Accurate calculation of the catch efficiency β is of paramount importance for any ice accretion calculation since β is the most important factor in determining the mass of ice accretion. A new scheme has been proposed recently in [1] for accurately calculating β on a discretized two-dimensional geometry based on the results of a Lagrangian droplet trajectory integrator (start and impact conditions).
This paper proposes an extension to the algorithm in Ref. [1], which is applicable to three-dimensional surfaces with arbitrary surface discretization. The 3D algorithm maintains the positive attributes of the original 2D algorithm, namely mass conservation of the impinging water, capability to deal with overlapping impingement regions and with crossing trajectories, computational efficiency of the algorithm, and low number of trajectories required to reach good accuracy in catch efficiency. At the same time, the new 3D algorithm avoids typical difficulties of other approaches to determine the catch efficiency β, like noisy β (results varying significantly between neighboring surface cells), catch efficiency of zero for surface cells surrounded by other cells with β > 0, jagged impingement limits, catch efficiency β not available on the discretized surface but only on an intermediate plane, or interpolation problems of β between an intermediate plane and the actual discretized surface.
The paper first reviews existing approaches in the literature to determine β, then describes in detail the extension of the algorithm in [1] to three dimensions and the steps taken to avoid the possible pitfalls in calculating β described above. The algorithm is then applied to two test problems, one being the wing/belly-fairing intersection of the Common Research Model (CRM) in clean configuration [2] and the other being a generic scoop intake. The paper closes with ideas for further development of the algorithm.