323 Twenty-Sixth Symposium (International) on Combustion/The Combustion Institute, 1996/pp. 323–329 NEGATIVE FLAME SPEED IN AN UNSTEADY 2-D PREMIXED FLAME: A COMPUTATIONAL STUDY INGE R. GRAN Department of Applied Mechanics, Thermodynamics, and Fluid Dynamics Norwegian University of Science and Technology N-7034 Trondheim, Norway TAREK ECHEKKI and JACQUELINE H. CHEN Combustion Research Facility Sandia National Laboratories Livermore, CA 94551-0969, USA This study analyzes a stoichiometric premixed methane flame perturbed by two-dimensional turbulence using direct numerical simulation. The chemistry is described with a detailed reaction scheme. Differential diffusion is accounted for by prescribing the Lewis number for each species. The turbulent Reynolds number based on the integral scale is 136 and the ratio of rms velocity to laminar flame speed u'/S L  12. When regions of steep scalar gradients are curved, a large second derivative is created in the direction tangential to the isoscalar lines. This opposes the distortion of the isolines by the imposed velocity field. Negative burning arises when the magnitude of the diffusive flux exceeds that of the adverse convective flux. In the present flow, this occurs in regions of high positive curvature. In these regions, both reaction and diffusion in the direction normal to the isolines generally contribute to decrease the negative flame speed. However, the contribution of diffusion in the direction tangential to the flame front by far exceeds the other contributions to the flame speed. The direct effect of chemical reaction on the flame speed is negligible compared to the effect of diffusion in the highly curved regions. The significance of using a detailed description of the chemistry and diffusion in the present context is that it allows the gradients in the flame to be computed with sufficient accuracy. Introduction The burning intensity and the propagation of pre- mixed flames is often described in terms of a single quantity denoted as the flame speed. The premixed flame, a nonpassive front, has a finite velocity relative to the local flow field that is governed by the local balance of transport and reaction within the flame. In the generic problem of the planar unstrained flame, both diffusion and convection act to transport reactants from the unburned gas side to the reaction zone (i.e., the flow velocity in the reaction zone is directed from the unburned gas to the burned gas). The analysis of Libby and Williams [1] and the com- putations by Darabiha et al. [2] show that under strong strain rates, the so-called partial extinction re- gime, the mean flow tends to transport reactants away from the reaction zone. The transport of re- actants back to the flame is governed by diffusion that counters the adverse flow. The flame then, is, said to have a negative speed. The diffusion of re- actants is governed partly by the steepening of gra- dients of the thinned flame. The notion of a negative flame speed pertains to the propagation of the flame relative to the flow and not to the actual rates of fuel consumption or heat release. In the following discussion, the flame speed associated with propagation is denoted as a displace- ment speed. The burning in the partial extinction regime is also strongly reduced because of incom- plete combustion in the thin confined flame [1,2]. In the analyses and computations by Libby and Wil- liams [1] and Darabiha et al. [2], global one-step ir- reversible reaction mechanisms are used to model the chemistry. Detailed chemistry calculations have identified other mechanisms of extinction that per- tain primarily to the role of the hydrogen atom [3]. This extinction is observed to occur on the unburned side of the stagnation flow where the displacement speed is positive. Moreover, until extinction, the flame structure is not significantly affected by strain- ing [3,4]; the balance of reaction and diffusion re- mains essentially unchanged in the reaction zone be- fore extinction. Therefore, it is not clear whether conditions of negative burning may be achieved with steady straining and detailed chemistry for hydro- carbon mixtures. More importantly, other mecha- nisms for generating negative displacement speeds