Combustion of droplets in plane mixing layers

The combustion of droplets in turbulence gives rise to complex phenomena that are still not completely understood. First, the droplets disperse driven by fluctuations in the gas velocity and evaporate driven by fluctuations in the vapor pressure. Second, the vapor mixes and reacts with the oxygen forming carbon dioxide and water. Previous studies revealed persistent clusters, which influence the evaporation of droplets and reaction of vapor. In particular, the studies showed that diffusion flames, which surround single droplets, coexist with premixed flames, which propagate through clusters.\footnote{Weiss, Bhopalam, Meyer, and Jenny, \emph{Physics of Fluids} \textbf{33}, 033322 (2021).}${ }^{,}$\footnote{Weiss, Doctoral thesis, ETH Zurich (2021).} \par In this talk, these phenomena are examined with direct numerical simulations of plane mixing layers. The gas is governed by the low Mach number equations, the droplets are governed by the point droplet equations, and the chemical reaction is modeled with a one-step mechanism.${ }^{1,2}$ The mixing layer consists of a hot, outer stream and a cold, inner stream laden with droplets.\footnote{Dai, Jin, Luo, Xiao, and Fan, \emph{Fuel} \textbf{301}, 121030 (2021).} The flow is examined with statistics of the gas and droplets. In particular, clusters and voids are identified with Vorono\"{i} tessellations, and diffusion and premixed flames are identified with Takeno's flame index.\footnote{Rycroft, \emph{Chaos} \textbf{19}, 041111 (2009).}${ }^{,}$\footnote{Yamashita, Shimada, and Takeno, \emph{26th Symposium on Combustion}, 27-34 (1996).} Our purpose is to better understand how parameters like the droplet loading and diameter affect the structure and evolution of the mixing layer.