Spinning disk atomization: Theory of the ligament regime

Abstract

A method of the mathematical modeling of the spinning disk atomization process as a whole, from the film flow on a rotating disk to the drop formation and detachment from the ends of the ligaments spiralling out of the disk’s rim, is formulated and the key results illustrating its implementation are described. Being one of the most efficient nozzle-free atomization techniques, spinning disk atomization is used in many applications, ranging from metallurgy to pharmaceutical industry, but until now its design and optimization remain empirical which is time consuming and costly. In the present work, the entire spinning disk atomization process is, for the first time, modelled mathematically by (a) utilizing all known analytic results regarding its elements, notably the film flow on the disk and the dynamics of outgoing spiral jets, where the flow description can be simplified asymptotically and (b) using the full-scale numerical simulation of the three-dimensional unsteady free-boundary flow in the transition zone near the disk’s rim which brings these elements together. The results illustrating the developed modeling approach reveal some previously unreported qualitative features of the spinning disk atomization process, such as the drift of the outgoing ligaments with respect to the disk, and elucidate the influence of physical factors on the size distribution of the drops and, where this is the case, satellite droplets. The comparison of the obtained results with available experimental data confirms the validity of the assumptions used in the modeling.