Numerical study of turbulent flame velocity

A premixed flame propagating through a combination of vortices in a tube/channel is studied using direct numerical simulations of the complete set of combustion equations including thermal conduction, diffusion, viscosity, and chemical kinetics. Two cases are considered, a single-mode vortex array and a multimode combination of vortices obeying the Kolmogorov spectrum. It is shown that the velocity of flame propagation depends strongly on the vortex intensity and size. The dependence on the vortex intensity is almost linear in agreement with the general belief. The dependence on the vortex size may be imitated by a power law ∝D2/3∝D2/3. This result is different from theoretical predictions, which creates a challenge for the theory. In the case of the Kolmogorov spectrum of vortices, the velocity of flame propagation is noticeably smaller than for a single-mode vortex array. The flame velocity depends weakly on the thermal expansion of burning matter within the domain of realistically large expansion factors. Comparison to the experimental data indicates that small-scale turbulence is not the only effect that influences the flame velocity in the experimental flows. Large-scale processes, such as the Darrieus–Landau instability and flame–wall interaction, contribute considerably to the velocity of flame propagation. Still, on small scales, the Darrieus–Landau instability becomes important only for a sufficiently low vortex intensity.