Rime- and glaze-ice accretion due to freezing rain falling vertically on a horizontal thermally insulated overhead line conductor

Abstract

A theory of atmospheric icing due to freezing rain on an overhead line conductor (OHLC) is developed. The rain falls vertically on a horizontal OHLC that is thermally insulated. It is assumed that the collection efficiency of the accretion surface is unity and that this surface is in thermodynamic equilibrium with the environment. For air temperature T A ⩽ 0°C and raindrop temperature T D ⩽ 0°C, the freezing rain accretes as rime ice, provided that the temperature of the ice surface T l < 0°C. The evolution equation governing the mass transfer at the accretion surface is solved analytically, yielding the shape of the rime-ice surface. Equations governing the thermal state of the rime-ice deposit are also given. These determine the onset of wet growth or glaze accretion at the upper stagnation line during suitable environmental conditions. For environmental conditions producing an ice surface at temperature T l = 0°gC, the freezing accretes as glaze. Equations governing the heat and mass transfer at the surface determine the shape of the glaze surface and the downward viscous motion of the unfrozen water. For T D < 0°C, glaze evolution equations are developed for T A ⩽ 0°C and T A 0°C. Analytical solutions of these equations are obtained. In particular, when T D < − T A < 0°C, the evolution equation predicts a novel limiting growth that is triangular in shape. Further study of the mass and heat transfer conditions, in the neighborhood of this final stage of glaze accretion, shows that it is maintained in thermodynamic equilibrium with its warm air environment.