Thermodynamic models of wet-snow accretion: axial growth and liquid water content on a fixed conductor

Abstract

For wet-snow accretion on overhead line conductors, occurring at positive air temperatures, the liquid water content of the snow matrix controls the strength of the capillary forces, promoting contact between ice granules, which leads to ice bonding. During this process of metamorphosis, the liquid water content of the snow matrix increases with time and, on reaching a level of 20–40 percent, the internal cohesive forces are greatly weakened, causing shedding of the accreted snow by aerodynamic and gravitational forces. The purpose of this paper is to construct thermodynamic models of wet-snow accretion, by axial growth on a fixed conductor, which estimate the liquid water content during the accretion process. The models depend upon assumptions concerning the wet-snow accretion factor, namely the proportion of mass of a snowflake that adheres on impact with the snow/conductor surface. Models are formulated assuming either that the accretion factor is constant or that it obeys a cosine law (adhesion proportional to the cosine of the angle between the impacting snowflake trajectory and the normal to the surface). A differential equation governing the variation of the liquid water content with deposit time is derived and solved numerically. Solutions of this equation are also obtained using analytical solutions of the evolution equation based on the assumption that the trajectory paths of snowflakes are rectilinear. For a range of meteorological conditions, critical cohesive “precipitation—air temperature” criteria are established for wet-snow shedding, leading to quantitative information on the sawtooth transient wet-snow loading of an overhead line conductor.