In the vortex-in-cell method combined with the penalization method, fluid particles are traced by continuously updating their positions and strengths from the grid solution. To evaluate particle velocity, the velocity field is computed by solving a Poisson equation for the vector potential, namely [Formula: see text], where [Formula: see text], and its computation can be greatly accelerated by the use of a fast Poisson solver. While this method offers an efficient way to simulate unsteady viscous flows, the computation of the boundary values when solving the Poisson equation can become a computation time bottleneck. Although adopting the fast multipole method can lead to saving further computation time, its disadvantage is that it requires complicated hierarchical data structures such as a quad-tree and oct-tree. In this paper, we introduce and assess an approximation method for specifying domain boundary values using splines. Using the proposed spline approximation method we achieve significant savings in both computation time and memory consumption.

a b s t r a c tThe present study aims to understand the energy conversion mechanism of a 100 kW horizontal axis tidal stream turbine by analyzing thrust, torque, and wake flow measurements. The scale ratio of the turbine model was 1/20 and model tests for power and wake measurements were conducted in a towing tank facility. Wake fields were measured by a towed underwater stereoscopic particle image velocimetry (SPIV) system. The chord-length based Reynolds number at 40% of the radius of the turbine ranged from 53,000 to 63,000 in the test conditions. The turbine model showed the highest power coefficient at a tip speed ratio (TSR) of 3.5, and the magnitude of power coefficient was 0.278. Three TSR conditions were selected for SPIV measurement after power measurement tests, representing heavy loading, highest efficiency, and light loading, respectively. In the wake field measurement results, conversion of kinetic energy of the turbine wake was investigated, decomposing it into effectively extracted work, loss due to the drag on the turbine system, kinetic energy of the time-mean axial flow, local flow structures, turbulence, and secondary flow loss. In high TSR conditions with a small angle of attack onto the turbine blade, the secondary flow loss was minimized.

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