Two enhanced models based on the enthalpy method for mixed-phase icing: PMEE and SFE

To address the limitations of the binary velocity assumption for liquid-water convective transport in mixed-phase icing based on the enthalpy method for icing, this paper proposes two enhanced models: the Porous-Media Enhanced Enthalpy (PMEE) model and the Slush-Film Enthalpy (SFE) 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 yields predictions of ice shape, maximum ice thickness, and icing limits that are closer to experimental measurements than those of the PMEE model; under rime ice conditions, both models produce consistent results that agree well with experiments. Further parametric studies based on the SFE model reveal that a decrease in freestream temperature enhances convective heat transfer and accelerates liquid water freezing, leading to a significant reduction in both the total ice enthalpy and the liquid water volume fraction, whereas an increase in the freestream liquid water fraction directly raises the 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.