The investigation of super-cooled droplet impingement characteristics is the most important step for aircraft icing and anti-icing/de-icing analyses. The Lagrangian method and the Eulerian method are widely used to compute the droplet motion and collection efficiency, and the two methods are considered to obtain almost the same results for surface impingement characteristics under icing conditions. The models and implementation approaches of the two methods were established in this work, and the simulations of droplet motion were carried out for a NACA 0012 airfoil, a 2D section of an A320 head, a multi-element airfoil, and an icing wind tunnel. The collection efficiencies of the NACA 0012 airfoil obtained by the present Lagrangian and Eulerian methods show good agreement with the results in the literature, validating the established methods. The droplet impingement characteristics of the two methods are consistent for the aircraft surfaces without upstream trajectory deflections. However, when the droplet motion is deflected by the frontal body before hitting the rear surfaces, the results obtained by the two methods are different whether the droplet trajectories intersect or not, which subverts the traditional opinion that the Lagrangian and Eulerian methods would obtain the same result of the droplet impingement characteristics. The reason is studied in detail according to the droplet motion results in the icing wind tunnel. The findings of this work are helpful for the accuracy of aircraft icing and anti-icing/de-icing simulations, and useful for the development of airworthiness certification.

Considering the transient heat and mass transfer process of the impinged water droplets during aircraft icing, an unsteady thermodynamic model was established to simulate the dynamic developments of the water film and the ice layer on aircraft surfaces. The unsteady model was discretized in an implicit scheme with a corresponding solution method. Icing simulations were performed for a NACA0012 airfoil, and the results show acceptable agreement with the data in the literature. Water film first appears near the stagnation point, and then, the film thickness increases, and the runback water region expands with time, affecting the icing rate, the surface temperature, and the ice type. The development of the water film is rapid, and the thickness and range of the film, along with the icing rate, reach a steady state in a short time. The stable characteristics obtained by the unsteady model are consistent with those of the Messinger steady model. Despite that the unsteady and steady models can obtain similar ice shapes in icing simulations, the dynamic developments of the water film and the ice layer should be considered at the initial stage of ice accretion or in the short-time icing simulations.