Implementation of EOQ and Lambert W function in 1-D engine simulation model for optimizing fuel injection in GDI engine

The aim of this study was to implement Economic Order Quantity method (EOQ) together with the Lambert W function in a 1-D engine simulation model in order to develop a fuel control strategy for a Gasoline direct injection (GDI) engine. Previous work of the co-author demonstrated the possibility of optimizing fuel injection quantity in GDI engine using the EOQ that is commonly used in supply chain of perishable products. This work extends the previous work and implements it in a 1-D, crank angle resolved, engine simulation model for the application of model based calibration process. The present work uses a validated engine simulation model, which is based on predictive combustion modelling approach, and couples the 1-D engine simulation model with SIMULINK to add the evaporation, wall- wetting and heat transfer models. It employs FORTRAN subroutines to modify the internal code of the 1-D simulation software in order to add crank angle resolved evaporation model. Finally, EOQ with Lambert W function was added to the model using MATLAB with special attention to the decimal control for the solution. This study demonstrated that EOQ and Lambert W functions together are a suitable method to develop fuel control strategy for a model based calibration procedure when implemented in crank angle resolved 1-D simulation model.