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Published June 2014 | public
Journal Article

An a priori model for the effective species Lewis numbers in premixed turbulent flames

Abstract

An a priori model for the effective species Lewis numbers in premixed turbulent flames 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 (Aspden et al., 2011). The conditional mean profiles of various species mass fraction versus temperature are evaluated from the DNS and compared to 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 the Lewis numbers of the different species. A transition from "laminar" Lewis numbers to unity Lewis numbers as the Karlovitz number increases is clearly captured. A model for those effective Lewis numbers with respect to the turbulent Reynolds number is developed. This model is derived from a Reynolds-averaged Navier–Stokes (RANS) formulation of the reactive scalar and temperature balance equations. The dependency of the effective Lewis numbers on the Karlovitz number instead of the Reynolds number is discussed in this paper. Unfortunately, given that the ratio of the integral length to the laminar flame thickness is fixed throughout this series of DNS, a change in the Karlovitz number is equivalent to a change in the Reynolds number. Incorporating these effective Lewis numbers in simulations of turbulent flames would have several impacts. First, the associated laminar flame speed and laminar flame thickness vary by a factor of two through the range of obtained effective Lewis numbers. Second, the turbulent premixed combustion regime diagram changes because a unique pair of laminar flame speed and laminar flame thickness cannot be used, and a dependency on the effective Lewis numbers has to be introduced. Finally, a turbulent flame speed model that takes into account these effective Lewis numbers is proposed.

Additional Information

© 2013 The Combustion Institute. Published by Elsevier Inc. Received 26 July 2013; Received in revised form 12 December 2013; Accepted 13 December 2013; Available online 17 January 2014. The authors gratefully acknowledge funding from the Air Force Office of Scientific Research (Award FA9550-12-1-0144) under the supervision of Dr. Chiping Li, and from the Natural Sciences and Engineering Research Council of Canada (NSERC Postgraduate Scholarship D). This work was also made possible by a collaboration with Dr. Andy Aspden, from the University of Portsmouth, who kindly shared with the authors the DNS data presented in Ref. [13].

Additional details

Created:
August 22, 2023
Modified:
October 25, 2023