Ates, M., Matthews, R., and Hall, M., "A Full-Cycle Multi-Zone Quasi-Dimensional Direct Injection Diesel Engine Model Based on a Conceptual Model Developed from Imaging Experiments," SAE Technical Paper 2017-01-0537, 2017, doi:10.4271/2017-01-0537.
A quasi-dimensional model for a direct injection diesel engine was developed based on experiments at Sandia National Laboratory. The Sandia researchers obtained images describing diesel spray evolution, spray mixing, premixed combustion, mixing controlled combustion, soot formation, and NOx formation. Dec  combined all of the available images to develop a conceptual diesel combustion model to describe diesel combustion from the start of injection up to the quasi-steady form of the jet. The end of injection behavior was left undescribed in this conceptual model because no clear image was available due to the chaotic behavior of diesel combustion. A conceptual end-of-injection diesel combustion behavior model was developed to capture diesel combustion throughout its life span. The compression, expansion, and gas exchange stages are modeled via zero-dimensional single zone calculations. The spray and combustion events were modeled with up to six separate zones, representing different phenomenological sequences in the conceptual model of Dec . The spray model was based upon correlations developed by Naber and Siebers  and Siebers . A full cycle simulation was used to capture the initial conditions of the closed portion of the cycle and predict the brake specific fuel consumption accurately . The model was calibrated with cylinder pressure data obtained from Southwest Research Institute for a 6 cylinder, 15 liter heavy-duty engine.