MECH 482 â Noise Control Week 11 Silencers and Muffling Devices
MECH 482 – Noise Control Week 11 Silencers and Muffling Devices March 23, 2015 Page 1 Introduction • A muffling device (silencer) allows the passage of fluid while at the same time restricting the free passage of sound. • Muffling devices may function in any one or any combination of three ways: suppress the generation of noise; attenuate noise already generated; carry or redirect noise away from sensitive areas. • Careful use of all three methods for achieving adequate noise reduction is important in the design of muffling devices. March 23, 2015 Page 2 Introduction • Muffling devices are commonly used to reduce noise associated with internal combustion engine exhausts, high pressure gas or steam vents, compressors and fans. • Muffling devices might also be used where direct access to the interior of a noise containing enclosure is required, but through which no steady flow of gas needs to be maintained. • For example, an acoustically treated entry way between a noisy and a quiet area in a building or factory might be considered as a muffling device. March 23, 2015 Page 3 Introduction March 23, 2015 Page 4 Measures of Performance • Two terms, Insertion Loss, IL, and Transmission Loss, TL, are commonly used to describe the effectiveness of a muffling system. • The insertion loss is defined as the reduction in sound power transmitted through a duct compared to that transmitted with no muffler in place. • The transmission loss is defined as the difference between the sound power incident at the entry to the muffler to that transmitted by the muffler. • These terms are similar to the terms Noise Reduction, NR, and Transmission Loss, TL, introduced when we talked about barriers and partitions in connection with sound transmission through a partition or barrier March 23, 2015 Page 5 Introduction • Muffling devices make use of one or the other or a combination of two effects in their design. Either, sound propagation may be prevented (or reduced) by reflection back towards the source or suppressed, or sound may be dissipated. • Muffling devices based upon reflection or source sound power output suppression are called reactive devices and those based upon dissipation (absorption) are called dissipative devices. March 23, 2015 Page 6 Measures of Performance • The performance of reactive devices is dependent upon the impedances of the source and termination (outlet). • In general, a reactive device will strongly affect the generation of sound at the source. • This has the effect that the transmission loss and insertion loss of reactive devices may be very different. • As insertion loss is the quantity related to noise reduction, it will be used here to describe the performance of reactive muffling devices in preference to the term transmission loss (TL). • However, TL will be also considered for some simple reactive devices. March 23, 2015 Page 7 Measures of Performance • Provided that the transmission loss of a dissipative muffler is at least 5 dB it may be assumed that the insertion loss and the transmission loss are the same. • This assertion is justified by the observation that any sound reflected back to the source through the muffler will be reduced by at least 10 dB and is thus small and generally negligible compared to the sound introduced. • Consequently, the effect of the termination impedance upon the source must also be small. March 23, 2015 Page 8 Measures of Performance • The performance of dissipative devices tends to be independent of the effects of source and termination. • In practical designs, reactive devices are generally favoured for the control of low-frequency noise, since they tend to have more compact than dissipative devices for the same attenuation (Helmholtz Resonators). • Conversely, dissipative devices are generally favoured for the attenuation of high-frequency noise, due to their simpler and cheaper construction and greater effectiveness over a broad frequency range (absorbing materials). March 23, 2015 Page 9 Classification of Muffling Devices March 23, 2015 Page 10 Lumped Element Model • Acoustic energy will pass through an orifice largely in the form of kinetic energy. • There will be a small volume of air, somewhat larger than the actual orifice, that will participate in the induced motion, depending on the shape of the orifice. • The bounds of this volume are quite arbitrary, but the volume can be imagined as a small cylinder of air of crosssection equal to the area of the orifice and some additional length. • This is taken into account in analysis by adding an “end correction” to each side of the orifice to give an “effective length”. March 23, 2015 Page 11 Lumped Element Model • Impedance of an orifice or a tube (side view): w the actual length of the orifice le = “Effective length” Tube with flange March 23, 2015 Tube without flange Page 12 Lumped Element Model • In general, a phase relation exists between the pressure and the particle velocity. • The complex impedance of the orifice is defined as … Z A RA jX A Resistance Reactance • Where R is the resistive part (acoustic resistance), and X is the reactive part of the impedance. • Relatively detailed equations define these terms (not presented here). March 23, 2015 Page 13 Lumped Element Model • The resistive part represents the various loss mechanisms an acoustic wave experiences. • For the case of propagation through a duct, wall vibrations and viscous forces at the air/wall interface (boundary layer) can also have a significant effect, especially at high frequencies. • For resistive effects, energy is removed from the wave and converted into other energy forms. • This energy is said to be 'lost from the system'. March 23, 2015 Page 14 Lumped Element Model • The reactive part represents the ability of air to store the kinetic energy of the wave as potential energy since air is a compressible medium. • It does so by compression and rarefaction. • The electrical analogy for this is the capacitor's ability to store and dump electric charge, hence storing and releasing energy in the electric field between the capacitor plates. • For reactive effects, energy is not lost from the system but converted between kinetic and potential forms. March 23, 2015 Page 15 Lumped Element Model • The end correction accounts for the mass reactance of the medium (air) just outside of the orifice or at the termination of an open-ended tube. • The mass reactance is the reactive part of the radiation impedance presented to the orifice. • The radiation impedance of any source depends upon the environment into which the source radiates. • The end correction will depend upon the local geometry at the orifice termination (there are many different equations that define this depending on the end conditions. March 23, 2015 Page 16 Side Branch Resonator • The side branch resonator functions by placing a very low impedance in parallel with the impedance of the remainder of the line at its point of insertion. • It is most effective when its internal resistance is low, and it is placed at a point where the impedance of the tone to be suppressed is significant. • A type of side branch resonator is the Helmholtz resonator, which consists of a connecting orifice and a backing volume, as indicated schematically on the next slide. March 23, 2015 Page 17 Side Branch Resonator • A particularly useful device for suppressing pure tones of constant frequency, such as might be associated with constant speed pumps or blowers is the side branch resonator. March 23, 2015 Page 18 Acoustic Circuits and Electrical Analogs R p v X I X C P = pressure/electrical potential v = volume velocity/electrical current (I) C = compliance/capacitance March 23, 2015 X = Reactance R = resistance Page 19 Acoustic Analogs of Kirchhoff’s Current and Voltage laws 1. 2. At any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node (or the algebraic sum of currents in a network of conductors meeting at a point is zero). The sum of the electrical potential differences (voltage) around any closed network is zero (or the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop). For acoustics: 1. 2. The algebraic sum of acoustic volume velocities at any instant and at any location in an acoustic system must be equal to zero. The algebraic sum of the acoustic-pressure drops around any closed loop in an acoustic system at any instant must be equal to zero. March 23, 2015 Page 20 Side Branch Resonator • The side branch Helmholtz resonator appears in an equivalent acoustical circuit above (the acoustic impedance, Zs , acts in parallel with the downstream duct impedance, Zd . • The quantity, Zu , is the acoustic impedance of the duct upstream of the resonator. March 23, 2015 Page 21 Side Branch Resonator Insertion Loss due to the side branch for a constant volume– velocity source (fixed volume displacement machines such as reciprocating pumps and compressors and IC engines, also speakers with air-tight backing cavities) is: IL 20 log10 1 Zd Zs For a constant acoustic-pressure source (induced pressure rise machine such as fans and impeller type pumps and compressors): IL 20 log10 1 March 23, 2015 Zu Z d Z s (Zu Z d ) Page 22 Side Branch Resonator • To maximize the insertion loss for both types of sound source, the magnitude of Zs must be made small while at the same time, the magnitude of Zd (as well as Zu for a constant pressure source) must be made large. • Zs is made small by making the side branch resonant (zero reactive impedance, such as a uniform tube one-quarter of a wavelength long), and the associated resistive impedance as small as possible (rounded edges, no sound absorptive material). • The quantities Zd and Zu are made large by placing the side branch at a location on the duct where the internal acoustic pressure is a maximum. March 23, 2015 Page 23 Expansion Chambers • A common device for muffling is a simple expansion chamber. • If the chamber is less than ½ wavelength long, wave propagation effects can be neglected. March 23, 2015 Page 24 Expansion Chambers • The expansion chamber can thus be treated as a lumped element. • The pipe extensions (x and y) will have no effect except at high frequencies (chamber length becomes greater than ½ wavelength. March 23, 2015 Page 25 Expansion Chamber Lumped Element Model • The elements in the acoustic system labeled a, b, c, and L are represented in the lumped element model as Za, Zb, Zc, and ZL. March 23, 2015 Page 26 Expansion Chamber The Insertion Loss due to the expansion chamber for a constant volume–velocity source is: Zc Z L IL 20 log10 1 Zb For a constant acoustic-pressure source: IL 20 log10 1 March 23, 2015 Z a Zc Z L Zb Zb Z c Zb Z L Page 27 Lowpass Filter • A device commonly used to suppress pressure pulsations in a gas flow is a low pass filter. • It is made of two expansion chambers (b and d) connected with a pipe (c). March 23, 2015 Page 28 Lowpass Filter Lumped Element Model • The equivalent lumped element model is… March 23, 2015 Page 29 Lowpass Filter The Insertion Loss for a constant volume–velocity source is: IL 20 log 10 L b d L d Zd LZL March 23, 2015 Page 30 Lowpass Filter b Z b d Z c Z d L Z L Zc Z L Z L Zc Z L IL 20 log10 1 Zb Z d Zb Zb Z d March 23, 2015 Page 31 Lowpass Filter For a constant acoustic-pressure source: p IL 20 log 10 L Z L p Z a b d L b Z b IL 20 log10 March 23, 2015 Za Za Za Zc Zc 1 1 Z d Z L Zb Z d Z L Page 32 Lowpass Filter Constant volume–velocity, long tailpipe termination: IL IL0 20 log10 AL 60 log10 ( / c) Constant volume–velocity, short tailpipe termination: IL IL0 20 log10 AL 20 log10 lL 80 log10 ( / c) Constant acoustic-pressure (long or short tailpipe): IL IL0 20 log10 Aa 20 log10 la 80 log10 ( / c) IL0 20 log10 VbVd lc 20 log10 Ac March 23, 2015 Page 33 Lowpass Filter The following iterative process can be used to design a lowpass filter that can be adjusted to achieve the desired Insertion Loss at any desired frequency. f OD highest resonance frequency Vb and Vd chamber volumes Ac cross - section area of tube c f OC calculated highest resonance frequency March 23, 2015 Page 34 Desired f0D Reduce Increase Chamber volumes Vb, Vd Increase Reduce Choke tube diameter, Ac Calculated f0C f0C = f0D Yes Design over No Yes March 23, 2015 f0C < f0D No Page 35 Addition of Dissipative Material The addition of dissipative material to the interior of a muffer can increase the TL by as much as 10 dB, but will also add fabrication cost and weight as well as increasing back-pressure by increasing flow resistance. March 23, 2015 Page 36 Plenum Chambers Plenum chambers are typically used to “smooth” flows from fans and blowers. The TL is largely dependent on the room constant for the chamber and therefore dependent on the average absorption coefficient of the chamber walls. March 23, 2015 Page 37 Next Time Final Exam March 23, 2015 Page 38
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