a b s t r a c tDirect numerical simulations of premixed n-heptane/air flames at different Karlovitz numbers are performed using detailed chemistry. Differential diffusion effects are systematically isolated by performing simulations with both non-unity and unity Lewis numbers. Different unburnt temperatures and turbulence intensities are used and their effects on the flame structure and chemical source terms are investigated. As the unburnt gases are preheated, the viscosity ratio across the flame is reduced and the Karlovitz number at the reaction zone is increased. The increase in turbulence intensity suppresses differential diffusion effects on the flame structure (i.e. species dependence on temperature). However, differential diffusion effects on the chemical source terms are still noticeable even at the highest Karlovitz number simulated. Simulations with differential diffusion effects exhibit lower mean fuel consumption and heat release rates than their unity Lewis number counterparts. However, the difference is reduced as the reaction zone Karlovitz number is increased. Transition to distributed burning is characterized by a broadening of the reaction zone resulting from enhanced turbulent mixing. Local extinctions in the burning rate are observed only in non-unity Lewis number simulations and their probability decreases at high Karlovitz numbers. These results highlight the importance of using the reaction zone Karlovitz number to investigate the effect of turbulence on the chemical source terms and to compare flames at different unburnt temperatures.

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Results from a series of direct numerical simulations (DNS) of a high Karlovitz, slightly lean (φ = 0.9), n-C 7 H 16 /air premixed turbulent flame are presented. The flame is statistically flat and is subjected to an inflow of homogeneous isotropic turbulence. A 35-species and 217-reaction mechanism [Bisetti et al. Combust. Flame 159 (2012) 317-335] is used to represent the chemistry. Two simulations have been performed: one with unity Lewis number to asses the effects of turbulence on the flame structure in the absence of differential diffusion, and the other with non-unity Lewis numbers to analyze how turbulence affects differential diffusion. The Karlovitz numbers are 280 and 220 respectively. The first simulation reveals that the flame is strongly affected by turbulence as enhanced mixing largely thickens the preheat zone. However, the turbulent flame structure (i.e. the correlation between species and temperature) is similar to that of a one-dimensional flat flame, suggesting that turbulence has limited effet on the flame in temperature space, in the absence of differential diffusion. In the second simulation, the flame structure is affected by turbulence, as differential diffusion effects are weakened. It is suggested that this result is attributed to the fact that turbulence drives the effective species Lewis numbers towards unity through an increase in effective species and thermal diffusivities. Finally, the reaction zones of both the unity and the non-unity Lewis number turbulent flames remain thin, and are locally broken (only to some extent for the unity Lewis number flame, and more strongly for non-unity).

Please cite this article in press as: B. Savard et al., A computationally-efficient, semi-implicit, iterative method for the time-integration of reacting flows with stiff chemistry, J. Comput. Phys. (2015), http://dx. Abstract A semi-implicit preconditioned iterative method is proposed for the time-integration of the stiff chemistry in simulations of unsteady reacting flows, such as turbulent flames, using detailed chemical kinetic mechanisms. Emphasis is placed on the simultaneous treatment of convection, diffusion, and chemistry, without using operator splitting techniques. The preconditioner corresponds to an approximation of the diagonal of the chemical Jacobian. Upon convergence of the sub-iterations, the fully-implicit, second-order time-accurate, Crank-Nicolson formulation is recovered. Performance of the proposed method is tested theoretically and numerically on one-dimensional laminar and three-dimensional high Karlovitz turbulent premixed n-heptane/air flames. The species lifetimes contained in the diagonal preconditioner are found to capture all critical small chemical timescales, such that the largest stable time step size for the simulation of the turbulent flame with the proposed method is limited by the convective CFL, rather than chemistry. The theoretical and numerical stability limits are in good agreement and are independent of the number of sub-iterations. The results indicate that the overall procedure is second-order accurate in time, free of lagging errors, and the cost per iteration is similar to that of an explicit time integration. The theoretical analysis is extended to a wide range of flames (premixed and non-premixed), unburnt conditions, fuels, and chemical mechanisms. In all cases, the proposed method is found (theoretically) to be stable and to provide good convergence rate for the sub-iterations up to a time step size larger than 1 μs. This makes the proposed method ideal for the simulation of turbulent flames.

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Supplemental material for B. Savard and G. Blanquart, Effects of dissipation rate and diffusion rate of the progress variable on local fuel burning rate in premixed turbulent flames

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