Self-similar propagation and turbulent burning velocity of CH₄/H₂/air expanding flames: Effect of Lewis number

In this study we clarify the role of differential diffusion characterized by effective Lewis number, Le_eff, on the self-similar accelerative propagation and the associated turbulent burning velocity of turbulent expanding flames. The turbulent flame trajectories of the CH₄/H₂/air mixtures were measured using a newly developed large-scale, fan-stirred turbulent combustion chamber generating near-isotropic turbulence. It is found that the normalized turbulent propagation speed scales as the turbulent flame Reynolds number, Re_T,f=(u_rms/S_L)(〈r〉/l_f), roughly to the one-half power for the stoichiometric CH₄/H₂ = 80/20 flames with unity Le_eff (=1), where the average flame radius, 〈r〉, is the length scale and the thermal diffusivity, α=S_Ll_f, is the transport property, S_L and l_f are the laminar burning velocity and flame thickness, and u_rms is the root-mean-square (rms) turbulent fluctuation velocity. The propagation of the fuel lean CH₄/H₂ = 20/80 flames with sub-unity Le_eff (<1) is still self-similar, however, the normalized turbulent propagation speed is much higher and the power exponent is greater than 1/2 even though these two flames have almost the same laminar burning velocity, flame thickness with S_L, l_f and experience the similar turbulence perturbations. The stronger self-similar propagation of the Le_eff < 1 flames is the consequences of the couple effects of the differential diffusion and the flame stretch on the local wrinkled flamelets within the turbulent flame brush. Based on the present experimental data, a modified possible general correlation for turbulent burning velocity is obtained in terms of the Le_eff and Re_T,f with differential diffusion consideration. This correlation is able to predict not only the present experimental data but also the previous turbulent burning velocities measured using both turbulent Bunsen flames and expanding flames at high pressures.