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Chapter 12
Acoustically Induced Vibration and Noise

## Excerpt

Although not the most costly, acoustically induced vibration is probably one of the most common vibration problems in the power and process industries. Vessels, piping systems, valve cavities, heat exchanger internals, ducts and many other components are potential resonators in which standing waves can form, while fans, pumps, valves, elbows, obstruction and discontinuities in flow channels, or even the addition or removal of heat all have the potential to excite these standing waves. Once the resonant conditions are met, the resulting sound intensity in most cases will require remedial action. In some cases, acoustic excitation can cause rapid fatigue failure of piping welded points, valve internal parts and other components.

The first requirement in acoustically induced vibration analysis is to calculate the velocity of sound in the fluid media. The velocity of sound in air at 68 deg. F (20 deg. C) and one atmospheric pressure is 13,500 in/s or 343 m/s. The velocity of sound at other temperatures can be readily calculated from the equation,

$c=(∂p∂ρ)s=γpρ=γGT∝Tγ=Cp∕Cv$
where T is the absolute temperature in either deg. R or deg. K, depending on which unit system is used. At atmospheric pressure and 0 deg. C (32 deg. F) the velocity of sound in water is 55,288 in/s or 1,404 m/s. The velocity of sound in water, steam or water-steam mixture at any given temperature and pressure combination can be calculated from information given in the ASME Steam Table (1979), as outlined in Examples 12.2 and 12.3. A table of velocity of sound in water at selected values of temperatures and pressures are given in Chapter 2, Table 2.1.

In a heat exchanger, the velocity of sound in the direction transversal to the tube bundle axis is decreased by the presence of the tubes. If c0 is the velocity without the tubes and c is the velocity in the presence of tubes, then

$c=c01+σ$
where σ is the ratio of the heat exchanger internal volume occupied by the tubes to the total volume.

• Summary
• Nomenclature
• 12.1 Introduction
• 12.2 Velocities of Sound in Material Media
• Velocity of Sound in Gases
• Velocity of Sound in Liquids
• Velocity of Sound in Water, Steam or Water/Steam Mixture
• Velocity of Sound in Solids
• Apparent Velocity of Sound Through a Tube Bundle
• 12.3 Standing Waves in Pipes and Ducts
• Slender Pipes with Both Ends Open
• Slender Pipes with Both Ends Closed
• Slender Pipes with One end Open and the other Closed
• Slender Annular Pipes and Pipes of Other Cross-Sections
• Example 12.1
• 12.4 Standing Waves in Cavities
• Enclosed Rectangular Cavities
• Rectangular Cavity Opened at End x=0, Closed at All Others
• Rectangular Cavity Opened at End x=0, L1, Closed at All Others
• The Annular Cavity
• Finite Cylindrical Cavity
• The Helmholtz Resonator
• Example 12.2
• Example 12.3
• Example 12.4
• 12.5 Heat Exchanger Acoustics
• Resonance Maps
• Sound Pressure Level
• Example 12.5
• 12.8 Thermoacoustics
• 12.9 Suppression of Acoustic Noise
• 12.10 Response of Structures to Acoustic Waves
• 12.11 Case Studies
• Case Study 12.1: Noise and Vibration Caused by Cavitating Venturi
• Case Study 12.2: Acoustic Noise Generated by a Spherical Elbow
• Case Study 12.3: Acoustic Resonance in Valve Cavity
• Case Study 12.4: Acoustic Resonance in Heat Exchanger
• Case Study 12.5: Valve-Generated Acoustic Waves in a Pipe
• Case Study 12.6: Thermoacoustic Vibration of a Gas Turbine Recuperator
• Appendix 12A: Scattering of Normal Incident Acoustic Wave by a Cylinder
• Reference
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