A Level Set/Vortex Sheet Method for Modeling Phase Interface Dynamics During Primary Breakup

The atomization of turbulent liquid jets and sheets can usually be divided into two subsequent processes: the primary breakup, where the jet or sheet initially breaks up into both large and small scale structures, followed by the secondary breakup, where these structures continue to break up into ever smaller drops, forming a spray. Considering numerical grid resolutions typical for Large Eddy Simulations (LES), the large scale liquid structures during primary breakup are well resolved, the liquid volume fraction can be of order one, and the phase interface can have any arbitrary complex shape. To correctly account for these characteristics, the phase interface has to be explicitly tracked on the numerically resolved scale and all phase interface dynamics on the subgrid scales have to be modeled. To derive such a Large Surface Structure (LSS) model, a level set/vortex sheet method is proposed. The level set/vortex sheet method tracks the phase interface by a level set scalar, so that topological changes of the interface, like breaking and merging, are handled automatically. Assuming inviscid fluids, the dynamics of the phase interface can be described by a vortex sheet located at the phase interface. The evolution equation for the vortex sheet strength then contains explicit local source terms for the physical processes at the phase interface, namely stretching terms, a surface tension term, and terms accounting for the differences in fluid density. The proposed level set/vortex sheet method thus provides a framework for the derivation of the primary breakup LSS subgrid models. Some preliminary results, namely the Kelvin-Helmholtz instability in the linear regime, the oscillations of liquid columns and spheres, and the three-dimensional breakup of a liquid/gas surface and a liquid sheet are presented in this paper. Introduction Atomization processes play an important role in a wide variety of technical applications and natural phenomena, ranging from inkjet printers, gas turbines, direct injection IC-engines, and cryogenic rocket engines to ocean wave breaking and hydrothermal features. The atomization process of liquid jets and sheets is usually divided into two consecutive steps: the primary and the secondary breakup. During primary breakup, the liquid jet or sheet exhibits large scale coherent structures that interact with the gas phase and break up into both large and small scale drops. During secondary breakup, these drops break up into ever smaller drops that finally may evaporate. Usually, the atomization process occurs in a turbulent environment, involving a wide range of time and length scales. Given today’s computational resources, the direct numerical simulation (DNS) of the turbulent breakup process as a whole, resolving all physical processes, is impossible, except for some very simple configurations. Instead, models describ∗Corresponding Author /∆x > 1 ` /∆x < 1 ` /∆x << 1 ` secondary breakup