6 fluid machine noise control

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Indian Institute of Technology Roorkee

Noise and Vibration Control

6. Fluid Machine Noise Control6. Fluid Machine Noise Control

Fluid machines-

examples : fans, pumps, compressors, turbines,internal combustion engines.

uses : transportation systems, in the process industry

to transport fluids in pipes and ducts, in homeappliances and in buildings.

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6.1 Classification of Fluid Machines

Fluid machines involve the exchange of mechanical energy or workwith a fluid medium.

3 basic ways in which this exchange can take place:i. via mechanical forces (pressure),ii. via volume displacementsiii. via heating.

Axial Fan

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The mechanical force is normally created by rotating

surfaces, e.g., propellers, blades or screws.

Examples: fans, turbines and compressors.

Rotating fluid machines can be split into: axial, radial andmixed flow.

Radial Fan Mixed Flow Fan

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Volume displacement machines : pistons, screws andgears.

Examples: compressors and pumps.

Fluid machines involving heating : mostly driven bycombustion.

combinations involving energy exchange via forces orvolume displacements.

Examples: (i) a gas turbine is driven by combustion which

then drives the compressor and the turbine.

(ii) an internal combustion engine in which a pistonmachine is driven by combustion.

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6.2 Noise Generated by Fluid Flow Machine

3 types of fundamental acoustic source mechanisms inunsteady flows:

1) Fluctuating (unsteady) volume flows; (monopole)2) Fluctuating (unsteady) fluid forces; (dipole)3) Free turbulence or fluctuating shear stress on fluid

particles; (quadrupole)

relative strength in terms of the acoustic power ( )Wgenerated by each of these sources:

2 4: : 1: :m d qW W W M M

where M is a characteristic Mach-number of the flow processproducing the sound.

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p

v

Laminar flow

Turbulent

boundary layer

Turbulent

eddiesOutside

Inside

Roof

p

Figure 2 The pressure fluctuations generated by the turbulent vortices

are responsible for noise both inside and outside of the vehicle.

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Table 1 The three fundamental types of flow acoustic sources.

Source type Physical mechanism Physical situation

Monopole fluctuating volume ormass flow

cavitation, inlets andoutlets of piston machines

(e.g., valves)

Dipole fluctuating force propellers, fans

Quadrupole fluctuating force couple free turbulence (jet flows)

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1. Monopole

the simplest type of point source.a multipole of zeroth order.sound field emitted by a monopole is spherically symmetric,For a harmonic time-variation, the general expression for a

spherically symmetric field is given as:

)()(),( krtikrti er

er

tr++ +=

AAp

With a monopole at the origin, in a free field without boundaries,only an outgoing wave exists.i.e., second term in the equation given above, can be

disregarded. In order to interpret a monopole physically, theamplitude A+ is related to what happens at the source.Note that the physical dimension corresponding to that amplitudeis [kg/s2], i.e., it represents the change in mass flow rate [kg/s] perunit time.

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For spherical symmetry, at a distance r, the volumetric flow rate is given by

tirr e

Q=Q

rr r uQ24= where

and where uris the particle velocity in the radial direction.

mass flow rate = volume flow rate density (fluid )

relation between the mass flow rate and the amplitude ofthe radiated spherical sound wave :

4

00 Q

Ai

=+

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The spherical sound wave radiated from a harmonicallyoscillating monopole is given by

ikrm e

r

i =

4

00 Qp

where the index m indicates a monopole and Q0 is called themonopoles source strength.

Assume an arbitrary distribution of monopoles in a free field;

the resulting sound field is then obtained through superposition,as

=n

ikr

n

nm

ner

i

4

0 Qp

nrv

where rv

is the position vector

from monopole n to the field point

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If the summation in above equation is interpreted

as an integral, then even cases of a continuoussource distribution can be treated.

vr

vr1

vrn

Qn

Q1

Figure 3 Sound field built up by superposition of monopoles.

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N i d Vib i C l


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The sound powerradiated by a monopole

20

20 ~

4Q

ckWm

=

The physical realization of a monopole closest to the ideal is that ofa small spherical shell, undergoing pure radial oscillations.

Small shell condition- requirement that the wavelength be muchlarger than the radius of the shell.

That is usually expressed by requiring that the Helmholtz number

He = ka be much less than 1, where kis the wave number and a theradius of the shell (or of the source).

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N i d Vib ti C t lill ti h i l h ll i th d di ti f


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oscillating spherical shell is the sound radiation fromcavitation bubbles.Such bubbles arise in a flowing liquid when the local

pressure is so low that it approaches the liquids vaporpressure.A cavitation bubble is unstable, and normally implodesshortly after it is generated

That implosion is a strong source of sound, because it occurs in avery short span of time,and the sudden local change in volume yields a high value of the

volume flow rate Q ~ d(

V)/dt, where

Vis the volume of thebubble before collapse.

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N i d Vib ti C t l


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valve

collapsing gas bubbles

low pressureVery high pressure

Figure 4 For sudden changes of the cross section in a pipe carrying

flowing medium, the pressure drop can be so large that cavitationbubbles arise. The sound generated by the imploding cavitationbubbles can be described using the monopole model.

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At low frequencies, atwhich the He number,based on the radius of thebox, is small, that sourcesacts as a monopole.

Figure 6 A loudspeaker element mounted in a box is an exampleof a sound source approximating a monopole in the low-frequencyregion.

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2. Dipole

From the monopole, which is the simplest type of point source,new types of sources can be created by superposition.

first superpose two monopoles with the same source strength,

but opposite phases Q and -Q.

If the He number based on the distance lbetween these twomonopoles is much less than 1, a dipole is obtained;

Such a source is also called a multipole of order one.

The process can be repeated to obtain multipoles of arbitraryorder.

For example, a multipole of second order, or a quadrupole as it isusually called, is obtained by the superposition of two dipoles ofequal strength, but opposite phase;

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To calculate the resultant field from a dipole, and to interpret

that source type physically, we now consider two harmonicallyoscillating monopoles Q and -Q

z

r1

r2

-Q

Q

lr

Figure 7 Dipole obtained by superposition of two monopoles (kl 1)

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=

21

021

4 r

e

r

eiikrikr

tot

Qp

field from a point source of the dipole type (index d) oriented inthe z-direction:

==

r

e

z

i ikr

ztotl

d

4lim0

0

Dpp

The sound powerexpressed as a dipole moment:

12

~240 z

dDckW =

For a dipole of finite size consisting of two closely spaced monopoles

Radiation from such a finite dipole with the sound powerthat a lone monopole of strength Q gives in the free field

1,3/)( 2


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loudspeakermembrane

Pressure equalisation overmembrane

Figure 8 If a loudspeaker is not mounted in a sealed speaker

box, the radiated sound power will be reduced due to thepressure equalization between the front and back sides of theelement.

enclosing the back sideof a common woofer(bass loudspeaker) in asealed box- a monopole source isobtained

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3. Quadrupole

Fr

Fr

F

r

l

r

and The quadrupole, or a multipole of second order, is obtainedby the superposition of two dipoles with source strengths

and

When the He number, based on the distance lbetweenthese two dipoles, is much less than 1, a quadrupole isobtainedthere are two basic types of quadrupoles:

the longitudinal, for which and are parallel,

zlF

M

the lateral, for which those two vectors are orthogonal.To obtain a quadrupole concentrated at a point, lzmust

approach zero, while constraining the productto be a constant value

(called the quadrupole moment) with the dimensions [Nm].

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x x

z

y y

z

lz

-lz

Fx

Fz-

Fzlz

-Fx-lz

2

2 2

2

longitudinell $ $M Fzz z zl= longitudinal lateral $ $M Fxz x z

l=

Figure 9 Quadrupoles obtained by superposition of two

dipoles (klz 1) in each case.

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z

0

lz

-lz

-Q

Q

-Q

Q

lz

lz

/2

/2

$ $M Qzz z zi l l= 0

z

0

-Q Q

lx

Q -Q

lx

lx lz$ $M Qxz x zi l l= 0

Longitudinal Lateral

Figure 10 Quadrupoles obtained by the superposition ofmonopoles ( klx, klz 1).

The radiated sound powercan then be calculated by integration

over a spherical surface, the result of which is

c

MkW zzzzq

0

24

,20

~

= W

k M

cq xz

xz

,

~

=4 2

060

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o se a d b at o Co t o

Q

-Q Q

-Q

quadrupole

Physical situation

Body in "rocking" motion ..F -F

Free turbulence

.....fluctuating forces

Church bell

Figure 11 Examples of physical situations that, at low frequencies

(He 1), constitute sources of quadrupole character.

The most important physical process - free turbulence.sound generation- fluctuating shear stresses acting on the fluidparticles of the turbulent flow fields.

These shear stresses comprise oppositely directed force couples,so that each fluid particle in the turbulent field acts as a quadrupolesource.Thus, there is a continuous distribution of quadrupoles, and theresultant sound field is obtained by summation (integration) over the

entire turbulent field.

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Gasstrm

Blandningsomrde

Gas flowMixing region

Figure 12 Free turbulence arises in so-called mixing zones between

gases with differing flow velocities. The greater the velocitydifference, the greater the sound generation.

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0

2 2cd U

cUd42

0 02 6 3

d U c

0

2 3

d U

02 5 2

d U c

0 2 7 4d U c

0

2 4d U c

02 6 3

d U c

02 8 5

d U c

Dimension Monopole Dipole Quadrupole

1-D

2-D

3-D

Table 1 Flow induced sound. Scaling laws for sound power in soundfields with different dimensions. U is a characteristic velocity, and da

characteristic length.

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Scaling laws for flow induced sound

2)(/ kdWW md 2)(/ kdWW dq and

where dis a length scale that indicates the size of the source

region.For flow generated sound, a rule of general validity is that thefrequency spectrum of the sound is proportional to afrequency fst, which is determined by a typical flow velocity U

and a typical size dof the source region, as

dUfst /=

That characteristic frequency fst, for flow generated noise, isusually called the Strouhal frequency

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Figure 3 For a cylindrical pole in an air flow, there is a periodic

shedding of vortices that gives rise to fluctuating forces. Soundgenerated in that way is called a Strouhal tone.

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case (I):

There is flow about a cylindrical barrier.

Around that barrier, a periodic vortex shedding begins at very

small Reynolds numbers (based on the diameter of the cylinder).

That shedding gives rise to fluctuating forces, which correspond

to dipole sources.

The Strouhal -frequency is obtained by choosing Uas the

velocity of the flow field and das the diameter of the cylinder.

The sound generated is relatively narrow banded;

except for large Reynolds numbers, it is a tone-like sound, the

Strouhal tone, with a frequency proportional tofst.

Reynolds number is defined as Re = Ud/v, where vis thekinematic viscosity

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second case (II):

a non-pulsating turbulent jet flow exits a duct.

The jet corresponds to a distribution of quadrupolesources.

The Strouhal frequency is obtained by choosing Uto be the jets velocity and d to be the diameter ofthe duct.

The sound generated is broad-banded, with afrequency content that is proportional to, fst.

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third case (III):

A propellor rotates in an otherwise still fluid,

at a rotational frequency f0.

The blades of the propellor generate time-

varying forces on the surrounding fluid,and thereby constitute dipole-type sources.

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From the perspective of a listener that does not movethrough the fluid, the time-variation of the forces has twocauses:

the blade rotation; and,

the turbulence in the flow fields around the blades.

The rotation brings about a periodic time dependence.

If all of the blades are alike, the blade force distribution is

repeated every time the propeller rotates through an angle2p/K, where Kis the number of blades.

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Choice of characteristic velocity, U, and characteristic length, d, forcalculating the Strouhal frequency, fst= U/d, in three different cases.

Case I Periodic vortex shedding

Vortex shedding frequency fvs = 0.2 U/d

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Case II Turbulent jet

Harmonics offst

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Case III Propeller

f0 Rotational frequency

K Number of blades

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To estimate the size of the source region, measured in the He number,

{ } MdUfc

dfkdHe st

st

2/2

=====

where M= U/cis the Mach number

2

/ MWW md

2/ MWW dq

and

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For Monopole:

20

20

~QckWm

cd

U

c

fk

st 22 ==

cUdWm 420

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For a dipole :

3620 cUdWd

For a quadrupole :

5820 cUdWq

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T bl Fl i d d d S li l f d i


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Table 4 Flow induced sound. Scaling laws for sound power insound fields with different dimensions. U is a characteristic

velocity, and da characteristic length.

02 2

cd U 02 4

d U c 02 6 3

d U c

0 2 7 4d U c02 3d U 0

2 5 2d U c

0

2 4

d U c 02 6 3

d U c 02 8 5

d U c

Dimension Monopole Dipole Quadrupole

1-D

2-D

3-D

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Most applications involve Mach-numbers much lessthan 1

Here, we first look for monopole type of mechanisms.

If there are no fluctuating volume processes involvedThe second or dipole type of mechanism will dominate.

This mechanism involves unsteady fluid forcesproduced by moving (rotating surfaces), but unsteadyfluid forces also occur around objects with flow separation.

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The weakest source for the low Mach-number case is the

quadrupole corresponding to free turbulence. Generally flow separation is involved ; this source isoften impossible to observe for the low Mach-number case.

Low Mach-number : The internal combustion (IC-) engine

Figure 2 An IC-engine exhaust system producing a pulsating volume

flow and representing a monopole type of source.

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The engine is a heat driven piston machine producing a volumeflow in the intake and exhaust systems.

This volume flow has a steady part plus an unsteady part

related to the number of cylinders and the details of the enginedesign.

The Mach-numbers involved (in the intake or exhaust pipes)

are typically less than 0.3.

This implies that there is 10 dB difference between themonopole and dipole type of sources.

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This is not very large so one should not entirely neglectsound from flow separation in the intake or exhaust

system.

However, the effect of the jetnoise at the outlet of theexhaust pipe should be of the order of 20 dB less than themonopole, so this is safe to neglect.

One can also note that if we consider the entire car ortruck the only monopole type of source comes from theIC-engine.

Since for low Mach-number applications this source isexpected to dominate the first thing one must put on anautomobile is a muffler!

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High Mach number range


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High Mach-number range

Mach-numbers of the order of 1

All three source mechanisms are equally important.

Mach-numbers > 1

shock-wave phenomena, (discontinuities in the flow field ,since flow field cannot travel faster than the local sound speed)

shock-waves are often non-stationary - they oscillate and changetheir shape or position in space.

During these motions the shock-wave surface will create bothunsteady volume flows and pressures,

represents a combination of monopole and dipole sources

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Figure 3 A modern high-by-pass ratio jet engine

Jet engine: a high Mach-number application.

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modern jet engines

high by-pass-ratio engines a high thrust is achieved using an exhaust jet with a largearea but with a reduced speed.

The engine consists of:

i. an inlet stage with a turbo-fan creating a by-pass flowoutside the gas turbine part.

ii. inlet compressor stages,

iii. the combustion chamber

iv. and then the outlet turbine stages.

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all three source mechanisms can play a role:

i. The combustion or unsteady heat release willgenerate changes in pressure and density and is amonopole type of source.

ii. The turbo-fan and the compressor/turbine bladesrepresent dipole types of source.

Also guide vane arrangements in the compressor/turbine

sections will generate unsteady fluid forces andcontribute to the dipole sound.

i. Finally, the exhaust jet which is a quadrupole type of

source.

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The case of liquids:


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The case of liquids:

The sound generating mechanisms are the same.

Mach-numbers are often much smaller than 0.1.

- since the speed of sound in most liquids is 4-5 timeshigher than in gases, and flow speeds involved aresmaller

This implies that sound produced by free turbulenceor quadrupole sound is not of interest.

However another phenomenon becomes important in the

liquid case and that is the possibility of a phase transition orcavitation.

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Important phenomenon - phase transition or cavitation.

Cavitation involves the creation of vapor bubbles inthe liquid, when the local (static) pressure is reducedto values close to or below the vapor pressure.

occurs in regions where the local flow speed islarge, e.g., at constrictions or at moving surfaces(propellers).

formation of a cavitation bubble - monopole type ofsource mechanism.

The pressure peaks generated by the rapidimplosion can also lead to mechanical wear (erosion).

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The periodic operation of a fluid machine implies that the

acoustic source processes also will be periodic.

Assuming that the machine has a cycle with time periodT0 then it will produce sound (and vibration) spectra which

contain harmonics of a fundamental frequency f0=1/T0.

Besides the periodic content there will always be non-periodic or random contributions to the sound from theturbulent part of the flow in the machine.

This will produce a broad-band contribution to thespectrum.

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f [Hz]

Level (dB)

f0 2f0 3f0

Broad-band part

Figure 4 Typical spectrum from a fluid machine

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6 3 Noise Control Techniques


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6.3 Noise Control Techniques

most efficient is always to modify the sources.

due to design limitations, economy or other reasons -

noise control along the transmission paths or at thereceivers

Sources

Transmission paths

Receivers

Figure 5 The chain source-transmission-receiver. Ideally noise

control should be done as early as possible in the chain

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2

W d U

where

= 4, 6 or 8 for the monopole, dipole and quadrupole,respectively.

W- Sound power,U- velocity,d-a length scale (size of source region) for noise control of the source - reduce the speed.

most pronounced for the jet noise case, where a 50%reduction in flow speed gives 24 dB reduction of the soundpower.

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Other noise control methods:

reduce the periodicity and the amplitude of theperiodic fluctuations by changing the geometry.

eg.(1) use fans with equal but unevenly spacedblades.

This will reduce the fundamental to the fan rpm and

will also give smaller amplitudes of the harmonics.

Creates a new problem : to properly balance the fan

negative effects on the aerodynamic performance.

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eg.(2) IC-engines,

use the intake or exhaust manifolds connecting thecylinders to shift the phase of the engine pulses tocancel certain engine harmonics.

For the intake side this kind of approach is not mainlyused for noise control but to tune the engine sound, e.g.,

to make it more sporty.

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Thank You

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6 fluid machine noise control

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