Aero acoustics of a flow pipe having a single small cavity

HAL Id: hal-01004729

https://hal.archives-ouvertes.fr/hal-01004729

Submitted on 11 Jun 2014

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Aero acoustics of a flow pipe having a single small cavity

Daniel Mazzoni, U. Kristiansen

To cite this version:

Daniel Mazzoni, U. Kristiansen. Aero acoustics of a flow pipe having a single small cavity. Forum

Acusticum 2011, Jun 2011, Aalborg, Denmark. http://www.fa2011.org/. �hal-01004729�

DanielMazzoni

LaboratoiredeMeaniqueetd'Aoustique,UPRCNRS7051,31heminJoseph-Aiguier,13402Mar-

seilleCedex20,Frane

UlfKristiansen

AoustisResearhenter,NTNU,O.S.Bragstadsplass2b,7491Trondheim,Norway.

Summary

The whistling of a pipe-avity system subjeted to an internal ow of uid is onsidered in this

paper.Thisphenomenononsistsinaself-sustainedosillationintheshearlayerthatdevelopsatthe

interfaebetweentheuidowinthepipeanduidintheavity.Somebasigeometrialrelations

regardingthesoundemissionareonsidered:theavitylength,andthedistanebetweentheairinlet

andtheavity.Thetestedpipeshadlengthsbetween

0 . 65

mand

1 . 459

m,andallthediameter

42

mm.

The maximumveloity was

30

m/s.A noise redutionexperiment isalso presented thatinvolvesa timeharmonisoundsuperposedonthewhistlingnoise.

PACSno.43.20.Ks,43.28.Ra

1. Introdution

Unstableowsanbeimportantnoisesouresorform

the basisof musialinstruments. A lassisystem is

the irular ylinder in a ross ow where Aeolian

tonesaregeneratedbyregularvortexshedding.Asys-

teminvolvinganunstableowandanaoustiavity

is the so-alledHelmholtz resonator, whih will pro-

duepuretoneswhenexposed toairow.

In this presentation we present resultsfrom mea-

surements on another simple and well dened aero-

aoustisystem:asmall avityattheend ofaylin-

drialpipe. Inthesimplest ase,the systemonsists

of two osillators, the shear layer above the avity,

and an aoustimode in the pipe. In our investiga-

tionwehaveonentratedonthelowermodesofthe

pipes;theaoustiwavelengthsarein allasesmuh

longerthantheavitydimensions.Withtheinuene

of sound, the shear layersabovethe avitiesare ex-

peted to behave in a modal fashion. These modes

mightbedesribedbywavelengthsoftheshearlayer

orresponding to the avity length, or, as is found

when the shear layers are exposed to strong aous-

tields andurlupinto separatevorties:numbers

ofvortiesrossingtheavityspanat thesametime

[2℄.

In part2 we present resultsfrom an investigation

ontheinueneofavitylengthonaspeiongu-

()EuropeanAoustisAssoiation

ration.Inpart3wegiveanexampleonhowamodal

tone generated by the ow might be strongly inu-

enedby an added aousti signalfrom an external

loudspeaker. Finally, in part 4,wehaveinvestigated

theinuene of the smoothpipe lengthupstream of

theavity.

2. Inuene of the avitylength on

the behavior of a whistling pipe

In this setion we fous on the aoustiresponse of

the pipe-avity system as a funtion of the stream-

wiselengthoftheavity.

The experimental system is presented in gure1:

Apipe-avitysystemisloatedontheupstreamside

of a box with a

32

^{m by}

32

^{m square setion and}

60

^{mlong.Downstreamofthisboxweuseavauum}

pumptoreateaowofair.Theboxontainsaloud-

speaker loated in front of the air outlet setion of

the pipe: This loudspeaker will be used in the next

setiontoreateanaoustiwavetravelingalongthe

pipe-avitysystem.Aradialavityofdepth

5

^mmand

variablelength

L c

^{in the}stream-wisediretion is in- sertedin the wallof thepipe. Theupstreamedge of

thisavityis loatedat

5

^{mmfrom theairinlet.The}

stream-wise avity length

L c

^{an vary} ontinuously from

0

^to

20

^{mm.Letusdenoteby}

L p

^{thelengthofthe}

pipewhenthe avityis absent(

L c = 0

^),

D = 4.2

^m

theinside diameter of thepipe,

U 0

^{is theowspeed}

measuredby athermal veloimeter at the enter of

Coustician, Sound: Template for EAA proceedings FORUM ACUSTICUM 2011

27. June - 1. July, Aalborg

Microphone

Velocimeter

Speaker

Lc L'c

Lt

L'c Acoustic Uo feedback

Uo

Figure1.Experimentalsystem

0 0.005 0.01 0.015 0.02

60 70 80 90 100 110 120 130

Cavity length (m)

Maximum SPL (dB)

V = 10 m/s ; L = 1.08 m ; Increasing Lc

mode 2 mode 3 mode 4

Figure2.MaximumSPLmeasuredinthepipe

1

mfrom theairinletasafuntionoftheavitylength

anvary from

0

^to

30

^{m/s. Theaousti pressureis}

measuredinsidethepipebyathinB&Kmirophone

sonde loated

1

^{m from the air inlet. The eigenfre-}

quenies

ν n

^{ofthispipeofaregivenby:}

ν n = c/(2 ∗ (L t + 0.8 ∗ D)) n = 1, 2, 3, ...

⁽¹⁾

where

c = 343

^{m/sisthespeedofsound,andnthe}

aoustimodenumber.

The gure 2 is obtained by measuring the maxi-

mum sound pressure level in a pipe

1.08

^{m long. It}

0 0.005 0.01 0.015 0.02

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Cavity length Lc (m)

Strouhal (f L

c

/ U

o

)

Strouhal of the maximun SPL increasing Lc

mode 2 mode 3 mode 4

Figure3.Strouhalnumbermeasuredinthepipe

1

mfrom theairinletasafuntionoftheavitylength

wasmeasuredinthepipe

1

^{mfromtheairinlet.fora}

owspeed

U 0 = 10

^{m/s, whentheavitylengthvary}

from

0

^to

20

^{mm.Thegure2showsthatthewhistling}

phenomenonstart when theavityin approximately

5

^mmlong:for

5

^mm

< L c < 12

^{mmthethird aousti}

modeofthepipeisexited.For

L c > 12

^mmthepipe

respondsonit'sseondaoustimode.Eahaousti

modeofthepipe(modes2,3,4)isexitedoverarange

ofavitylengths.Thesamebehaviorispresentedby

Erdem &al. in [3℄ when inreasing thespeedof the

ow:theavitymodesofthepipeareexitedbymul-

tiplerangesofowspeeds.

Forthe sameexperiment as presentedin gure2,

Figure 3 presents the Strouhal number based upon

theavitylength

f L c /U 0

^{plottedasafuntionofthe}

avity length

L c

^{. The gure 3 presents 3 segments}

with onstant slope

f /U 0

^{, the jumps between these}

segmentsrepresentahange oftheaoustimodeof

thepipe.onsideration

3. Inuene of an aousti wave on

the whistlingpipe

Thesoundattenuationin whistlingowpipesisstill

hallenging: In [3℄ the authors propose a redution

methodbasedondierenesinthelengthoftheinlet

andof theoutlet ofthepipes.In[4℄the authorsuse

aompression driverhanneledto theavity leading

edge to redue the avity ow tone. In [5℄ a loud-

speakerisusedtoperformnoiseattenuationinaor-

rugatedpipe.Inaverysimilarexperimentpresented

by [5℄,weusein this paperaloudspeakerloated in

front of the airoutlet setion of the pipe (see gure

1) to reate a tonal aousti wave traveling in the

TableI.Table givingthedetailsofpipesandavitylength.

L

p

L

c

L

t

= L

p

+ L

c

U

0

gure2

1 . 08

m 0to

20

mm

1 . 08

m

< L

t

< 1 . 1

m

10

m/s

gure3

1 . 08

m 0to

20

mm

1 . 08

m

< L

t

< 1 . 1

m

10

m/s

gure4

1 . 451

m

8

mm

1 . 459

m

11 . 5

m/s

0 1000 2000 3000 4000 5000

10 20 30 40 50 60 70 80 90 100 110

frequency Hz

dB

L

T

=1459mm, L

C

=8mm, V=11.5m/s

SPL without control

SPL with harmonic control at 3086Hz

Figure4.Additionofanharmonisoundatfrequeny

3086

Hz to the singing pipe: SPL vs frequeny measured at

13

mfromtheairinlet

pipe.Varyingthefrequenyandtheamplitudeofthis

tonal wave, we measure the aousti pressure when

the pipe is exited by the ow in a whistling speed

region. For this experiment, we use a pipe of total

length

L t = 1.459

^{mandaavityoflength}

L c = 8

^mm

exited at

U 0 = 11.5

^{m/s.Thesound pressurelevelis}

measuredonamirophonewallmountedin thepipe

at

13

^{mfrom theairinlet(seegure1).}

Theresultsarepresentedongure4:theblueurve

isthesoundpressurelevelmeasuredat

U 0 = 11.5

^m/s.

Awhistlingtonesoundwithamaximumsoundpres-

sure level of

108

^{dB at the frequeny}

462

^{Hz an be}

observed. Thistonal sound orrespondto thefourth

eigenmode of the pipe. The red urve is the sound

pressurelevelmeasuredonthesamemirophonewhen

anharmoni ontrolsound isgenerated bythe loud-

speakerat the frequeny

3086

^{Hz : the amplitude of}

thisontrolsoundisdeterminedempiriallybytuning

the amplier in order to observe theowtone noise

andtheontrol noiseatapproximatelythesamelev-

els.On theredurve,oneanseethat theowtone

noise of the whistling pipe has been redued from

108

^{dB to}

76

^{dB. Similar results are presented by [4℄}

foradierentgeometry:aavityowtonenoiseon-

4. Inuene of pipe length upstream

of avity

Somemeasurementswere doneto seewhat inuene

thesmoothpipesetionupstreamoftheavitywould

haveonthegeneratedtones.Forthesetests,theavity

length was kept onstant at 10mm at the end of a

645mmlongpipe.

4.1. 10mmlongavitywith 15mmand40mm

upstreamsetions

Someinitialtestingdemonstratedthatthepipewould

not sing (for veloities up to

U 0

^{= 26 m/s ) if the}

smoothupstreampipelengthwasshorterthan 5mm

or longer than 40mm, that is,

5mm ≤ L upstream ≤ 40mm

^{wasfoundtobeaneessaryonditionforgen-}

eratingthepipetones.

Figures5and6showresultsfortwo

L upstream

^on-

gurations,

15

^{mm and}

40

^{mm. The upper panel in}

eah gure show the sound pressurelevelas afun-

tionoftheaxisowveloity

U 0

^{.Thesoundpressures}

weremeasured

30

^{minfrontofthetube'sowentry}

setion,and

10

^{moaxis.Inthelowerpanelisplot-}

tedtheStrouhal number (

f · L cavity /U 0

^)againstthe

veloity.

Ingure5isseenthatthetonegenerationstartsat

about

6.5

^{m/s. The rst tone generated orresponds}

to the rst longitudinal pipe mode. With inreas-

ing veloity the tone rst jumps to the third modal

frequeny, before it lowers to the seond with even

higherveloities.Atthesametimeitisseenthatthe

Strouhalnumbersdesendwithinreasingveloityfor

eahmode.

Forthepipehavingalongerupstreamsetionitis

seen that the tone generation starts at about

9

^m/s

withtherstandseond modesgeneratedatlowve-

loities. Between

12

^and

16.5

^{m/s there is no sound}

generation.The 3rdand 2nd modes are then gener-

atedbeforethesystemjumps tothe4thmodeatthe

highveloities.ItisagainseenthattheStrouhalnum-

bersdesendmonotoniallyforeahmode.

Withtheinueneofsound,theshearlayersabove

theavitiesareexpetedto behavein amodal fash-

ion. Assuming the hydrodynami wave speed to be

approximatelyequaltohalf theaxisveloity,andas-

sumingtheavitylengthequal to onehalf hydrody-

namiwavelengthfor thersthydrodynami mode,

the orresponding Strouhal number equals

0.25

^{, [1℄.}

Also,undertheinueneofstrongaoustields,the

Coustician, Sound: Template for EAA proceedings FORUM ACUSTICUM 2011

27. June - 1. July, Aalborg

5 10 15 20 25

20 40 60 80 100

L

p

5 10 15 20 25

0.2 0.4 0.6 0.8

U

0

[m/s]

f L

c

/ U

0

Figure 5. Sound pressure level and Strouhal numberas

funtionof

U

0 ^for

10

mmavityhavinga

15

mmupstream setion. Mode 1(

240

Hz, ross), mode 2(

485

Hz, square), mode3(

715

Hz,irle),mode4(

955

Hz,star).

hydrodynamimodesanthenbeunderstoodasone,

ormorevortiespassingtheavitylength[2℄.

TheStrouhalnumbersin thepresentinvestigation

are seen to fall into groups desending towards

0.2

^,

0.4

^,and

0.6

^.Thehydrodynamimotionausingtonal generation is therefore indiated to represent one of

thethreelowesthydrodynamimodes.

Ingure7wehaveplottedthesoundpressurelevel

alongtheaxisgoingintothepipeaboutonehalfwave-

length.Thiswasdonebymovingamirophonesonde

intothepipe.Thedierentongurationsaregivenin

table II.Thelastolumn ofthistablegivestheratio

ofaoustipressureatthedownstreamavitysetion

dividedbythepressuremeasuredattherstpressure

antinode.Fromthegureitisseenthattheantinodal

pressuredereaseswithupstreampipelengthandbe-

omesmore"noisy".Itisalsointerestingtonotethat

forthedierentsituationspresented,theavityislo-

atedatverydierentloationsalongtherstpartof

thestandingwave.

Figure 5 was experimentally found by dereasing

theveloitiesthroughtherange.Around

11.5

^m/sthe

third mode was found to be stable. If the opposite

proedure was hosen, i.e. inreasing the veloities

through the region, the rst mode would be heard

atthesameveloity.Itwasobservedthatbothsitua-

tionswerestable. Itwashoweverpossibletogofrom

the low tone to the high by giving the ow an im-

pulse,likemovingthehandarosstheinowopening;

and from thehigh tone to thelowbysinginga tone

around

240

^{Hzintothepipeopening!Thetwospetra}

10 15 20 25

40 50 60 70 80 90

L

p

10 15 20 25

0.1 0.2 0.3 0.4 0.5 0.6

U

0

[m/s]

f L

c

/ U

0

Figure 6. Sound pressure level and Strouhal number as

funtionof

U

0^for

10

mmavityhavinga

40

mmupstream setion.

0 500 1000 1500 2000

0 20 40 60 80

Frequency [Hz]

L

p

[d B re . 2 0 µ P a ]

0 500 1000 1500 2000

0 20 40 60 80

U

Pi tot

=11.5m/s, L

front

= 15mm, L

cavi ty

= 10mm

Frequency [Hz]

L

p

[d B re . 2 0 µ P a ]

Figure8.Twostableonditions measuredforpipe"b"

5. CONCLUSIONS

It has been shown that a ow pipe having a single

small avity loseto theopeningwill sound at rela-

tivelyhighsoundpressurelevels.Forthepipetested,

itwasshownthattheavitylength,andthelengthof

thesmoothpipesetionupstreamoftheavity,have

tobewithinertainlimits.TheStrouhalnumbersal-

ulatedindiatethatthesoundgenerationinvolvethe

three lowest hydrodynami modesof the shear layer

−10 0 10 20 90

95 100 105 110 115 120 125 130

Pipe "b"

−10 0 10 20

90 95 100 105 110 115 120 125 130

Pipe "a"

Lp [dB re 2.10 −5 Pa]

−10 0 10 20

90 95 100 105 110 115 120 125 130

Pipe "c"

−10 0 10 20

90 95 100 105 110 115 120 125 130

Pipe "d"

Figure7.Soundpressurelevelmeasuredintopipealongaxisfor4dierentgeometries.x-axisisinm.Positionofavity

ismarkedwithvertiallines.

TableII.Tablegivingthedetailsofpipestestedingure3.

P ipe U

0

L L

upstream

L

cavity

F requency p

cavity

/p

max

"a" 13.6m/s 650mm 5mm 10mm 755Hz 0.44

"b" 11.5 660 15 10 740 0.52

"" 17.1 660 40 10 715 0.77

"d" 24.4 680 40 10 944 -

tonesoundfromaloudspeakerwouldreduetheow

generatedtoneonsiderably:a

32

^{dBredutionofthe}

whistling was observed in our experiment. As this

might havepratial appliations, we plan to inves-

tigate this eet more systematiallyin the time to

ome.

Referenes

[1℄ A.ChaigneandJ.Kergomard:Aoustiquedesinstru-

mentsdemusique.EditionsBelin2008.

[2℄ D. Tonon and B.J. Landry and S.P.C. Belfroid

and J.F.H. Willems and G.C.J. Hofmans and A.

Hirshberg: Whistling of a pipe system with multi-

plesidebranhes:Comparisonwithorrugated pipes.

JournalofSoundandVibration329210, 1007-1024.

[3℄ D. Erdem, D.Rokwell, P.Oshkai, M. Pollak.Flow

tones inapipeline-avitysystem:eetofpipeasym-

metry.JournalofFluidsandStrutures17(2003)511-

523.

[4℄ M. Debiasi, J. Little, E. Caraballo, X. Yuan, A.

StohastiEstimationontheControlofSubsoniCav-

ity Flow ? A Preliminary Study. AIAA Paper 2006-

3492,3rd AIAAFlow Control Conferene,San Fran-

iso,CA,June2006.

[5℄ V.F. Kopiev, M.A. Mironov, V.S. Solntseva. Sound

generation, ampliation and absorption by air

ow throughwaveguide withperiodially orrugated

boundary.Pro.ForumAoustium,Budapest,2005.