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Review Article

Flow-Excited Acoustic Resonance Excitation Mechanism, Design Guidelines, and Counter Measures

[+] Author and Article Information
Samir Ziada

e-mail: ziadas@mcmaster.ca

Philippe Lafon

Laboratoire de Mécanique des Structures
Industrielles Durables (LaMSID),
UMR EDF-CNRS-CEA 8193,
EDF R&D,
Clamart, France 92141

1Permanent address: Mechanical Engineering, McMaster University, Hamilton, ON L8S 4L7, Canada.

Manuscript received September 21, 2012; final manuscript received October 15, 2013; published online December 03, 2013. Editor: Harry Dankowicz.

Appl. Mech. Rev 66(1), 010802 (Dec 03, 2013) (22 pages) Paper No: AMR-12-1053; doi: 10.1115/1.4025788 History: Received September 21, 2012; Revised October 15, 2013

The excitation mechanism of acoustic resonances has long been recognized, but the industry continues to be plagued by its undesirable consequences, manifested in severe vibration and noise problems in a wide range of industrial applications. This paper focuses on the nature of the excitation mechanism of acoustic resonances in piping systems containing impinging shear flows, such as flow over shallow and deep cavities. Since this feedback mechanism is caused by the coupling between acoustic resonators and shear flow instabilities, attention is focused first on the nature of various types of acoustic resonance modes and then on the aeroacoustic sound sources, which result from the interaction of the inherently unstable shear flow with the sound field generated by the resonant acoustic modes. Various flow-sound interaction patterns are discussed, in which the resonant sound field can be predominantly parallel or normal to the mean flow direction and the acoustic wavelength can be an order of magnitude longer than the length scale of the separated shear flow or as short as the cavity length scale. Since the state of knowledge in this field has been recently reviewed by Tonon et al. (2011, “Aeroacoustics of Pipe Systems With Closed Branches”, Int. J. Aeroacoust., 10(2), pp. 201–276), this article focuses on the more practical aspects of the phenomenon, including various flow-sound interaction patterns and the resulting aeroacoustic sources, which are relevant to industrial applications. A general design guide proposal and practical means to alleviate the excitation mechanism are also presented. These are demonstrated by two examples of recent industrial case histories dealing with acoustic fatigue failure of the steam dryer in a boiling water reactor (BWR) due to acoustic resonance in the main steam piping and acoustic resonances in the roll posts of the Short Take-Off and Vertical Lift Joint Strike Fighter (JSF).

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References

Figures

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Fig. 1

Schematic presentation of flow-excited acoustic resonance mechanism

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Fig. 2

Flow visualization and acoustic particle velocity at two different instants during the acoustic resonance cycle of a deep cavity. Reprinted from Ref. [13] with permission from ASME.

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Fig. 3

Various arrangements of closed side-branches and associated acoustic pressure (p) distributions of the first acoustic mode. The arrows in the bottom figures indicate the acoustic flux of the resonant acoustic modes. Reprinted from Ref. [35] with permission from Elsevier Publishing.

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Fig. 4

T-junction with a transition zone to combine the flow from two branches into a main pipe. The length of the transition piece is 2LT. The top figure shows the lowest trapped mode along the branches.

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Fig. 5

Ducted shallow cavity, or two orifice plates, together with the pressure distributions of the lowest three longitudinal modes of the duct

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Fig. 6

Ducted axisymmetric shallow cavity showing (a) main dimensions; (b) longitudinal section showing contours of the acoustic pressure of the first trapped cross mode; (c and d) acoustic pressure distributions along the duct length and across the cavity for the first and second cross modes. Adopted from Ref. [67] with permission from Elsevier Publishing.

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Fig. 7

Simulation results of an axisymmetric cavity-duct system with and without mean flow showing contour plots of the radial particle velocity amplitude for the first diametral mode. The contours scale is similar in both figures. L/h = 1 and h/D = 2/12, Adopted from Ref. [69] with permission from Elsevier Publishing.

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Fig. 8

Flow visualization of the lowest three shear-layer modes (m = 1–3) for (a) a coaxial side-branch resonator and (b) two orifice plates in a pipeline. Insets (a1 and a2) are from Ref. [34] with permission; (a3) from Ref. [70] with permission; and (b1–b3) from Ref. [71] with permission from Elsevier Publishing.

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Fig. 9

Finite element simulation of acoustic particle steam lines near a baffle in a pipeline

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Fig. 10

Flow structures during acoustic resonance in a T-junction combining the flow from two pipes into a single downstream pipe (Fig. 4). Top figure shows the lowest observed shear-layer mode A, which produces the strongest acoustic resonance, whereas bottom figure shows a higher shear-layer mode B, producing a weaker resonance than that produced by mode A. Adopted from Ref. [72] with permission from ASME.

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Fig. 11

Acoustic response of coaxial side-branches with sharp edges [29]. n is the acoustic mode number and m is the hydrodynamic mode of the shear layer. Reprinted from Ref. [29] with permission.

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Fig. 12

Pressure contours showing acoustic pressure level as function of frequency and flow velocity for ducted axisymmetric cavity. L/d = 1, h/D = 1/6; n is the acoustic diametral mode number, and m is the hydrodynamic mode number of the shear layer. Reprinted from Ref. [67] with permission from Elsevier Publishing.

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Fig. 13

Resonance characteristics of a pipeline containing double orifice plates (adopted from Ref. [71] with permission from Elsevier Publishing). Solid lines correspond to shear layer modes (m), and dashed lines represent the pipeline acoustic modes (n).

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Fig. 14

Normalized acoustic pressure (P/1/2 ρVB2) of the primary acoustic mode f1 as a function of reduced velocity (VB/f1LT) based on half the transition zone length LT. Reprinted from Ref. [72] with permission from ASME.

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Fig. 15

Normalized acoustic pressure (P/1/2 ρV2) as a function of Strouhal number (fnL/V) for a ducted axisymmetric cavity. L/h = 1, h/D = 1/6. All modes are trapped diametral modes. Reprinted from Ref. [67] with permission from Elsevier Publishing.

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Fig. 16

Acoustic response of coaxial side-branches showing the effect of the branch length LB (i.e., the effect of acoustic attenuation). Δ, LB = 61 cm, test pressure 3.5 bar; ○, LB = 110 cm, test pressure 4 bar; ▲, LB = 158.5 cm, test pressure = 4 bar. Adopted from Ref. [35] with permission from Elsevier Publishing.

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Fig. 17

Design chart of critical Strouhal number (So = f d/Vo) at the onset of resonance for closed side-branches in various arrangements and diameter ratios. Reprinted from Ref. [35] with permission from Elsevier Publishing.

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Fig. 18

Design chart for critical Strouhal number (So = fnL/Vo) at the onset of resonance of the longitudinal resonance of pipelines with axisymmetric shallow cavity as illustrated in Fig. 5

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Fig. 19

Design chart of critical Strouhal number (So = f L/Vo) at the onset of resonance of the trapped cross (or diametral) modes for an axisymmetric shallow cavity in a duct as illustrated in Fig. 6. Data extracted from Ref. [67].

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Fig. 20

Model of the aeroacoustic source resulting from the interaction of a shear layer at the mouth of a deep cavity with the particle velocity u associated with an acoustic resonance in the cavity. Reprinted from Ref. [39] with permission from ASME.

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Fig. 21

Experimentally determined aeroacoustic source for a shear layer at the opening of coaxial side-branches as illustrated in Fig. 3(c). The aeroacoustic source term Q is presented in the Q-complex plane with the acoustic particle velocity (u/V) and the Strouhal number (St) taken as parameters. Reprinted from Ref. [39] with permission from ASME.

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Fig. 22

Oscillation amplitude as function of flow velocity for different depth modes for coaxial branches. The resonance frequency is 137 Hz in all four cases. The symbols indicate measured data, and the lines are computed from the experimentally determined source term presented in Fig. 21. + LB1 = LB2 = 0.6 m; ○ LB1 = 0.6 m and LB2 = 3LB1; • LB1 = 0.6 m and LB2 = 5LB1; × LB1 = LB2 = 1.8 m. Reprinted from Ref. [39] with permission from ASME.

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Fig. 23

Model of the aeroacoustic source resulting from the coupling of the shear layer at a cavity opening with the particle velocity u associated with a longitudinal resonance mode of a pipeline

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Fig. 24

Experimentally determined aeroacoustic source for a cavity shear layer coupling with longitudinal acoustic modes of a pipeline as illustrated in Fig. 5(a). The aeroacoustic source term Q is presented in the Q-complex plane with the acoustic particle velocity (u/V) and the Strouhal number (St) taken as parameters. Reprinted from Ref. [57] with permission from ASME.

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Fig. 25

Real part of source term Q for a cavity shear layer coupling with longitudinal acoustic modes of a pipeline as illustrated in Fig. 5(a). Real (Q) is plotted as function of Strouhal number with the acoustic particle velocity (u/V) taken as a parameter. Reprinted from Ref. [57] with permission from ASME.

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Fig. 26

Oscillation amplitude as function of flow velocity for longitudinal acoustic resonance of a pipeline housing a cavity. The symbols indicate measured data, and the lines are computed from the experimentally determined source term presented in Fig. 25.

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Fig. 27

Pulsation amplitudes P1 and P2 at the closed ends of asymmetrical side-branches of length L1 and L2. (a) Coaxial side-branches. (b) Two tandem side-branches in close proximity with ℓ/L=0.15. The length of one side-branch was increased/decreased in steps while the other branch was shortened/elongated accordingly by an equal length to keep the resonance frequency constant. D = 89 mm, d = 51 mm, (L1 + L2) = 1.57 m. Adopted from Refs. [12] and [41] with permission.

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Fig. 28

Effect of upstream edge geometry on the excitation of trapped cross modes of the axisymmetric ducted cavity. (a) Effect of rounding off the upstream edge with a radius r = 0.2 L; (b) effect of a 17 deg chamfer of length 0.38 L; (c) effect of curved tooth and delta spoilers. Cavity parameters as shown in Fig. 6 are L/h = 1, h/D = 1/6, D = 152 mm.

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Fig. 29

Photographs of the curved tooth and the delta spoilers attached to the upstream cavity corner. The arrows indicate the flow direction. Reprinted from Ref. [82] with permission from ASME.

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Fig. 30

Effect of the curved tooth and delta spoilers on the pressure drop over the cavity. Cavity parameters as shown in Fig. 6 are L/h = 1, h/D = 1/6, D = 152 mm. Reprinted from Ref. [82] with permission from ASME.

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Fig. 31

Schematic of the upper section of a boiling water reactor (BWR) showing the steam separator, steam dryer, inlet nozzle to a main steam line (MSL), and the path of steam flow through the dryer and into the MSL. Reprinted from Ref. [92] with permission from the US NRC and ASME.

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Fig. 32

Steam dryer assembly of Quad Cities unit 2 (top left) and details of the acoustic fatigue failure on the outer hood. Reprinted from Ref. [95] with permission from Exelon Nuclear and GEH.

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Fig. 33

Power spectral density of fluctuating pressure on the dryer showing the tonal excitation near 150 Hz. Reprinted from Ref. [96] with permission from Exelon Nuclear.

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Fig. 34

Locations of the safety relief valves on the main steam lines. Reprinted from Ref. [13] with permission from ASME.

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Fig. 35

Geometry of the standpipe of safety relief valves. Left: original design; middle: alternative design but impractical in the present case; right: final solution with acoustic side-branch [99].

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Fig. 36

Rolls-Royce Vertical Lift System® showing the engine and roll posts configuration of the joint strike fighter.2

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Fig. 37

Geometry of test section showing the inner cylinder, splitter plates, and microphone locations m1 and m2. The splitter plates were not used in the original design but were added later as a countermeasure. Reprinted from Ref. [36] with permission from Elsevier Publishing.

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Fig. 38

Frequency spectrum and mode shape for the first acoustic mode f1. Reprinted from Ref. [36] with permission from Elsevier Publishing.

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Fig. 39

Overview of the system acoustic response. Top figure shows acoustic resonance (lock-in) frequency, with the straight lines presenting the Strouhal numbers St = 0.55 and 0.27, and bottom figure shows dimensionless acoustic pressure as functions of flow velocity. Reprinted from Ref. [36] with permission from Elsevier Publishing.

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Fig. 40

Sound pressure level in dB measured at the branch closed end. Reprinted from Ref. [36] with permission from Elsevier Publishing.

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Fig. 41

Pressure spectra at the end of (a) the shortened and (b) the unchanged branches for V = 30 m/s, ΔL/LB = 42%. (c) Acoustic pressure (□) at f'1 in the unchanged branch and (×) at f"1 in the shortened branch for ΔL/LB = 42%. Reprinted from Ref. [36] with permission from Elsevier Publishing.

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Fig. 42

Acoustic pressure of the duct with and without splitter plates. Reprinted from Ref. [36] with permission from Elsevier Publishing.

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