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The effect of cavitation on the natural frequencies of a

hydrofoilO. de la Torre, X. Escaler, E. Egusquiza

Technical University of Catalonia

M. Dreyer, M. FarhatÉcole Polytechnique Fédérale de Lausanne.

13th – 16th August 2012 Singapore

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• Introduction• Objective• Experimental methodology• Results & Discussion• Conclusions

Summary

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• Structural natural frequencies come up as paramount variables in engineering design phase.

• When dealing with submerged bodies AM

Introduction

𝒇=√ 𝒌𝒎𝒎

𝒇 𝒇=√ 𝒌𝒎𝒎+𝒎𝒇

Vacuum Submerged in a fluid

FRRFrequency

Reduction Ratio

𝐹𝑅𝑅=|𝑓 𝑓 − 𝑓 𝑎𝑖𝑟|

𝑓 𝑎𝑖𝑟

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• How does it work when we have a two-phase flow? i.e. Cavitation– Submerged structures (offshore

platforms…)– Hydraulic machinery (pumps,

turbines…)

Introduction

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• To study the effect of partial sheet cavitation and supercavitation on the three first natural frequencies of a NACA0009 hydrofoil in a cavitation tunnel.

Objective

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• Choose and test a suitable excitation system:– Enough excitation force– Adequate frequency range excitation– On board system (embedded in the

hydrofoil)– The flow is not perturbed

Experimental methodology

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• PZT Patches:– Flexible Mountable on non-flat

surfaces– Based on piezo effect Used as

actuators or sensors– Easiness to isolate the electrical

connectors– They accept different excitation signals

Experimental methodology

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• Test rig and hydrofoil dimensions:– LMH High Speed Cavitation Tunnel

• Test section of 150 x 150 x 750 mm• Tests at 14 m/s free stream velocity

– NACA0009 aluminum hydrofoil

Experimental methodology

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Experimental test definition:• Still air/water tests (Reference)

– Air – Water– Half wetted

• Flowing water tests– Partial cavitation (l/c=X)– Supercavitation

Experimental methodology

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• Frequency extraction methods:

Experimental methodology

Response signal

Excitation signal

Chirp (from f1 to f2 linearly in ∆t)

Crosscorrelation + Spline

STFT

Natural frequencie

s

Good agreeme

nt

CDIFUPCResults &

Discussion• Still air/water tests• All the frequencies are reduced with water• The FRR for half-wetted is closer to water

condition than to air condition• The FRR is different depending on the

modef1 f2 f3

Hz FRR Hz FRR Hz FRR

AIR 270,2

0 1018,6

0 1671,0

0

HALF WETTED 163,0

0,40

755,0 0,26

1113,6

0,33

WATER 130,2

0,52

614,8 0,40

886,0 0,47

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• Flowing water tests• The presence of partial cavitation has an effect in

all the modes• The FRR decreases when the cavity grows• Supercavitation shows the minimum FRR close to

air condition• The FRR depends on the mode, the cavity size and

the angle

Results & discussion

f1 f2 f3Incidende angle

1° Hz FRR Hz FRR Hz FRRPartial Cavitation

(l/c = 0,44) 135.4 0,50 677.6 0,33 996.8 0,40Supercavitation 248.7 0,08 918.4 0,10 1460 0,13

f1 f2 f3Incidence angle

2° Hz FRR Hz FRR Hz FRR

Partial Cavitation (l/c = 0,75) 142.0 0,47 720,3 0,29 1050,

3 0,37

Supercavitation 235,2 0,13 879,9 0,14 1402,3 0,16

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• FRR comparison at 2º for the three modes

Results & discussion

CDIFUPCConclusions

• A system based on PZT patches has been developed and used to perform hydrofoil experimental modal analysis without altering the flow field.

• The three first natural frequencies of the hydrofoil have been found under partial cavitation and supercavitation conditions.

• A partial cavity provokes a reduction of the added mass effect with respect to the still water case.

• Supercavitation presents the minimum added mass effects closer to air conditions than to half wetted conditions.

• The added mass effect depends on the particular mode of vibration, but other variables also play a role:

• The density of the two-phase flow inside and outside the cavities

• The surface of the hydrofoil covered by the cavity and its location

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…Questions?