Droplet heating and evaporation−recent results and unsolved problems

Recently developed approaches to the hydrodynamic, kinetic, and molecular dynamic modeling of fuel droplet heating and evaporation are reviewed. Two new solutions to the heat conduction equation, taking into account the effect of the moving boundary during transient heating of an evaporating droplet, are discussed. The first solution is the explicit analytical solution to this equation, while the second one reduces the solution of the differential transient heat conduction equation to the solution of the Volterra integral equation of the second kind. The new approach predicts lower droplet surface temperatures and slower evaporation rates compared with the traditional approach. An alternative approach to the same problem has been based on the assumption that the time evolution of a droplet's radius, Rd (t), is known. For sufficiently small time steps, the time evolutions of droplet surface temperatures and radii predicted by both approaches coincide. A simplified model for multi-component droplet heating and evaporation, based on the analytical solution to the species diffusion equation inside droplets, is discussed. Two new solutions to the equation, describing the diffusion of species during multi-component droplet evaporation taking into account the effects of the moving boundary, are presented. A quasi-discrete model for heating and evaporation of complex multi-component hydrocarbon fuel droplets is described. The predictions of the model, taking into account the effects of the moving boundary during the time steps on the solutions to the heat transfer and species diffusion equations, are discussed. A new algorithm, based on simple approximations of the kinetic results, suitable for engineering applications, is discussed. The results of kinetic modeling, taking into account the effects of inelastic collisions, and applications of molecular dynamics simulations to study the evaporation of n-dodecane droplets are briefly summarized. The most challenging and practically important unsolved problems with regard to the modeling of droplet heating and evaporation are summarized and discussed