Prediction method of tip vortex circulation based on hydrofoil load

Abstract

In this paper, a theoretical derivation from the perspective of the force on the slender bodies arranged along the hydrofoil span is performed to explain why the vortex circulation Γvortex should theoretically be equal to the maximum bound circulation Γ0 around the hydrofoil. Then, a more accurate and operable prediction formulation based on hydrofoil load, Γvortex=kΓ0‾, is proposed, where k = 0.9–1. Γ0‾ is the averaged hydrofoil circulation along spanwise direction and its value can be obtained easily from hydrofoil load. To validate our new formulation, two typical vortex flows, i.e., tip leakage vortex (TLV) flow and tip vortex (TV) flow, are simulated with large eddy method. Our numerical results confirm that the variations of hydrofoil load along span would lead to streamwise vorticity, and then the rolling-up of latter leads to the vortex formation (Green, 1995). However, since the influential region of vortex is limited that not all streamwise vorticity could be entrained into the vortex and there are viscous and dissipation effects, the actual Γvortex cannot reach Γ0 but it is quite close to Γ0‾. The prediction formulation agrees well with the numerical results and available measured data.