Two main approaches are available when studying droplet dynamics for in-flight icing simulations: the Lagrangian approach, in which each droplet trajectory is integrated until it impacts the vehicle under study or when it leaves it behind without impact, and the Eulerian approach, where the droplet dynamics is solved as a continuum. In both cases, the same momentum equations are solved.
Each approach has its advantages. In 2D, the Lagrangian approach is easy to code and it is very efficient, particularly when used in combination with a panel method flow solver. However, it is a far less practical approach for 3D simulations, particularly on complex geometries, as it is not an easy task to accurately determine the droplet seeding region without a great number of droplet trajectories, dramatically increasing the computing cost. Converting the impact locations into a water collection distribution is also a complex task, since droplet trajectories in 3D can follow convoluted paths. One of the advantages of the Lagrangian approach is the crisp definition of the shadow zone as it is clearly defined by the first trajectory to graze the surface of the vehicle.
The Eulerian approach is much simpler to use with complex geometries, solving the entire domain as a whole, using the same grid as for the airflow, and there is no need to seed trajectories. For this reason, it is the preferred approach in most 3D icing solvers. One of its disadvantages, however, is that discontinuities, such as shadow zone limits or impingement limits, are usually not very sharply defined, with smoothing due to numerical dissipation and the grid, optimized heuristically for the airflow calculation, not being sufficiently fine in regions of solution discontinuities in the droplet solution.
This paper presents a refined approach in the use of Eulerian algorithms for icing simulations by introducing a mesh adaption process simultaneously based on the airflow solution and the droplet solution. The results show the great potential of this approach in capturing the solution discontinuities very sharply, significantly reducing the uncertainty in determining shadow zone heights and impingement limits.