Phenomenological models for prediction of spray penetration and mixture properties for different injection profiles

•Phenomenological model for prediction of spray penetration.•Model capable of predicting multiple pulse and ramped up ROI profiles.•Transient calculation of spray velocity profile for various ROI.•Transient prediction of mean equivalence ratio for various ROI.

Accurate and quick prediction of spray characteristics such as penetration length, mean axial velocity profile and equivalence ratio distribution inside combustion chamber are important for the understanding and control of air–fuel mixing process in a compression ignition (CI) engine. In this study phenomenological model has been developed for prediction of spray penetration, air–fuel ratio and spatial distribution of velocity profile in terms of available analytical solution for steady sate, constant velocity sprays with variable radial profile for a characteristics injection velocity. Phenomenological model is able to accurately predict the transient spray tip penetration for single pulse, multiple pulse and linearly ramped up fuel injection profiles. Predicted values of mean axial spray velocity profile and mean axial equivalence ratio distribution by this model were following the trends of reference numerical model for various rate of injection (ROI) profiles.