Spray modeling techniques have evolved from the classic DDM (Discrete Drops Method) approach, where the continuous liquid jet is discretized into “drops” or “parcels” till advanced spray models often based on Eulerian approaches. The former technique, although computationally efficient, is essentially inadequate in highly dense jets, as in the near nozzle region of compression ignition engines, while the latter could lead to extreme levels of computational effort when resolved interface capturing methods, such as VoF (Volume of Fluids) and LS (Level-Set) types, are used. However, in a typical engineering calculation, the mesh resolution is considerably coarser than in these high fidelity computations. If one presumes that these interfacial details are far smaller than the mesh size, smoothing features over at least one cell ultimately results in a diffuse-interface treatment in a Eulerian framework. Therefore, it is explained that currently the greatest interest is focused on the development of diffuse interface computational models which use a variable called surface density of the interface (Σ), solved using an averaged or filtered transport equation, to model the atomization process. However, in this type of approach a single-fluid formulation is used solving a single momentum equation but neglecting some features of the relative velocity between the liquid and the gas phases. This practice is not an issue for diesel sprays under nominal operating conditions of current engines, i.e., under high injection pressure and chamber density. Nevertheless, in certain combustion strategies, due to lower ambient densities (highly premixed combustion) or the usage of substitute fuels, the slip between phases becomes more important and must be fully considered. In this work, we propose a new developed Σ-Y Spray Atomization Model that accounts for diffusion due to Drift-Flux velocities, providing a predictive behavior under all engine conditions. In addition, the proposed formulation creates a mechanism by which the interfacial dynamics can impact the transport of the liquid mass fraction, therefore, making the interfacial density an active scalar, fully coupled with the rest of the flow, overcoming the limitations of previous formulations.
