Data assimilation of the near-field dynamics of the hydrofoil tip vortex

Abstract

Tip vortex cavitation is a critical issue in marine hydrodynamics, yet its prediction is hampered by challenges in capturing the complex, unsteady flow in the hydrofoil near-field. Conventional experimental and numerical methods often struggle to resolve the unsteady structures and the physically consistent pressure–velocity coupling associated with vortex instability. This study applies an established continuous-adjoint data-assimilation (DA) framework to a new hydrofoil-tip-vortex application by assimilating time-resolved tomographic particle image velocimetry measurements into the spatially filtered Navier–Stokes equations. The DA step reconstructs a physics-constrained three-dimensional velocity field; pressure is subsequently estimated from that velocity field by solving a pressure Poisson equation. The flow is examined at angles of attack (AoA) of 5°, 10°, and 15° under non-cavitating conditions. Increasing AoA strengthens the reconstructed vortex, lowers the mean core-pressure estimate, and increases vortex wandering and pressure fluctuations. Proper orthogonal decomposition (POD)/extended POD reveals a change from a monopole-like pressure-fluctuation pattern at low AoA toward a dipole-like displacement pattern at higher AoA. These patterns are interpreted as qualitative indicators of pressure-based cavitation susceptibility. The DA framework therefore provides a physics-constrained approach for investigating near-field vortex velocity and pressure dynamics that are difficult to obtain from experiments or under-resolved simulations alone.