Three-dimensional evolution and turbulent kinetic energy transport of tip vortex from an elliptical hydrofoil

A non-cavitating tip vortex generated by an elliptical hydrofoil is investigated utilizing tomographic particle image velocimetry (TPIV). Focus is placed on its three-dimensional evolution over a relatively large streamwise region, as well as the transport process of turbulent kinetic energy (TKE). Based on the variations in vortex structure and related vortex properties, three main stages of tip vortex evolution can be identified: formation stage, persistence stage, and decay stage. The boundary between the formation and persistence stages is the position where tip vortex cavitation (TVC) is more prone to incept, attributed to the rapid growth in vortex circulation and vortex-center axial velocity, along with high turbulent fluctuations. During the tip vortex evolution, its swirling momentum significantly influences the axial flow pattern, likely by altering the pressure gradient along the vortex path. TKE transport equation is employed to analyze the turbulent properties of the tip vortex. Flow near the hydrofoil tip is highly turbulent and unsteady, with the local TKE at an excessive level. The local high TKE tends to diffuse into surrounding flow rather than being concentrated within the tip vortex as it moves downstream. TKE is mainly produced on the suction side of hydrofoil, potentially due to local boundary-layer behaviors, and is subsequently transported into the vortex core. As the tip vortex propagates further downstream, the in-core TKE exhibits a decreasing trend, and a relaminarization process appears to occur in far wake region. The flow topology of the tip vortex is examined with the invariants of velocity gradient tensor, providing insights into the topological features during the vortex evolution.