Turbulent Flame Motion in a Pancake Chamber via a Lagrangian, Two-Dimensional Vortex Dynamics Simulation

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Abstract
A flame ball growing into a turbulent mixture exhibits a speed which is proportional to its size- this effect is a consequence of the distorted flame surface and the resulting distributed volume expansion effect. A simple two-dimensional, zero-thickness flame model interacting with defined eddies illustrates how rapidly this flame distortion occurs after a spark ignition. The simulated two-dimensional flow configuration mimics a pancake engine chamber. The distorted flame exhibits exponential growth until about half of the mass is consumed, at this point the burnt gas appears to almost nil the chamber; a density ratio of four across the flame has been used- The next phase of flame motion occurs without further growth of flame surface as unburnt cusp features are consumed. In the final phase there is a rapid loss of flame surface: the flame consumes the many isolated pockets which are created by a distorted flame which has a distance from the wall comparable to the distortion amplitude. Now, however, the wall proximity greatly reduces the volume expansion effect upon flame motion, that is, the zero normal velocity condition at the wall counteracts the distributed volume expansion effect that dominated the freely propagating flame. Throughout the entire flame motion, the concept of a turbulent flame speed does not seem appropriate. The mass burning rate depends upon the flame burning velocity SL and the amount of flame area, and the area development depends upon the distributed volume expansion and its location with respect to the chamber walls. The turbulent generation of flame area is not a local property in this reacting flow.