A 3D icing simulation code is developed in the open-source CFD toolbox OpenFOAM. A hybrid Cartesian/body-fitted meshing method is used to generate high-quality meshes around complex ice shapes. Steady-state 3D Reynolds-averaged Navier-Stokes (RANS) equations are solved to provide the ensemble-averaged flow around the airfoil. Considering the multi-scale nature of droplet size distribution, and more importantly, to represent the less uniform nature of the Super-cooled Large Droplets (SLD), two droplet tracking methods are realized: the Eulerian method is used to track the small-size droplets (below 50 $\mathsf{\mu }$m) for the sake of efficiency; the Lagrangian method with random sampling is used to track the large droplets (above 50 $\mathsf{\mu }$m); the heat transfer of the surface overflow is solved on a virtual surface mesh; the ice accumulation is estimated via the Myers model; finally, the final ice shape is predicted by time marching. Limited by the availability of experimental data, validations are performed on 3D simulations of 2D geometries using the Eulerian and Lagrangian methods, respectively. The code proves to be feasible and accurate enough in predicting ice shapes. Finally, an icing simulation result of the M6 wing is presented to illustrate the full 3D capability.

The impact of supercooled water droplets is the cause of aircraft icing, and the acquisition of impingement characteristics is the key to icing prediction and the design of ice protection systems. The introduction of water droplet collection efficiency is required to obtain the characteristics for the Lagrangian method. In this work, a traditional flow tube method, a local flow tube method, and a statistical method are established to calculate the local collection efficiency, based on Lagrangian droplet trajectories. Through the numerical simulations of the air–droplet flow field around an NACA 0012 airfoil, the accuracies of the three methods in regard to collection efficiency are verified. Then, these three methods are applied to obtain the results for water droplet trajectories and the collection efficiency of an S-shaped duct, a 2D engine cone section and an icing wind tunnel. The results show that the distributions of water droplet collection efficiency obtained by the three methods are consistent and the three methods are all feasible when the water droplets do not overlap or cross before hitting the aircraft surfaces. When the water droplets are shadowed by upstream surfaces or blown by air injection, the droplet trajectories might overlap or even cross, and the local collection efficiencies obtained by the traditional flow tube method, local flow tube method, and statistical method might differ. The statistical method is relatively accurate. However, not all the droplet impingement characteristics obtained by the three methods are different due to these effects, and the non-crossing of the droplet trajectories is not a necessary condition for the use of the flow tube method. The effects of trajectory crossings are analyzed and discussed in detail in different situations for the three methods. This work is helpful for understanding and accurately calculating the droplet impingement characteristics and is of great significance for simulations of the aircraft icing process and anti/de-icing range.