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Research Papers: Multiphase Flows

# Experimental Study on the Effect of Number of Bubble Occurrences on Tip Vortex Cavitation Noise Scaling Law

[+] Author and Article Information
Jisoo Park

Department of Naval Architecture and
Ocean Engineering,
Seoul National University,
599 Gwanak-ro, Gwanak-gu,
Seoul 151-744, South Korea

Woojae Seong

Professor
Department of Naval Architecture and
Ocean Engineering,
Seoul National University,
599 Gwanak-ro, Gwanak-gu,
Seoul 151-744, South Korea
e-mail: wseong@snu.ac.kr

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 30, 2016; final manuscript received December 24, 2016; published online April 5, 2017. Assoc. Editor: Satoshi Watanabe.

J. Fluids Eng 139(6), 061303 (Apr 05, 2017) (15 pages) Paper No: FE-16-1204; doi: 10.1115/1.4035929 History: Received March 30, 2016; Revised December 24, 2016

## Abstract

A novel scaling law for the tip vortex cavitation (TVC) noise was determined, employing the Rankine vortex model, the Rayleigh–Plesset equation, the lifting surface theory, the boundary layer effect, and the number of bubbles generated per unit time $(N0)$. All terms appearing in the final derived scaling law are well known three-dimensional (3D) lifting surface parameters, except for $N0$. In this study, the dependence of $N0$ with inflow velocity and hydrofoil dimension is investigated experimentally while trying to retain the same TVC patterns among different experimental conditions. Afterward, the effect of $N0$ on the TVC noise is analyzed. Optimal TVC observation conditions are determined from consideration of cavitation number and Reynolds number of two comparable conditions. Two geometrically scaled hydrofoils are concurrently placed in a cavitation tunnel for the hydrofoil size variation experiment. Wall effects and flow field interaction are prevented with the aid of computational fluid dynamics. Images taken with a high‐speed camera are used to count $N0$ by visual inspection. The noise signals at all conditions are measured and an acoustic bubble counting technique, to supplement visual counting, is devised to determine $N0$ acoustically from the measured noise data. The broad-band noise scaling law incorporating $N0$ and the International Towing Tank Conference (ITTC) cavitation noise estimation rule for hydrofoil are both applied to estimate the TVC noise level for comparison with the measured noise level. The noise level estimated by the broad-band noise scaling law accounting for the acoustically estimated $N0$ gives the best agreement with the measured noise level.

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## Figures

Fig. 1

Photos of overall experimental setup and angle of attack adjusting device

Fig. 2

(a) Axial velocity and (b) pressure distribution following the tip vortex line for various simulation conditions

Fig. 3

Top view of foil locations in the cavitation tunnel (computational environment: 0.6 m (W) × 1.25 m (L))

Fig. 4

Flow field around the rear hydrofoil for 3 m/s inflow velocity (reference condition)

Fig. 5

Flow field calculation results: (a) standard, Δy=31 cm; (b) case 1, Δy=26 cm; (c) case 2, Δy=21 cm; (d) case 3, Δy=16 cm; and (e) case 4, Δy=11 cm

Fig. 6

Final arrangement of two foils: (a) top view and (b) side view

Fig. 7

TVC patterns at developed TVC conditions with inflow velocity variation for 30 cm span hydrofoil

Fig. 8

TVC patterns at developed TVC conditions with inflow velocity variation for 45 cm span hydrofoil

Fig. 9

TVC patterns at developed TVC conditions at fixed inflow velocity of 3.5 m/s for (a) 15 cm and 30 cm and (b) 15 cm and 45 cm span hydrofoils

Fig. 10

Elongated bubble developed from one nucleus. Images were obtained at developed TVC condition for 45 cm span hydrofoil and 3.5 m/s inflow velocity.

Fig. 11

Number of generated bubbles per unit time with inflow velocity variation for (a) 30 cm and (b) 45 cm span hydrofoils after time averaging. Arrows indicate the representative intervals selected from each condition.

Fig. 12

Number of generated bubbles per unit time with hydrofoil dimension variation for (a) 15 cm and 30 cm and (b) 15 cm and 45 cm span hydrofoils after time averaging. Arrows indicate the representative intervals selected from each condition.

Fig. 13

Number of bubbles generated per unit time with (a) inflow velocity variation at selected intervals as representative value for 30 cm and 45 cm span hydrofoils and (b) hydrofoil dimension variation at selected intervals as representative value for 3.5 m/s inflow velocity

Fig. 14

(a) Spectrogram at developed TVC condition for 3.5 m/s inflow velocity and (b) pressure amplitude in time domain, integrated over 2–100 kHz frequency range. A span length of hydrofoil is 45 cm.

Fig. 15

Number of bubbles generated per unit time with inflow velocity variation estimated using the acoustic bubble counting technique. Span lengths of hydrofoils are (a) 30 cm and (b) 45 cm.

Fig. 16

Signal processed time-series data

Fig. 17

PSD with development of TVC for (a) 15 cm, (b) 30 cm, and (c) 45 cm span hydrofoils at 3.5 m/s inflow velocity

Fig. 18

Estimated target noise from the ITTC noise estimation rule and the broad-band noise scaling law, and comparison with the measured target noise: Δf = 1 Hz. Span lengths of hydrofoils are (a) 30 cm and (b) 45 cm. The number of generated bubbles is visually measured.

Fig. 19

Estimated target noise from the ITTC noise estimation rule and the broad-band noise scaling law, and comparison with measured target noise; Δf = 1 Hz. The inflow velocity is fixed as 3.5 m/s. The number of generated bubbles is visually measured.

Fig. 20

Estimated target noise from the ITTC noise estimation rule and the broad-band noise scaling law, and comparison with the measured target noise: Δf = 1 Hz. Span lengths of hydrofoil are (a) 30 cm and (b) 45 cm. The number of generated bubbles is acoustically estimated. Maximum error range: (a) 4.4 dB and (a′) 4.3 dB and (b) 7.37 dB and (b′) 2.05 dB.

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