Cavitation in Ka´rma´n Vortex Shedding From 2D Hydrofoil: Wall Roughness Effects

The present study deals with the shedding process of the Ka´rma´n vortices in the wake of a NACA0009 hydrofoil at high Reynolds number, Re_h = 25·10³ − 65·10³. This research addresses the effects of the foil leading edge roughness on the wake dynamic with a special focus on the vortex shedding frequency, vortex-induced vibration and three-dimensionality of vortex shedding. For smooth leading edge, the shedding frequency of Ka´rma´n vortices occurs at constant Strouhal number, St = 0.24. The wake exhibits 3D instabilities and the vortex induced vibration signals strong modulation with intermittent weak shedding cycles. Direct relation between vibration amplitude and vortex spanwise organization is shown. In the case of rough leading edge, the Ka´rma´n shedding frequency is notably decreased compared to the smooth one, St = 0.18. Moreover, the vortex induced vibration level is significantly increased and the vibration spectra sharply peaked. The occurrence of vortex dislocations is shown to be less frequent with the roughness. The shedding of the vortices is considered on the whole as in phase along the hydrofoil span. Obviously, the shedding process of the Ka´rma´n vortices is highly related to the state of the boundary layer over the entire hydrofoil. It is believed that in the case of smooth leading edge, slight spanwise non-uniformities in the boundary-layer flow lead to slight instantaneous variation in vortex shedding frequency along the span which is enough to trigger vortex dislocations. On the contrary, for the rough leading edge, the location of transition to turbulence is uniformly forced which leads to the reduction of the spanwise boundary-layer non-uniformities and therefore to the enhancement of the coherence length of the Ka´rma´n vortices.