On the use of thermodynamic modeling for predicting cycle-to-cycle variations in a SI engine under lean conditions

We propose a procedure by which a two-zone thermodynamic model combined with a flame propagation sub-model can used for predicting the cycle-to-cycle variations of combustion in a spark ignition (SI) engine operating at very lean and high exhaust gas residual conditions. Under such conditions, the variations have been shown to consist of both deterministic and stochastic components. The deterministic component is inherent to the non-linear nature of the combustion efficiency variation with equivalence ratio (or dilution level) while the stochastic component results primarily from noise associated with the parameters (that are inevitable in a mechanical system) that affect combustion. Since the overall dynamics of the instabilities are driven by the low order deterministic component, if a model can be made to capture this component, the stochastic component is easily modeled by adding noise to the parameters. A method for extracting the deterministic component from experimental pressure data was proposed in a series of past publications [10, 13, 14, 12, 15]. In this paper, we attempt to use this deterministic component to modify the flame speed correlations correlations used in two-zone thermodynamic models. The procedure involves adjustment of parameters in the flame propagation sub-model model proposed by Blizard and Keck [23]. The values of parameters resulting from this procedure indicate the following possibilies when the inlet equivalence ratio is at or below 0.73 and in the presence of moderate residual levels. The combustion transitions from flamelet mode to distrubuted mode. As the equivalence ratio is lowered gradually, the combined effect of flame stretch and heat losses to walls/electrodes can lower the flame propagation speed significantly and even cause misfires before the lean flammability limit is reached. The effect of dilution also seems much more significant at such conditions than at near-stoichiometric conditions.