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TECHNICAL PAPERS

Cavitation Influence on von Kármán Vortex Shedding and Induced Hydrofoil Vibrations

[+] Author and Article Information
Philippe Ausoni, Mohamed Farhat

 Laboratory for Hydraulic Machines, EPFL, Ecole polytechnique fédérale de Lausanne, Avenue de Cour 33bis, 1007 Lausanne, Switzerland

Xavier Escaler, Eduard Egusquiza

Center for Industrial Diagnostics, UPC,  Universitat Politecnica de Catalunya, Avenidad Diagonal 647, 08028 Barcelona, Spain

François Avellan

 Laboratory for Hydraulic Machines, EPFL, Ecole polytechnique fédérale de Lausanne, Avenue de Cour 33bis, 1007 Lausanne, Switzerlandfrancois.avellan@epfl.ch

J. Fluids Eng 129(8), 966-973 (Mar 16, 2007) (8 pages) doi:10.1115/1.2746907 History: Received June 27, 2006; Revised March 16, 2007

The present study deals with the shedding process of the von Kármán vortices at the trailing edge of a 2D hydrofoil at high Reynolds number Reh =25×103 –65×103 . This research focuses mainly on the effects of cavitation and fluid-structure interaction on the mechanism of the vortex generation. The vortex shedding frequency, derived from the flow-induced vibration measurement, is found to follow the Strouhal law provided that no hydrofoil resonance frequencies are excited, i.e., lock-off. For such a regime, the von Kármán vortices exhibit strong spanwise 3D instabilities and the cavitation inception index is linearly dependent on the square root of the Reynolds number. In the case of resonance, the vortex shedding frequency is locked onto the hydrofoil eigenfrequency and the spatial coherence is enhanced with a quasi-2D shape. The measurements of the hydrofoil wall velocity amplitude and phase reveal the first torsion eigenmotion. In this case, the cavitation inception index is found to be significantly increased compared to lock-off conditions. It makes clear that the vortex roll-up is amplified by the phase locked vibrations of the trailing edge. For the cavitation inception index, a new correlation relationship that encompasses the entire range of Reynolds numbers, including both the lock-off and the lock-in cases, is proposed and validated. In contrast to the earlier models, the new correlation takes into account the trailing edge displacement velocity. In addition, it is found that the transverse velocity of the trailing edge increases the vortex strength linearly. This effect is important in the context of the fluid-structure interaction, since it implies that the velocity of the hydrofoil trailing edge increases the fluctuating forces on the body. It is also demonstrated that cavitation developing in the vortex street cannot be considered as a passive agent for the turbulent wake flow. In fact, for fully developed cavitation, the vortex shedding frequency increases up to 15%, which is accompanied by the increase of the vortex advection velocity and reduction of the streamwise vortex spacing. In addition, a significant increase of the vortex-induced vibration level is found at cavitation onset. These effects are addressed and thought to be a result of the increase of the vorticity by cavitation.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

EPFL high speed cavitation tunnel

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Figure 2

Blunt truncated NACA 0009 hydrofoil

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Figure 3

Sketch of the double laser optical probe

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Figure 4

Location of the hydrofoil vibration amplitude measurement points

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Figure 5

Waterfall spectra of the laser vibrometer signals for different upstream velocities

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Figure 6

Shedding frequency of von Kármán vortices and vibration amplitude of the hydrofoil trailing edge for different upstream velocities

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Figure 7

Survey of the hydrofoil wall vibration amplitude for lock-in condition; Cref=12m∕s

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Figure 8

von Kármán vortices cavitation inception index versus the square root of the Reynolds number

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Figure 9

Difference between the cavitation inception number in lock-in condition and the value derived from the linear regression of the cavitation inception numbers in lock-off condition versus the square of the hydrofoil trailing edge vibration velocity scaled by the upstream velocity

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Figure 10

Relative vortex strength for lock-in condition versus the hydrofoil vibration amplitude

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Figure 11

Top-view photographs of von Kármán vortex street cavitation in lock-off conditions

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Figure 12

Waterfall spectra of the laser vibrometer signals for different values of cavitation index and for lock-off condition

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Figure 13

Reduced advection velocity of the vortices and spacing ratio of the vortex street versus cavitation index for lock-off condition

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Figure 14

Top-view photographs of cavitation von Kármán vortex street for lock-in condition (first torsion mode)

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Figure 15

Frame series of von Kármán vortex street for lock-in condition (first torsion mode; Cref=12m∕s) and for two cavitation indices (left) σ∕σi=0.85, (right) σ∕σi=0.7

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Figure 16

Waterfall spectra of the acceleration signals for different values of cavitation index at 12m∕s upstream velocity

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Figure 17

Shedding frequency of von Kármán vortices versus cavitation index at 12m∕s upstream velocity

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