Two Improved Thermodynamic Icing Models for Mixed-Phase Accretion: PMEE and SFE

To address the deficiency of the binary assumption for liquid water convective transport in mixed-phase icing within Malik’s enthalpy model, this paper proposes two improved models: the Porous-Media Enhanced Enthalpy (PMEE) Icing Model and the Slush-Film Enthalpy (SFE) Icing Model. The PMEE model introduces a porous-media resistance term, establishing a continuous functional relationship between the liquid water volume fraction and the average velocity. The SFE model constructs a dual-layer structure based on a critical liquid water volume fraction, distinguishing between a static slush ice layer and a dynamic surface water film, thereby characterizing the water retention and runback mechanisms within the ice layer. Through sensitivity analysis, the recommended value for the critical liquid water volume fraction in the SFE model is determined to be 0.05. Validation results indicate that under high freestream liquid water fraction conditions, the SFE model outperforms the PMEE model in predicting ice shape, maximum ice thickness, and icing limits. Under rime ice conditions, both models yield consistent results that agree well with experiments. Further analysis based on the SFE model reveals that a decrease in freestream temperature enhances convective heat transfer intensity and accelerates liquid water freezing, leading to a significant reduction in both the total ice enthalpy and the liquid water volume fraction. An increase in the freestream liquid water fraction directly raises the total liquid water supply impinging on the wall, thereby increasing the total ice enthalpy and enhancing the runback effect. The SFE model effectively captures the coupled influence of the above parameter variations on the mixed-phase thermodynamic accretion process, providing a more effective computational tool for numerical simulations of mixed-phase icing.