead of the Reynolds number was studied and is discussed in this paper. These changes in effective Lewis numbers have significant impacts. First, the laminar flame speed and laminar flame thickness vary by a factor of two through the range of obtained effective Lewis numbers. Second, the regime diagram changes because a unique pair of laminar flame speed and laminar flame thickness cannot be used. A dependency on the effective Lewis numbers have to be introduced.

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