Monte Carlo method for predicting a physically based drop-size distribution evolution of a spray
Résumé
We report in this paper a method for the evolution of a physically-based drop size distribution of a spray, by coupling the Maximum Entropy Formalism and the Monte Carlo scheme. Using the discrete or continuous population balance equation, a Mass Flow Algorithm is formulated taking into account interactions between droplets via coalescence. After deriving a kernel for coalescence, we solve the time dependent drop size distribution equation using a Monte Carlo method. We apply the method to the spray of a new print-head known as a Spray On Demand (SOD) device; the process exploits ultrasonic spray generation via a Faraday instability where the fluid/structure interaction causing the instability is described by a modified Hamilton's principle. This has led to a physically-based approach for predicting the initial drop size distribution within the framework of the Maximum Entropy Formalism (MEF): a three-parameter generalized Gamma distribution is chosen by using conservation of mass and energy. The calculation of the drop size distribution evolution by Monte Carlo method shows the effect of spray droplets coalescence both on the number-based or volume-based drop size distributions.