A Numerical Study Promoting Algebraic Models for the Lewis Number Effect in Atmospheric Turbulent Premixed Bunsen Flames

This numerical investigation carried out on turbulent lean premixed flames accounts for two algebraic – the Lindstedt–Vaos (LV) and the classic Bray–Moss–Libby (BML) – reaction rate models. Computed data from these two models is compared with the experimental data of Kobayashi et al. on 40 different methane, ethylene and propane Bunsen flames at 1 bar, where the mean flame cone angle is used for comparison. Both models gave reasonable qualitative trend for the whole set of data, in overall. In order to characterize quantitatively, firstly, corrections are made by tuning the model parameters fitting to the experimental methane–air (of Le = 1.0) flame data. In case of the LV model, results obtained by adjusting the pre-constant, i.e., reaction rate parameter, C_R, from its original value 2.6 to 4.0, has proven to be in good agreement with the experiments. Similarly, for the BML model, with the tuning of the exponent n, in the wrinkling length scale, L_y = C_l⋅ l_x(s_L/u′)ⁿ from value unity to 1.2, the outcome is in accordance with the measured data. The deviation between the measured and calculated data sharply rises from methane to propane, i.e., with increasing Lewis number. It is deduced from the trends that the effect of Lewis number (for ethylene–air mixtures of Le = 1.2 and propane–air mixtures of Le = 1.62) is missing in both the models. The Lewis number of the fuel–air mixture is related to the laminar flame instabilities. Second, in order to quantify for its influence, the Lewis number effect is induced into both the models. It is found that by setting global reaction rate inversely proportional to the Lewis number in both the cases leads to a much better numerical prediction to this set of experimental flame data. Thus, by imparting an important phenomenon (the Lewis number effect) into the reaction rates, the generality of the two models is enhanced. However, functionality of the two models differs in predicting flame brush thickness, giving scope for further analysis.