A Computational Investigation of Water Droplet Trajectories

Abstract

The work of Langmuir and Blodgett is widely referenced among researchers in the field of ice accretion who are interested in the impingement characteristics of cloud and spray droplets on circular cylinders. In this paper we check the accuracy of those early calculations by integrating the droplet trajectories on a modern digital computer. We then demonstrate the changes which result when an improved formulation for the drag coefficient is used. Our results verify that the original Langmuir and Blodgett calculations are essentially correct for most practical purposes. Except for inertia parameters between 0.125 and 0.25, the relative differences between their results and our new ones do not exceed 10%. At very low collision efficiencies, however, the relative error is larger, with Langmuir and Blodgett tending to overpredict the collision parameters. Tables of our newly calculated data and fitting functions for the collision parameters are presented. We recommend them for future use because they are more accurate and more convenient to use than their Langmuir and Blodgett equivalents. A discussion of some of the limitations of Langmuir and Blodgett's theory is also given.