Unsteady force and torque correlations for prolate spheroids pitching at large inclination angles in transitional flows

This study investigates the unsteady hydrodynamic forces and torques acting on a prolate spheroid with aspect ratio 6. It undergoes small-amplitude pitching oscillations about a large inclination angle at Reynolds numbers 50 minus 300 50 − 300 50 - 300 and dimensionless pitching frequencies 0.03 minus 0.16 0.03 − 0.16 0.03- 0.16 . This operating regime, situated near the onset of laminar flow separation, features strong coupling between added-mass effects and viscous dissipation. We numerically resolve the time-dependent vortices, and quantify the force and torque responses across a range of pitching frequencies and Reynolds numbers. The results reveal significant deviations from quasi-steady predictions, particularly in the phase lag and amplitude effects of unsteady loads, which are attributed to the nonlinear interaction between incipient separation vortices and periodic body motion. The unsteady force and torque correlations for pitching prolate spheroids are proposed, incorporating both inertia-driven and viscous contributions, to capture the dominant mechanisms governing unsteady loads.