A mixing and deformation mechanism for a supercritical fuel droplet

A model is developed of the dispersion of a vapor fuel droplet that is suddenly set in motion in a gaseous environment that has a density similar to that of the fuel vapor. The objective of the analysis is to describe the mixing and deformation process encountered by a supercritically preheated fuel droplet that is suddenly injected in a gaseous environment that is well above the thermodynamic critical temperature and pressure of the fuel. The initial droplet injection process is modeled by instantaneously creating a potential flow around a moving spherical gaseous droplet, i.e., initially imposing a harmonic vortex sheet at the droplet surface. In the analysis, the transient, axisymmetric, stream function-vorticity and species equations are solved to determine the evolution of the vorticity distribution, species mixing, and the distortion of the initial interface. A time series expansion solution is developed for small times, and a fully numerical procedure is used to extend it to longer times. Specific results are obtained for Reynolds numbers of 50 and 200. They show that the initially spherical gaseous fuel droplet is extensively distorted, adopting a mushroom-like shape. This is caused by the evolution of the vorticity distribution that tends to form a ring vortex. It is also shown that the vapor mixing process is greatly enhanced around the vortex ring. These effects are stronger for the higher Reynolds number.