Effect of the vortical structures on the hydrodynamic performance of a pitching hydrofoil

The objective is to study the vortical structural behaviors of a transient pitching hydrofoil and their effects on the hydrodynamic performance. The pitching motion of the hydrofoil is set to pitch up with an almost constant rate from 5° to 15° and then back to 5°, with the Reynolds number 4.4×10⁵ and the frequency 2 Hz. The results show that the main coherent structures around the pitching hydrofoil include small-scale laminar separation bubble (LSB), large-scale second vortex (SV) and trailing edge vortex (TEV) which are all vortical. The relationship between the vortical structure and the lift is investigated with the finite-domain impulse theory. It indicates that the major part of the lift is contributed by the LSB, whereas the shedding and the formation of the SV and TEV cause the fluctuation of the lift. The proper orthogonal decomposition (POD) method is applied to capture the most energetic modes, revealing that the LSB mode occupies a large amount of energy in the flow field. The dynamic mode decomposition (DMD) method accurately extracts the dominant frequency and modal characteristics, with the first mode corresponding to the mean flow, the second mode corresponding to the LSB structure and the third and fourth modes corresponding to the vortex shedding.