Correlation of flame speed with stretch in turbulent premixed methane/air flames

Direct numerical simulations of two-dimensional unsteady premixed methane/air flames are performed to determine the correlation of flame-speed with stretch over a wide range of curvatures and strain rates generated by intense two-dimensional turbulence. Lean and stoichiometric premixtures are considered with a detailed C₁-mechanism for methane oxidation. The computed correlation shows the existence of two distinct stable branches. It further shows that exceedingly large negative values of stretch can be obtained solely through curvature effects, which give rise to an overall nonlinear correlation of the flame speed with stretch. Over a narrower stretch range, -1 ≤ Ka ≤ 1, which includes 90% of the sample, the correlation is approximately linear, and, hence, the asymptotic theory for stretch is practically applicable. Overall, one-third of the sample has negative stretch. In this linear range, the Markstein number associated with the positive branch is determined for different initial turbulence intensities. For high turbulence intensity, the large eddy turnover time becomes shorter than a flame time, and the flame propagation becomes less responsive to unsteady straining. Reductions in strain Markstein numbers by as much as 37% from comparable steady counterflow computations are reported. In addition to the conventional positive branch, a negative-branch is identified. This negative branch occurs when a flame cusp, with a center of curvature in the burnt gases is subjected to intense compressive strain, resulting in a negative displacement speed. Negative flame speeds are also encountered for extensive tangential strain rates exceeding a Karlovitz number of unity, a value consistent with steady counterflow computations. In both situations, consistent with earlier findings, the source of the reduction in flame speed is attributed to an imbalance between diffusion and reaction.