Abstract
•A coupled Σ-Y Eulerian model is formulated based on the drift velocity.•The present formulation makes the interfacial density Σ an active scalar.•The interfacial density can now impact the liquid transport, overcoming limitations of previous formulations.•A noticeable improvement on spray tip penetration and liquid length predictions is shown.•The new coupled Σ-Y model specifically improves cases with large liquid-to-gas density difference.
Modeling of spray in a dense near-nozzle region remains a great challenge, because of the large scale separation between the small features of the interface and the overall jet. Diffuse-interface treatment in a single-fluid Eulerian framework, in which the interfacial surface area density (Σ) is used to describe the atomization process, has attracted interest for its potential in providing a manageable and still accurate model. In this work, we propose a new formulation of the Σ-Y spray atomization model that accounts for liquid diffusion due to drift-flux velocities, correctly predicting the behavior under all relevant engine conditions. Additionally, the present formulation allows the interfacial dynamics to impact the transport of the liquid mass fraction, thus making the interfacial density an active scalar fully coupled with the rest of the flow, overcoming limitations of previous formulations. The new model is implemented in the OpenFOAM framework and validated against experimental measurements under non-vaporizing and vaporizing environments, and at reacting conditions.