From droplets to particles: Transformation criteria

International audienceAtomization of liquid fuel has a direct impact on the production of pollutant emission in engineering propulsion devices. Due to the multiple challenges in experimental investigations, motivation for numerical study is increasing on liquid-gas interaction from injection till dispersed spray zone. Our purpose is to increase the accuracy of the treatment of droplets in atomized jet, which are typically 100 times smaller than the characteristic injection length size. As the characteristic length reduces downstream to the jet, it is increasingly challenging to track the interface of the droplets accurately. To solve this multiscale issue, a coupled tracking Eulerian-Lagrangian Method exists [1]. It consists in transforming the small droplets to Lagrangian droplets that are transported with drag models. In addition to the size transformation criteria, one can consider geometric parameters to determine if a droplet has to be transformed. Indeed, the geometric criteria are there for two reasons. The first one is the case where the droplets can break if there are not spherical. The second one is about the drag models that are based on the assumption that the droplet is spherical. In this paper we make a review of the geometric criteria used in the literature. New geometric criteria are also proposed. Those criteria are validated and then discussed in academic cases and a 3D airblast atomizer simulation. Following the analysis of the results the authors advise the use of the deformation combined with surface criteria as the geometric transformation criteria. Introduction Atomization is a phenomenon encountered in many applications such as sprays in cosmetic engineering or aerospace engineering for jet propulsion [2]. In the combustion chamber, the total surface of the interface separating the two phases is a key parameter. Primary and secondary breakup have been extensively investigated in the literature. However, in order to fully describe the complete process, one has to capture droplets in dispersed zone 100 times smaller than jet diameter. Atomization is then a multiphase and a multiscale flow phenomenon which is still far from being understood. Due to this wide range of scale, the Direct Numerical Simulation (DNS) of such process requires robust and efficient codes. DNS is an important tool to analyse the experimental results and go further into the atomization understanding. In the past few years, numerical schemes of Interface Capturing Method (ICM) have been improved but faced numerical limitation. For instance, the treatment of the small droplets is the most challenging part when the entire process is treated in DNS. When dealing with unresolved structures we face different problems such as the dilution or the creation of numerical instabilities. To avoir them, a strategy is to remove small structures during the simulation, see Shinjo et al. [3]. But, those methods do not collect information on smallest droplets in atomization application. Introduction of Adaptive Mesh Refinement (AMR) in DNS is a first answer to this issue, it consists in refining unresolved area under numerical concept and focus on the interface between two phases instead of refining the entire domain. In dense spray, AMR tends to refine the entire zone and becomes as expensive as a full domain refinement. A solution is to transform the smallest droplets into point particles and remove AMR in this area. This strategy is called Eulerian-Lagrangian coupling [1], it assumes that small droplets will no longer break during the simulation and that the Lagrangian models reproduce correctly the droplet transport. These physical assumptions are implemented to answer numerical issue and improve the computational cost. This Eulerian-Lagrangian coupling is based on transformation criteria that defines when an ICM structure has to be transformed into Lagrangian particle and when a Lagrangian particle has to be transformed back into ICM. The main purpose of the present communication is to provide a detailed analysis of the ICM to Lagrangian transformation criteria. The geometri