In modern turbocharged direct-injection, spark-ignition engines, proper calibration of the engine control unit is essential to handle the increasing variability of actuators. The physically based simulation of engine processes such as mixture homogenization enables a model-based calibration of the engine control unit to identify an ideal set of actuator settings, for example, for efficient combustion with reduced exhaust emissions. In this work, a zero-dimensional phenomenological model for direct-injection, spark-ignition engines is presented that allows the equivalence ratio distribution function in the combustion chamber to be calculated and its development is tracked over time. The model considers the engine geometry, mixing time, charge motion and spray–charge interaction. Accompanying three-dimensional computational fluid dynamics, simulations are performed to obtain information on homogeneity at different operating conditions and to calibrate the model. The calibrated model matches the three-dimensional computational fluid dynamics reference both for the temporal homogeneity development and for the equivalence ratio distribution at the ignition time, respectively. When the model is validated outside the calibrated operating conditions, this shows satisfying results in terms of mixture homogeneity at the time of ignition. Additionally, only a slight modification of the calibration is shown to be required when transferring the model to a comparable engine. While the model is primarily aimed at target applications such as a direct-injection, spark-ignition soot emission model, its application to other issues, such as gaseous exhaust emissions, engine knock or cyclic fluctuations, is conceivable due to its general structure. The fast calculation enables mixture inhomogeneities to be estimated during driving cycle simulations.
