Experimental Determination Simonnet

8/12/2019 Experimental Determination Simonnet

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Chemical EngineeringScience62 (2007) 858866

www.elsevier.com/locate/ces

Exerimental!eterminationo"the!ragcoe"#cientinaswarmo"$%$$les

&.Simonnet'C.entric'E.lmos'*.&i!o%x

LaboratoiredesSciencesduGnieChimique,UPR6811,CNRS-ENSC-NPL, 1 rueGrand!i""e,#P$%&'1,'&%%1Nanc(Cede),*rance+eceive! 2,-%ne 2005 receive! in revise! "orm2, -%l2006 accete! 6cto$er2006

1vaila$leonline26cto$er 2006

Abstract

Sim%ltaneo%s meas%rements o" li%i! velocit$ laser 3oler velocimetr an!$%$$le velocit' !iameter' an! voi! "raction$ a!o%$le oticalro$eareer"orme! ina$%$$lecol%mn tost%! the in4%enceo" thevoi! "ractionon the relativevelocito"aswarmo"gas

$%$$les. %$$le !iameters db var "rom 2 to 0mm an! local voi! "ractions loc can reach 5. t is "o%n! that' "or loc


2/15

./Simonneteta"/0Chemica"EnineerinScience6$ 2$%%348'85866 85@where n is o"ten re"erre! to as Hthe +ichar!son an! Ga9iexonentI an! is a "%nction o" thearticle +enol!s n%m$er.

V is the velocit o" an isolate!$%$$le in a %iescent li%i!

an! can$e calc%late! %sing' "or instance' the correlation o"

-amialahma!ietal.(@@,)?

V= Vb0 Vb2 ' (2)V2 +V2

:heresentexerimental st%!aimsat testing thealica>

$ilit o" the a$ove>mentione! correlations to$%$$le col%mns

oerate!overawi!e rangeo"voi! "ractionan! toroosea

relia$lean!contin%o%s!ragcorrelation.

2. Experiments$/1/E)erimenta"setu

with

Vb0 =

0b b2

l+ ggd2

:heexerimentalset%(;ig.)consistso"as%are$%$$le

col%mn with a 0. 0. m2 cross>sectional area an! atotal height h o" m.1%m is %se! to circ%late the li%i!

hase

an!

8 lb g+2 l (!emineralie! water)' at a s%er#cial velocit Jl % to 0

cm/s. e"ore reaching the test section'waterasses thro%ghacon> vergent an! across two gri!s which ens%re %ni"orm

ro#leso" water velocities. :he gas hase (air) is inDecte!thro%gh caillaries (8 cm long an! 0.,, mm internal!iameter).e"ore

Vb2 = 2 g db+

.

enteringthesecaillaries'airassesthro%ghacalmingcham>

db( l+ g) 2Correlation(2)willtherea"ter$e%se!tocalc%latetheslive>

locito"anisolate!$%$$le.

$%lent 4ow regimes. :he !rag "orm%lation o$taine! has$een

teste!$rien$ergeran!=o"mann(@@2)inanE%lerianC;3

co!e$%t no imrovement in the mo!elre!ictions' comare!

to those achieve! with a !rag coe"#cient $ase! on thera!ial ositioninthecol%mn'was"o%n!.

:hero$lemo"all therece!ingcorrelations is that therel>

ativevelocitsho%l!$e$ase!onthelocalvoi!"raction'rather

thanontheglo$alonesincethe$%$$le$ehaviorisgoverne!$

localhenomena. :he can' however'$e %se! to sim%late the

4owh!ro!namics in thehomogeneo%s regimeo" the$%$$le

col%mn'when localan!glo$algashol!>%saree%al' since

$er containing aoro%slate' allowing all the nee!les to$e s%lie! %ni"orml with the gas. Fith this artic%larinDection sstem' a %ni"orm an! mono!iserseo%lation o"

$%$$lescan $e"orme! (arnieretal.'2002). tcanmoreover$e mo!i#e!' "or examle' to c%t o"" the s%l o" air in acaillar' in!een> !ent o" the others. :he s%er#cial gasvelocitJg can$evarie! "rom 0 to 8cm/s' correson!ing toa glo$al voi! "raction$e> tween0an!5aroximatel.


3/15

3emineral

iEe!

water +eservoir

Vrel =V(0/6

loc) (,)

"or loc


4/15

860 ./Simonneteta"/0Chemica"EnineerinScience6$ 2$%%348'85866$/$/Loca"measurementso7"iquid!e"ocit(andashasecharacteristics

0.4

0.35

gl

o

b

glob Pressure probesJ l

= 0 cm/s

$/$/1/Liquid!e"ocit(shi"te!$meanso"araggcell too$tain the

velocitsign.

0.3

0.25

0.2

0.15

0.1

0.05

0

loc Opticl probe Jl= 0 cm/s

glob Pressure probes Jl= 10 cm/s

loc Opticl probe Jl= 10 cm/s

0 1 2 3 4

Jg!cm/s"

rio!inarticles (!iameter 5 m' !ensit aro%n! 0009g/m6 )

are%se!asli%i!hasetracer$eca%setheirsettlingvelocitis

negligi$le comare! to the meas%re! velocities. :he !ata rate

mainl !een!s on the voi! "raction consi!ere! an! can var

"rom0 to500=.:hecomarison o" the!ata rateso$taine!

with an! witho%t see!ingarticles has shown the small in4%>

ence o" the$%$$les on the signal. :he ac%isition time o" all

themeas%rementser"orme!with s%re! with the oticalro$e are local mean val%es on a

n%m> $er o" $%$$les correson!ing aroximatel to theac%isition timeo"00s ta9enwith !ates the local voi! "raction meas%re!$ the otical

ro$e.

$/$/$/$/#ubb"e!e"ocit(/ :he$%$$levelocitiscalc%late!$inter>correlating the signal o$taine! "rom the #rstro$e to

thatemitte!$ the secon!ro$e.:hemaxim%mo" the inter>

correlation "%nction correson!s to the most li9el

resi!ence time o"$%$$le$etween the tworo$es. 3ivi!ing

the vertical !istance searating thero$e tis$ this timegivesthemean vertical$%$$levelocit.Vg has$eenchec9e!

$ comarison with the morerecise res%lts o$taine! with a

high>see!cam> era%ncertaint"o%n!wasa$o%t5.

$/$/$// #ubb"e equi!a"ent diameter/ :he average c%tchor! length o" a$%$$le crossing the !%al oticalro$e can

$ecal> c%late!"rom

Vg loc$/$/$/1/ Gasho"d-u/ 3ivi!ing the resi!ence time o"$%$$lesontheoticalro$e$thetotalac%isitiontimegivesthelocalvoi!"raction.

dchor! =2

' (6)bf

1tlows%er#cialgasvelocities'theregimeishomogeneo%s

in the col%mn' an! the satial$%$$le !istri$%tion is

%ni"orm

(Gahra!ni9 et al.' @@7 hole an! -oshi' 2005 :horat an!-oshi'200,). n this case' the time average voi! "raction loc '

o$taine! "rom local meas%rementser"orme! with the otical

ro$e'sho%l!$enearle%altotheglo$alvoi!"raction.Com>

arisonscanthere"ore$ema!e$etweenthislocalvoi!"ractionan! theglo$alvoi! "ractioncalc%late! "romress%remeas%re>

ments' to test theacc%raco" the!o%$leoticalro$e res%lts.

:heglo$alvoi!"ractioniso$taine!"romtworess%rero$essearate!$a9nown!istance(hres =60cm)as"ollows?

P


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where fb is the$%$$le "re%enc (&%rn et al.' 2005 :angetal.' 2005).:hisaverageierce! lengthcan$e relate! to themeanvertical$%$$le!iameterdvert $

2dchor! = dvert . (7)

E. (7) is$ase! on a statistical calc%lation o" the mean verti>

calchor!o"anellisoi!alo$Dect.;romtheanalsiso"ict%res

o$taine! with the high>see! camera' in the range o"

$%$$le !iametersst%!ie!'theratioE$etweentheverticalan!horion> tal $%$$le !iameter is "o%n! to $e constant an!

aroximatel e%al to 0.6. :his asect ratio is comrise!

$etween theval>

glo$ =lghres ' (5) %eso$taine!in%rewateran!theonesmeas%re!incontami>

nate!me!ia(Cli"tetal.'@78).:he9nowle!geo"Ean!o"the


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./Simonneteta"/0Chemica"EnineerinScience6$ 2$%%348'85866 86vertical!iameter#nall lea!s to themeanvol%mee%ivalent

!iametero"the$%$$le?

db=dvertE2/6 . (8)$/$//9eterminationo7themeanre"ati!e!e"ocit(andthedracoe7:cient

:he9nowle!geo" the$%$$levelocit'meas%re!$ theo>

ticalro$e' an! the li%i! velocit' meas%re!$ erimentall(3hotreetal.'200,)an!n%mericall

$solving

;ig. ,.


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ro#les. :his "actallows%stoass%methatthevariationo"the

$%$$lerelative


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862 ./Simonneteta"/0Chemica"EnineerinScience6$ 2$%%348'858660.5

0.4

0.3

0.2

0.1

0

Jl= ' cm/s

,r-ier et l. !2002"

*ocett & irptric !1'5"

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35loc

;ig. 5.%$$le relativevelocit vs. localvoi!"raction.

#tte! $ correlation () o$taine! exerimentall $

crit ' the variation o"relative velocit resents a s%!!en change? it increases

rai!l with the local voi! "raction an!$ecomes m%chgreaterthanV.:hisincrease is mainl !%e to three main

e""ects? coalescence o" $%$$les asiration o"$%$$les inwa9es o" therece!ing ones lea!ing to a rai! acceleration

an!thet%r$%lencein!%ce!$$%$$les.

:hecoalescenceo"$%$$leslea!stoanincreaseinthemean

$%$$les!iameters. n theconcerne! !iameter range' an in>

crease in the$%$$le !iameter in!%ces an increase in its

slivelocit.%tcomare! to the isolate!$%$$levelocit

(;ig. 5)' the meas%re! increase in the relative velocit

o" $%$$les is m%ch more rono%nce!. :he coalescence

alone canconse%entlnotexlainthetren!weo$serve!.

:heentrance o"$%$$les in thewa9e o" other$%$$lescan

lea! toa rai!acceleration$eca%se the s%!!enl%n!ergo

a!e> creaseintheir!ragan!areasirate!(shiian!G%$er'

@7@ ertola et al.' 200,) $ the rece!ing $%$$les.

Jrishnaetal.

velocit'resente! in Section .' will$e the conse%ence o"changesinthelocalvoi!"ractionan!not!%etolocalrecirc%la>tionatternsocc%rringin$%$$lecol%mnswitho%t"orce!li%i!4ow.1llthemeas%rementsresente!werethere"oreer"orme!at x/L = 0 an! y/L = 0' z/ h = 0.2' where the!istri$%tor e""ectsarenomorere!ominant'an!where the4atra!ialro> #leso" li%i!velocit an!voi! "ractionens%re theexistenceo" anhomogeneo%s regime in thecol%mn%ntilJg =5 cm/s (i.e.' the largestgass%er#cialvelocitst%!ie!"orJl=0 cm/s)an! whatevertheval%eo"Jg "orJl=0cm/s.// Re"ati!e!e"ocit(o7bubb"esin;uenceo7the!oid7raction

n ;ig. 5' the in4%ence o" the local voi! "raction on therelative velocit o"$%$$les is shown ( caillaries "e!an! Jl = @ cm/s). :his variation exhi$its two !istinct

$ehaviors. ;irst' "or a local voi! "raction less than acritical val%e' crit aro%n! 5' the relative velocit

!ecreases slowl when the voi!"ractionincreases.;ors%chcon!itions'therelativeveloc> it is$elow the velocit o" anisolate!$%$$le with the same !iameter (calc%late! "romcorrelation (2) with the $%$$le !i> ameter "rom ;ig. ).:hismeansthat"or loc


9/15

(@@@) have meas%re! an! sim%late!' %sing the vol%me

o" 4%i! metho!' the rise velocit o" a swarm o" large gas

$%$> $les. :he "o%n! that the acceleration "actor$etween

$%$$les inaswarman!isolate!$%$$lesco%l!lieintherange

o" 6 "or$%$$le>cas. :his tren! was also o$serve!$

Massaloan! J%mar(@@@)'whomeas%re!arelativevelocit!een!ing on $oth !iameters an! voi! "raction (0 ation when theass on the t%r$%lent e!!ies

si!es' instea! o" $eing entrae! $ e!!ies when the

t%r$%lence is not s%"#cient.

:he$ehavior we evi!ence is conse%entl in accor!ance with

the%$lishe! literat%re'$%t since themean !iameter increaseswith thevoi! "raction' thecontri$%tiono"eacharametercan>

not$e estimate!. ;or this reason' as exlaine! in Section .5'

meas%rementswerecarrie!o%twithconstant$%$$le!iameters

while increasing the local voi! "raction' to !etermine the onl

e""ecto"thelocalvoi!"ractionontherelativevelocit.

/&/Re"ati!e!e"ocit(o7bubb"es"iquid!e"ocit(in;uence:ost%! thein4%enceo"theli%i!velociton thevariation

o"therelativevelocit'exerimentshave$eencarrie!o%twith

vario%s s%er#cial li%i! velocities in the range 00cm/s.

;ig.6showsthattherelativevelocito"$%$$lesistotallin!e>

en!ento"theli%i!velocitinthecol%mn.:hishenomenon

is con#rme! $ arnier et al. (2002). Even when the

li%i! sweeing velocit is set to ero' the relative velocit

!oesnot


10/15

./Simonneteta"/0Chemica"EnineerinScience6$ 2$%%348'85866 860.'

0.(

0.

Jl= 0 cm/s Jl

= 2 cm/s J l=

cm/s Jl= '

cm/s

2

1.5

0.%

0.5

0.4

0.3

0.2

0.1

0 0.1 0.2 0.3 0.4

1

0.5

0

b % mm

% b mm

b ( mm

( b ' mm

' b 10 mmull ertio-

0 0.05 0.1 0.15 0.2 0.25 0.3loc

loc

;ig.6.%$$lerelativevelocitvs. localvoi!"ractionNli%i!velocit in4%>

ence.

;ig. 7. *ormalie! $%$$le relative velocit vs. local voi! "raction"or

Jl=@ cm/sNin4%ence o" the$%$$le!iameter.

exhi$it signi#cant change in comarison with exeriments

wherea li%i!4ow is imose!.;oro%rcol%mn con#g%ration'

we can there"ore concl%!e that the local li%i! recirc%lations

have a negligi$le e""ect on the relative $%$$le velocit

com> are!tothein4%enceo"thelocalvoi!"raction.

/'/9istributorin;uencee)erimentsithconstantbubb"ediameter

ne wa o" 9eeing the$%$$le !iameter constantwith var>io%s voi! "ractions is to mo!i" the n%m$er o" caillaries "e!

withair'"romtheHcaillariesIcon#g%rationinitiall%se!.

Conse%entl'$changing$oth thes%er#cialgasvelocitan!

then%m$ero"caillariess%lie!withair'ithas$eenossi$le

2

1.5

1

0.5

0

b mm

b mm

0 0.05 0.1 0.15 0.2 0.25 0.3

loc

to"orm$%$$leswithconstantmean!iameter(50.5 mm)over alarge range o" voi! "ractions this co%l!$e !one "or !iame>

ters varing "rom 6 to 0mm. :o show the onl in4%ence o"

the voi! "raction on the relative velocit' we investigate! the

ratio$etween the relative velocit meas%re! in the swarm o"

$%$$les an! the %ni%e$%$$le velocit "rom E. (2). ;ig.

7 shows the a$ove normalie! relative velocit as a "%nction

o" the local voi! "raction "or the !i""erent$%$$le !iameterval%es an! "or the H caillariesI con#g%ration (H"%ll

aerationI in the legen!' o$taine! "romolnomial #tting o"

therece!ing res%lts).

;rom ;ig. 7' we can #rst o$serve' consi!ering the$ehavior

o"theswarmo"67mm$%$$les'thatthevoi!"ractiononlin>

!%cesthe!ecreasingvelocit.;orthis!iameterrangean!voi!

"raction greater than 5' meas%rements cannot$eer"orme!

witho%rcaillaraerator.:hetransitiontowar!stheincreasing

velocit has conse%entl not$een o$serve!' with this$%$$le

sie.%tre"erring tootherwor9s(e.g.theexerimentalcontri>

$%tion$ arnier et al.' 2002' an! the n%merical aroach o"

ertolaetal.'200,'relingonthevol%meo"4%i!metho!)'we

cans%osethatthe$%$$lerelativevelocitwo%l!contin%eto!ecreasei"thelocalvoi!"ractionwas"%rtherincrease!'%sing

;ig. 8. *ormalie! $%$$le relative velocit vs. local voi! "raction"or

Jl=0 cm/sNin4%ence o" the$%$$le !iameter.

another gas "ee!ing !evice "or instance. arnier et al. (2002)

haveo$serve!thehin!rancee""ect%ntillocalvoi!"ractions%

to5with$%$$le!iameters$elow5.5mm.

;oraswarmo"$%$$leso"db>7mm'therelativevelocithas the same variation as the one o$serve! "or the Hcaillar> iescon#g%rationI? it!ecreases%ntil crit =5an!

increases $eon!' showing that the wa9e e""ects $ecome

re!ominant in comarison to the$%oanc re!%ction when

thevoi!"raction increases.&oreover'wecano$servethatthe

hin!rance e""ect on one han!' an! the acceleration e""ect on

theotherhan!'are in!een!ento" the$%$$le!iameter(as"ar

asitisgreaterthan

7mm"ortheacceleratione""ect).

:herece!ingo$servationshave$eenma!e"orJl=@ cm/s'an! theare similar to theoneso$taine!witho%t "orce!4owo" li%i! reresente! in;ig. 8.:he slight scatter o$serve! in

these#g%res(eseciallin;ig.7)islin9e!totheexerimental


11/15

%ncertainties.


12/15

86, ./Simonneteta"/0Chemica"EnineerinScience6$ 2$%%348'8586610 0.4

0.35

(0.3

%

0.25

0.2

6ter

6ter + 7ut-ol 0.04 8ol. 9

4 0.15

6ter2 6ter + 7ut-ol 0.04 8ol. 9

0.1

0.05

00 0.1 0.2 0.3 0.4

loc

00 0.1 0.2 0.3 0.4

loc

;ig. @. %$$le !iameter vs. local voi! "raction "or Jl=0 cm/sNe""ect o"$%tanola!!ition.

;ig.0.%$$lerelativevelocitvs.localvoi!"raction"orJlo"$%tanola!!ition.

=0 cm/sNe""ect

/6/n;uenceo7thesur7acetension:heresence o" alcohol in the li%i!hase is 9nown to

ma9e$%$$les more sherical as it !ecreases their sie' than9s

to a !ecrease o" the s%r"ace tension o" the !emineralie!

water (-amialahma!i an! &P ller>Steinhagen' @@2).:hishe>

nomenon has$een chec9e! here$ vis%aliations o" the$%$>

$les $ %sing a high>see! camera. :he vertical !iameter

o" the $%$$le is there"ore ass%me! to $e e%al to the

e%ivalent !iameter o" a sherical $%$$le. &oreover' the

lower s%r"ace tension with a!!ition o" alcohol re!%ces thesigni#cance o" the coalescence henomena' an! $%$$le

!iameterswill$esmaller than in %re water. n the resent

case' a!!ition o"$%tanol at0.0,vol to!emineralie!water(givingas%r"acetension

:,506*/m0 )ma!eitossi$leto9ee$%$$le!iame>

ters$elow5mm"orlocalvoi!"ractions%to5intheH

caillariesIcon#g%ration(;ig.@).

:he meas%rement o" the relative velocit o" $%$$les' in

theresence o"$%tanol' reveals that the hin!rance e""ect can

$e o$serve!$eon! the critical voi! "raction "o%n! a$ove

(;ig.0).

/3/


13/15

./Simonneteta"/0Chemica"EnineerinScience6$ 2$%%348'85866 8651.%

1.4

1.2

1

0.(

0.%

0.4

0.2

0

:a$le

;)perime-tl results

5'the"ollowing!ragcorrelationcan$e%se!"ortheair%rewatersstem?

m 2/m

b / '!imensionless

fb $%$$le"re%enc's0

g acceleration!%etogravit'm/s2

h heighto"thecol%mn'm

hres !istance$etweentheress%resensors'mJ s%er#cialvelocit'm/s

CDCD

=( loc) ( loc)m+ ,.8 loc . loc

()

L lengtho"thes%aresection'm

m exonentinE.()'!imensionlessn +ichar!sonan!Ga9i(@5,)exonent(E.())'

t is vali! "or$%$$le !iameters ranging "rom 5 to 0mm (oncon!ition thatdb>7mm "or loc >5)an! localvoi! "rac>tion less than 0. :he exonent m is chosen in s%ch a wathat the transition$etween the increasing an! !ecreasing !ragcoe"#cientocc%rs"oragiven crit .;orinstance';ig.shows

!atawithm=25'whichlea!to crit =5.4. Conclusion

nthisaer'theexerimentalst%!o"therelativevelocit

inaswarmo"$%$$leshas$eencarrie!o%t. thas le! to the

!eterminationo"thein4%enceo"thelocalvoi!"ractiononthe

$%$$lerelativevelocit.;or$%$$le!iameterslargerthan7mm'

it is "o%n! that' "oragashol!% lower thanacriticalval%e

near 5' the relative velocit is s%$Decte! to the

hin!rance e""ectan!!ecreaseswhenthevoi!"raction

increases.eon! thiscriticalval%e' theasiration in the

$%$$leswa9es res%lts inanincreasingrelativevelocitwith

thelocalvoi!"raction. :he rolelae!$ the$%$$le!iameterin thesevariations is !etermine!$ 9eeing it constant

(mo!i#cation o" the n%m$er o" caillaries aerate!) an!

varing the voi! "raction. &osto"theaers!ealingwith

thiss%$Decthavemeas%re!a


14/15

!imensionless

P ress%re!i""erence'KaV verticalcomonento"thevelocit'm/s

Vb0 'Vb2 arametersinthe-amialahma!ietal.(@@,)cor>

relation(E.(2))'m/s

Vrel relativevelocito"a$%$$le'm/sx'y'z !irections

Gree="etters

voi!"raction'!imensionless

!ensit!i""erence' = l g'9g/m6!namicviscosit'Kas

!ensit'9g/m6

s%r"acetensiono"li%i!'*/m

Subscrits

g gashasel li%i!hase

loc local

glo$ glo$al

crit critical re"erstoanisolate!$%$$leinanin#niteme!i%m


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866 ./Simonneteta"/0Chemica"EnineerinScience6$ 2$%%348'85866References

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Experimental Determination Simonnet

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