This work presents an implementation and evaluation of the Σ-Y atomization model for Diesel spray CFD simulations. The Σ-Y model is based on an Eulerian representation of the spray atomization and dispersion by means of a single-fluid variable density turbulent flow within a RANS framework. The locally homogeneous flow approach has been applied in order to develop a spray vaporization model based on state relationships. A finite-volume solver for model equations has been created using theOpenFOAM CFD open-source C++ library. Model predictions have been compared to experimental data from free Diesel sprays under nonvaporizing and vaporizing conditions. High-speed imaging, PDPA, and Rayleigh-scattering measurements have been used in order to assess the CFD model. Accurate predictions of liquid and vapor spray penetration, as well as axial velocity and mixture fraction profiles, can be simultaneously achieved for a wide range of injection pressure and ambient conditions, despite only having qualitatively correct predictions of droplet size. The success of these predictions supports the mixing-limited vaporization hypothesis. Model accuracy is better for high ambient density and injection pressure conditions. It is proposed that under low ambient density and injection pressure conditions, interfacial dynamics become more important and the single velocity field assumption is less appropriate.

A computational study was performed to investigate the influence of transient needle motion on gasoline direct injection (GDI) internal nozzle flow and near-field sprays. Simulations were conducted with a compressible Eulerian flow solver modeling liquid, vapor, and non-condensable gas phases with a diffuse interface. Variable rate generation and condensation of fuel vapor were captured using the homogeneous relaxation model (HRM). The non-flashing (spray G) and flashing (spray G2) conditions specified by the Engine Combustion Network were modeled using the nominal spray G nozzle geometry. Transient needle lift and wobble were based upon ensemble averaged X-ray imaging preformed at Argonne National Lab. The minimum needle lift simulated was 5 µm and dynamic mesh motion was achieved with Laplacian smoothing. The results were qualitatively validated against experimental imaging and the experimental rate of injection profile was captured accurately using pressure boundary conditions and needle motion to actuate the injection. Low needle lift is shown to result in vapor generation near the injector seat. Finally, the internal injector flow is shown to be highly complex, containing many transient and interacting vortices which result in perturbations in the spray angle and fluctuations in the mass flux. This complex internal flow also results in intermittent string flash-boiling when a strong vortex is injected and the resulting swirling spray contains a thermal * Corresponding author

This work evaluates the performance of the Σ-Y Eulerian atomization model at reproducing the internal structure of a diesel spray in the nearfield. In the study, three different computational domains have been used in order to perform 3D and 2D coupled simulations, where the internal nozzle flow and external spray are modeled in one continuous domain, and 2D decoupled simulations, where only the external spray is modeled. While the 3D simulation did the best job of capturing the dense zone of the spray, the 2D simulations also performed well, with the coupled 2D simulation slightly outperforming the decoupled simulation. The similarity in results between the coupled and the decoupled simulation show that internal and external flow calculations can be performed independently. In addition, the use of spatially averaged nozzle outlet conditions, in the case of an axisymmetric (single-hole) convergent nozzle, leads to a slightly worse near-field spray predictions but to an accurate far-field ones. Finally, a novel constraint on turbulent driven mixing multiphase flows is introduced which prevents the slip velocity from exceeding the magnitude of the turbulent fluctuations through a realizable Schmidt number. This constraint increased model stability, allowing for a 4x increase in Courant number.

Despite great practical interest in how sprays emanate from fuel injectors, the near-nozzle region has remained a challenge for spray modelers. Recently, Eulerian models have shown promise in capturing the fast gas-liquid interactions in the near field. However, with the inclusion of compressibility, it can be difficult to maintain consistency between the hydrodynamic and thermodynamic variables. In order to resolve numerical inconsistencies that occur in segregated solutions of Eulerian spray model equations as well as to provide good scalability and stability, a new construction of a Σ-Y model is introduced. This construction is built around an IMEX-RK3 algorithm which offers accuracy and efficiency. The new algorithm is compared to an existing implementation for speed and is validated against experimental measurements of spray evolution in order to test the accuracy. The predictions of the new construction are slightly more accurate and, when tested on 256 processors, are 34 times faster.

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