Large eddy simulation of liquid jet atomization

International audienceIn the past decade, numerical methods for two-phase flows, which are now capable of fully describing both phases and the interface, have progressed to a state of maturity. At present, direct numerical simulations (DNS) are possible even for complex configurations such as atomization processes. However, the numerical resources necessary to completely compute the atomization up to the formation of the final spray are still out of reach. Therefore, the LES approach is very appealing for two-phase flows. Depending on the assumption concerning the relative size of the LES filter compared to the characteristic scale of interface wrinkles, two classes of LES methods have emerged: the first class of LES method is required close to the injector while the second class is needed far from the injector when the spray is formed. The present work describes a modeling proposal that solves this problem by focusing on the transition between these two classes of method for LES of two phase flows. A postulated transport equation of the surface density is used to describe the subgrid spray formation ranging from interface wrinkling, ligaments, and sheets up to the droplets. Issued from RANS formalisms, this transport equation extends the usual spherical geometry given to the liquid structures that compose the subgrid spray. This equation contains several source terms that act on the creation and destruction of the liquid/gas interface. Considering that major breakup processes are due to turbulence in the field near the injector, an appropriate source term is proposed. This source term, also derived from RANS models, introduces a local critical value of surface density related to a critical Weber number that provides information concerning the local equilibrium between turbulent kinetic energy and surface energy. Concerning the velocity field, a standard Smagorinsky approach is considered. The initial results, obtained through the simulation of the atomization of a liquid jet, confirm that the subgrid term of the liquid volume fraction transport equation determines the transition between the resolved interface and the subgrid spray. A LES model for continuous two-phase flows, termed CLES in this paper, is proposed. The CLES model allows for a better description of the liquid dispersion within the calculation domain from both qualitative and quantitative points of view when compared with the usual LES formalism that does not consider subgrid terms for the interfacial contribution. Mean liquid volume fraction profiles are well captured with CLES when compared to '{\it a posteriori}' DNS simulations, and only a weak grid dependency is observed. Grid dependency is generally a major drawback when carrying out LES of interfacial flows. The surface density and behavior are well estimated and described by using a dedicated transport equation. Based on this parameter and thanks to a good estimation of the critical Weber number value, relevant characteristic scales of the subgrid spray in the atomization regime can be obtained