Finite Volume Droplet Trajectories for Icing Simulation

During a Lagrangian icing simulation a large number of dropl et trajectories are calculated to determine the water catch, and as a result it is impor tant that this procedure is as rapid as possible. In order to arrive at a method with min imum complexity, a finite volume representation is developed for streamlines a nd extended to incorporate the equations of motion for a droplet, with all cells being cr ossed 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 degrad e performance. An implicit method is therefore implemented by carrying out iterations to olve for the crossing of each CFD cell, so that the droplet motion is tightly couple d 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 costl y searches or containment checks is eliminated and the resulting method is efficient. T he implicit system is solved using functional iteration, which is feasible for the dropl et system (which can be stiff) by using a particular factorisation. Stability of this iter ation is explored and seen to depend primarily on the maximum power used in the empirical r el tionship for droplet drag coefficientCD = CD(Re), while numerical tests confirm the theoretical orders of accuracy for the different discretisations. Final resul ts are validated against experimental and alternative numerical water catch data for a NACA 23012 aerofoil. Email address: thomas.rendall@bristol.ac.uk (T.C.S. Rendall) Preprint submitted to International Journal of Multiphase Flow August 21, 2013