Effective Implementation of Microperforated Panel Absorbers

David HerrinUniversity of Kentucky

Effective Implementation ofMicroperforated Panel Absorbers

September 18, 2020

Vibro-Acoustics Consortium


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Microperforated Panel Absorbers

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Advantages

• High temperature resistant

• Chemically stable

• Non-combustible

• Wear resistant / Rugged

• Fiber free

• Washable

• Aesthetic appearance

• Acoustically tunable

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Hindrances to Use

• More expensive than traditional absorbers

• Properties must be measured

• Requires thoughtful integration into the product

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Suggested Design Process

• Select a MPP and measure transfer impedance.

• Consider the environment the MPP is placed in.

• Partition the backing cavity so it behaves in a locally reactive sense.

• Vary the depth of the backing cavity to improve low and broadband frequency attenuation.

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MPP and MSP Absorbers

0.89 mm

3.75 mm

Thickness

Thickness


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Thin layer with flow resistance 𝜎 𝑡 where 𝜎 is the flow resistivity and 𝑡 is the thickness.

𝜎 𝑡 2𝜌𝑐 for each case

Long, 2014 based on Ingard, 1994

Porous Absorbers Basics for Designers

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𝑑

𝐷

Plane wave

Air Cavity

𝑧

Sound Absorption of MPP

𝑧 𝑧 𝑗 cot 𝑘𝐷

𝑝 ,𝑢 𝑝 ,𝑢𝑧

1𝜌𝑐𝑝 𝑝𝑢


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MPP Transfer Impedance

Grazing Flow

High SPL

Allam and Åbom, 2013

𝑟 Re𝑗𝜔𝑡𝜎𝑐 1

2𝜅 𝑗

𝐽 𝜅 𝑗𝐽 𝜅 𝑗

2𝛽𝑅𝜎𝜌𝑐

𝑢𝜎𝑐

𝐾𝑀𝜎

𝑥 Im𝑗𝜔𝑡𝜎𝑐 1

2𝜅 𝑗

𝐽 𝜅 𝑗𝐽 𝜅 𝑗

0.85𝑑𝜔𝐹 1 𝑢𝜎𝑐

𝜎𝑐

𝜅 𝑑𝜔4𝜈

𝑅2

2 𝜂𝜌𝜔

𝐹1

1 12.6𝑀

𝑧 𝑟 𝑗𝑥


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𝐷 cavity depth

𝑑 hole diameter

𝜎 porosity

𝑡 thickness

𝐽0 zeroth order Bessel function

𝐽1 first order Bessel function

𝛽 2 for rounded and 4 for sharp edged holes

𝐾 0.15±0.0125

𝜈 kinematic viscosity

𝜂 dynamic viscosity

𝑀 grazing flow Mach number

𝑢 peak particle velocity

Symbols


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Maa’s EquationMaa, 1975

𝑧32𝜂𝑡𝜎𝜌𝑐𝑑 1

𝛽32

232 𝛽

𝑑𝑡 𝑗

𝜔𝑡𝜎𝑐 1 3

𝛽2 0.85

𝑑𝑡

𝛽 𝑑𝜔𝜌4𝜂

𝐷 0.1 m𝑡 1.0 mm

Given

0.0

0.2

0.4

0.6

0.8

1.0

0 200 400 600 800 1000 1200 1400 1600

Soun

d Ab

sorptio

n Co

efficient (α

)

Frequency (Hz)

0.20 mm

0.25 mm

0.40 mm

0.45 mm


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𝑍 𝜌𝑐𝑧 𝑍 𝑍

𝑍

Sample

Loudspeaker

Microphones

Measure Transfer ImpedanceWu, Cheng, and Tao, 2003

𝑍


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Assumptions:1. A MPP can be simulated using Maa’s equation with an effective holediameter and porosity.2. Measured absorption coefficient 𝛼 is accurate.

Measure 𝛼

Assume porosity and diameter

Calculate 𝛼 using Maa’s Equation

Compare in aLeast Squares Sense

Minimize the error to find effective porosity and holed diameter.

Procedure (Liu et al., 2014)

Determine Equivalent ParametersLiu et al., 2014


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0

0.2

0.4

0.6

0.8

1

0 1000 2000 3000 4000

Abso

rptio

n C

oeffi

cien

t

Frequency (Hz)

Measured

NLLSF

0

1

2

3

4

0 1000 2000 3000 4000

Nor

mal

ized

Tra

nsfe

r Im

peda

nce

Frequency (Hz)

Real (Measured)Real (NLLSF)Imag (Measured)Imag (NLLSF)

Fitted Hole Diameter: 0.242 mmFitted Porosity: 4.11%

Determine Effective Parameters


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0

2

4

6

8

10

12

0 0.1 0.2 0.3 0.4 0.5

Poro

sity

(%)

Hole Diameter (mm)

0.0

0.2

0.4

0.6

0.8

1.0

0 1000 2000 3000 4000 5000

Abso

rptio

n C

oeffi

cien

tFrequency (Hz)

2% Porosity8% Porosity

Manufacturing Variability


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Air Compressor

Airbrush

Powder container

Spray booth

MPP

Filter

Air Flow

Spray Booth

Impedance Tube

Effect of Contamination


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0

0.2

0.4

0.6

0.8

1

0 1000 2000 3000 4000

Abso

rptio

n C

oeffi

cine

t

Frequency (Hz)

1.4% Porosity, 0.3 mm Diameter




0

0.2

0.4

0.6

0.8

1

0 1000 2000 3000 4000

Abso

rptio

n C

oeffi

cine

t

Frequency (Hz)

0.9% Porosity, 0.2 mm Diameter2.0% Porosity, 0.2 mm Diameter2.3% Porosity, 0.2 mm Diameter2.0% Porosity, 0.2 mm Diameter4.2% Porosity, 0.2 mm Diameter

Effect of Contamination

1.0 mm thick MPP with slit perforations 0.6 mm thick MPP with circular perforations

Liu et al., 2014


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Test Case

1. Without MPP (Reference)2. With MPP3. With MPP + Partitioning

3 Cases

𝐼𝐿 𝐿no mpp 𝐿mpp

54 Measurements on Plane in front of MPPx

y

z


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Measurement Setup

Cardboard Partitioning


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Partition the Backing Cavity

-10

0

10

20

30

0 200 400 600 800 1000

Frequency (Hz)

IL (d

B)

MPP with PartitioningMPP

(1,0,0) (0,1,0)(2,0,0)

(0,0,1)

(2,1,0)

(1,0,1)(3,0,0)

(3,1,0)

(4,0,0)

(0,0,2)(0,3,0)

-10

0

10

20

30

0 200 400 600 800 1000

Frequency (Hz)

IL (d

B)

MPP with PartitioningMPP

(1,0,0) (0,1,0)(2,0,0)

(0,0,1)

(2,1,0)

(1,0,1)(3,0,0)

(3,1,0)

(4,0,0)

(0,0,2)(0,3,0)

Liu and Herrin, 2010


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100 mm

Baseline

Vary the Cavity Depth

100 mm

10 mm

40 mm

33.33 mm

Three-Channel


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0

0.2

0.4

0.6

0.8

1

0 400 800 1200 1600

Abso

rptio

n C

oeffi

cien

t

Frequency (Hz)

MeasurementPlane Wave

Empty Airspace

0

0.2

0.4

0.6

0.8

1

0 400 800 1200 1600Ab

sorp

tion

Coe

ffici

ent

Frequency (Hz)

Measurement

Plane Wave

Three Channel

Impedance Tube Measurements


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• AAP Reverberation room: 10.87 m3 with no parallel walls, and the noise source was a distributed loudspeaker

• Humidity: 56%~ 60%, temperature: 21ºC

• Box: 60 cm X 40 cm

• 24 cells (10 cm X 10 cm)

Reverberation Room Test


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Design ConfigurationsPartitioned Three channel

Half Three channel


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0.00

0.20

0.40

0.60

0.80

1.00

100 1000 10000

Abso

rptio

n C

oeffi

cien

t

Frequency( Hz)

MPP only

Partition0.00

0.20

0.40

0.60

0.80

1.00

100 1000 10000Ab

sorp

tion

Coe

ffici

ent

Frequency( Hz)

MPP only3-channel (full)3-channel (half)

Partition and Three-Channel


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100 mm

MPP

12 mm

Double Leaf Configuration

0

0.2

0.4

0.6

0.8

1

0 400 800 1200 1600

Abso

rptio

n C

oeffi

cien

t

Frequency (Hz)

MeasurementPlane Wave

Normal Incident Sound Absorption


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30

0.00

0.20

0.40

0.60

0.80

1.00

100 1000 10000

Abso

rptio

n C

oeffi

cien

t

Frequency( Hz)

MPP only

Double leaf

Double Leaf Configuration


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Ultra Thin MPP

• Much thinner than a traditional MPP• Ideal for use as a fiber cover

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Curve Fit to Determine Parameters

Effective ParametersThickness: 0.65 mm;Hole diameter: 0.23 mm;Porosity: 8.0%

0

0.2

0.4

0.6

0.8

1

0 1000 2000 3000 4000

Abso

rptio

n C

oeffi

cien

t

Frequency (Hz)

Measured

Fitted

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Silencer with MPP

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0102030405060708090100110120

100 1000

Transm

ission Loss (d

B)

Frequency (Hz)

56”48”

Absorptive(Perforated, Fibrous Material)

Transmission Loss Measurement


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References

1. Maa, D. Y., Theory and Design of Microperforated-Panel Sound-Absorbing Construction, Scientia Sinica XVIII, pp. 55-71, 1975.

2. Allam, S., Guo, Y., and Åbom, M. Acoustical Study of Micro-Perforated Plates for Vehicle Applications, SAE Noise and Vibration Conference, Paper No. 2009-01-2037, St. Charles, IL, 2009.

3. Allam, S. and Åbom, M. A New Type of Muffler Based on Microperforated Tubes, ASME Journal of Vibration and Acoustics, Vol. 133, 2013.

4. Herrin, D. W., Liu, W., Hua, X., and Liu, J., “A Guide to the Application of Microperforated Panel Absorbers,” Sound and Vibration, Vol. 51, No. 12, pp. 12-20 (December, 2017).

5. Herrin, D. W., Liu, J., and Seybert, A. F., “Properties and Applications of Microperforated Panels,” Sound and Vibration, Vol. 45, No. 7, pp. 6-9 (July, 2011).

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Effective Implementation of Microperforated Panel Absorbers