Rigorous Reformulation of Rime/Glaze Ice Accretion and Reassessment of the Messinger/Myers Model under Unsteady and Variable Conditions

Aircraft icing involves complex interactions between multiphase heat transfer, phase change, and environmental variability. This study reassesses the classical Messinger/Myers model for rime ice accretion by introducing unsteady conduction, variable ice properties, and surface sublimation, all of which are often simplified in traditional models. The Stefan condition, applied alone at the ice-air interface, neglects sensible heat and assumes linear temperature profiles, leading to underprediction of surface temperature and glaze ice transition time. We identify three regimes of rime ice formation: R1, saturated rime ice with finite thickness; R2, continuous but finite rime growth; and R3, transition to glaze ice. The transitions between these regimes depend on the balance of thermal and mass fluxes, characterized through nondimensional parameters. The original Myers model performs well in some regimes due to compensating simplifications, but it fails in cases with strong unsteadiness or variable properties. A modified Myers model is proposed to improve predictive accuracy across a wider range of icing conditions.