Xue, Q., Battistoni, M., Som, S., Quan, S. et al., "Eulerian CFD Modeling of Coupled Nozzle Flow and Spray with Validation Against X-Ray Radiography Data," SAE Int. J. Engines 7(2):1061-1072, 2014, doi:10.4271/2014-01-1425.
This paper implements a coupled approach to integrate the internal nozzle flow and the ensuing fuel spray using a Volume-of-Fluid (VOF) method in the CONVERGE CFD software. A VOF method was used to model the internal nozzle two-phase flow with a cavitation description closed by the homogeneous relaxation model of Bilicki and Kestin . An Eulerian single velocity field approach by Vallet et al.  was implemented for near-nozzle spray modeling. This Eulerian approach considers the liquid and gas phases as a complex mixture with a highly variable density to describe near nozzle dense sprays. The mean density is obtained from the Favreaveraged liquid mass fraction. The liquid mass fraction is transported with a model for the turbulent liquid diffusion flux into the gas. Simulations were performed in three dimensions and the data for validation were obtained from the x-ray radiography measurements Kastengren et al.  at Argonne National Laboratory for a diesel fuel surrogate n-dodecane. The quantitative and time-resolved data consisting of fuel mass distribution and spray velocity in the near nozzle dense spray region are used to validate the coupled Eulerian approach. A standard k-ε Reynolds Averaged Navier Stokes based turbulence models is implemented in this study and the influence of model constants are evaluated. The effect of grid size is also evaluated by comparing the fuel distribution against experimental data. Finally, the fuel distribution predicted by the coupled Eulerian approach is compared against classical Lagrangian spray model results. The coupled Eulerian approach provides a unique way of coupling the nozzle flow and sprays so that the effects of in-nozzle flow can be directly realized on the fuel spray.