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Research Papers: Fluid-Structure Interaction

Flow-Excited Acoustic Resonance of Trapped Modes of a Ducted Rectangular Cavity

[+] Author and Article Information
Michael Bolduc, Samir Ziada

Department of Mechanical Engineering,
McMaster University,
Hamilton, ON L8S 4L8, Canada

Philippe Lafon

IMSIA/EDF R&D,
Clamart 92141, France

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received August 21, 2015; final manuscript received December 4, 2015; published online February 5, 2016. Assoc. Editor: Tomomichi Nakamura.

J. Pressure Vessel Technol 138(3), 031303 (Feb 05, 2016) (14 pages) Paper No: PVT-15-1196; doi: 10.1115/1.4032281 History: Received August 21, 2015; Revised December 04, 2015

Flow over ducted cavities can lead to strong resonances of the trapped acoustic modes due to the presence of the cavity within the duct. Aly and Ziada (2010, “Flow-Excited Resonance of Trapped Modes of Ducted Shallow Cavities,” J. Fluids Struct., 26(1), pp. 92–120; 2011, “Azimuthal Behaviour of Flow-Excited Diametral Modes of Internal Shallow Cavities,” J. Sound Vib., 330(15), pp. 3666–3683; and 2012, “Effect of Mean Flow on the Trapped Modes of Internal Cavities,” J. Fluids Struct., 33, pp. 70–84) investigated the excitation mechanism of acoustic trapped modes in axisymmetric cavities. These trapped modes in axisymmetric cavities tend to spin because they do not have preferred orientation. The present paper investigates rectangular cross-sectional cavities as this cavity geometry introduces an orientation preference to the excited acoustic mode. Three cavities are investigated, one of which is square while the other two are rectangular. In each case, numerical simulations are performed to characterize the acoustic mode shapes and the associated acoustic particle velocity fields. The test results show the existence of stationary modes, being excited either consecutively or simultaneously, and a particular spinning mode for the cavity with square cross section. The computed acoustic pressure and particle velocity fields of the excited modes suggest complex oscillation patterns of the cavity shear layer because it is excited, at the upstream corner, by periodic distributions of the particle velocity along the shear layer circumference.

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References

Figures

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Fig. 1

Illustration of the fluid-resonant feedback mechanism [5]

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Fig. 2

Geometry of cavity–duct setup [1]

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Fig. 3

Dimensions of cavity geometry and locations of pressure transducers

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Fig. 4

Detailed exploded assembly of the cavity–duct system including cavity side walls, pipes, and flanges

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Fig. 5

Mode shapes of the four trapped acoustic modes at the center of the rectangular, W/H = 0.9, cavity

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Fig. 6

Schematic of uniform acoustic particle velocity, Ua, triggering an axisymmetric shear layer at upstream separation edge

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Fig. 7

Top left: dimensionless acoustic pressure distribution; top right: acoustic particle velocity magnitude; bottom left: radial acoustic particle velocity distribution; and bottom right: radial acoustic particle velocity along shear layer circumference. All figures correspond to 0.2 mm downstream from the inlet of the cavity.

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Fig. 8

Radial profile of mean flow velocity measured one pipe diameter upstream from the edge of the square cavity at resonance conditions (flow velocity = 61 m/s)

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Fig. 9

Sound pressure level (reference: 20 μPa) contour plot of the aeroacoustic response for the W/H = 0.9 cavity

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Fig. 10

Aeroacoustic response of the rectangular, W/H = 0.95, cavity. The recorded value is the maximum acoustic pressure from each of the four dynamic pressure transducers at the associated natural frequency. Modes 1–3 recorded from PT3 and PT4; mode 4 recorded from PT1 and PT2.

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Fig. 11

Aeroacoustic response of the rectangular, W/H = 0.90, cavity. The recorded value is the maximum acoustic pressure from each of the four dynamic pressure transducers at the associated natural frequency. Modes 1–3 recorded from PT3 and PT4; mode 4 recorded from PT1 and PT2.

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Fig. 12

Aeroacoustic response of the square, W/H = 1, cavity. The recorded value is the maximum acoustic pressure from each of the four dynamic pressure transducers at the associated natural frequency. Modes 1–3 recorded from PT3 and PT4; mode 4 recorded from PT1 and PT2.

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Fig. 13

Dimensionless acoustic pressure distribution 0.2 mm downstream from the upstream edge and radial acoustic particle velocity distribution along the shear layer circumference for the first (top) and second (bottom) acoustic modes for the rectangular, W/H = 0.9, cavity

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Fig. 14

Spectra (a) and time signals (b) taken simultaneously to demonstrate the simultaneous excitation of the third (PT3) and the fourth (PT2) acoustic modes for the square cavity at 92 m/s

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Fig. 15

Dimensionless acoustic pressure distribution 0.2 mm downstream from the upstream edge and radial acoustic particle velocity distribution along the shear layer circumference for the third (top) and fourth (bottom) acoustic modes for the square, W/H = 1, cavity

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Fig. 16

Instantaneous time signals at 63 m/s detailing the degenerate acoustic mode's spinning behavior. Pmax is the maximum pressure obtained from corner pressure transducers.

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Fig. 17

Summed orthogonal modes 0.2 mm from upstream edge, normalized by maximum amplitude from the resultant spinning mode

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Fig. 18

Instantaneous pressure contours of the spinning degenerate mode with phase, θ, represented through the summation of two orthogonal modes with a 90 deg temporal phase shift

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Fig. 19

Instantaneous radial particle velocity contours of the spinning degenerate mode with phase, θ, represented through the summation of two orthogonal modes with a 90 deg temporal phase shift

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