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IntroductionIn the flamelet approach of turbulent premixed combustion, the flames are modeled as a wrinkled surface whose propagation speed, termed the "displacement speed," is prescribed in terms of the local flow field and flame geometry [l]. Theoretical studies [2] suggest a linear relation between the flame speed and stretch for small values of stretch, where 5' : is the laminar flame speed, l i a = m 5~/ S i is the nondimensional stretch or the Karlovitz number, and M a = L/SF is the Markstein number. The nominal flame thickness, S F , is determined as the ratio of the mass diffusivity of the unburnt mixture to the laminar flame speed. Thus, the turbulent flame model relies on an accurate estimate of the Markstein number in specific flame configurations. Experimental measurement of flame speed and stretch in turbulent flames, however, is extremely difficult. As a result, measurement of flame speeds under strained flow fields has been made in simpler geometries [3,4], in which the effect of flame curvature is often omitted.In this study we present results of direct numerical simulations of unsteady turbulent flames with detaiIed methane/air chemistry, thereby providing an alternative method of obtaining flame structure and propagation statistics. The objective is t o determine the correlation between the displacement speed and stretch over a broad range of Karlovitz numbers. The observed response of the displacement speed is then interpreted in terms of local tangential strain rate and curvature effects. Numerical MethodThe numerical scheme is based on the solution of the Navier-Stokes, species and energy equations for a compressible gas mixture with temperature dependent properties. The explicit finite difference algorithm uses a fourth-order low storage Runge-Kutta scheme for time advancement and an eighth-order explicit spatial differencing scheme [5]. The chemical mechanism is based on a detailed C1 mechanism by Warnatz [6] with 17 species and 68 reversible reactions. The species mass diffusion is determined by prescribing the Lewis numbers of each species [7]. The molecular viscosity of the mixture is temperature dependent, while the thermodynamic properties (enthalpy, specific heat) are temperature and composition dependent. The Prandtl number is taken to be 0.708.The computations are initialized with a one-dimensional steady laminar flame profile. A fuel-lean mixture (equivalence ratio of 0.7) of methane/air is preheated to 800 K in the reactant freestream. The profiles are obtained from a one-dimensional steady code PREMIX [SI, and the solntion is allowed to adjust t o the simplified transport in a one-dimensional DNS.The turbulence is prescribed by an initial two-dimensional turbulent kinetic energy spectrum function [9] which is superimposed on the laminar flame. The ratio of the turbulence intensity, u', to S i is taken to be 10, and the ratio of the integral eddy scale, L11, to SF is 2.77. The turbulence Reynolds number based LI1 and the unburned gas properties at 800 K is 181. The computationa...

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