Bi-modal size distributions predicted by maximum entropy are compared with experiments in sprays

A theoretical formulation based on maximum entropy principles is presented to predict the droplet size and velocity distributions of sprays in an isothermal environment. The joint droplet distribution function is derived subject to the constraints of mass flow rate, momentum flux, and two modes of energy fluxes (kinetic and surface). A simpler model, which reduces the number of constraints by three, is derived by choosing an adequate velocity integration range. This maximum entropy principle spray model is tested by comparing the calculated distributions with experimental measurements presented by the authors for a hollow cone, non-swirl spray nozzle and the experimental results obtained by other researchers for hollow cone, swirl spray nozzles. For a specific droplet size, the droplet velocity distribution is Gaussian. The droplet size distribution is much more complicated; three types of distributions may occur-positively skewed mono-modal, uniform size (in the limit approaching a delta function), and bi-modal. This study is concerned mainly with the bi-modal size distribution.