Finite-volume droplet trajectories for icing simulation

During a Lagrangian icing simulation a large number of droplet trajectories are calculated to determine the water catch, and as a result it is important that this procedure is as rapid as possible. In order to arrive at a method with minimum complexity, a finite-volume representation is developed for streamlines and extended to incorporate the equations of motion for a droplet, with all cells being crossed in a single timestep. However, since cells vary greatly in size, the method must be implicit to avoid an awkward stability restriction that would otherwise degrade performance. An implicit method is therefore implemented by carrying out iterations to solve for the crossing of each CFD cell, so that the droplet motion is tightly coupled to the underlying flow and mesh. By crossing every cell in a single step, and by using the mesh connectivity to track the droplet motion between cells, any need for costly searches or containment checks is eliminated and the resulting method is efficient. The implicit system is solved using functional iteration, which is feasible for the droplet system (which can be stiff) by using a particular factorisation. Stability of this iteration is explored and seen to depend primarily on the maximum power used in the empirical relationship for droplet drag coefficient C_D = C_D(Re), while numerical tests confirm the theoretical orders of accuracy for the different discretisations. Final results are validated against experimental and alternative numerical water catch data for a NACA 23012 aerofoil.