MECH 482 – 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.
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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.
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Introduction
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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
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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.
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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.
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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.
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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).
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Classification of Muffling Devices
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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”.
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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
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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).
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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'.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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).
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Page 28
Lowpass Filter Lumped Element
Model
• The equivalent lumped element model is…
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Lowpass Filter
The Insertion Loss for a constant volume–velocity source is:

IL  20 log 10 
 L



   b  d  L
 d Zd  LZL
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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
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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
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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
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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
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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.
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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.
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Next Time
Final Exam
March 23, 2015
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