Fie ld an d La b or atory Studies of Mixing Tubes for Mar ine Outfall s
hy
©Ramdas N.Gowda,a.Eng.
Athesis submitt edtothe SchoolofGraduateStudies illpartialfulfillment ofthe requirementsfor the degree of
Master of Engineering
Faculty ofEngineeringandAppliedScience MemorialUnive rsityofNewfoundla nd
Ma.v, 1992
St. John's Newfoundland Canada
11+11
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ACKNOW LEDGEMENTS
Iamhighlyindebted toDr.J.J .Sh arpforhis rXl'rll l' ntSl1 l11'lTi~i<ll land~lIid,lI1n' duri ngthe cou rse of my studies .Iabo wouldliketo thankhimforLln-slI pl'"rllu- providedallthesetimes.
I amverygratefultoDr. C.A.Sha rpe,theAssociateDean,0(<':r,1<lu;llpSI,ll<lil's.
Dr.G.R.Peters ,the DeanofEngineeringandDr.T.II. Cllari,1.11l'Assurial., ·1)";111
or
Engineeringfortbc financial supportintheform of GrMluol.t,· Fellows hipalld Teach ingAssistantshipswhichmadethis workpossible.I amthankfulto myfriends for their support.Thanksarealso11111.'to Lll<'l.1',·hni,·,,1 steffespeci all y Mr.K.Gr iesand~Ir.D.Tilley,who had l-eon part.iculru-lyIwlpful intheexperimentalwork.
Finall yIwouldliketo than kmyfamily membersforthe-irlovoandillfl'd io ll.
Abstract
Irll:Tl"L~einlandcostsdue to urhanizalionhas led many coastal communities to- wnr,ls mar-ineontfal!s1I.Sa convenientmeansof disposing of domestic am] non toxic w••st,·.~.It bas ken commonpractice to usc submerged outfalla forsmalldischarges l<,li\k(~advantageoftile immediatedilutionavailableas theeffluent rises to the surface.Theprimeobject ive ofthe marineoutfall installationis to maximize the totaldilut ionofthewaste andto minimizeimpactonthemarine environment.Jet pumps or mixing tubes may be usedtoimprove theinitialdilution and to promote plumesubme rgence insmall outfalls. Theoretical and experimentalstudieshave hl,rncarried out hutfieldtria lshave beenvery limited.
St.llflies ha ve shownthatverylimited improvementin dilution;5obtainedwith conventionalmixing tubes. The basicreason for thisis that. the combinationof in- cn~IL,«~dflowand increased diameter of themixing tubemodifythe values of density' difference, relative depthanddensimetric Fronde number. Dueto these changes k·s.~mixing rakes place betweenthe end ofthe mixing tubeand the sur facethan wouldhavetaken place in theoriginaljet. discharged withouta mixingtube, The combinnrlon of increased dilutionwithinthemixingtube and decreased dilutionin thebuoyant jet has beenfoundtolimit the improvement factorof overall dilution
10,1factor of about two.
In this thesisexperiments on anovel shapeor mixing tube are described . This was designed to overcome the problems discussedabove andused a tra nsitionfrom a square sectio n atent ry to a two dimensiona lslotat the exit.The studyshowed thatbetter performan cecan be acheivedat lowvalues oftheFroudenumber.The improveme nt of overalldilutionwitha slotmixing tubecompared tothecircular mixingtubewashowever,fairly limited.
Littleinformationis availableto describethefieldperformanceormixingtubes, This lackwasrectifiedbyitfieldstudy run par alleltothelaborator ywork ,In this stu dy acirc ular mixing tubewasbuiltandinstalled on a smalloutfall located at Spaniardsbay ontheeast coast of theisland ofNewfoundland. Dye studies were do ne atthisinstallation to checkthe dilutionachieved inthe field.Comparisons were made between the performanceofa horizontal jetwith and witho ut themixing tubebutliul eimprovementin overall diluti on was acheivedwiththemixing tube. It wasfoundthatthemixing tubes performedbette r in the fieldthanwas theoretically predic ted .
iii
Contents
ListofFigures
List of Tables
1 Introducti on
2 Literat ur eReview 2.1 Jets ,plumeslindbuoyant.jds
2.1.1 General .
2.1.2 Buoyant jet .
2.1.3 Vertical buoyantjet. 2.U Twodimensionalbuoyantj~t 2.2 Factorsaffectingdilution.
ix xiii
Ifi
:!!J
2.2.1 Effecl of current .
2.2.2 Effect of waves 2.3 Met hodsof incre&!lingdilution.
2.3.1 Gent:ral . .
iv'
:17 :17
2.:J..I r1uoYl\l1t walljot
2.,1 ~kt!lo,ls
or
predilution.:U.2 2.:1.:1
2..1. \ 2.·1.2
Mult i-portdiffusers .
VCUlurielTcct Pre-dilution devices•
!\.li:<i l1~ lu bn
12 42
"
••• • • • ••• • ·1:1 2.LI !.imita.tionsorpre-dilution devices andmixi nglubes 4&
3 FieldStudiesofanExisti n g OceanOutfall :J.I Introduc tion..
:l.:! Spillli;jr<ls11a)' Outrilll :J.2.1 Out fall design. :1.2.2 Pumpcha mber
:1.:1 Preliminarypreparationfor fieldwork.•. .
50 50 ij[
.')1 . 53 5;
3.3.1 Sitevisit.•.• • •.•. .. .... .•.•..•. . .. • . 5;
3.3.2 Plan ningordyestudy 5;
;1,.1 rin;t FieldStudy . . .•..•. . .• . 3.3.3
:1.3..1 :1.3.5
Selectionord}'e.. Spectrcphctcm et cr Preliminaryarrangements
58 58 59 59 3..1.1 Init ial preparation .. . . .. . . . .. . ... . . . •. 59
:1..1.2 Tt'!ilsetupatoutfall sill'. :1.·1.:1 Ihtl"'of,lyr injf'("lion . :1.·1.-1 IniliaI Adj llsl llll-III Q£ 1<.,.1""l-llp. :1.·1.5 Prepa rarlon
or
rI~·.·solutio n3..1.6 Pumpingcycle •.
;1.;; Analysisof samples .. . :1.6 Theoreticaln~rificil.t ion. :1.7 Second field l'Lud)·.
:1.7.1 Initialprepa ration
;1.7.2 Putupiugcycle :1.7.;) Theor eticalwririra tioll_ :J.S FieldstudyormixingtllIM'S __
:I.S.I Designofmixingtubes_ :J.8.2 Thirdfieldstudy
;1.8.3 Theoreticalverificatio n. 3.8.·1 Removalormixingtubes. 3.9 Discus.~ion._. . . _ . _. . ._... ..
4 De velopmen toftwo dime nsionalslotmixingtube 4.1 Introduction•. . . . .
4.1.1 Multiplejcts .
4.2 Slotmixingtube •.. .. . ... ..
Iii
\.1 'i:1
Ii i
. ' . • , ,." ,
!Is
!t!1 1111
116
JJlj IJ7 I:! J
1.:1 Ex!H·rilllent....llI1C.KldSoftwodimensionalslot lIlixinJl;tubes. 12:)
:')La bor a tory studyorslotmixingtubes 134
;j.1 E:<pf'rilw'lJlalarrange ments :1.1.1 Experimentalset-up
5.1.2 Flowmiller ."i.I.:! Prdiminaryex perime nts
rd.·'
Samp lingmet hods .'U.S SllltlpJingdevice. .';.1.6 l-l" linilYmete r.. :'i.2 Experimenta lprocedure.'i.2.1 G"flNal .').:!.2 Saltwater preparation :').2.3 Tel'tprocedure
1:11
•••• •••• • •••• • 1:j.J 1:);"1 I:l!) [-12
••• • • • • • • •• •1·15 H~
I-I!.!
1·19 I.,)()
5.:1Analysisor!k\mples•.• •..••. . . • •. . • • .• . .'i.·1Calculationordilution...
5.5 Second set orexperiments.•.
5.6 Calculatio nor overall dilution 5.7 Discu ssion. . .
6 Concl us io nandRecomm en datio ns 6.1 FieldStudy •..
6') ExperimentalStudy .
vii
163
!61
'9.
194 195
Ii.:l He-onuueudetiousforIurtlu-r [,lh"ral"ryn's"arrh
7 Ref er-enc e s
8 App e n dix
...iii
1%
:m·l
List of F ig ures
:!.l lnttlal dilutio n afterHawn ,Bower m an and Brooks, (1%0 )
oJ" Crosssectional profile of a buoyantjet(Abra ham, 1963) II.
:!.:J Zoneof1101'1establishmentandZOI\l)ofestablished flow [Albertso n
t-Lal.,I~J.''jO) 12
'.!..l l'redioticn ofsurfac e dilu t ion ofItbuoyantjet afterAbraham(1%:1) II :?..'i (;"llC'ralisf"[d\1l.rlofvariousworker sforsurfacedilut ion of abuoyant
jcl(Li sl'lh.l!JiO) . Ii
:?f; Flowpa ra me tersinvolvedin thetheoreticalanalysis ofbuoyan tplume
(Mor t on ctal.,19.')6). 18
'2."j Generalsolutionfor11'10dimensionalbuoyantjet Abraham(1!J65) . 28 2.MDilution of slotbuoyantjets in stagnantuniformenvironments(Fan
andBrook s,19(9).. 30
2.9 Grap hicalre presenta t ion ofcentre'line dilutionfortwo dlmenslonal buoyantje tinstagnantenvironmentandco m pariso nwithexpert-
mental data (Ccderwall,1971).. . . . • , 31
2.10 Basic methodsclincreasingthe surface dilutionof buoyant jet (Rawn
Iltal.,1960) 38
2. 11ImprovementFactorsofsurfacedilution usingDissi:"ators(Snook,
W69). 41
2.12Circular mixingtube(Argaman etal.,1975) . ,15
ix
2.13Improvement factors for overa lldilutionu~ i l1ga eircularrni .~ illgln hl '
(Arg am a n e t al.1975) Hi
:].1 locationofSpania rds Bayo\1tfall. ;)~
3.2 Cross secrlon showing the depthof till'outfall .",1 3.3 Cross sect ionshowingthe details oftoe disrlm rgillp;nm:",I,'!!atI,Ill'
rnltfull ~
:3." Crosssectionofpumpcha mber alongwithautomaticl1oatllpl'r;lt.,~1
switches ;,li
a . . )
Testset- up attheout fallsite Ii:!:J.6 Calibra tioncha r t ofspect re photomet e rused.Illring lirs t;Ul,l '~!'''''lld
field st udies li7
:1.7 Dimension softhecircular mixinglubeinstalledduringlhinlIh·ld
study. !II
:1.8 Photograph. of theactualMixingTubeinstallednt Spaniardshily :1;, 3.9 Photograph of themixing lube after being removed fromthe~"a. lOti 3.10Experimentalscatt er in measured dilutionwhencompa red tocalrn-
lated theoreticaldilutionfor verticalandhorizonta l lIozz1,'s . Ill:!
3.11Experimentalscatter in measureddilution whenco mpa red tocnh:u- lated theoretical dilutionfo r circularmixing tube IU....I
4.1 Arrangementof multiplejets. II!!
4.2 Development of the slotmixingtube 111
4.3 Basiclengthsof the slotmixing tube l'l.'i
·1..1Actual dimensions of the Model Xl 11~
4.5 Photograph oftheModel Xl.. 1:!!J
Hi Dimensionsof the i\'lodclXl . 130
,U Pholograph oftheModel X2, .. 131
Ul Dimensions c,fthe Model VI . L32
.I.!J Photogra phofthe~IodelVI. 133
:;.1 Experimenta lSet-up 1;16
.'",.:.1. Photogra ph of theExperimentalSet-up. 137
.'l.:l Photogra ph
or
theFlowmeter.. 138riA Flowpatter nwith in the slotmixing tube duringthe nrsttest(~Iodel
Xl) loll
!;. :; Baines used todividethe flowwithinthe slotmixingtube 1-11 .'"J.!i Flowpatternwit hi nlite slotmixingtubewit h threebaffles[Model
xn ,
1·13.'j.7 Flow pauemwithbellsha ped sides and central baffle(ModelXl). 1,13
!j.S Photogra phofthe mixingtubeandsamplingdevice inplace . H7
5.!J Flowpara meters
or
a slot mixingtube 156!j.IOVariati onofdilut ionnwithinthe mixing tube with the Areara tio. 159 5.11Variationof dilutionnwithinthe mixing tube wit h theArea ra tio . 160 5.12VariationofinitialdilutionnwithjetFronde number 162 5.13Variati on ofdilutio nnwithinthemixingtubewit hjetFrondenum-
berFduri ngthesecond set of Experiments(ModelXlandXl) .. 165 S.l ·lVariation ofdilutio nnwit hinthemixing tubewit hjetFroude num-
berF(ModelYI). 168
xi
5.15 Graphicalreprese ntat io nofcenter-linedilution rurtwollillll'n~iun;,1 buoyantjet in stagnant enviroumcur and comparisonwithI·X\>t-ri·
mentaldata[Cederwall etal.1911).. .. I7n
5.16Improve me ntofover a lldilutio nof~Iotmixing tul....lllo ~ lc-IsXI;,n,1 X2whencompare dto circularmixing till... 17,·, 5.17Im provementofoveralldilutionofslotmixingtub e mOII"1YI\\'IU'n
comparedtocircularmixingtube .. . IiIi
S.l SamplingpointsforModelsXIand ;.(2 :!lJ:,
8,2 SamplingpointsforModelYl, :!nrl
xii
Lis t of T ables
:U TheoreticalimprovementfactorsforYo/d<O.5F6, (Sharp, 1978) 49
a.l Inllow fateofsewage intothe pumpingchamber. 74' :1.2 Calibration table of spectra-photomete rused duringfirst and second
r,ddstudies... . .. . 75
:\.:l Analysisof samplescollected at the sea during the first field study. T6 :1.-1 Analysis of samplescollectedat the pumpchamberduringfirstfield
study. . . ii
;).5 Measureddilutionduringfirst fieldstudy . 78
3.6 Calculation of inflowrate and outflow rateof theoutfall during first
fieldstudy. 79
3.7 Calculatedtheoretical dilut ion forthe verticalnozzleinstalledatthe
outfallduringfirst fieldstud y . . . ... 80
:1.8 Analysis of samplescollected atthe sea duringthe second fieldstudy86 :
3.9 Analysis of samplescollectedat the seaduringthesecond fieldstudy 87 :1.10 Analysisofsamples collectedatthepumpchamberduringsecond
fieldstudy, , . 88
:1.11Ana.lysisofsamplescollectedatthepumpchamberduring second
ficldetudy. . . ., ..,.. . . 89
xiii
3.12 Measured dilutio nduri ngsecond Iidllstudy ~111
;J.13Measureddilutio n du ring secondHeldstudy !H
3.14Calculationofinflow rate andout flowrnw oftheoutfall(tu riu!!;M',',
ondfield study !1:.!
3.15Calculated theor et icaldilut ion for thehor izont al1101.1.1,·ins t all..,lat theout fall duringseco ndfieldstudy... ~l:l 3.16 Calibrationtableofspectro-photomet e r useddur ingtIll't.h irdf..l,!
study. IlH;
:l.I7Analysisofsamplescollectedat thesell.duringthethirdli..I,1sl.II<1.v 107 :J.l8 Analysisofsa m plescollected at theseaJuringtilethird11,,1,1slluly IIlH 3.19 Analysis ofsamplescollectedatthe pumpchamberdurillgt.hinl lipid
study. IO!)
3.20Analysisof samples collectedatthepumpchamberdllrinl-\thir,1li(,ld
study. 110
3.21Measureddilutio ndurin gthirdfieldstudy III
3.22Measureddilu t iondur ingthird field study II:.!
3.23 Calcul ation of inflow rateandoutflowrateof the out fa ll,luring thir d
fieldstudy .. 11:1
3.24 Calcu late d theo reti caldilut ionfor thecircula rmixing tuncat tllf' outfalldu ring thirdfieldstudy .. , . . . .... IJ.I 3.25 Summaryof calculatedandmeasur eddilut ionsduri ngtil(!lid d~tll, tyIl:i
4.1 Typica lvaluesof the lengthTLianddivergence ungle0ofMuddXI
t:w
5.1 Salin ity ofsamplesatQ
=
4.72XIO-JmJ/.~measureddu r ing thetest6 . ][H
5.2 Avera gedilut ion withinthe slot mixing tube during testa1 to-1 17!J
.'i.:l Avenlh'Cdilutionwithinthe slotmixing tube during te:sts .5to 9 180
!;A Averagedilutionwithin the slotmixingtubeJuring test s10to14.181 ',..'j Averagedilution within th ...slotmixing tube (luring test sIS to19. 182
!j.G Averagedilutlon withinthe slotmixing tube during tests20to 24 .183
"i.7 Average dilutionwithintheslot mixingtube during second seriesof
tests2.) Lo28 ••. 184
!i.l3 Average dilution withi ntheslotmixingtube during second seriesof
test s 2!)to:j:l 185
.'i.9 Avcfil.gcdilutionwithintheslo t mixing tube during second seriesof
tc-sts34 to 38.. IS6
0.10Averagedilutionwithin theslo t mixingtubeduringsecond seriesof tests:l9 to4:J.. .... . . ... lSi
;j. l[Averagedilutionwith in theslot mixing tube duringsecondseries of
tests",Ito·18 .... . ... .• • . IS8
5.12Averngediluti onwithin theslot mixingtubeVIduring tests49to.')2189 5.13Average dil utio nwithi nthe slotmixingtube duri ng secondse ries of
tests53to 56 190
f).ltIPredicted overalldilutionoftheslotmixingtubeModelsXl and X2191 5.15Improvementof overalldilutionof Mode l XlandX2 whencompared
tocircular mixingtube ... . , . .. .. .. 192
5.16Pre d ictedoverall dilutionor the slotmixingtube (ModelVI)... 193 5.17Improvementofoveralldilut ion ofMode lVIwhencompared to cir-
cularmixing tube . 193
Chapter 1 Introduction
Asland costs continue10escalate due to incecnscd IIt1l1l1l1;(1I.t10I1,morr-and111U I"'-
coastal communitie sate turning tomarine01l1fa1l5as a('tJIl H'l l il' III Ilt P ilIiS["I"dis- posingof domesticandnontoxicindustrialwa~ll's . Theproo'sainvolvr-sSO li I!' pretreatme nt onsho re to removesuspendedsolidsam] Iloaling man.rinlsr' llIuw('r1 bydischa rgeoffshore at adepthwellbelowlow water. Theprimeubj,'divl'
<lr
tlu- marine outfallis tomaximise physicaldilutio n ofthewa.~ll·to protl'rltIll''llI;l li ty ofthemarine environment.Followingdilutionanddisperaicu, organic wastesJUI' stabil izedbynat uralprocesses which .withproper<lesign, occurwit houteuvlron- men t aloraesthe ticdamagetotheenvironment.Comparisonsbetweenthe performance oflandbasedsecondarylr"atnwnlplauts and oceanoutfallsare often made asiftheywere comparisonsbetweenfull trent. men tandtotallack o(treatment. Thisapproach 10the problemis misleadingand irra tional becausetheprima rydiffere nce betweenthetwo liesinthe location,"HI not inthe manner oftreatment.Ina secondarytreatment plan tsCWIl.W~wllsksar"
stnhlllzed hy theecucn ofbacteria and other micro-organismsin enclosedbasins,In thf:seathe sa llieresult is obtainedI>ycssentially similarprocesses[albeit natural) Iml thesizeofthe treatment zoneis increased while the concentrationofpollutants is re-duced.Onemajor differenceis thedegree of controlexertedover thetwo types of trea tment, Landtreat mentplants havecloselycontrolled purification processes whereastheonlycontroloverthe nat uraltreatmentwhich occursinthe ocean lies in the choice of the outfallsite.thedesign ofthe outfalland the permissib leload- lug. Thus,dilution is very importantinthe design of ocean outfalls. Not only does it decreasethe concentrationof wastes,italso provides an ambientsourceor' dissolvedoxygen sothat aerobicbacteriaandhigherformsof lire flourishwithout depletingthe dissolved oxygenconcentr ation.Ithasbeendocumentedthatunder suit ab lewind,wave andcurrentconditions,ocean outfallsprovide favo urablere- duct .ioninBODatless cost(ClonghandCannon,1981)andatless damageto the environm ent(AllenandSharp, 1987)thanland based treatmentplants.
Itis oftenassumed,for example,thatland treatmentprovidesa pure effluent with110~idceffects.Howeverliquidwastesfollowingtreat mentareusuallyrich in nutrientsand,when dischargedtothe sea , the relativelyclear outflow concealsthe foodimmediatelyavailable foralgaegrowth.Thlaisnot thecase when effluentis dischargedth rough an outfalL Underthese cond itions tbe organicmatteris widely dispersedandbreaksdown slowly. Thesametotalamountofnutrient isavailable butthisisreleased slowlyoverawidearea.Oceanoutfalls seem tobe particularly suitableto small,remote. coastalcommunities wheredomestic sewageco nstitutes themajor partoftheeffluent .In additionan outfallis an alter nativebecause mostofthecostis forcapital works andthe syst em needsverylittle maint enance
whenco mpared toasecondary treatment plant.·1'I11'simp ll'Slsp'l,·mof,l is ll<~i' lp;
of effluent ,commoninthe('ase of sma ll disdlilrg.:s.rcuxistsofIwadw"l·kaml a longpipewhichrunsfrom theshore IiIII' towe-ll1,..lowtIl'·1,,11'wnternuu-k.TIl<' effluen tisdischargedthroughacircularT10Z~lcal lin- ,'n,1"fIh.·pip,"Tllt'llI'i,,1 work usuallyconsistsofgritchambersto remo ve~llspt-· l1.I,·dsoli d s illlda[mill!, chambe r. Automaticpumpswithfloatoperated swithesaw1IS( ' .1topumplilt' collect e dsewageatnregular in t e r valof time, For'iltgt~rlIowsit.is"0111111011hi ll S"
amultiportdiffuser inwhicheffluentisdis('hlltp;, ~ dthrnug hits,' rip:<ofIMlrl,1i10";11" ,1 along the lengthofthe diffuserpipe.Th is met ho dlim;Iw,'nIIs"dslltTl'ssftlllyfur decades but,therehasalso been cunsiderabicinterestillt.hed,·v"ltJlllI\t"lIl.
or
uflu-r- deviceswhich,bysomemeansofpremi xi ng,Increase thediloriou"",'ulllun'thall(,1I1lbe achievedbymult iport diffusers.
VarioustYI"JCsofbarnes andobstructionstothef10 lY havehl~,tl l r i " dinan ..rfurL 10 increas edilutio n above thatwhichcanheobtained hy a simplejr-t,lisdlilrp;(~,.let- pumps, or mixingtubes , have also been advocated on varlens()cnl.';inn ~(S ill'l'Sr"r 1967,Argaman , etal., 1975, Agg,ctal.,U1H),Theseoperatewi thdllill·nt.Iwiuv, discharged from anozzleintoalargerdiameterpipe,themixing tuhe, inSlIrl l;~
way thatreceivingwaterisent ra ined 11,1entrythusdilutin gthedIluentwitluntlH~
mixingtubeitself.However,it hasbeenshownboth theoretically(Shar p,I!J7H) and experimentally(Argaman,ot11.1.,197.'))that the increase in <lillltio ll':'l.lIsl'r1I,y uscof thesemixingtub esislimit ed to a factorof abouttwo.This isbecause, pn-.
dilutionchangesthe characterist icsof the jet suchthatsubsequentdillltif)lIIJI~h'''l~'Jl themixi ngtub e and thesurfaceislessthan the dilutionwhichcouldhenb t airl<'d withoutthe tube. The gainindilution withinthetube isthns olfse tlIyared uction
in dilutionbetweenthe tu nelUlUthe surface.
'I' h isthl$i~fJf!Sni b(~sfiddandlaboratorystudiesrelatedtoth euseandeffectiveness
"fmixiugtubes.Despite some previoustheo reticaland laborato ry work on cylin- drinJmixing Luhcs. nofielddatahas beencollected or reportedto showwhether laboratoryresultscan be scaledupforuse inthefie ld,Tore medy this lack.cylin- drica lmixingtubes weredesigned andinsta lledon asmall out fall onthe east coast
of~'?I\"foll n dlalld. Dye stu dies we re undertaken to determ ine whe t her dilutions
measured inthefieldwere the same asthosewhichcouldbe predictedfrom prc-.
viouslyrep orted la boratory studies.The lubeswere lefl inplaceoverthe winter months nn dwere thenexamined todetermi newhe t herthe designwas adequate towid-st.aridthe winter wea ther.Alongside thisfieldworka laboratorystudy was undertakenfor anovelshape ofmixing tube.Thiswasdesigned tooverco me the problcue whichw(;'re responsible forlimitingthe improvementof a cylindricalmix- ing tubeto afactor of about2.0. Twodiffere ntshapes ofmixi ng tube werestudied in thelabo r-atoryandmeasu rements weremadeof the predilution obtained within eachtube.The tu beswere designed toconve rttheflowfrom a circula rjet ente ring th elubeint o a twodlmens lonalflo wfrom aslot atthe end of thetube.Previous
~tlldiesoftwo dime nsionaljets thenmade itpcsslbleto calc ulatethe overa lldilu- tiou whichcould beobtained.It sh ould beemphasizedhowevertha tthe primary intentionofthis st udywasto dete r minewh et her the shapechosenrepresenteda fC'as ible alter nativetothemorecommon cy lind rical tuberatherthanto prov ide a detailed de signforpractica l use.
Chapter 2
Literature Review
2. 1 J et s, plume s a n d buoyant jet s
2.1. 1 GeneralWhenflu id is dis ch a rgedfr o m acir cu lar nozzle lat o a!lotherlIuid.tile n'1illl till/!,1I" IV maybe described as a pure(or momentum) jet,a hlloyanlplumeor aItI1ll)"' Ull. j l'l..
When no c.ensitydifferenceexistsbetweenthetwo fluids thert'silltiugII,)\\'L"\t!l il l of a pure je t . The trajectory isa straightline in the rilrccfiouoftill'11m:;,,),·;\~is and mixingoccursbecauseof the initialmomentu m givento tlwnownsitI.·;\\',,,~
the nozzle . Ifa densitydifferenceexists,huttherei~noinitial momentu m,l!1(' res ultingBowis calleda buoyant plume.Thisisunusualin practicel)l'(aIlSf~sonll' initialmomentum is almostalway spresent.However theflow ofIwal,·,1air[nnu a warmpo int source(eg.a cigaretteend) orofmel ti ng...aterfromafresh wall'r glaciersubmergedinsea water would be very plumelike. III a true plumetheflowb vertical.Wben densitydifferenceandinitialmomentumare hull!prl~f'liltllf'fluw
isIl'rJIKotlahllopulljet.Momentum dominatesneuthedischargenozzleand the fluwinlhillr<'.!~iolli'l similarto that
or
a pureje t.However,Allthe initial ll1olllC'ntum isl1i,,~i p",h..I,hlloyancybeeomesmore importan t. The flowpassesthrougha stage wherebothmomentu mandbuoyancyareimpo rt antbutasdislan ce fromthe nozzle iur reases buoya ncybecomesmore andmore domina nt.\Vith sufficientdepththe initial mom e ntummayhecompletelydissipatedendthefluidthen rises underthe actionofbuoyancyalone.lnthisregion theHowisalmilar10that ofabuoyant1'11i1Ill',
This thesisrdall~primar ilyto theeffectof mixingtubesonoceanoutfallsdischerg- iug ...llIuentwithbuoyan cyand momentum.Theliter ature surveywilltherefore rono-ntratcOilhuuyallt jels and mixingtubes. Plumesandmomentum jetswillhe considered on lyin!IOfar as tht'irunde rstan dingimpactsonan Undl'tslan(lingor bnop.ntjt:'ls.
2.1.2 Bu oya nt jet
Whena buoyanteffluent flowsinto stillwaterCromtheendof a horizontalpipe,it is immedia telyacted uponby a buoyantforce,themagnitude of whichdependson thedensitydifference betweenthe effluentandthe receiving water.Thiscausesthe jet ofeffluen t to be deflected and accelerated towardsthesurface. As shear stress es arcset up betw eentherisingjetand thesurrou nd ing wate r, tur bulenceisgenerated and mixingtakesplace,first aroundthe periph er y orthejet and finally througho u t thewhole colu mn.With continuedmixing,thedensitydifferencebetweenthejet or effluent andthe surrounding waterdecreases in proport iontothe amountor mi.o:ing.
Sincemixingismost pronouncedarOIHU[tlu-,·d.!!,·:;uf thed., ill,a; n,1111Ll1l.itisIhis partof theco lumn which isd...cd,'wl,'drtluslrapi,lI,I'.Ih11s"'ll in~III'"''''''l1d,'f,1 shea r stressesandca us ingturbulent I1lbdll,a;th rtl ll!!;bulit t11l'"Illjrt·"nlmll ll,
TheearliestexperimentsOilbuoyant j,·t s were "olldnd ,'dhyHHI\'1l;1I 11[l'nlun-r (1930)who cantileveredanozz lefroma raft lu Los "\llgd ,'14 harbour ;Hul,'"11",,,,·,[
dyesamplesatthe boilofthej<,t,iI.!l·aSllrl'mt' ntsufslIffa...'dilutiou11"'n 'millt., and some empirical formulaewere der iver].Itwaslall 'rfoundLlratth,'"lllpir i";,1 formu laewerenot universallyapplicable.
Thedatncolle ctedbyHawnandPalmerwrrt-fl"'i1llaIF I'<tbyH,1WU.111J\\'NIWlIIillid Brooks(1!)60 )whocalculat edthedl'usinll'trkFro ml!'11111111,,,1'.
/.'0..
til"1I"yl,,)I,'-' number,!l..an d therela tive depth}'~ /dforeachl,':<t.I;silll;I'ilrti;'['1Il'11.\'sis111<'y showedthatSf> dil u t ionof the jetfluiddefinedas the ratioofceucentrnrion
ofthejetfluidatany pointto theconc ent rat ion of thejetfluidat thedischargepoint FA densimetricFrondenumberdefined as
Q/t ..f71'J!
R.. Reynoldsnumberde fined as
Q/t/ll?
Q rateofdisch argefromthejet /I kinematic viscosity
g/ gt!.e.
9 gravitationalacceleration
6.p differencein densit y betwee n thedischarging fluidandthe surrou n di ng fluid density
or
thereceivingfluid(:L1)
By.:a refu lil.Jlalysi~ofth esamples Rawncr al., wereable to show that theReyn olds 1I11mlw rhnduosigllifican t inilueneeon the dilutio n. providedthejf-t.11011'wasfully turhuient. HecausetheReynoldsnumber ca lculat e d usingHawn'sdata was always
!!ir'~;ltf'rthnu.'lOOnmak ingtheflow10 he fullyturbulent,itwasconclude dthat HI'Yl1flld~numberhadnoapprecia blesign ificance onthe in itialsurfac edilut io nS~.
Thus ll1l'IulSic equationnamely, (Erlua t io n:1.1)red ucedto
(2.2).
A gt a p hicalsolu ti on(F ig u re 2.1) for the availabledatawas developedto determine
:\kilSlln'lm~nl sfo rcentrelinedilutionwere madeby Cctler w all(196:3)bymeansofa eou.luctivhyprobe placed within1'1.salt waterjet injected tofreshwa ter.~laximl1m ronrr-nt rntion wasobser ve d alongtheaxis ofthejet. Comparisonsofthese dilutions withHawn,BowermanandBrooksshowe d thatat large densimetri c Frcude num- ht'l'1lthepredicteddilutionsofRawnetI'll.(1960),weregreaterthanthe measured nnnlmumcentre -line di lution.
FrankelandCum ming(HI65)ca rriedoutaseriesofexperimentsonbuoyantjets illa stillreceivingwater,A graphical solutionforconce n trations withinthejet was developedwiththeaidofnon dimensi onalrelationships ,It wasfoundthat the distributionacrossthe jetclosely approximatethe gaussian dist rib u tion, Various angles ofjetdischargewere also testedand itwasfoundthat th e horizontal jrt
\\',15the11l0~tefficientandthe vertical jetleast efficient. Frankeland Cumming
Figure 2. 1:InitialSolutionefterRaw»,BowermanandBro oks,(1960)
10
also studied theeffect of surface proximi ty onmixing in the surface trans itionzone.
M,·itSU~IIlCnt5of concenrrerionwere takenallthesurfaceandatsomedeptbbelow
it.They concluded that theelfeclivl"'dilutingdepthtodiameter rat io is cons iderab ly r.~'1t.ha nthe ava.ilable Iiudacede pt h todia me ter ratio.As a resul t,the dilu tionat thecentre-li ne oftheplumecannotbe calculatedeelclyas afunct ionof thedep th ofnozzle belowthe surface.TIIt:Y estimated theeffective mixingdepthto be as llulcestwothirdsofthe availabledept hin someinstances.
1\compre hens ivestudyor buoyant jetphenomena was done by Abraham{Abre-.
ham, 1963,1965).Ill'assumed thatthevelocityandbuoyancyprofiles wereof&
gaussiannature. Emp iricalrelationsforvelocitydistributi onanddist ribution of rrecerconcent ra tio n at anycres s sectionofthe jetwere developed.n amely
(2.3 )
(2.4)
where
UQ centrelinevelocity ofthe jet, U, velocity ata distan cer fromthe centr e line Co centre line coucentrat ion
Cr concenlrat ionatII.distancerfrom thecentreline I'adial distancemeasuredfromthe centre line axial distance of the plane fromthe nozzle I'.k dimeo!ionlesll coefficients
y
--;=t:::,,=~-I---L_----_x
o
Figure2.2:Cross sectionalprofileof a buoyant jet (Abraham,1963) Atypica l sketchshowing all the above parametersisshown in Figure 2.2.
11
The flow establishment forpure jetsa.soutlinedby Albertson,ct., al.,(1956)wa.~
used to explainthe flow pattern. Figure 2.3 shows the Zone of flowestablishment and the zoneofestablished flow.Itwas foundtha tthelengthof the zone of flow establi shmentwas equal to 6times the diameterof thejet.The analysiswasbased onthe assumptionthat thebuoyan tjet had jetlikecharacte rist ics inthe zone-of flow establishmentand plumelikecharacteristicsin thezoneof establishedflow.
Values for the constant!kandJ.Iweregivenby therelation
12
r
u _
•
Figure 2.3:Zone offlowestablishment andzone ofestablishedflow(Albertsonet nl., 1956)
wherej3wasdefined astheangle thejet axismakeswiththehorizontalil l. 'lll) point distance's'alongtheaxis ofthejet(Figure 2.2).TIll)rateofl'ul ra illlll1'lll was represented as afunct ion of the axial dlstnnceofthejet axls.TIll'1,11l'orl'l.k al·
solutionsdevelopedwereverifiedby experimental results. ,\ graphk id solution (Figure 2A)wasdevelopedforthe predictionof theslIrf;H't! ,1iI11tioll .
Comparisonof Abraham 'spredic ted dilut ionswithHawntuulPaluu-r(I~J:ln).~I Il,\\·,·, 1 that there was considerableagreeme nti~tlowerdcnshuet.ticFron, ],)uuruln-rsbut, at largevalues, Abraham's dilutionswere lower thanHawnnndl'alnn-r. This was discussedbySharp(Sharp,19(8) whostate dtha1 thisumylu~,hI("III1,lw perfectstill water conditionsof Abraham's measurementswhen compared11) fi,·I.1 measurementsof Rawnand Palmer.hwould alsobedifficulttoaccurately10f ill l' the point of minimumdilution dur ing thesampling done byHawuanr]Palmer, againresulting in anoverestimate ofdilut ion.
Improvements onthese theoreticalsolutionsweremadehy ran undHrco ks(I!Hlfj ).
They assumedthat the rate ofentrainmentWMproportionalto1ht~lot i'Llt:h ;" r;Lcr.t~r
istic velocityUmand thelocalcharacteristicradiusofthe jet orplume'I.'alldfly followingthe techniqueusedsuccessfully by Morton eta].(l9.'i6)theyJln~~I'lIl.<'.I,
0 --1:
1---t::- I- +
~ ,.' I -
~~
o~tO 1'\
~ '1'\
0
.
,
, I
,
."
lOso~oGOBO 100ec so
.. v.
F.
Figure2.4:Prediction ofsurface dilutionof a buoyantjet afterAbraham (1963)
(:!,ti)
wherea=a dimensionlesscons tantof proportlouallty.
Thevelocityand concent rationprofileswere presented illil.~liKlJll'yllilf,'!"pul Ionn than that ofAbraham 's equationnamelyEqua j.ion(2.:1)11.11,1('l.·I)a~
('L j )
(:! ..'i)
HereA is a dimensionless spread ratio and'b' is thehalfwidth uf I!I<' j,,1..
Asetoffour ordinarydifferent ia l equat ions namelyContinuity, Momentum,Buoy- ancyflux andthe geometryof the jetwe re developedbasedontherateofill':t!'1~~"
involu meflux (Equation2.6).One principle advantageofthucntrnintueutequation over Abrabam's approachis thatitis more flexible andcanbeusedfora varid.yof problem s such asthose involving buoyantjetsand plumesinasLra tilie<1environ- ment .Thisisbecause theplumewidthand the distance'5'need notIj(~sru~:i li"ll inadvanc ebutcanbe derived fromequatio nsofmotion and continuity.
In1968 Cederwall (1968) developed a set ofanalyt icalequat ionsto predict rjilution achieved in ahorizonta lbuoyantjet,namely
[ ] " "
s,
=a.M FA(Y./d) FA16
i\ll1l
. - [ (I;/J) ]'"
."i..=O,a-IF4 O.:J8""""F;"""+0.66 for Y./d>O.5F~ (2.10)
A generalisedcharl(Figurc 2.5) wasdevelopedby Liseth(1970)com biningthe work ofvarious workers.Hefound that thefield data predicts ahigherdegree of dilu tion tha nshownby alli\lyticalresults The reasonfor thisisduetolateralmixingwithin till'transitionzonewhich tendsto increase the dilut ion. Healso found thatthe sf>led,("(! dimensionlessparameterin hisfigure would show less scatt er than plotting' withothe rdimensionlessparam eters.
The lalerwo rkinthisareahastendedto dealwithrefinement softhernathem1Llical modelsof Pan andI\braham and has generallyconfirmed the...aliditycf the solutt ons shown in Figure2.5.More recentwork,whichwillbe presentedlater.hasdeAlt withtheeffects of currents,stratificati on and wave.
2.1.3 Vert icalbuoyantjet
Stu dieson buoyantplumesweredonebyMorton,Tayl or andTu rner
V
vlort onet al.,1956) using the followingassump tionsIThe entrainmentat anycross sectionisrelatedto somecharact eristic velocity at that section.
~Thevelocityandbuoyancyprofiles acrosstheplumeare of simila r format differentheight s.
17
4
~~r~~ae~::lr:;~
"\.lisethI
2_ Franktl . Cllmm;n\l
"",""):
.
.-.-~=::~....=:~~~
~~ ~.~... ""
0
. -
e
/ ' . .... 1 /
6
...
1/
Theo,el,ca I 5011l1l0n1:Ceder" o ll
4 Abrahom
:I-..-f onondBrooks
2
II
I
4 6
,
10 20 4000.1 0,2 0.4 0,6 1.0 2
~/Fil
Figure 2.5: Generalisedchartof various wor kersfor surfacedilutionof a hlloYll.nl jet(Liset h, 1970)
18
Atsectionx . x:-
U(z,r) U=Vertica l velocity p(.x,r) p=Density of the Plume b{x) b
=
Radiu s ofthe plume1'" Den sityof ambientFluid
outsidePlume
PI> Ini tia lden sity ofplume
a Constant relatin ginflow velocity at edgeof plume to vertic al velocityinsidethe plume
Figure2.6:Flowparame tersinvolved in thetheoreticalana lysisof buoyantplume (Mortonct al.,1956)
3 Local variations indensityaresmallincomparisonto the density ofthe ambient fluid atthesource .
Usingthenotationshownin Figure 2.6theywereable toshow that,
DyprincipleofConservat ionofvolume
by princ ipleof conservation or mass
and by the principleof conservationof densityIlilrl·rl·IlCt·
where
verticalvelocity b radiusof theplume P density ofplume
P~ densityofambientfluidolltsilleplume Po initia l density of plume a constantrelating inflowvelocityat('dge
ofplume to verticil lvelocityinside plume
Theseequat io ns werederived wit hanassumpt ionthatvelocityandhuoynncyfllrn- across theplumewe re const ant.Expressionsforvdodtyauddilutio niLlol1Ktill'jt'l axiswerederivedbyrearr anging the above equationsto give
and
wbereQ=constant
g(Po-P)
=
~(.E....QQ) lf~ ;t._'1/3P 60 10
(:l.l l)
(l.ll)
Thissolut ionWA:!comparedwilhexperiment alr~ll [tsandalso with resultspro- vi,lf'(l hySchmid t (1!H1 1And Rouse etat (1952) Theproportionalityconstant
Itwasfoundtohan' a valueof 0.093and the\'{'rtiCRIvd ncityand concent ra tion ,Ii~triblltion:swereshownto begaussianandgivenby
(2.13)
(2.H)
WILI'rc
II ", vertic alvelocityonaxis of jetatdistance "fromorigin
r'" concen trationon axisof jetatdistance xfromorigin
c...= ~P.-Po
IIandc are theverticalvelocity and concentration atApointdistancerfromthe axisandadistan cexIrcm theorigin.
Abraham (1963) analyzed jet diffusion inaliquid of greater densityand suggested tha t the factor"in theabove equations shouldbe replacedby (x+2d ) for a jet of finite initialdiameterD and velocityU•.He also sta testhatthe valueofQinboth equ ationsis given by
Q=~J'u.(P.-
p .l
4 P. (2.15)
~I
becausethedensimctricFrondellumb('risgivenhy
Equations2.11 and2.12were rewritten as:'
" ( r )-' ''' [
'>]
~=3.6;jF~ -l/J _ ,., up-Sll(-)'I
1.10 ,+ w .I'
c >> ( r )-' ''' [ '>
I
~='.J.7f'tJ. -2/J ~ ('.tll_SII(_)'l
Co rl+_ r
t~·II;}
('!.Ii)
I'!. IS)
WhereUoandCQareinitial velocityandconcentrationofll,,~j"la.~itl"i1\ "I 'SIll!' nozzle.
Velocity and concentrationon the axisofthejet callbe1'11.11'11IaL\:dusing"'plid,i"IIS 2.17and2.18and atany otherpoint on thejet bylIsin~r-quationa'!.1:1.11 1,1'!.I·l.
A recentanalysismakesuseof the conceptof characteristiclengths[Flseherdal..
1979),an approach whichseemsto be becoming more popularthantho traditiollal dimensional ana lysisbased on the individualvariab[e~involved. Thebasicpamnu-.
tors which determinethe flow in ajctor a plume arceonsidered to bet.1l1:1\r1:illit.illl fluxesofvolume, momentumandbuoyancyrepresentedasQ,M.and/Jnepect.ivr-ly, The distance'z' along the axis ofthe jet isincludeda.~abasic parameter. FlIrII
vertical jet of diameterddischargingwitha velocity ofwinto areceivinglIuidwith a density difference ofAp,theinitial fluxesof volume,momentum and buoyancy
Thuswecall writeany Howvariable(nolldimenainnalizvd]a~,1functlcnoftill''''' variables.lieneevelocityof thebuoyantjC't'U',~.(allhI'writtena~
Q_
[Ml/J: J{lll]IV",J(-
f
Q 'J)l('l (:!.:!I )Consideringthelimiting condit ions wherenowhasbot hmomentum M <l1l,1],UllY' ancvB,butno initial volumcIluxQ,the abovesolut ionforilroundj" lwmde!t;ll.;l·
the form
Fischer(19i9 )showedthatequat ion
2.:n
couldbedeveloped togivi'and
(:!.:!1)
where(1andC:lare empericalconstants. Tire r-atio1,Y1J/~I IJ If11isddill,~,1asa charecteristiclengthf",.Forz
«
1mtheHowislikea jetiwlfor.~:»I,~llll~f1" w is like a plume.The dilution of a vertical buoyant jet(So)mayhecalculated uslng thedinu:IIlIicml,·ss values(Fischer,etal.,1979)of thevolumeflux(ii)anddistance Iromthejdorifil:f~
;"p fJ=y(-)Q
p,
~ ~ravilati ()nfl.laccelerat ion
II diameterof the jet l:ip fI~-fl l
fl1 densityofthe rece iving Iluid (II dnnsity oflilt'fluid hl'illgdischarged
Thll ~thedimensions ofQ,B.end~1willbe
The hlLNic equa tion of thevariables involved invertical buoyan t jet phenomenaCRn t.hr-nhewrittenas
o(Q,M, B,,)= O (2.19)
Fortheabove basicequation thenondimensional equationcan be written as
( M I/2;:A/3/4 ) _
¢ Q 'Bin -0 (2.20)
Thefirstof these parameter sincludes momentumandvolume fluxandis impor tant in theanalysisof momentumjets , whilethesecondincludesthe efffectof buoyancy.
24
whe re
'4
plumeRichardso n numbe requalto 0.557 R" jdRichardsonnu mber for aroundjetdefinedas(f) ""1;-
fo'1J, dcneimctric Frondenumbe r
(2.25 )
LIII.'dillllm~iuJ1 lcssvalueorvolumeIluxis given (Fischeret al.,19i 9)as a function, of(,n
ji=( for
«
Iwhere(isgivenby
r" plum e coefficientequalto0.25 (Fis cher etal., 1979) Il,. plumeRichardsonnumberequal to0.557
(2.26)
(2.27)
2.1.4 Twodimensional buoyantjet
A theoret ical solu tionforthe case ofa two dlmcnsioua l horizcutnlhuoyaut.j",ill stagnant,homogeneouswate r has beenpresentedby Abrah<llll(Abra lliUllI!lli;",) . Thisapproach assumesthatd;c lat eral velocityandbuoyancyprotilps.H'·ill'l'rux i.
mately gaussian . Thesimilarity profilesforvelocityand concoutrntionforhllrh:tlul" l two dime nsionalbuoyantjetswere presentedas
(2.:!X)
(2.2'1)
where
U" cent relinevelocity of thejet U. velocit y ata distancer fromthecentr eline Co centr e lineconcentration
CT concentr at ion ata distance rFrom thecent reline dist ancemeasu red fromthe axis ofthejf~l axial distance of the plane from thenozzle
Jj,k dimensionless coefficients
thevalue ofdimensionlesscoefficients weregivenbythe empirica l equa tionsnatunly
(2.:lnJ
26
t3
3 fJ~Il=-2A(;)-1.8(; ) +0.50
wherefjwasIll'finedas theanglethe jet axis ma keswiththehorizontal atthe requiredpoint (Fig ure2.2).Thetheoryis basedonempi ricalfunctio nsfor the spreadofmassandmoment um wherethe rate ofspread is introduc edas a function or the localangleof inclinat ion of the jettraject ory.
Therollowing equationshavebeen solved : Twomomentum flux cquatlcns,namely
Horizontal momentumflux;
Verticalmoment um nux;
( 2I ' )'/'
PoU.2ssin fJ=:M.sinH.+913r
,(P,-Po)(' )'/' 2k
C.sd.s whereaxialdistanceof theplane from thenozzle .4, le ngt h offlowestablis hment
f3. {Jat3=3.
M. fAp1.l1dAat
,, =
s.M" fAPu2dAat s
=
0 J] depthofthe jetCeomet ric relationsfor thej~ttre jectcry, nault'l)"
Conlinuity equa tion,namely
Anumericalsolutiontothissyst emofequationsWASpr{'SI'ntl'C!h;L~('dOiltht·IJUII~i".
nesqapproxim ation,that is,thatdensityrlillercncesrnuheignored illalllI'rll1~
except thegra\'ity term.Ageneralsolutionwasdevelopedfor ,1,'Sign purpuse'llali<I the dilut ionalongthe axis ofthc jel(S~),WI\.'lplot tedlL~afunc tion ofFrullll.·
number(F)andrelativedepth(y/D)asshowninfi~urc"1.7.
ImprovementofAbra ha m',theoryfor diffusion
o r
Atwo dimensionalhuuyantjo·t in uniform andlinear lystr atifiedenvironme ntWA.:ldonebyFan and Brooks(J~J(j~IJ.The theorywas basedontheprinciple of entrai nment,first proposed byMurtulj etaI.,(1956)which was ad vocated. byFa nilndOroo~, a:~moresimpleandUlli n'
logicalfromphysical pointofvie w.Theequation ssolvedinthi:.theoryWr.ff~
Continuityequation,namely
-i;(ub)
=
2oll/.;i Two momentu m fluxequationshorizont al momentum;
.
~--...
28
verficelmom entum;
Geometricrelations Corthejet lrajl'ctory niu ndy
NumericalintegrationwascarriedoutusingHunge-kut te-glllIIl1'll1011.TIIl't"l'lll r,:
line dilution {or a horizontalbuoyantjetWallplctte das afunctionllfFron d ,·1I1l1lt1ll'r
andrelat ivedepthand is shownin Figure2.~,
Experimentswere conducted by Ced erwall[Cedcrwal laeal.,19j1) to\wifyIIIl' above theories
or
horizontaltwodime nsionalbuoyAnljelillJ'ita)!;IIi\llten vireuuu-nt, The graphical representatio n ofthetheo reticalcentrelinedilurlonandcom[M.ri!lt>ll withexperimental datai,showninfigure 2.92 .2 Factors affec t ing dilution
2.2.1 Effect ofcur re ntAny turbulenceordisturbance causedinthe receiving waterwillincreas etIll!dilu- tionof theoceanoutfall.Two differentlypCllof approaches,nam ely mathemaurnl andempiricalapproachesexistfordeterminingtheeffectofcurrent011the dilution.
MortonetaI.,(1956)originatedtheint.cgralmomentumlechn i'lueCorsillgll:jl~l
20
lD~IO
~8
'0
6
~ "
2
I 0.8 0.6 0.5
0.50.6 0.8 I 2
30
Figure 2.8:Dilutionof slotbuoyant jets instagna ntuniformenvironments (Fan andBrooks, 1969)
:11
( J..) -'lZ
S", B 1.0
0.5L-Ll...l..JLL_LL...L...L--'---'----l
0.5 1.0 2 3 4 5
I y )"2
"2/Sla
·F~H!...,)Figure2.9 : Grap hical representation ofcentre-linedilution fortwo dimens ional buoyantjet insta gnantenvironmentIIIId co mpariso n withex periment al data{Ced- erwall,1971)
32
.Iisc:h:trgcs.Fa n(1967 ) followed the iruegral techniquedevisedbyMor to n et al., (1956) and developedalrloflintordertlilTe-Te ntia!cquat ion ~whichcouldbenu- lTX'ficaJly inl.egra tedlI!iingtheRunge-K utta-Gillmethod.l'r.ssumptionswere mad e lbdflow wasincompressibleandturb u lent.that thedensitydifference wassmall and lhat longit udinalconvectionwasmuchlarger thanlongitudinalturb ulenttrans- port.Velocityprofileswere consi dered tobesimilaral allcross section snormalto theaxisand theentrain mentco efficient was assumed constant. Alam et aI., (198 2) compared thre eEnviro nmental Protecti onAge ncy(EPA)models(PLU;\.IE,OUT·
PI.M,andDKIIPLM)andmo d elsof Fan and Brooks,AbrahamandRoberts .He' concl u ded thatOUTPLMwas oflittle use, pe rhapsbecauseithadinitially been develo pedforcoolingtowersplume analysis.Themodels developed by Fan and Brook s andPI.UME model gavegoodresultsforstill waterwhileDKH PLMgevc ronsist cntlylo wer valuesthan measuredin bot hstill and movingwater.Results rromAbraham'smodelvarieddependingonthe currentmagnitudeandReber t's model sil;llilicantJ,underpredicteddilutions.
U,illgdatacollectedatfivemarineout fall,aroundtheCOAlItofEngland,Agg and Wakefor d (1972) devel o ped anequationformin imumcentre linedilutio nas
(2.31 )
Where
S.. mini mumcentrelinedilutionattill'sur'[are
S. stillwaterdilution un deridc ut.irelconditionsof 111'111_11 ,11ll1,!l·lIsil.v,lilr" n'Ill""
U. velocity of amblcutcurrent Vj velocity ofjet at outfall
Basedonthe stud iesconductedon the long st' aoutfallatllasli ll~s011 IIll' south coastof England,Benne tt(Wl:ll,L!l83)developed anl'lIIpi rka l rd llliol1sltipfurtl1O' ratio of moving watertostillwater dilu t ion.IIcUS(' I!(;('(\('rll"al1'11equnfionfmtl", stillwat e r dilut ionand present e d his correct ionfactoraar-
where
Sm mov ingwaterdilution S. stillwaterdilut ion
CF correction factor(Sm/S. )appfiedtostillwaterllilnt ion U. curre nt velocity
V veloci tyofthe jet
Yo
dept hofrecei vingwaterHe also usedline arregressiontoobtain themeasured moving waterdilutlon directly as afunctionofV.,~andVjorQ,thedischarge.Thisgave the cqunt i" ll:'
He recommend ed tbie fo rmula.inpreferen ceofEfJU<1tion (2.:Il)for prnct.ir-n]dr'sil!,11
Usingthecomplete dat a base, comprisingbothsets ofdat anamely Agg andWakf'-
34
ford's and Be nnett's,an effortwas made by Sharp andMoore(Sharpand Moore 1!l87)todevelopanewequation.Anumber of forms of equationswere considered ....1It!after somepreliminaryanalysis,theyadoptedaform based onCederwa lf's st ill-w aterdilution andpresentedtheirequationas:-
(2.34)
where
Sin movingwater dilution S" st illwaterdilution U~ current velocity V velocityof the jet }' depth ofreceiving water
Comparisonsofallthesedifferentempiricalequationswerelaterdone and they concluded that bestpredictionsfortheset of field data was fromEquatio n(2.34) with Aggand Wake ford'sEquation (2.31)pro viding generallysimilar resultswith slightly increasedaccuracy but decreased precision. they found thatBennet's mod- lflcd equatio nsignificantly lessaccurateandless precisethan either oftheothers.
Theupdated EPAmodelsnamely UOUTP LM,UDKHPLM,UMERGEwerecho- sellIor com par ison by Sharp andMoore(1989)whoconcludedthateachof the models tende d to overpredictdilutio n.Theysuggest edthat the increase indilu- Ilondue toacurrentshouldbelooked onasabonusto improvetheperforma n ce of theout fallandthat designers shouldnotre lyentirel yontheeffectofa curre nt toprove theaccepta bility
o r
anoutfall.2.2 .2 Effectof wav es
The effect sofwaveshavereceived milch lessat tentlonthan11111S('nf rurrr-nts.S"lllt·
quan tita tive work has been ca rriedoutin order\.0dl?\'p lnpanul1<II'I"S1.;l IHlill.l!;
lJr
lIlt' phenomenonandsome predict orequa tionshaveIwenll~vdOlll'd.(:l'l lI' m llyWl1\',' effectshavebeen sho wnto dependstr onglyonthetypeofl.h ~11'<1.\....lll't'lJwnt r-r waveeffect sbeingsignificant lydifferentfrom thoscofshallowwa ter .Early studie s weredoneby Shuteand Ti(IOj.,)whodl'wlupecl{'lllpiril'll!l'lluatious.
based onequationspreviouslydevelopedfor je t sdischargedinto aI'fUSS('urrt'ntamI modifiedonthe basis ofexperi mentscarried outwit h slllall[ctsdi~l'h;u~('dumb-r sta nding wa ve s in a0.5 rnwide wa vechanne l.'l'lu-yf011l1l1I.Imlsllrra n'.lilut.lou.
S,ucouldbedescrib edby
('.!.:n )
where
Y.. depthofdischarge
H waveheight
F dischargeFrcudenumbereUjJ(!JD)lfl D diameterofthe jet
g gravitationa lacceleration
a entrainmentcoefficient de pendentprimarilyOilWI\ VI:condition Uj velocityofthe jet
Ger(1979) proposed asomewhatmore comple x arrangementidentical withadif-
. 16
f('nmt ontrelnmentcoefficient.Th !s equation gavecentreline dilutio nslISa linear functio no(th...horiacnt.al co-ordinate , X,althepointofmeasureme nt .Thus,
(2..16)
WlU!TC0'is give nillter m sof the waveand jet veloci t ies.
Qualit<l.tivc experimentswerecon ducted by Sharp(1986) who showedthatthe jet st ructureundersha llow waveswas quill.'differentfromtha t experie nc edwithdeep waves. Inpar tic ular, under sha llow wave actionthejet brokeintotwodistinct' doudsofdiluentwhereas indeep water...avesthest ructurewassome whatsimilar tothatexperiencedinst illwater . This suggestedthatII.singletheorycould not be valid for nilwavetypes.
H(~rcnt J yChill(Chin,198;)used dimensionalanalysis wit hIIlengthscale ap p roach hi\.'I(!l!011Fischer' s work(Fischerct at,1979)to ide n tify therelevantlength scales.
linpresent edthe function alrelationship
s./s:
1+6.15(U.../Uj ) (2.37)whereS,uis the average surface dilutionwith waves and5isthe averagesurface dilution withoutwaves.U",uisthemaximum horizontal wave-indu cedvelocity at thedischar gepointgiveninterms ofthe waveparameters;He weveheight,Leewave length.)'~ =depth, T= waveperiod ,g= gravitationalacceleration.
U"",r = ·)(~1'(hll(~)
_.'M I,2.3 Methods of increasing dilution
2.3.1 General;lj
t:.!·:ISl
Tomaximise theperformance of anoceanoutfall,dcsigncl'sIliI}'part.icularcou ...-ru tothedilutionwhichwillbe expe r iencedbythediluent;lft c'rt1i~('harl!;C'.TIll'overall- dilutiondepend sonthe initialmixing thattakes placeinthe risin.u;c'OIUlll lloftill' buoyantjdandtheturbulentmixingthat ti\kclSplacewhentill'pllllll!'is fMric',1 anddispersed by oceancurrents.Becauseadequat e initialdilntlon;s~uimpo rtillil in the designofamarine outfallvar iousdraft shaveIW'~l1111,1,[,-1.0incn-asr- .lillilillli withou tsignifica ntly incrcasing thecostof the operatio n. ~lllChattentionh;\~
beendevoted to improvingthe initialdilutionbyehangillgtheg''<JlIwt ryofth,~
discharging jet.
Rawnetal.,(1960)lookedat howdilutio ncouldbe increasedhychangingth.~dcosiv;u parametersand showedtheeffects ofthesechangesina almplifledversion(Iftheir dilutioncbart.Thissim p lifiedversion is showninFigure2.10. Toalter thedilution itisnecessaryto changeeithertherela ti ve depth, \'old.orthe-lenaimetr lcFwllth!
number,}"!J.,However,because thede ns it y difference atthesite ill fixed bytho siteconditions(approx i matelyeq ualtothatbetweenFres hWille rand sea water], variationinthe valueofFAcan onlybeachievedbyvaryingthedischargeorthl!
outfalldiameter.Ingen eral,the dischargeisfixe d ,atleas tto till!extenttha titis
38
Figure 2.10:Hasie method,of increasingthesurface dilution of buoyant jet(Ra wn d 1\1.,1960)
limited between thelower and upper limits of thedischargeflow.However itwould hepossibletomodify the dischargeto some extent by discharging ataconsta nt rai l"overiI.carefullysdeeted per iod oftime.Thiswouldrequireconst ructionof
~loragcponds. eithertoholdback theeffluentwhile the outfallisnotdischar gingor 10bala nce outtheOowso that the effluentcouldbe dischargedata constantrate.
However this wouldinvolve excessive costs in building thestorage ponds andthe
!lmdlnuisancebecause ofthestorage. Thisalternativewhich ispracticedin many Jllac('9illshownin Figure2.10aslineAD.Increasing dilut ionby cha ngingthedepth
obtainedonlyby run ni ng theoutfallfur t he rolf~liott·will.n...lIhi llF;...,.;1inn"i'''' ''' due totheextrale ngth of ou tfallrequired.I)...·rra~i llt>tilt'.liallll'lI·rilln.·) ,,,"'"1" ,.,,1 lossesandff'>\ull.5inincreasedpumpingcosts.Th,~'illt "rl1ati\"l'!<ar,'SIIl'WIIil~Ii....
AEandACrespectivelyin Figure2.10.
2.3.2 M ulti-port d iffusers
Variousmethods havebeen devisedtoprocurehigll{'r diluti o llsthi UIwould1,,"
obtained bydischargingclllucntthrougha.~i llgk'n01.zk·IUl";II"datlIlt'.1"Wl\~'tt·ill1l endof thesewer,Themost com mo n ilpl'rolI.chi1tto1l1\Ca. 1II111Ii·I,urt.Iilfll ~'· rill wh ich the eJfluentisdischa rged throughi\!>I'riM;o(IMlrhItM'al c..1UII.·illl"rsi.I.·
alcug the lengthofthedilluse rpipe.ThehO[I~iUl'pl"Cl'l1litlthatjets.Iisdliu~, · ho rizo ntal ly and aresepara tedbydistanceslargeenulI~htoellSUR'111.11IhillIII'"
jetswiltnotmixwit h each other.Bydoing thisa simple flischarl!,cis '·.mv'·rh'llt"
anumberofseparatedischarg eseachiltalargerl~/tl al1data..Iilft·t<~ntvilliit' IIf FtJ,Theincreasein dilut ioncan heseenbythelineAUinFigllI'C'2.111.TIll'Ill'll 'flf amultipartdiffuseris a common approach in Illtgeoutfalls.S" lIleti ll":li ilisill..., common tobury the outfallpipeanddischargethroughport slocaL.~1flllv" rl in t]
risers .Thisis part icularlytr uefor outfa lls designed toco pe withlilrw~Howrill,'S fromcoolingwatersys te ms ofthermalor nuclearflower stations,
'0
2.3.3 Baffle s
Variousatlemplshave been madeto increasedilutionbypromoti ngadditional turbulence inthejelaftertheeffluent has beendischarged. Baffles and other devices to obstructtheflow.Ofaltertheflowpatt ern, werereportedbyHa nsen [Hanse nand Schroder,1968 ) andadvocatedbySnook(Snook,1969).Thede vices reported arc illustrat ed in Figure 2.11toge th er withtestdeta ils.Amongallthe devices tested,itCfll~:2and 3, (Figure 2.1I) inwhich the flow is divided intotwo or morecom ponentsbyplxclngtheobst ructions,doubled thelevelof dilution. Spiral"
inser tsin theendsect ionofthepipeshowed litt leimpro vemen t and increased the Ill,,(<Ilossinthe system.Onedevicetested was actuallydetrimental andreduced dllurlon.
2.3.4 Buoyan twalljet
Whenabuoyanteffluentisdischargedtothemarineenvironment,itrises and mixeswiththe receivingfluid duetothe format ion ofturbulenteddies.However, ifthe jetisdischargedveryclosetohorizontal solid boundary,it will be subjected
\0the coandaeffectwhichcausesitto ding totheboundary forsome distance beforerising.Thistype ofjetis calleda buoyant walljet .A preliminarystudy of the buoyant walljet was done by Sharp(1915)and Sharpand Vyas(1977) to measure the increasein dilution achievedwhencomparedto thatofa horizontaljet.
Experimentalworkshowedthat the surface dilutionofsuch ajetwas approximately twice thatobtained inanequivalentfreejet.
"' _ .. .,,, .. _ .... " ~ '.
" 4~0
0 ~~
, - _ ,oq lll.."I..:. ,12 30 10 1 (1)'GJ
1200110"" "'. .,G''''''"921HI0 2 '·' 1"
'@
CD :::
tl..2~,I...'. " 21 23 10 1e'\)
.~o,lOpt"SI1"'"I,...,"
23101..l..il",.
@ ,
2.... _ " '.. " _ _•"
231."'_ 0 1 ...
®
" n••'~ ... 2 _ """... ... _
_ *00'
'i "'...
"..:.21" . .
22n11
, . .
.~,Figure2.11:ImprovementFactor sofsurfacedilutionU~i llgDissipaters(Snook, 1969)
2.4 Methods of pre dilution
2.4.1 Vent u rieffectPredilutiundevicesoperatebydisturbingtheRow patternoftheje tsissuing from theoutfallOfby drawingreceiving water intothe pipetherebydilut ingthe effluent beforeitis discharged. Mostoftheideas presented have not beendetailed Cur- 1lll'fthantheexperimenta lstages.The earliest andsimplestmethodemployedwas the venturiprincip le advocated by Nece (1966).Inthismet hodthe diamete rwas' fl'!llridcdover a sectionofthe outfall pipe.Duetothe increase inveloci tyand reduc tioninpressureAtthe reduced section the ambientRuid was sucked through the ports locat edinthe conduitwall.Results indicated thal the concentrat ionill the onlfallplpeWMreducedby50%.No measurements were madefor thesubsc- qucntdilution bet ween outfalland surfacebutthegener&! effe<: tof pre-dilutioncan heesrlmatedfromFigure 2....A decrease in concentration of 50%impliesthat the dischargeisdoubled and thatthe densitydifference ishalved.This thereforerep- resentsanincreMe(by&(actorof
v'2)
inthe discharge densimetricFroude number.Thisincreasein densimetr ie Frnudenumberwillhaverelatively little effectbut may hedetrimental ,Thus pre-dilutio n withinthe outfallmay be,tosome extent,offset byareduction insubsequent dilut ionbetween tbe dischargepointandthesurface.
'1'111.'deviceinvolvedsubstantial head lossesandwouldbeprobablynot.be suitable Iorthis reasonalone.
2.4.2 Pre-dil ut iondevic es
Six possibledesignsfor devices10 achieveprc-dihulonof~1'\I'a!-\\'Iwfo1"l'Ilt'ill~,lis charge dfrom a submergedoutfall wereshlllil,,1by:\gg and Whill'(AI-(Io:.uu]\\'hill', 1974).Ofthe methodsinvestiga ted forinducingmixing,m,l dilut.iun, till'I'lll,lIISI'· ful wasItdevicewitha shape ofittruncat ed cone, Av,' ragedlhuienfa('t.tlr~,wit.ltln the mixing device,were foundto be aboutII fur low ellluentIlmv~iLIUI1"'1.\\" "'11 4-and6 athighe r dischargerates.An asscsua-nt of overall dilutionthai,'0111,11,,- achieved usingthismixingdevice under~drlconditionsWlISlllllll-lIsill,!!;L]u-dat;, or.
Aggand Wakeford(1972). An ovornllimprovementilldilutlouofilppru xOI11;,I,-ly twowasobtained inshallow water ,hillatla rgerdepthstln-,ulv;lIlt;ll-\l'oftlu-d"I'in- was lessma rked.
2.4.3 Mix in g tube s
Researchon mixingtubes attheUnive rsity of W,-slern Ausl ra liaw;~~dOlI!'l,y Silveste r .Dilutionsof moretha ntwo were obtainedwit hinth,' mi:d ngtnlll's(Silo vester ,1957)using relatively highvelocityjetsand wit hthen!(l~ivingwau-r al re-st, Model testswere also conductedhySilvester and Patarapanieh(I!172)forlh,~liS"
of jet pumpsin oceanout falls.Itwasrecom mendedthattheleng t h ofthel1Jixill~
tube .oustbe seventimes the diameterof the mixingtubeandthatt1lt~rlisd1ar~i llg nozzle shouldbe placedatleastone diameter fromthe mixingtube.WatNW;L~
used inthemodel experimen tsbut,altho ughtheresults have hcen illterp rt'te,1in relation to sewagedischargedfro meubrn erged outlalls,no accountSf~~ I11!1tohave beentakenof the possible effect
or
densitydilfefl'lII~cOilthe mixingmechanism.The maximumoverall dilutionfactor appeared to be less thantwo althoughthe
"xl'l~ri n]('ntalresu ltsfor ver-ticaljetssuggestedthatthe predictio nswereronserva- rive. Analyticalcompariso ns weremadefor outfalls with andwithoutmixinglubes and itwa.~observedthat the overalldilutionbetweenthe outfalljetandthesurface
\WI,'1im proved hy afactor of no more thantwo.
Onlyone field installation ofamixingtubehas been reportedbut few details were giwn [Anon 1!166).This devicewas installedat a smalloutfalldischargingsewage fromSurfer's paradis eintothe NerangRiverin south EastQueenslandand was.
d(~sigllciltopre-dilutethe effluentby a factorof2,.'ipriorto discharge.Thesystem workl'llsatis factorily, the onlydisadvan tagebeing a slight increase in head on the
Laborato rytestswerecond uctedbyArgaman(197.'») bothinuniformand stratified rcccivlng fluidswitha mixingtubehaving thegeometryshownin the Figure2.12.
The purposeofthese testswasto measure the theprimary dilutionachievedwithin themixingtube. Basedonthese experimentsa linear relationshipwas developed to predict the primary dilut ion achievedilli~mixingtube havinga circularcross sect ion. This was given as
(2.39)
1\ primarydilutionwith in the mixingtube IJ diameter of themixing Lube d diameterofthe nozzle
The110 11dimensional constants 1\,and1\2were determined from theexperimental results tobe0.8 and 0.7resp ectively. The subsequentdilut ion achieved between
I.".
Figure:!.I:!:Circularmlxiug tube(,\rg,'lIIlul
.· t
al..1!lj;",)the outletorthe mixingtubelindthesurfnceWitS('alr lllah 'dusill~til"(·...h-rw..lr~
equations:!.9 and 2.10.1\r~l\manalsoccmbim-dllw'''lll:ltinll rurinitial ,Iilillill"
(Equat ion2.:J9) withtheCcderwaU's cqllation(l%..'I}tll I'ru\"i.II·;.!'iim\,liti...I' ''lll;'' tiontocalculatetheove ralldilutionas:-
12.-1lI)
in whichS....
=
overall dilution obtai nedwitha lI1ixiligtube,wIFI!J, :;:dl!llllinwiril:Frondenumber orRow throughnoasle. Improvementractorswerecaklllilt.~1r"r
4'
2.2 a: 2.0 0
%" 2•
....
0;;:
1.8....
1.6z 1.6
'"
~
1.4>0 2.2
g:
1.2'li
1.0
0.2 0.5 1.0 5.0 10.0
Y I.
~
FigilH':u;~ :lnrprcvcmcnt factorsforoveralldilut ion usinga circularmixingtube (..\q:;il ll li\ ll t'l <lI,I !Ji Ii )
,litf('f l'nl /JIllrati os.Here,the improvement factor(IF)is defined as the ratio ofthe overall dilutionachieved witha mixing tube tothe cvcrelldilution achieved without a mixingtube attached underthe same experimentalorfield conditions.The depth parameterYfd{F~)andthe improvementfactor If' were plottedfor differentOld ratios (Figure2.13.Theimprovementfactorincreasedwiththe reduction ofDjd ratiosand depthfactorYld(F,),).
2.4.4 Limit a t ionsof pre-dilut ion devicesandmixing tubes
Experimentalstud iesto improvetheoveralldilut ionusing pre-dilutiondevices have 111'('11re por ted.The earlierstudies wereundertakenbySilvester who didexperi- mental studies on a circular mixing tube.Themaximumimprovement achieved
by hisdevice wasagain limitedtoa factoroftwo.Lan-r~tlldi .'~··..illl,Iilr" r"ul shapes ofmixing devices weredoneby'\M<t1l,1 Whitt'(l!)jl)who\\W,·,lh\.' 10 echleveinit ial ave rage dilutio n ofI! withinthemixill!!;d,'\'in'1>111llll' "\'I'ralldi- lutionbe tween thedisch a rgenozzleand thewa terl\ll rr~l C{'lI'a~limite-dfuIIr;1l'lm of approxim atelytwo. The yalso Iouudtha tthe overall illlprlll'I'llH'IILn'dlln'~with the dept hof water.La boratory tests oncircularmixingtubesha~,',l011Sih·..~ll'r'~
designwas done byArga ma n(l915),The,,(fed ofmixiull:lulu'sen u\wHllllillll.iI!l1 was exam inedby comparingthe dilut ions oh ta in", 1Ilyil!limp!" ulIl!,'lwith "fI,1 wit hou t ,amixi ng tu be. From Figure 2.13itwasconcludedthntthelllil\ i ll~1,11 1", imp rove me ntfac to rinc reases with decreasein till'dialllL'l,'rratiuIJjd"fIIll'1ll ixill~
tu be tothe dischar gi ngnozzle. Theyalsofou nd tllilt tit" ituproveuu-utis~f{'ld"~1 asDjdapp roaches 1.0. The maxim umimp rovement fa,·tn tthat.\l'a.~fl'1'"rl,·,1\\,;,s app roxim atel y two.
Reasonsfor the expe rime nta llyobser vedlimitn ti onson tIll'maximumvnhu-"I'111I proveme nt facto rwe restudiedthecretlv allyby Sha rp(Sharp,I!Jil'l).lJsi nl; "'11101' tionsdeveloped by Albertso n etal., (1% 6) Lisruh(UHO)andl'edNwall(l~ lf i''\ ll lI descri bethedilutio n of je tsandplum es.he conclud edthal till' ituptovcmentfHr tu r duetopre-dilu t ionliesin therange
Where
