Stretch effects on the burning velocity of turbulent premixed hydrogen/air flames

Unsteady stretch effects on the laminar burning velocity of unsteady premixed hydrogen/air flames are studied using two-dimensional direct numerical simulation (DNS) with detailed chemical kinetics and transport. Preferential diffusion-unsteady stretch interactions are studied by varying the fuel mass equivalence ratio from fuel-lean to fuel-rich conditions. The correlation of the burning velocity with strain, curvature, and stretch is determined along with other flame propagation statistics. Different definitions of the burning velocity are compared. It is found that definitions based on heat release and fuel consumption lead to different correlations of burning velocity with curvature for some fuel-lean conditions. For fuellean and fuel-rich conditions corresponding to unstable and stable mixtures, classical diffusive-thermal effects are recovered in correlations of burning velocity with strain and curvature. It is also observed that the theory for flame propagation in the limit of weak stretch is more widely applicable to turbulent stretch conditions. As such, the strain contribution to the Markstein number is computed from the DNS data and compared against experimental and numerical counterflow data. Good agreement between all three approaches is found in terms of the crossover value of the equivalence ratio from negative to positive Markstein numbers and for fuel-lean stoichiometries. It is found from DNS that strong stretch-preferential diffusion interactions exist in the turbulent flame, with computed Markstein numbers varying between - 5.34 and 2.85 and area-weighted mean burning velocities as high as 2.43 times the laminar velocity. It is further observed that over a wide range of mixture stoichiometries, as the ratio of the characteristic turbulence to flame transit time decreases, the flame response to stretch is attenuated, resulting in a marked decrease in Markstein number. This is consistent with linear theory and recent unsteady counterflow computations.