Tomographic particle image velocimetry investigation on flow characteristics and pressure–velocity relation of a near-field tip vortex

The non-cavitating tip vortex in the near field of an elliptical hydrofoil is studied utilizing tomographic particle image velocimetry. Both the instantaneous and time-averaged flow fields are analyzed to elucidate the flow characteristics of the near-field tip vortex. The tip vortex is mainly formed on the suction side of hydrofoil and exhibits a tube-like shape. The turbulence intensity is at a relatively high level around the hydrofoil tip due to the roll-up process of the separated shear layers from the pressure side. With increasing angle of attack, the initiating position of the tip vortex moves upstream along the hydrofoil outline. In the near field, the axial flow within the tip vortex manifests a jet-like profile at higher angles of attack (α≥10°), and the majority of the vorticity is contained within the vortex core. A special position is identified during the streamwise evolution of the tip vortex, where the vortex circulation reaches its local maximum for the first time and the tip vortex cavitation is more prone to incept. In the vicinity of this crucial position, the pressure–velocity relation is derived along the vortex centerline by combining the three-dimensional measured velocity fields with the governing equations. It is revealed that the mean static pressure is directly related to the local mean axial velocity, adhering to the form of Bernoulli's equation. Conversely, corresponding pressure fluctuation depends on both the mean and fluctuating parts of the local axial velocity.