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Review Article

Review of Flow-Excited Resonance of Acoustic Trapped Modes in Ducted Shallow Cavities

[+] Author and Article Information
Kareem Aly

Mechanical Engineering,
Cairo University,
Giza 12613, Egypt

Samir Ziada

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

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received July 24, 2015; final manuscript received December 5, 2015; published online April 28, 2016. Assoc. Editor: Tomomichi Nakamura.

J. Pressure Vessel Technol 138(4), 040803 (Apr 28, 2016) (16 pages) Paper No: PVT-15-1168; doi: 10.1115/1.4032251 History: Received July 24, 2015; Revised December 05, 2015

Flow-excited resonances of acoustic trapped modes in ducted shallow cavities are reviewed in this paper. The main components of the feedback mechanism which sustains the acoustic resonance are discussed with particular emphasis on the complexity of the trapped mode shapes and the strong three-dimensionality of the cavity flow oscillations during the resonance. Due to these complexities of the flow and sound fields, it is still difficult to theoretically or numerically model the interaction mechanism which sustains the acoustic resonance. Strouhal number and resonance amplitude charts are therefore included to help designers avoid the occurrence of resonance in new installations, and effective countermeasures are provided which can be implemented to suppress trapped mode resonances in operating plants.

Copyright © 2016 by ASME
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References

Figures

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Fig. 1

Diametral and circular acoustic modes of cylindrical duct. Areas with same color are in-phase and areas with different colors are out-of-phase.

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Fig. 2

Variation of the first trapped mode frequency with the length of the main pipes. L/d = 1 and d/D = 2/12 [30].

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Fig. 3

Mode shapes of the first, second, and third acoustic trapped modes. L/d = 1 and d/D = 2/12. The gray scale indicates the relative pressure amplitude with the maximum equal to ±1.0 [30]. (a) First diametral mode, (b) second diametral mode, and (c) third diametral mode.

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Fig. 4

Contour plots of the radial particle velocity for a cavity depth to length ratio = 1 and cavity depth-to-pipe diameter ratio = 1/6 [30]

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Fig. 5

Contour plots of the amplitude of the vertical particle velocity for the first trapped mode of a planar cavity–duct system. The contours demonstrate the relative amplitude of the particle velocity. The color scale indicates the relative pressure amplitude with the maximum equal to ±1.0 [47].

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Fig. 6

Growth rate for different perturbation Strouhal number: o—axisymmetric nozzle and x—plane nozzle [73]

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Fig. 7

Strouhal number of the impinging free shear layer oscillation as a function of the dimensionless impinging length [84]

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Fig. 8

Strouhal number of cavity oscillation over a range of Mach number. Different data symbols correspond to different sources [87].

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Fig. 9

Vortical structure of the first free shear layer mode at the mouth of a resonant closed side-branch [21]

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Fig. 10

Vortical structure of the second free shear layer mode at the mouth of a resonant closed side-branch [21]

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Fig. 11

Schematic presentation of a high-pressure by-pass control valve [8]

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Fig. 12

Strouhal numbers and sound pressure level as functions of the flow rate for the two lowest resonance modes of the model valve [8]

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Fig. 13

Water fall plot and 2D pressure contours for an axisymmetric ducted cavity with a length-to-depth ratio of 1 and a depth-to-pipe diameter ratio of 2/12. m is the diametral mode number, and n is the free shear layer mode [30].

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Fig. 14

Dimensionless acoustic pressure as function of the Strouhal number for an axisymmetric ducted cavity with a length-to-depth ratio of 1 and a depth-to-pipe diameter ratio of 2/12 [30]

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Fig. 15

Effect of cavity length (L) on the maximum dimensionless pressure for the first diametral mode (n = 1) of an axisymmetric ducted cavity with a length-to-depth ratio of 1. n is the free shear layer mode [30].

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Fig. 16

Strouhal numbers of cavity shear layer modes recorded at the maximum resonance amplitude of axisymmetric ducted shallow cavities [30]

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Fig. 17

Maximum dimensionless acoustic pressure of the first diametral mode for different ratios of cavity depth-to-pipe diameter (d/D). (a) Resonance excited by the first shear layer mode (n = 1) and (b) resonance excited by the second shear layer mode (n = 2) [30].

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Fig. 18

Acoustic pressure distributions of degenerative modes of a square cavity attached to circular ducts [48]

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Fig. 19

Distribution of the acoustic pressure amplitude over the outer perimeter for a partially spinning fist mode of an axisymmetric ducted cavity. Results are generated for an amplitude ratio of 0.4 between the two degenerative modes [46].

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Fig. 20

Distribution of the acoustic pressure phase over the outer perimeter for a partially spinning fist mode of an axisymmetric ducted cavity. Results are generated for an amplitude ratio of 0.4 between the two degenerative modes [46].

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Fig. 21

Instantaneous pressure distribution of the spinning mode of a square cavity over half the oscillation cycle [48]

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Fig. 22

Instantaneous radial acoustic particle velocity distribution of the spinning mode of a square cavity over half the oscillation cycle. The images correspond to Fig. 21 [48].

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Fig. 23

Mapping of the shear layer vorticity during the degenerative mode resonance: (a) schematic of the geometry showing the image field and (b) vorticity contours at four azimuthal locations taken at different phase angles along the acoustic resonance cycle [109]

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Fig. 24

Cavity edge chamfer geometry

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Fig. 25

Example of leading edge spoilers used to suppress the excitation of trapped modes in an axisymmetric ducted cavity [110]: (a) curved spoiler and (b) delta spoiler

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