Chapter 10 Sound in Ducts - University of Kentucky dwherr01/ME510_Old/Chapter_10_Sound_in_Du ...

download Chapter 10 Sound in Ducts - University of Kentucky dwherr01/ME510_Old/Chapter_10_Sound_in_Du  Chapter

of 49

  • date post

    19-Aug-2018
  • Category

    Documents

  • view

    224
  • download

    0

Embed Size (px)

Transcript of Chapter 10 Sound in Ducts - University of Kentucky dwherr01/ME510_Old/Chapter_10_Sound_in_Du ...

  • Slides to accompany lectures in

    Vibro-Acoustic Design in Mechanical Systems 2012 by D. W. Herrin

    Department of Mechanical Engineering University of Kentucky

    Lexington, KY 40506-0503 Tel: 859-218-0609

    dherrin@engr.uky.edu

    Chapter 10 Sound in Ducts

  • ME 510 Vibro-Acoustic Design 2 Dept. of Mech. Engineering University of Kentucky

    1. Dissipative (absorptive) silencer:

    Sound is attenuated due to absorption (conversion to

    heat)

    Sound absorbing material (e.g., duct liner)

    Duct or pipe

    Types of Mufflers

  • ME 510 Vibro-Acoustic Design 3 Dept. of Mech. Engineering University of Kentucky

    2. Reactive muffler:

    Sound is attenuated by reflection and cancellation of sound waves

    Compressor discharge details

    40 mm

    Types of Mufflers

  • ME 510 Vibro-Acoustic Design 4 Dept. of Mech. Engineering University of Kentucky

    3. Combination reactive and dissipative muffler:

    Sound is attenuated by reflection and cancellation of sound waves + absorption of sound

    Sound absorbing material

    Perforated tubes

    Types of Mufflers

  • ME 510 Vibro-Acoustic Design 5 Dept. of Mech. Engineering University of Kentucky

    Transmission loss (TL) of the muffler:

    Wi

    Wr

    Wt Anechoic Termination Muffler

    Performance Measures Transmission Loss

    ( )t

    i

    WWTL 10log10dB =

  • ME 510 Vibro-Acoustic Design 6 Dept. of Mech. Engineering University of Kentucky

    IL (dB) = SPL1 SPL2 Insertion loss depends on : TL of muffler

    Lengths of pipes Termination (baffled vs. unbaffled) Source impedance

    Muffler

    SPL1

    SPL2

    Note: TL is a property of the muffler; IL is a system performance measure.

    Performance Measures Insertion Loss

  • ME 510 Vibro-Acoustic Design 7 Dept. of Mech. Engineering University of Kentucky

    24 12

    12 2 6 Source

    -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

    Example TL and IL

  • ME 510 Vibro-Acoustic Design 8 Dept. of Mech. Engineering University of Kentucky

    Source Su Any acoustic system

    Su

    P (sound pressure

    reaction)

    Zt

    Input or load impedance

    Termination impedance z =

    PSu

    = r + jx zt =PtSut

    = rt + jxt

    Acoustic System Components

  • ME 510 Vibro-Acoustic Design 9 Dept. of Mech. Engineering University of Kentucky

    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.

    Summary 1

  • ME 510 Vibro-Acoustic Design 10 Dept. of Mech. Engineering University of Kentucky

    Named for: Hermann von Helmholtz, 1821-1894, 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

    The Helmholtz Resonator

  • ME 510 Vibro-Acoustic Design 11 Dept. of Mech. Engineering University of Kentucky

    F = PSB

    x

    V

    SB

    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)

    Helmholtz Resonator Model

    Mx +Kx = PSB x = juB x =uBj

    j M K

    "

    #$

    %

    &'uB = PSB

    zB =PSBuB

    = j 1SB2

    "

    #$

    %

    &' M

    K

    "

    #$

    %

    &'

    VScK Bo22

    =

    LSM Bo =

    VLSc

    MKz BB

    == when0

  • ME 510 Vibro-Acoustic Design 12 Dept. of Mech. Engineering University of Kentucky

    A 12-oz (355 ml) bottle has a 2 cm diameter neck that is 8 cm long. What is the resonance frequency?

    Helmholtz Resonator Example

    ( )( )( )

    Hz1821035508.0402.0

    2343

    2 62

    =

    =

    =

    n

    Bn

    fVLScf

  • ME 510 Vibro-Acoustic Design 13 Dept. of Mech. Engineering University of Kentucky

    V = 0.001 m3 L = 25 mm SB = 2 x 10-4 m2 S = 8 x 10-4 m2

    fn = 154 Hz

    Anechoic termination

    0

    5

    10

    15

    20

    0 50 100 150 200 250 300

    Frequency (Hz)

    TL (d

    B)

    35 Hz

    Helmholtz Resonator as a Side Branch

    ( )

    +=

    2

    21021log10dB

    VcSLScTL

    B

  • ME 510 Vibro-Acoustic Design 14 Dept. of Mech. Engineering University of Kentucky

    Can we make ZB zero?

    zA V

    P

    zB

    z

    z zA

    zB (any system)

    (Produces a short circuit and P is theoretically zero.)

    Network Interpretation

    AB

    AB

    zzzzz+

    =

    zB =PSBuB

    = j 1SB2

    !

    "#

    $

    %& M

    K

    !

    "#

    $

    %&

    VLSc

    MKz BB

    == when0

  • ME 510 Vibro-Acoustic Design

    A Tuned Dynamic Absorber

    K1

    M1 x F

    K1

    M1 x F

    K2

    M2

    Original System

    /1

    |x/F|

    Original system

    Tuned dynamic absorber M2/M1=0.5

    K2M2

    =K1M1

    tune

    Tuned Dynamic Absorber

    15 Dept. of Mech. Engineering University of Kentucky

  • ME 510 Vibro-Acoustic Design

    Resonances in an Open Pipe

    P = 1 Pa

    Lp= 1 m source

    First mode

    Second Mode

    etc.

    1 = 2Lp =cf1 f1 =

    3432 1( )

    =171.5 Hz

    2 = Lp =cf2 f2 =

    3431 1( )

    = 343 Hz

    16 Dept. of Mech. Engineering University of Kentucky

  • ME 510 Vibro-Acoustic Design

    SPL at Pipe Opening No Resonator

    17 Dept. of Mech. Engineering University of Kentucky

  • ME 510 Vibro-Acoustic Design

    Example HR Used as a Side Branch*

    V = 750 cm3 L = 2.5 cm (L= 6.75 cm) DB = 5 cm (SB= 19.6 cm2) D = 10 cm (S = 78.5 cm2)

    fn = 340 Hz

    Anechoic termination

    _____ * e.g., engine intake systems

    ( )

    +=

    2

    21021log10dB

    VcSLScTL

    B

    18 Dept. of Mech. Engineering University of Kentucky

  • ME 510 Vibro-Acoustic Design

    SPL at Pipe Opening with Resonator

    19 Dept. of Mech. Engineering University of Kentucky

  • ME 510 Vibro-Acoustic Design 20 Dept. of Mech. Engineering University of Kentucky

    The Quarter-Wave Resonator has an effect similar to the Helmholtz Resonator:

    zB

    L

    S

    SB

    The Quarter Wave Resonator

    ( ) ( )( )

    += 2

    22

    10 44tanlog10B

    B

    SSSSklTL

    zB = jocSB

    cot L c( ) = 0 when L c = n 2 n =1,3, 5...

    n =nc2L

    fn =nc4L

    or L = nc4 f

    = n 4"

    #$

    %

    &'

  • ME 510 Vibro-Acoustic Design 21 Dept. of Mech. Engineering University of Kentucky

    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.

    Summary 2

  • ME 510 Vibro-Acoustic Design 22 Dept. of Mech. Engineering University of Kentucky

    18

    2 2 6 where m is the expansion ratio (chamber area/pipe area) = 9 in this example and L is the length of the chamber.

    The Simple Expansion Chamber

    ( ) ( )

    ++= klm

    mklTL 22

    210 sin

    1cos441log10

    0

    5

    10

    15

    20

    25

    30

    0 100 200 300 400 500 600 700 800

    Frequency (Hz)

    TL (d

    B)

  • ME 510 Vibro-Acoustic Design 23 Dept. of Mech. Engineering University of Kentucky

    2

    9 18

    2 2 6

    Quarter Wave Tube + Helmholtz Resonator

    0

    5

    10

    15

    20

    25

    30

    0 100 200 300 400 500 600 700 800

    Frequency (Hz)

    TL (d

    B)

  • ME 510 Vibro-Acoustic Design 24 Dept. of Mech. Engineering University of Kentucky

    18

    2 2 6 9

    (same for extended outlet)

    Extended Inlet Muffler

    0

    5

    10

    15

    20

    25

    30

    0 100 200 300 400 500 600 700 800

    Frequency (Hz)

    TL (d

    B)

  • ME 510 Vibro-Acoustic Design 25 Dept. of Mech. Engineering University of Kentucky

    9 9

    4 6

    Two-Chamber Muffler

    0

    10

    20

    30

    40

    50

    0 100 200 300 400 500 600 700 800

    Frequency (Hz)

    TL (d

    B)

  • ME 510 Vibro-Acoustic Design 26 Dept. of Mech. Engineering University of Kentucky

    Source

    Engine Pump Compressor (intake or exhaust)

    Area change

    Expansion chamber

    Helmholtz Resonator

    Quarter-wave resonator

    termination

    We would like to predict the sound pressure level at the termination.

    Complex System Modeling

  • ME 510 Vibro-Acoustic Design

    The sound pressure p and the particle velocity v are the acoustic state vari