Modeling of Pressure and Non-Stationary Effects in Spark Ignition Engine Combustion: A Comparison of Different Approaches

Published experimental data obtained in well-defined simple cases are discussed in order to qualitatively test various models of premixed turbulent combustion, utilized in multi-dimensional numerical simulations of SI engines. An analysis of such data indicates that there exist several unresolved issues important for flame propagation in SI engines. Two of them, pressure dependence of turbulent flame speed S_t and turbulent flame development, are discussed in the paper.

First, existing experimental data indicate an increase in S_t by pressure despite the marked decrease in the laminar burning velocity S_L by P. Although this well established trend appears to be of substantial importance for SI engine applications, many combustion models utilize S_L as the sole mixture characteristic and, hence, predict similar dependencies both of S_t and of S_L on P, contrary to the aforementioned experimental results. The ability of various models to correctly predict the effects of pressure on turbulent combustion is assessed by qualitatively comparing analytical expressions for fully developed, 1D, planar flame speed, resulting from the models, with the available experimental data. The following approaches (1) Flame Speed Closure model [4, 5 and 6], (2) CFM2 [12], (3) the thickened flamelet model by Peters [9], (4) the pair-exchange model by Kerstein [59], and, maybe, fractal model by Zhao et al. [18], are shown to be the most promising.

Second, experimental data indicate the non-stationary nature of turbulent flames: in most laboratory and industrial burners and in SI engines, in particular, both S_t and mean flame brush thickness δ_t develop with time after ignition. By analyzing experimental data, phenomenological approximations of S_t(t) and δ_t(t) are singled out and a self-similar regime of turbulent flame propagation is emphasized. The ability of various models to describe this regime and, in particular, to yield the qualitatively different time-dependencies of S_t(t) and of δ_t(t), indicated by experimental data, is assessed both analytically and numerically. The results show that the emphasized difference is a challenge for many current combustion models but the Flame Speed Closure model is well tailored to simulate it and other emphasized trends of turbulent flame development.