Modeling Evaporating Droplets in Complex Unsteady Flows

In many applications, a moving fluid carries a suspension of droplets of a second phase which may change in size due to evaporation or condensation. Examples include liquid fuel drops in engines and raindrops or ice-crystals in a thunderstorm. If the number of such particles is very large, and, if further, the flow is inhomogeneous, unsteady or turbulent, it may be practically impossible to explicitly compute all of the fluid and particle degrees of freedom in a numerical simulation of the system. Under such circumstances Lagrangian Particle Tracking (LPT) of a small subset of the particles is used to reduce the computational effort. The purpose of this paper is to compare the LPT with an alternate method that is based on an approximate solution of the conservation equation of particle density in phase space by the method of moments (MOM). Closure is achieved by invoking the assumption that the droplet size distribution is locally lognormal. The resulting coupled transport equations for the local mean and variance of the particle size distribution are then solved in conjunction with the usual equations for the fluid and associated scalar fields. The formalism is applied to the test case of a uniform distribution of droplets placed in a non homogeneous temperature field and stirred with a decaying Taylor vortex. As a benchmark, we perform a direct numerical simulation (DNS) of high resolution that keeps track of all the particles together with the fluid flow.