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A two-dimensional second-order positivity-preserving finite volume upwind scheme is developed for a semi-coupled algorithm involving the air and droplet flow fields in the Eulerian frame in which shares the grid for each phase. Special emphasizes are placed on the computational modeling, which is induced from a strongly coupled algorithm, that satisfies the strict hyperbolicity and its numerical scheme based on the HLLC solver preserving the positivity to handle multiphase flow in the Eulerian frame, respectively. The proposed modeling associated with the semi-coupled algorithm including the Navier-Stokes and droplet equations takes into account different boundary conditions on the solid surface for each phase. The verification and validation studies show that the new scheme can solve the air and droplet flow fields in fairly good agreement with the exact analytical solutions and experimental data. In particular, it accurately predicted the maximum value of the droplet impingement intensity near the stagnation region and the droplet impingement area.

A Computational Modeling for Semi-Coupled Multiphase Flow in Atmospheric Icing Conditions