A physics-based sphericity, drag coefficient and Nusselt number model of a partially-melted ice crystal

Partially melted crystals can lead to ice accretion on heated surfaces including the inside of turbofan engines. To model the ice accretion due to partially melted crystals, the trajectory of the crystals must be modeled based on their drag, which is correlated with the shape of the crystals. The melting rate of an ice crystal is subject to the heat transfer coefficient, which is influenced by the geometry of an ice crystal. The geometries of partially melted crystals are related to their percentage melting. To study the correlation between the geometry and the percentage melting of a crystal, a levitating test rig is used to study the melting process of a single crystal under natural convection. The percentage melting is measured using luminescent Rhodamine B. A transient collapse in the shape of a single ice crystal is observed in the experiment during the melting process. The shape variation is predicted by a physics model based on the surface energy at the interface between air, ice and water. The model shows that the critical percentage melting forcing the crystal to become spherical is independent of the initial shape of the crystal. The average critical percentage melting that collapses the crystal to a spherical shape was experimentally measured to be 68.6%. A physics based model predicts such critical percentage melting to be 62.2%, verifying the proposed model. A two-stage drag coefficient model is also developed to capture the transient crystal shape at the predicted critical percentage of melting.