An investigation into empirical ice density formulations for dry ice growth on cylinders

Abstract

This paper describes an investigation into the empirical accreted icing density formulations, namely the numerical fits by (Makkonen and Stallabrass, 1984) and (Jones, 1990). Typically, the icing severity is estimated by the masses of the accreted ice, however, for this study the focus is primarily on the accreted ice densities and thicknesses for the main purpose of estimating the ice loads, in particular for the cases when the ice mass measurements are not readily available and other indirect measurements such as observed ice thicknesses can to be used as an estimate. The results were obtained for both the analytical and numerical modeling in comparison with the icing tunnel experiments. Seven different diameters of cylinders ranging from 20 to 298 mm are used. Analysis show that Makkonen and Stallabras (M&S) fit tends to have good agreement with the smaller cylinders, while it tends to underestimate the icing thicknesses for the larger cylinder diameters. On the other hand, the Jones ice density formulation shows consistently better results for almost all tested cases and especially for the larger cylinder diameters. The results with the MVD approximation show good agreement mainly for smaller diameter cylinders whereas the agreement for the larger cylinders is not good primarily due to low values of droplet inertia parameter K, which puts the results using the MVD approximation outside of the verified range of the current icing theory. Thus, calculations with the full droplet distribution spectrum are recommended.