Muffler and Silencer Designvac.engr.uky.edu/.../Webinars/06_VAC_Muffler_Design.pdfMuffler and...
Transcript of Muffler and Silencer Designvac.engr.uky.edu/.../Webinars/06_VAC_Muffler_Design.pdfMuffler and...
Muffler and Silencer DesignVibro-Acoustics Consortium Web Meeting
University of Kentucky
Vibro-Acoustics Consortium
June 25, 2020
Vibro-Acoustics Consortium
Overview
2
• Fundamental Concepts
• Illustrative Examples
• Conceptual Design
• Detailed Design
• Prototyping / Testing
Vibro-Acoustics Consortium
Performance Measures Transmission Loss
3
Transmission loss (𝑇𝐿) of the muffler:
𝑊
𝑊𝑊 Anechoic
Termination
1 2
𝑇𝐿 10 log𝑊𝑊
Vibro-Acoustics Consortium
Performance Measures Insertion Loss
4
𝐼𝐿 𝑑𝐵 𝐿 𝐿
Insertion loss depends on : • Muffler• Lengths of pipes• Termination (baffled vs. unbaffled)• Source impedance
Muffler
𝐿
𝐿
Note: TL is a property of the muffler; IL is a “system” performance measure.
𝐿
Vibro-Acoustics Consortium
Example Transmission and Insertion Loss
5
2412
122 6Source
-50
-40
-30
-20
-10
0
10
20
0 200 400 600 800 1000
Frequency (Hz)
TL a
nd IL
(dB
)
Insertion LossTransmission Loss
Pipe resonances
Inlet Pipe Outlet Pipe
Expansion Chamber Muffler
Dimensions in Inches
𝜆𝑐𝑓
343 m/s𝑓
Acoustic Wavelength
Vibro-Acoustics Consortium
Reactive Muffler
6
Helmholtz Resonators
Quarter wave tube
Vibro-Acoustics Consortium
Reactive and Dissipative Muffler
7
Sound absorbing material
Perforated tubes
Neck
Volume
Vibro-Acoustics Consortium
The Helmholtz Resonator
8
𝐹 𝑝𝑆
𝑥
𝑉
𝑆
𝐿 𝐿 is the equivalent length of the neck (some air on either end also moves).
Damping due to viscosity in the neck are neglected
(resonance frequency of the Helmholtz resonator)
𝑘𝜌 𝑐 𝑆𝑉
𝑚 𝜌 𝑆 𝐿
𝑚𝑥 𝑘𝑥 𝑝𝑆 𝑥 𝑗𝜔𝑢 𝑥𝑢𝑗𝜔
𝑗 𝜔𝑚𝑘𝜔 𝑢 𝑝𝑆
𝑧𝑝
𝑆 𝑢 𝑗1𝑆
𝜔𝑚𝑘𝜔
𝑧 → 𝜔𝑘𝑚 𝑐
𝑆𝐿 𝑉
Vibro-Acoustics Consortium
The Helmholtz Resonator
9
𝑉 0.001 m3
𝐿 25 mm𝑆
2 x 10-4 m2
𝑆 8 x 10-4 m2
Anechoic termination
0
5
10
15
20
0 50 100 150 200 250 300
Frequency (Hz)
TL (d
B)
35 Hz
𝑇𝐿 10 log 1𝑐 2𝑆⁄
𝜔𝐿 𝑆⁄ 𝑐 𝜔𝑉⁄
Vibro-Acoustics Consortium
Quarter Wave Resonator
10
𝑧
𝐿
𝑆
𝑆 𝑇𝐿 10 logtan 𝑘𝑙 4 𝑆 𝑆⁄
4 𝑆 𝑆⁄
𝑧𝑗𝜌 𝑐𝑆 cot
𝜔𝐿𝑐 0
𝜔𝑛𝜋𝑐2𝐿 𝑛 1,3,5, …
𝑓𝑛𝑐4𝐿
𝐿𝑛𝑐4𝑓 𝑛
𝜆4 𝑛 1,3,5, …or
𝜔𝐿𝑐
𝑛𝜋2 𝑛 1,3,5, …and
Vibro-Acoustics Consortium
Parallel Impedance
11
Side Branch
𝑧
𝑧𝑧
𝑢 𝑝𝑧 𝑧
𝑧𝑝𝑆𝑢
𝑧 𝑧𝑧 𝑧
𝑧 0
𝑧 0
Vibro-Acoustics Consortium 12
𝑧Incident Wave
Reflected Wave
Transmitted Wave
𝑝 𝑝
𝑢 𝑢
𝑝 𝑝
𝑢
𝑧𝑝 𝑝𝑆𝑢
Series (Transfer) Impedance
Vibro-Acoustics Consortium
Muffler Elements
13
Straight Pipe𝐿
S
𝑆
LB
Quarter Wave TubeCone
𝑧
𝑧
𝑉
𝐿𝑆
Helmholtz Resonator
Perforate
Vibro-Acoustics Consortium
Overview
14
• Fundamental Concepts
• Illustrative Examples
• Conceptual Design
• Detailed Design
• Prototyping / Testing
Vibro-Acoustics Consortium
Muffler Elements Simple Expansion Chamber
15
18
2 26
0
5
10
15
20
25
30
0 100 200 300 400 500 600 700 800
Frequency (Hz)
TL (d
B)
Dimensions in inches
𝑇𝐿 10 log14 4 cos 𝑘𝐿 𝑚
1𝑚 sin 𝑘𝐿
where 𝑚 is the expansion ratio (chamber area/pipe area) = 9 in this example and L is the length of the chamber.
If 𝑚 10
𝑇𝐿 10 log14 𝑚 sin 𝑘𝐿
𝑚 𝑑 𝑑⁄
Vibro-Acoustics Consortium 16
Muffler Elements Quarter Wave Tube
29 18
2 26
Dimensions in inches
0
5
10
15
20
25
30
0 100 200 300 400 500 600 700 800
Frequency (Hz)TL
(dB)
Vibro-Acoustics Consortium
A Note on Quarter Wave Tubes
17
𝑧
𝑧 𝑧
Vibro-Acoustics Consortium 18
Muffler Elements Extended Inlet
18
2 269
0
5
10
15
20
25
30
0 100 200 300 400 500 600 700 800
Frequency (Hz)
TL (d
B)
Dimensions in inches
(similar for extended outlet)
Vibro-Acoustics Consortium 19
Muffler Elements Extended Inlet and Outlet
9 9
4 6
0
10
20
30
40
50
0 100 200 300 400 500 600 700 800
Frequency (Hz)
TL (d
B)
Dimensions in inches
Vibro-Acoustics Consortium 20
Muffler Elements Extended Inlet and OutletDimensions in inches
0
10
20
30
40
50
60
0 500 1000 1500 2000
Tran
smis
sion
Los
s (d
B)
Frequency (Hz)
𝐿
𝐿/2
𝐿/4
Simple expansion chamberSide branch 1Side branch 2
Expansion Chamber
Side Branch 1
Side Branch 2
Vibro-Acoustics Consortium 21
Munjal, 2011
Double Tuned Expansion Chamber
Vibro-Acoustics Consortium
Overview
22
• Fundamental Concepts
• Illustrative Examples
• Conceptual Design
• Detailed Design
• Prototyping / Testing
Vibro-Acoustics Consortium 23
Plane Wave Modeling
𝑝𝑆 𝑢
𝑝𝑆 𝑢
𝑝𝑆 𝑢
cos 𝑘𝐿𝑗𝜌 𝑐𝑆 sin 𝑘𝐿
𝑗𝑆𝜌 𝑐 sin 𝑘𝐿
𝑆𝑆 cos 𝑘𝐿
𝑝𝑆 𝑢
Vibro-Acoustics Consortium 24
𝑆
𝑆
1 2
𝑝 𝑝 𝑝
𝑆𝑢 𝑆 𝑢 𝑆𝑢
𝑧𝑝𝑆 𝑢
𝑝𝑆 𝑢
𝑆𝑢𝑝𝑧 𝑆𝑢
𝑝𝑆 𝑢
1 01 𝑧⁄ 1
𝑝𝑆 𝑢
Parallel Impedance
Transfer Matrix
Vibro-Acoustics Consortium 25
𝑧Incident Wave
Reflected Wave
Transmitted Wave
𝑝 𝑝
𝑢 𝑢
𝑝 𝑝
𝑢
𝑧𝑝 𝑝𝑆𝑢
Series (Transfer) Impedance
𝑝𝑆 𝑢
1 𝑧0 1
𝑝𝑆 𝑢
Transfer Matrix
Vibro-Acoustics Consortium
Empirical Equations Perforated Panel
Sullivan and Crocker (1978)
𝑧 1 𝜌𝑐𝜎⁄ 2.4 𝑗0.02𝑓
𝑧 1 𝜎⁄ 0.006 𝑗𝑘 𝑡 0.75𝑑
Sullivan and Crocker (1978))
Rao and Munjal (1986)
26
𝑧 1 𝜎⁄ 7.337 10 1 72.23𝑀 𝑗2.2245 10 𝑓 1 51𝑡 1 204𝑑
𝑓
𝑀
frequency
flow Mach number
𝜌 density of air𝑐 speed of sound in air
𝜎 porosity𝑡 panel thickness 𝑑 hole diameter
𝑘 wave number ( ⁄ )
Vibro-Acoustics Consortium 27
For each element:
Overall:
𝑝𝑆 𝑢
𝑇 𝑇𝑇 𝑇
𝑝𝑆 𝑢
𝑇 𝑇 𝑇 𝑇 ⋅⋅⋅ 𝑇 𝑇 𝑇𝑇 𝑇
Combining Elements
𝑇𝐿 10 log𝑆
4𝑆 𝑇𝑆 𝑇𝜌𝑐
𝜌𝑐𝑇𝑆
𝑆𝑆 𝑇
Transmission Loss
Vibro-Acoustics Consortium 28
Plane Wave Modeling Virtual DesignPlane Wave Modeling (Virtual Design)
Source
In course work
A real muffler
Vibro-Acoustics Consortium
Plane Wave Modeling Tips
29
1. Examine the muffler to be modeled and determine a direction of sound propagation. This will normally be the direction having the longest cross-dimension and is also usually the same as the flow path.
2. Details like welds, seams, and fillets that are small compared to an acoustic wavelength can be ignored. However, leaks should be included.
3. Identify and include quarter wave tubes. Often in the case of right-angle turns, quarter wave tubes are unintentionally included. Additionally, be sure to include mass effects in the case of extended inlets or outlets.
Vibro-Acoustics Consortium
Plane Wave Modeling Tips
30
4. The shape of the cross-section, whether circular, elliptical, or rectangular will have no effect.
5. Sound will be reflected due to changes in the cross-sectional area. Significant area changes should be accounted for. Gradual changes in cross-sectional area can be modeled as cones.
6. If the porosity (perforation rate) exceeds 30%, a perforate can generally be ignored and treated as open.
Vibro-Acoustics Consortium
Example Small Engine Muffler
31
Perforated
Vibro-Acoustics Consortium
Example Small Engine Muffler
32
Flow Path
Vibro-Acoustics Consortium
Example Small Engine Muffler
33
Quarter Wave TubesQuarter Wave Tubes
Vibro-Acoustics Consortium
Example Small Engine Muffler
34
SIDLAB Model
Vibro-Acoustics Consortium
Example Small Engine Muffler
35
Vibro-Acoustics Consortium 36
A Note on Perforates and Flow
Frequency (Hz)1000 2000 3000 40000
Frequency (Hz)1000 2000 3000 40000
Frequency (Hz)1000 2000 3000 40000
Frequency (Hz)1000 2000 3000 40000
40
30
10
20
Tran
smis
sion
loss
(dB)
40
30
10
20
Tran
smis
sion
loss
(dB)
30
10
20
Tran
smis
sion
loss
(dB)
40
30
10
20
Tran
smis
sion
loss
(dB)
40
No flow M=0.01
M=0.03 M=0.04
Vibro-Acoustics Consortium
Example Cross Flow Muffler
37
InletOutlet
: Propagation: Quarter-wavelength tube: Cross-flow: Helmholtz resonator
Vibro-Acoustics Consortium
Example Cross Flow Muffler
38
1st chamber2nd chamber3rd chamber
Vibro-Acoustics Consortium
Example Cross Flow Muffler
39
0
20
40
60
80
100
120
0 100 200 300 400 500 600
Tran
smis
sion
Los
s (d
B)
Frequency (Hz)
Measurement
SIDLAB
MAP
Vibro-Acoustics Consortium
Overview
40
• Fundamental Concepts
• Illustrative Examples
• Conceptual Design
• Detailed Design
• Prototyping / Testing
Vibro-Acoustics Consortium 41
Determination of Transfer Matrix
3-D Waves
Plane Waves
𝑝𝑆 𝑢
𝑇 𝑇𝑇 𝑇
𝑝𝑆 𝑢𝑝
𝑆 𝑢
𝑝𝑆 𝑢
Vibro-Acoustics Consortium 42
Determination of Transfer Matrix
𝑝𝑆 𝑢
𝑇 𝑇𝑇 𝑇
𝑝𝑆 𝑢
3-D Waves
Plane Waves
𝑝𝑆 𝑢
𝑝𝑆 𝑢
𝐴 𝑝,
𝐴 𝑝,
𝐴 𝑝,
𝐴 𝑝,
𝑇 𝐴 /𝐴 𝑇1𝑆 𝐴
𝐴 𝐴𝐴
𝑇 𝑆1𝐴 𝑇
𝑆𝑆
𝐴𝐴
Vibro-Acoustics Consortium 43
Example Cross Flow Muffler
Virtual prototyping using acoustic BEM (MAP software)
Vibro-Acoustics Consortium
Overview
44
• Fundamental Concepts
• Illustrative Examples
• Conceptual Design
• Detailed Design
• Prototyping / Testing
Vibro-Acoustics Consortium 45
Transmission Loss Standards
ASTM E2611-09, “Standard Test Method for Measurement of Normal Incidence Sound Transmission of Acoustical Materials Based on the Transfer Matrix Method,” American Society of Testing and Materials, Philadelphia, 2009.
Vibro-Acoustics Consortium 46
Example Cross Flow Muffler
0
20
40
60
80
100
120
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Tran
smis
sion
Los
s (d
B)
Frequency (Hz)
Experiment
SIDLAB
3D MAP
Vibro-Acoustics Consortium 47
Example Cross Flow Muffler
InletOutlet
: Propagation: Quarter-wavelength tube: Cross-flow: Helmholtz resonator
123
Vibro-Acoustics Consortium
VAC Meeting May 15-16, 2014
Muffler Design
48
Example Helmholtz Resonator Included
Vibro-Acoustics Consortium
Summary
49
• Muffler fundamentals introduced.
• Recommend the use of plane wave simulation in the early design stages.
• Numerical simulation is useful for finalizing the geometry and details.
• Prototyping using 3D printing is recommended for an initial test.
Vibro-Acoustics Consortium
References• ASTM E2611-19, “Standard Test Method for Measurement of Normal Incidence
Sound Transmission of Acoustical Materials Based on the Transfer Matrix Method,” Philadelphia, 2019.
• D. A. Bies, C. H. Hansen, and C. Q. Howard, Engineering Noise Control, 5th Edition, CRC Press, 2018.
• H. Bodén, U. Carlsson, R. Glav, H-P Wallin, and M. Åbom, Sound and Vibration, The Marcus Wallenberg Laboratory, KTH, Stockholm, 2011.
• D. W. Herrin, X. Hua, Y. Zhang, and T. Elnady, “The Proper Use of Plane Wave Models for Muffler Design,” SAE International Journal of Passenger Cars –Mechanical Systems, Vol. 7, No. 3 (2014).
• M. L. Munjal, Acoustics of Ducts and Mufflers, 2nd Edition, Wiley-Interscience, United Kingdom, 2014.
50
Vibro-Acoustics Consortium 51
List of Variables
𝑓
𝑀
frequency
flow Mach number
𝜌 density of air𝑐 speed of sound in air
𝜔 angular frequency
𝜎 porosity𝑡 panel thickness 𝑑 hole diameter𝜐 air kinematic viscosity
𝑘 wave number
𝐶 end correction coefficient𝐽 Bessel function of the first kind of order 1𝑏 the distance between two neighboring holes in axial directionsℎ the distance between two neighboring holes in circumferential directions
If either 𝑚 or 𝑛 is equal to zero, 𝜀 1; otherwise, 𝜀 0.5; 𝜀
Vibro-Acoustics Consortium
Eq. 5 (Ji, 2010)
𝑍 1 𝜎⁄ 1 𝑡 𝑑 8𝑘𝜐 𝜌𝑐⁄⁄ 𝑗𝑘 𝑡 𝐶 𝑑
𝐶4𝜋
1𝜁𝜂 ⁄ 𝜀
𝐽 𝜋 𝑚𝜁 𝑛𝜂
𝑚 ℎ 𝑏⁄ 𝑛 𝑏 ℎ⁄⁄
𝜁 𝑑 𝑏⁄ , 𝜂 𝑑 ℎ⁄
Eq. 4 (Rao and Munjal, 1986)
Empirical Equations Perforated Panel
52
𝑍 1 𝜎⁄ 7.337 10 1 72.23𝑀 𝑗2.2245 10 𝑓 1 51𝑡 1 204𝑑
Vibro-Acoustics Consortium53
Eq. 6 (Allam and Åbom, 2011)
the absolute value or the peak particle velocity inside the holes
𝑟 Re𝑗𝜔𝑡𝜎𝑐 1
2𝜅 𝑗
𝐽 𝜅 𝑗𝐽 𝜅 𝑗
2𝛽𝑅𝜎𝜌𝑐
𝑢𝜎𝑐
𝑥 Im𝑗𝜔𝑡𝜎𝑐 1
2𝜅 𝑗
𝐽 𝜅 𝑗𝐽 𝜅 𝑗
𝛿 𝜔 1 𝑢𝜎𝑐
𝜎𝑐
Surface Resistance 𝑅12 2𝜂𝜌𝜔β is equal to 2 for holes with rounded edges and 4
for holes with sharp edges
Dimensionless shear wave-number𝜅 𝑑 𝜔 4𝜐⁄
𝑍 𝑟 𝑗𝑥
End correction𝛿 0.85𝑑
Empirical Equations Perforated Panel