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TECHNICAL PAPERS

Unsteady Tip Leakage Vortex Cavitation Originating From the Tip Clearance of an Oscillating Hydrofoil

[+] Author and Article Information
Masahiro Murayama, Yoshinobu Tsujimoto

 Osaka University, Graduate School of Engineering Science, 1-3, Machikaneyama, Toyonaka, Osaka 560-8531, Japan

Yoshiki Yoshida1

 Osaka University, Graduate School of Engineering Science, 1-3, Machikaneyama, Toyonaka, Osaka 560-8531, Japankryoshi@kakuda.jaxa.jp

1

Author to whom correspondence should be addressed. Current address: Japan Aerospace Exploration Agency, Institute of Aerospace Technology, Kakuda Space Center, Koganezawa 1, Kimigaya, Kakuda, Miyagi 981-1525, Japan.

J. Fluids Eng 128(3), 421-429 (Oct 20, 2005) (9 pages) doi:10.1115/1.2173290 History: Received February 23, 2004; Revised October 20, 2005

Tip leakage vortex cavitations originating from the tip clearance of an oscillating hydrofoil were observed experimentally. It was found that the delay between the unsteady and the steady-state results of the tip leakage vortex cavitation increase, and that the maximum cavity size decreases when the reduced oscillating frequency increases. To simulate the unsteady characteristics of tip leakage vortex cavitation, a simple calculation based on slender body approximation was conducted taking into account the effect of cavity growth. The calculation and experimental results of the cavity volume fluctuation were found to be in qualitative agreement.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Top view of the cavitation tunnel

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Figure 2

Scheme of the test section

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Figure 3

Configuration of the flat plate hydrofoil

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Figure 4

Cross section of the equipment used to produce the pitching oscillation

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Figure 5

Schematic showing the three-bar linkage used to produce the oscillation of the angle of attack, and variation of the angle of attack compared with the sinusoidal curve, for αm=4deg and Δα=2deg

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Figure 6

Photographs of the tip leakage vortex cavitation with various frequencies, for k=0,0.45,0.90, σ=1.0, αm=4deg and Δα=2deg (uncertainty in α=0.1deg, k=0.005). (a) k=0. (b) k=0.45. (c) k=0.90.

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Figure 7

(a) Cavity radius R of the tip leakage vortex cavitation at Z∕C=0.5 and Z∕C=1.0. (b) Blade cavity length l on the blade surface at mid-span. (c) Influence of the oscillating frequency on variation of the cavity radius R at Z∕C=0.5 and Z∕C=1.0, for σ=1.0, αm=4deg, and Δα=2deg (uncertainty in R=0.2mm, α=0.1deg, k=0.005). (d) Influence of the oscillating frequency on variation of the cavity length l at mid-span, for σ=1.0, αm=4deg, and Δα=2deg (uncertainty in l∕C=0.02, α=0.1deg, k=0.005) at k=0.45 and k=0.90 (e) Comparison of the delay of cavity radius R of the tip vortex cavitation with cavity length l at mid-span, for σ=1.0, αm=4deg, and Δα=2deg (uncertainty in α=0.1deg, k=0.005) at k=0.45 and k=0.90.

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Figure 8

Sketch for explanation of the cross plane and the unsteady pressure difference across the tip clearance

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Figure 9

Coordinate of the pitching oscillation of a thin flat plate foil and typical unsteady pressure distribution for Δα=2deg, k=0.90, and t∕T=0. (a) Pitching oscillation of flat plate foil. (b) Unsteady pressure distribution.

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Figure 10

Calculation results of the tip leakage vortex cavitation with various oscillating frequencies, for k=0,0.45,0.90, σ=1.0, αm=4deg, and Δα=2deg, compared with the experimental results shown in Fig. 6. (a) k=0, (b) k=0.45, (c) k=0.90.

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Figure 11

Cavity trajectory at various angles of attack for k=0,0.45,0.90, σ=1.0, αm=4deg, and Δα=2deg (experimental uncertainty in X∕C, Z∕C=0.05, α=0.1deg, k=0.005). (a) Calculation, (b) Experiment.

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Figure 12

Comparison of the variation of the cavity volume between the experiments and calculations, for k=0,0.45,0.90, σ=1.0, αm=4deg, and Δα=2deg. Cavity volume is limited from the leading edge to the length of the two chords (experimental uncertainty in V=200mm3, α=0.1deg, k=0.005). (a) Experiment. (b) Calculation.

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Figure 13

Total amount of the shed vortices ΣΓ∕UC compared between steady (k=0) and unsteady (k=0.90) condition, for σ=1.0, αm=4deg and Δα=2deg

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Figure 14

Comparison of the circulation ΣΓ∕UC on the crossflow plane at the trailing edge (Z∕C=1.0) between the steady (k=0) and unsteady (k=0.90) condition, for σ=1.0, αm=4deg, and Δα=2deg

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