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Research Papers

Numerical Investigation Into the Influence on Hydrofoil Vibrations of Water Tunnel Test Section Acoustic Modes

[+] Author and Article Information
Wei Wang

College of Water Resources and Civil Engineering,
China Agricultural University,
Beijing 100083, China
e-mail: 1943459226@qq.com

Lingjiu Zhou

College of Water Resources and Civil Engineering,
China Agricultural University,
Beijing 100083, China;
Beijing Engineering Research Centre of Safety and Energy Saving Technology for Water Supply Network System,
Beijing 100083, China
e-mail: zlj@cau.edu.cn

Zhengwei Wang

Department of Thermal Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: wzw@mail.tsinghua.edu.cn

Xavier Escaler

Department of Fluid Mechanics,
Universitat Politècnica de Catalunya-Barcelona Tech,
Barcelona 08028, Spain
e-mail: xavier.escaler@upc.edu

Oscar De La Torre

School of Marine Science and Engineering,
Plymouth University,
Plymouth PL4 8AA, UK
e-mail: oscar.delatorre@plymouth.ac.uk

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received September 14, 2018; final manuscript received May 22, 2019; published online June 17, 2019. Assoc. Editor: Sheryl M. Grace.

J. Vib. Acoust 141(5), 051015 (Jun 17, 2019) (8 pages) Paper No: VIB-18-1397; doi: 10.1115/1.4043944 History: Received September 14, 2018; Accepted May 28, 2019

High-speed water tunnels are typically used to investigate the single-phase and two-phase flows around hydrofoils for hydraulic machinery applications but their dynamic behavior is not usually evaluated. The modal analysis of an NACA0009 hydrofoil inside the test section was calculated with a coupled acoustic fluid–structure model, which shows a good agreement with the experimental results. This numerical model has been used to study the influence on the hydrofoil modes of vibration of the acoustic properties of the surrounding fluid and of the tunnel test section dimensions. It has been found that the natural frequencies of the acoustic domain are inversely proportional to the test section dimensions. Moreover, these acoustic frequencies decrease linearly with the reduction of the speed of sound in the fluid medium. However, the hydrofoil frequencies are not affected by the change of the speed of sound except when they match an acoustic frequency. If both mode shapes are similar, a strong coupling occurs and the hydrofoil vibration follows the linear reduction of natural frequency induced by the acoustic mode. If both mode shapes are dissimilar, a new mode appears whose frequency decreases linearly with speed of sound while keeping the acoustic mode of vibration. This new fluid–structure mode of vibration appears in between two hydrofoil structure modes and its evolution with sound speed reduction has been called “mode transition.” Overall, these findings reinforce the idea that fluid–structure interaction effects must be taken into account when studying the induced vibrations on hydrofoils inside water tunnels.

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Figures

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Fig. 1

Cavity density (oblique line) and speed of sound (another line) as a function of void ratio in a bubbly air/water mixture at atmospheric pressure

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Fig. 2

(a) Top view of the computational domain and (b) top view of the hydrofoil surface and measurement points (LE = leading edge and TE = trailing edge) [21]

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Fig. 3

Comparison of numerical and experimental mode shapes for fs1 in (a) air and (b) still water

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Fig. 4

Comparison of numerical and experimental mode shapes for fs2 in (a) air and (b) still water

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Fig. 5

Comparison of numerical and experimental mode shapes for fs3 in (a) air and (b) still water

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Fig. 6

Natural frequencies and mode shapes of the seven first acoustic modes of the water cavity as a function of the speed of sound for a long domain (right-hand side plots and dotted lines) and for a short domain (left-hand side plots and continuous lines)

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Fig. 7

Natural frequencies of the six first hydrofoil modes and of the seven first acoustic modes of the water domain as a function of the speed of sound ratio for the long (a) and the short (b) domains

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Fig. 8

Evolution of the natural frequencies as function of cf for acoustic and structure modes with similar mode shapes: (a) ff2 versus fs1—1st bending, (b) ff5 versus fs2—1st torsion, and (c) ff7 versus fs3—2nd bending

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Fig. 9

First mode transition line with varying cf

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Fig. 10

Second mode transition line with varying cf

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