Spectral formulation of turbulent flame speed with consideration of hydrodynamic instability

Effects of Darrieus-Landau (DL) instability on the structure and propagation of turbulent premixed flame fronts are considered. By first hypothesizing separation of time scales of instability and turbulence, we estimate whether the instability can develop in the presence of turbulence of given flow rms-velocity and integral length scale. As a result, we modify the standard turbulent premixed combustion regime diagram by introducing new boundaries, limiting the domain where the instability influences the global flame shape and speed. Based on this analysis, a "turbulence-induced DL cutoff" as a function of turbulence and instability parameters is introduced, which when combined with a turbulent flame speed without DL instability yields the turbulent flame speed accounting for the instability. The consumption turbulent flame speed for no DL instability is formulated from the spectral closure of the G equation, thus accounting for the scale-dependent "turbulent" nature of the problem. Finally, an analytical form of the turbulent flame speed is derived, which is found to agree well with the corresponding experimentally measured turbulent flame speed from literature over wide ranges of normalized turbulence intensities and length scales.