Turbulent liquid gas flows remain an active field of research in fluid mechanics despite several decades of research and numerous applications. In particular numerical simulation is very attractive to explore such flows. Indeed, experiment can be very difficult, very often high velocity of the liquid may damage any physical probe, optical diagnostics suffer from the diffraction of the light at the liquid-gas interface. However, new diagnostic techniques such X-ray measurement (in particular at Argonne) has emerged to provide new insight in such flows. From the numerical point of view, two limit cases are addressed. In the first case, wrinkles of the interface can be resolved directly because of relatively large time scale and length scale compare to available mesh resolution. In this case interface capturing method (ICM) have reached a high degree of precision in particular during the last decade using for instance VOF, Level Set, Ghost Fluids method on parallel computer. In the other limit, one of the phases is very simplified to be represented as a set of discrete particles (DPMethod) with appropriate simplified behavior laws.

In this presentation the case of atomization is considered. ICM can be used initially to determine first instabilities of the cylindrical liquid jet. Eventually, a spray is formed that can be described with DPM. However, the process of atomization is exactly the description of the destabilization of the jet that occurs continuously from ICM to DPM approaches. A large consensus have emerged to conclude that due to the large range of scales implied in this process, it is unaffordable to use ICM all the way from the initial liquid jet to the final droplet. To keep a continuous numerical approach it is necessary to deal with poorly resolved interface that cannot be described with ICM but with a very complex surface geometry to apply DPM. The pioneering work of Vallet and Borghi (Vallet and Borghi 1999; Vallet, Burluka et al. 2001) draws the bases of an appropriate model base on surface density equation, the so-called ELSA model. This presentation will present some works on this approach and some achievements that shows the possibility to use the ELSA model as a bridge between ICM and DPM to describe turbulent liquid-gas flow for any regime from the dense to dilute regime.
Vallet, A. and R. Borghi. "Modélisation Eulerienne de L’atomisation d’un Jet Liquide." C. R. Acad. Sci., Paris, Sér. II b 327: 1015–1020, 1999.
Vallet, A., A. A. Burluka and R. Borghi. "Development of a Eulerian model for the "Atomization" of a liquid jet." Atomization and Sprays 11(6): 619-642, 2001.