A systematic approach to calibrate spray and break-up models for the simulation of high-pressure fuel injections

Abstract

A novel calibration methodology is presented to accurately predict the fundamental characteristics of high-pressure fuel sprays for Gasoline Direct Injection (GDI) applications. The model was developed within the Siemens Simcenter STAR-CD 3D CFD software environment and used the Lagrangian–Eulerian solution scheme. The simulations were carried out based on a quiescent, constant volume, computational vessel to reproduce the real spray testing environment. A combination of statistic and optimisation methods was used for spray model selection and calibration and the process was supported by a wide range of experimental data. A comparative study was conducted between the two most commonly used models for fuel atomisation: Kelvin–Helmholtz/Rayleigh–Taylor (KH–RT) and Reitz–Diwakar (RD) break-up models. The Rosin–Rammler (RR) mono-modal droplet size distribution was tuned to assign initial spray characteristics at the critical nozzle exit location. A half factorial design was used to reveal how the various model calibration factors influence the spray properties, leading to the selection of the dominant ones. Numerical simulations of the injection process were carried out based on space-filling Design of Experiment (DoE) schedules, which used the dominant factors as input variables. Statistical regression and nested optimisation procedures were then applied to define the optimal levels of the model calibration factors. The method aims to give an alternative to the widely used trial-and-error approach and unveils the correlation between calibration factors and spray characteristics. The results show the importance of the initial droplet size distribution and secondary break-up coefficients to accurately calibrate the entire spray process. RD outperformed KH–RT in terms of prediction when comparing numerical spray tip penetration and droplet size characteristics to the experimental counterparts. The calibrated spray model was able to correctly predict the spray properties over a wide range of injection pressure. The work presented in this paper is part of the APC6 DYNAMO project led by Ford Motor Company.