1. Design of Mufflers and Silencers
Lesson 11
Design of Mufflers and Silencers
D. W. Herrin, Ph.D., P.E.
University of Kentucky
Department of Mechanical Engineering
Slides © 2006 by A. F. Seybert

2. Types of Mufflers 1. Dissipative (absorptive) silencer: Duct or pipe
Sound absorbing material
(e.g., duct liner)
Sound is attenuated due to absorption (conversion to heat)
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3. Types of Mufflers 2. Reactive muffler:
Sound is attenuated by reflection and “cancellation” of sound waves
Compressor discharge details
40 mm
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4. Types of Mufflers 3. Combination reactive and dissipative muffler:
Sound absorbing material
Perforated tubes
Sound is attenuated by reflection and “cancellation” of sound waves + absorption of sound
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5. Performance Measures Transmission LossWi Wt
Anechoic
Termination
Muffler Wr
Transmission loss (TL) of the muffler:
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6. Performance Measures Insertion Loss
SPL1
SPL2
Muffler
IL (dB) = SPL1 – SPL2
Insertion loss depends on :
TL of muffler
Lengths of pipes
Termination (baffled vs. unbaffled)
Source impedance
Note: TL is a property of the muffler; IL is a “system” performance measure.
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7. Example TL and IL Source 2” 6” 24” 12” 12” Expansion Chamber Muffler
Inlet Pipe
Source
Outlet Pipe 2” 6”
24”
12”
12”
Pipe resonances
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8. The Concept of Impedance
Flow variable
Generalized impedance of a system Z and power supplied W : +
SYSTEM
Effort variable _
System Type
Effort Variable
Flow Variable
Impedance Z
Power supplied W
Electrical
Voltage (E)
Current (I)
E/I
EI = E2/Z
Mechanical
Force (F)
Velocity (V)
F/V
FV = F2/Z
Acoustic
Pressure (P)
P/V
PVS = P2 S /Z
Fluid
Volume Flow Rate (Q)
P/Q
PQ = P2/Z
Thermal
Temperature (T)
Heat Flow Rate/Deg (Q’)
T/Q’
TQ’ = T2/Z
* For acoustic systems we must multiply by the area S
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9. Network Interpretation Electrical and AcousticZ V Z
source
load
source
load
Electrical System
Acoustical System
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10. Acoustic System Components
Source V V
Any acoustic system P Zt
(sound pressure reaction)
Input or load impedance
Termination impedance
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11. Summary 1
Dissipative mufflers attenuate sound by converting sound energy to heat via viscosity and flow resistance – this process is called sound absorption.
Common sound absorbing mechanisms used in dissipative mufflers are porous or fibrous materials or perforated tubes.
Reactive mufflers attenuate sound by reflecting a portion of the incident sound waves back toward the source. This process is frequency selective and may result in unwanted resonances.
Impedance concepts may be used to interpret reactive muffler behavior.
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12. The Helmholtz Resonator
Named for:
Hermann von Helmholtz, , German physicist, physician, anatomist, and physiologist.
Major work: Book, On the Sensations of Tone as a Physiological Basis for the Theory of Music, 1862.
von Helmholtz, 1848
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13. Helmholtz Resonator ModelV x L
L’ is the equivalent length of the neck (some air on either end also moves). SB
F = PSB
Damping due to viscosity in the neck are neglected
(resonance frequency of the Helmholtz resonator)
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14. Helmholtz Resonator Example
A 12-oz (355 ml) bottle has a 2 cm diameter neck that is 8 cm long. What is the resonance frequency?
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15. Helmholtz Resonator as a Side Branch
Anechoic termination
35 Hz
V = m3
L = 25 mm
SB = 2 x 10-4 m2
S = 8 x 10-4 m2
fn = 154 Hz
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16. Network Interpretation
(any system) zB V zB zA z zA
Can we make ZB zero? z
(Produces a short circuit and P is theoretically zero.)
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17. The Quarter Wave Resonator
The Quarter-Wave Resonator has an effect similar to the Helmholtz Resonator: L Sb zB S
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18. Summary 2
The side-branch resonator is analogous to the tuned dynamic absorber.
Resonators used as side branches attenuate sound in the main duct or pipe.
The transmission loss is confined over a relatively narrow band of frequencies centered at the natural frequency of the resonator.
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19. The Simple Expansion Chamber
18” 2” 6” 2”
where m is the expansion ratio (chamber area/pipe area) = 9 in this example and L is the length of the chamber.
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20. Quarter Wave Tube + Helmholtz Resonator2” 9”
18” 6”
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21. Extended Inlet Muffler
18” 2” 6” 9”
( same for extended outlet )
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22. Two-Chamber Muffler 9” 4” 6” Dept. of Mech. Engineering
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23. Complex System Modeling
We would like to predict the sound pressure level at the termination.
Source
Engine
Pump
Compressor
(intake or exhaust)
Area change
Expansion chamber
Helmholtz Resonator
Quarter-wave resonator
termination
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24. The Basic Idea
The sound pressure p and the particle velocity v are the acoustic state variables 2
For any passive, linear component:
any acoustic
component 1 or
p2, v2
p1, v1
Transfer, transmission, or four-pole matrix
(A, B, C, and D depend on the component)
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25. Combining Component Transfer Matrices
Transfer matrix of ith component
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26. Performance Measures Transmission LossWi Wt
Anechoic
Termination Wr 2 1
Transmission loss (TL) of the muffler:
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27. The Straight Tube L A S B p2, v2 p1, v1 (x = L) (x = 0)
must have plane waves B
p2, v2
p1, v1
(x = L)
(x = 0)
Solve for A, B
in terms of p1, v1
then put into equations for p2, v2.
(note that the determinant A1D1-B1C1 = 1)
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28. Straight Tube with Absorptive Material
k’,zc
(complex wave number and
complex characteristic impedance)
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29. Area Change S2 S1 2 1 Dept. of Mech. Engineering 29
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30. Expansion Chamber Muffler
straight
tube S S’ S
area changes
(m = S’/S is called the expansion ratio of the muffler)
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31. Expansion Chamber Muffler
18” 2” 6”
(m = 9)
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32. Transfer Matrix of a Side BranchSB S 2 1
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33. Helmholtz Resonator ModelV x L
L’ is the equivalent length of the neck (some air on either end also moves). SB
F = PSB
Damping due to viscosity in the neck are neglected
(resonance frequency of the Helmholtz resonator)
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34. Summary 3
The transfer matrix method is based on plane wave (1-D) acoustic behavior (at component junctions).
The transfer matrix method can be used to determine the system behavior from component “transfer matrices.”
Applicability is limited to cascaded (series) components and simple branch components (not applicable to successive branching and parallel systems).
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