Circulation budget analysis of the leading-edge vortex in a Wells turbine under steady inflow conditions

Due to the narrow operating range with the high efficiency of Wells turbines, the performance of Oscillating Water Column (OWC) systems is extremely limited by the stall issue. In this study, a detailed investigation on the flow physics at three typical flow rates corresponding to the design, stall inception, and deep stall conditions is performed, aiming to explore the mechanisms governing the evolution of the leading-edge vortex in terms of the circulation budget analysis. For this purpose, 3D unsteady Reynolds-averaged Navier-Stokes equations with the shear-stress-transport turbulence model are solved for a monoplane Wells turbine with high solidity under the steady-state inflow conditions. The numerical results show encouraging agreement with the available experimental data. The transient flow behaviors of stall inception and deep stall mode are captured by the Proper Orthogonal Decomposition (POD) method. Furthermore, the contributions of the spanwise convection of the vorticity gradient, vorticity tilting term, and the shear layer flux to the circulation of the leading-edge vortex are quantitatively determined within the spanwise control surface. The results indicate that, for stall inception condition, the high turbulent kinetic energy regions are attached to the leading edge of the suction surface with a disturbance of 0.33 times of the rotor frequency. The leading-edge vortex appears after the turbine stall, and its stable development time is less than 1/4 of the rotor period. Although leading-edge vortex occurs periodically after the first shedding with a significant decrease of circulation, it is almost not reattached to the blade surface, which speeds up the shedding and vorticity dissipation. The first shedding of the leading-edge vortex is related to the increase of radial vorticity gradient, but not directly related to the radial velocity. Furthermore, the spatiotemporal distribution of the circulation is similar to the spanwise convection, but there is a phase difference. In addition, the tilting term changes greatly in the evolution of the leading-edge vortex, indicating that the tangential and axial vorticity are tilted, which is verified by the spatial streamlines.