Numerical investigation on vortex dynamics of flow around a pitching hydrofoil via the finite-domain impulse theory

The behaviors of unsteady flow structures and corresponding hydrodynamics for a pitching hydrofoil are investigated numerically and theoretically in the present paper. The aims are to derive the total lift by finite-domain impulse theory for sub-cavitating flow (σ = 8.0) and cavitating flow (σ = 3.0), and to quantify the distinct impact of individual vortex structures on the transient lift to appreciate the interplay among cavitation, flow structures, and vortex dynamics. The motion of the hydrofoil is set to pitch up clockwise with an almost constant rate from 0° to 15° and then back to 0°, for the Reynolds number, 7.5 × 10⁵, and the frequency, 0.2 Hz, respectively. The results reveal that the presence of cavities delays the migration of the laminar separation bubble (LSB) from the trailing edge (TE) to the leading edge (LE), consequently postponing the hysteresis in the inflection of lift coefficients. The eventual stall under the sub-cavitation regime is the result of LSB bursting. While the instabilities within the leading-edge LSB induce the convection of cavitation-dominated vortices under the cavitation regime instead. Having validated the lift coefficients on the hydrofoil through the finite-domain impulse theory using the standard force expression, the Lamb vector integral emerges as the main contribution to the generation of unsteady lift. Moreover, the typical vortices’ contributions to the transient lift during dynamic stall are accurately quantified. The analysis indicates that the clockwise leading-edge vortex (−LEV) contributes positively, while the counterclockwise trailing-edge vortex (+TEV) contributes negatively. The negative influence becomes particularly pronounced after reaching the peak of total lift, as the shedding of the concentrated wake vortex precipitates a sharp decline due to a predominant negative lift contribution from the TEV region. Generally, the vortices’ contribution is relatively modest in sub-cavitating flow, but it is notably more significant in the context of incipient cavitating flow. (Figure presented.)