A Quasi-Dimensional Fuel Distribution Model for a Radially Stratified Engine

Several combustion strategies leverage radial fuel stratification to adapt cylinder composition between the center of the chamber and the outer regions independently. Spark-assisted compression ignition (SACI) relies on careful tuning of this radial stratification to maximize the combined performance of flame propagation and auto-ignition. Established techniques for determining in-cylinder fuel stratification are computationally intensive, limiting their feasibility for control strategy development and real-time control. A fast running model for radial fuel stratification is developed for control-oriented objectives. The model consists of three submodels: spray penetration, fuel distribution along the spray axis, and postinjection mixing. The spray penetration model is adapted from fuel spray models presented in the literature. The fuel distribution and mixing submodels are validated against injection spray results from an large eddy simulation (LES) three-dimensional (3D) computational fluid dynamics (CFD) reference model for three test points as a function of crank angle. The quasi-dimensional model matches the CFD results with a root-mean-square error (RMSE) for equivalence ratio of 0.08–0.11. This is a 50% reduction from the 0.16–0.20 RMSE for a model that assumes a uniform fuel distribution immediately after injection. The computation time is 230 ms on an Intel (Santa Clara, CA) Xeon E5-1620 v3 to solve each case without optimizing the code for execution speed.