The initial size and growth of the plasma and flame kernel just after spark discharge in S.I. engines determines if the flame becomes self-sustainable or extinguishes. On the other hand the development of the kernel during the initial phases has non-negligible influences on the further combustion. For example cyclic variations often find their origin in the beginning of combustion and determine the working limits of the engine and the driving behavior of the vehicle. These factors demonstrate the crucial importance of the knowledge of the initial growth of the plasma and flame kernel in S.I. engines.

A complete model is developed for the growth of the initial plasma and flame kernel in S.I. engines, which takes into account the fundamental properties of the ignition system (electrical energy and power, geometry of the spark plug, heat losses to the electrodes and the cylinder wall), the combustible mixture (pressure, temperature, equivalence ratio, fraction of residual gasses, kind of fuel) and the flow (average flow velocity, turbulence intensity, stretch, characteristic time and length scales).

The proposed model distinguishes three phases: the prebreakdown, the plasma and the initial combustion phase. The model of the first two phases is proposed in a previous article of the same authors (Willems and Sierens, 1999), the latter is exposed in this article. A thermodynamic model based on flamelet models and which takes stretch into account, is used to describe the initial combustion phase. The difference between heat losses to the electrodes and the cylinder wall is considered. The burning velocity varies from the order of the laminar velocity to the fully developed burning velocity. The evolution is determined as well by the life time as by the size of the kernel. The stretch (caused by turbulence and by the growth of the kernel), the non-adiabatic character of the flame and instabilities have influence on the laminar burning velocity.

Validation of this model is done using measurements of the expansion in a propane-air mixture executed by Pischinger at M.I.T. The correspondence seems to be very well.

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