# A New Ice Accretion Model for Aircraft Icing Based on Phase-Field Method
###### Abstract  
Aircraft icing presents a serious threat to the aerodynamic performance and safety of aircraft. The numerical simulation method for the accurate prediction of icing shape is an important method to evaluate icing hazards and develop aircraft icing protection systems. Referring to the phase-field method, a new ice accretion mathematical model is developed to predict the ice shape. The mass fraction of ice in the mixture is selected as the phase parameter, and the phase equation is established with a freezing coefficient. Meanwhile, the mixture thickness and temperature are determined by combining mass conservation and energy balance. Ice accretions are simulated under typical ice conditions, including crime ice, glaze ice and mixed ice, and the ice shape and its characteristics are analyzed and compared with those provided by experiments and LEWICE. The results show that the phase-field ice accretion model can predict the ice shape under different icing conditions, especially reflecting some main characteristics of glaze ice. numerical simulation; phase-field method; aircraft icing; ice accretion model +
Footnote †: journal: Applied  
0000-0002-4000-0000-0000-0000-0000-0000-0000-0000-0000-0000-0000-00000-00000-  
of residual liquid water flows under the action of external airflow and gradually freezes. The structure of glaze ice is relatively compact, with higher density and a transparent appearance, which does not easily fall off. In the process of ice accretion, horn ice may form on the leading edge of the wing, which has a great influence on the aerodynamic characteristics. Mixed ice is a mixture of rime ice and glaze ice, which has the characteristics of both ice types. Similar to glaze ice, mixed ice may also seriously damage the aerodynamic performance and pose a threat to flight safety. At present, the approaches to studying aircraft ice accretion can be classified into two categories: experimental research with ground or flight tests [6; 7; 8] and numerical simulation methods [9; 10]. In the process of research, each has its own advantages and disadvantages. In recent years, with the development of computer technology, the efficiency, economy and flexibility of numerical simulation methods are more and more prominent, and have been widely studied and applied. Since the 1940s, a number of icing simulation codes have been developed, such as LEWICE [11], ONERA [12], DRA [13], CIRAMIL [14] and FENSAP-ICE [15; 16]. These icing simulation codes generally consist of three major modules, including calculating the airflow field, droplet trajectory and ice accretion. In 1953, the Messinger model was first established based on energy balance [17]. Subsequently, [PERSON] [18] and [PERSON] [19] improved the Messinger model by considering the temperature rise caused by compressible flow and adding an energy source at the substrate, which improved the applicability of the Messinger model. In order to build the Messinger model, the following limitations need to be adopted: the ice and water layers are isothermal. The heat is not allowed to be transferred from the interface of ice and water, and the energy can only be balanced by the latent heat generated during ice formation. Hence, [PERSON] [20] introduced heat conduction in the ice layer into the classical Messinger model. These methods are relatively complex and difficult to implement in the icing code in a simple manner. However, these improvements have not changed the basic form of the Messinger Model. The Messinger model can accurately predict the ice shape of rime ice, but the prediction results for glaze ice and mixed ice need to be improved. [PERSON] [15] introduced the shallow water icing model (SWIM) into the icing calculation and established the differential equation of continuous water film flow on the icing surface. The SWIM can describe the morphology and distribution of liquid water on the ice surface in more detail, and improve the accuracy of ice prediction.