A Dynamical Instability of Spark-Ignited Engines

A simple model for spark-ignited engines is proposed in which the residual exhaust gases of a combustion event affect ignition of the subsequent charge. The model is an example of a one-dimensional, discrete, nonlinear mapping of an interval. Laminar flame correlations incorporated within models for ignition exhibit Arrhenius kinetics. Small variations of the ignition time with respect to the expansion cycle alter the work produced by each cycle, thereby altering the exhaust-gas temperature. It is shown that the mixing of hot residual gases with a fresh charge is a sufficient mechanism to produce an instability of the ignition process, resulting in oscillatory behavior. When this instability is compounded with the effects of mixture turbulence, one obtains a novel picture of the well-known phenomenon of ``cyclic dispersion'' exhibited by such engines.