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A phenomenological zero-dimensional spray penetration model was developed for diesel-type conditions for a constant volume chamber. The spray was modeled as a protruding cone which is well-mixed at its tip after passing through initial primary and secondary breakup zones. The resulting cone model is strictly dependent on injection parameters; density ratio, injection and chamber pressure, nozzle characteristics, and cone angle. The proposed model was compared with data from three different sources and performed well in most cases except for low density environments.

The methodology for predicting the transient mixing rate is presented for a direct injection, quiescent chamber diesel. The mixing process is modeled as a zero-dimensional, large-scale phenomena which accounts for injection rate, cylinder geometry, and engine operating condition. As a demonstration, two different injection schemes were investigated for engine speeds of 1600, 2100, and 2600 rpm. In the first case, the air-fuel ratio was fixed while the injection rate was allowed to vary, but for the second case, the injection duration was fixed and the air-fuel ratio was allowed to vary. For the former case, the resulting mixing rate was also compared with the experimentally determined fuel burning rate. These two quantities appeared to be correlated in some manner for the various engine speeds under investigation.