Cavitation in Kármán Vortices and Flow Induced Vibrations

The shedding process of the Kármán vortices at the trailing edge of a 2D hydrofoil at high Reynolds numbers is investigated. The focus is put on the effect of the cavitation on the vortex street morphology. A direct insight is also provided on the role of the structural vibration on the cavitation inception. The shedding frequency, derived from the measurement of flow induced vibration, is found to follow the Strouhal law as far as none of resonance frequencies of the hydrofoil is excited. For lock-off condition, PIV measurements in cavitation free regime and high speed visualizations for developed cavitation reveal strong spanwise 3D instabilities. The comparison of instantaneous velocity fields in cavitation free regime and images of cavitating vortices does not show notable influence of the cavitation on the vortex street morphology. It is also observed that the cavitation inception index increases linearly with the square root of the Reynolds number. For Reynolds numbers ranging from 35’000 to 40’000, the torsion mode of the hydrofoil is excited with a substantial increase of the vibration level. In this case, the spatial coherence of the Kármán vortices is enhanced with a quasi 2D shape and the shedding frequency is locked onto the vibration frequency. The cavitation inception index is found to be significantly increased compared to lock-off conditions. It is thought that the vortex roll-up is amplified by the phase locked vibration of the trailing edge. Former model, successful in describing the cavitation inception for fixed bluff bodies, is extended for taking into account the hydrofoil trailing edge vibration velocity. In addition, we have found that the vortices strength increases for lock-in condition and is directly related to the vibration velocity of the trailing edge normalized by the upstream velocity. INTRODUCTION Vortex shedding is a dominant feature of twodimensional body wakes. Although the wakes have been extensively studied for flow around cylinders or wedges, only few experimental works are related to the effect of cavitation on the Kármán vortex shedding process. It is known that the cavitation is not a passive agent for the visualization of the turbulent wake flow. But as matters stand, the influence of the cavitation on the wake morphology has remained unclear. The role of the cavitation in vortices 3D aspect is indeed an open question. The wake cavitation inception is also investigated. The role of the structural vibration on both the cavitation inception and vortex strength is pointed out. Placed in a fluid stream, bluff bodies generate separated flow over a substantial proportion of their surface that extends to their wake. The detachment of the boundary layers on both upper and lower surfaces forms two shear layers generating, above critical values of Reynolds number, a periodic array of discrete vortices termed Kármán street. In a range of upstream velocity, the vortex shedding frequency is known to follow the Strouhal law. From a hydrodynamic point of view, the instability of the shear layer separating from a circular cylinder has been extensively investigated; see Williamson [14] for a comprehensive review. Many authors observe that the wake structure may exhibit 3D aspect even if the obstacle and the upcoming flow are 2D. Gerrard [7] observes curved vortices and suspects that the cylinder end conditions might be the cause. Gerich et al. [5], Prasad et al. [10] and Williamson [13] find that the spanwise end conditions control the primary