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The method has been tested on a NACA0012 hydrofoil at two different submerged depths (s=1.03 and s=1.29 chord). The angle of attack is in both cases 5 degrees. The submergence is measured from the mid chord of the foil to the undisturbed free surface. The physical domain is ten chords deep, and has a length in the stream-wise direction of 13.5 chords. The inflow boundary is located 5 chords upstream the leading edge of the foil. The domain is discretized on a mesh with 280 grid lines in the stream wise, and 91 grid lines in the lateral direction. At the bottom boundary an impermeable wall is used as a boundary condition. A fine mesh has to be used close to the free surface and to the foil. In the present case, 71 grid lines are used between the free surface and the foil.

Downstream the foil, the distribution of grid lines in stream-wise direction is uniform, with a spatial distance of 0.05 chord length. With this distribution of grid lines, one wave length is resolved in approximately 20 grid lines. The initial mesh in the vicinity of the foil for the s=1.29 case is shown in Figure 1.

The present computations are compared with experiments, Duncan [11] and numerical simulation, Hino [7]. Duncan performed experiment in a towing tank, the foil was towed at a speed of 0.8 m/s and the chord was 0.203 m , giving a Reynolds number, , The Froude number was Fr=0.567 in both cases. Hino did computations of the same cases, the results of the computations are shown in the figures for comparison.

Figure 2 show the results at s=1.03, and Figure 3 at s=1.29. The foil is located between x=0 and x=1 in both cases. The wave length and phase show good agreement with the experiments, the amplitude of the predicted waves are however slightly under estimated by the present method. The agreement between the simulation by Hino and the present simulation is very good for both cases. Hino explains the discrepancy between the simulations and the experiments by the fact that the foil in the experiments are located very close to the bottom of the towing tank. The distance between the foil and the tank bottom are only 0.82 chord in the experiments of Duncan.

Figure 4 and 5 show pressure distribution of the s=1.03 case and s=1.29 case respectively.

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