“main” — 2010/5/3 — 18:15 — page 521 — #1 AnaisdaAcademiaBrasileiradeCiências(2010)82(2): 521-537 (AnnalsoftheBrazilianAcademyofSciences) ISSN0001-3765 www.scielo.br/aabc Lower nappe aeration in smooth channels: experimental data and numerical simulation EUDES J. ARANTES1, RODRIGO M. PORTO2, JOHN S. GULLIVER3, , ALBERTO C.M. LIMA4 and HARRY E. SCHULZ25 1UTFPR,CampusCampoMourão,CaixaPostal271,87301-005CampoMourão,PR,Brasil 2DepartamentodeHidráulicaeSaneamento/EESC/USP, Av. TrabalhadorSão-carlense,400,13566-590SãoCarlos,SP,Brasil 3DepartmentofCivilEngineering,UniversityofMinnesota,2ThirdAvenueS.E,55455Minneapolis,MN,USA 4UniversidadedaAmazônia,Av. AlcindoCancela,287,Umarizal,66060-000Belém,PA,Brasil 5NúcleodeEngenhariaTérmicaeFluidos/EESC/USP, Av. TrabalhadorSão-carlense,400,13566-590SãoCarlos,SP,Brasil ManuscriptreceivedonSeptember14,2008;acceptedforpublicationonSeptember30,2009 ABSTRACT Bed aerators designed to increase air void ratio are used to prevent cavitation and related damages in spillways. Air entrained in spillway discharges also increases the dissolved oxygen concentration of the water,whichcanbeimportantforthedownstreamfishery. Thisstudyconsidersresultsfromasystematic series of measurements along the jet formed by a bed aerator, involving concentration profiles, pressure profiles, velocity fields and corresponding air discharges. The experimental results are, then, compared, withresultsofcomputationalfluiddynamics(CFD)simulationswiththeaimofpredictingtheairdischarge numerically. Comparisonswithjetlengthsandtheairentrainmentcoefficientsfromtheliteraturearealso made. It is shown that numerical predictive tools furnish air discharges comparable to measured values. However,ifmoredetailedpredictionsaredesired,verificationexperimentsarestillnecessary. Keywords: spillwayaerators,airentrainment,air-waterflows,multiphaseflows. INTRODUCTION Bottomaeratorsareatechniqueusedtopreventcavitationerosiononspillwaysandtoenhancetheoxygen contentofthewater. Airventedthroughthebottomaeratorsisentrainedintotheflowingwater,increasing thecompressibilityoftheair-watermixtureandloweringthevelocityofpressurewaves. Whenimplosion ofcavitationbubblesoccurs,thehighercompressibilityofthesurroundingfluiddampenstheimpactofthe pressure waves. Additionally, the bubbles increase the contact area between air and water, improving the oxygendissolutionintothewaterandtheDOcontentdownstreamofthespillway. Correspondenceto: Prof. HarryEdmarSchulz E-mails: heschulz@sc.usp.br;harry.schulz@pq.cnpq.br;harryeschulz@gmail.com AnAcadBrasCienc(2010)82(2) “main” — 2010/5/3 — 18:15 — page 522 — #2 522 EUDES J. ARANTES et al. Experimentalinvestigationsonspillwayairentrainmentbybottomaeratorshaveresultedinempirical designequations. SchwarzandNutt(1963)presentedatheoreticalequationforthejetlengthformedafter the ramp. Pan et al. (1980) and Pinto et al. (1982) related the air discharge to geometrical parameters of the jet. Additionally, Tan (1984) and Rutschmann and Hager (1990) explained the dependence of the air dischargeonthejetlength. ThejetlengthpredictionsobtainedbyTan(1984)areclosetothoseofSchwarz andNutt(1963). InBrazil,thestudiesonaeratedspillwayswereintensifiedduringtheconstructionofthehydropower damsinthe1970and1980decades. ThefirstrelevantconclusionsforspillwayswerepresentedbyPintoet al. (1982),whileBorsari(1986)andFuentes(1992)furnishedreviewsofimportantstudiesandprocedures. These aerator studies helped in the establishment of locally adopted procedures. Some early studies, like Volkart (1980) and Wood (1985), added important conceptual contributions for the understanding of aeratedflows. Practicalapplicationsoftheresearchresults,however,requiremoredetailedmeasurements andthereviewofexistentresults. KökpinarandGögüs(2002)conductedanextensiveexperimentalstudy and furnished correlations not only for the jet length, but also for the air entrainment in lower and upper nappes, and a graphical presentation of the effect of ramp heights and bed slopes. The redistribution of flowvelocityintheaerationzonewasconsideredbyToombesandChanson(2005),whilethedetailsofthe geometryoftheair-waterinterfacewereusedtoproposetheconceptof“entrappedair”byWilhelmsand Gulliver(2005). AsimilarentrappedairconceptwasusedbyLimaetal. (2008)toexplainmeasurements ofairvoidratiosinlowernappeaeration. This paper seeks to compare CFD simulations with a detailed experimental study of the lower nappe of a jet generated by an aerator in a laboratory chute. Measurements of velocity fields, pressure and air concentration(voidratio)profileswillbecomparedtoCFDresults. TheCFDsimulationsofairdischarges were comparable to the measured values. It is also shown that, if a more detailed description is needed, experimentsarestillnecessary. EXPERIMENTALMETHODS The experiments were conduced in a chute built in the Laboratory of Environmental Hydraulics of the . SchoolofEngineeringatSãoCarlos,Brazil. Thechutehadaslopeof14 5◦,anusefullengthof5.0m,with arectangularcrosssection0.20mwideand0.50mhigh. Thebedaeratorwascomposedofarampwitha . lengthof23.0cm,afinalheighttr = 4 0cmandanangleof10◦ relativetothechute. Thechamberunder thejethadadepthof12.0cm,alengthof18.0cmandawidthof20.0cm. Theairdischargewasmeasured in the air supply tube, which had a diameter of 71.65mm. Air velocities were obtained from pressure measurements,withamicromanometerhavingonesideopenedtotheatmosphereandtheotherfixedina pre-calibratedpositioninthetube. TheconcentrationmeasurementsintheflowweremadewithaCesium 137probe,asshowninFigure1. Calibrationwasmadewiththechannel a)fullwithwaterand b)empty. TheCesium137radiationwasprojectedperpendicularlytotheflowinthechannelandacounterregistered the remaining radiation after passing the mixture of air and water and the glass walls. The concentration measurements thus consider the entire width of the channel. Air concentration profiles were obtained by positioningtheprobeandradiationcounteralongtheverticalofeverystudiedcrosssection. Eachobtained concentrationisahorizontalmeanvaluetransversetotheflowdirection. AnAcadBrasCienc(2010)82(2) “main” — 2010/5/3 — 18:15 — page 523 — #3 BED AERATION IN SMOOTH CHANNELS: EXPERIMENTS AND NUMERICAL SIMULATION 523 Fig. 1–EquipmentusedfortheconcentrationmeasurementswithCesium137probe. An electromagnetic flow meter was used to measure the water discharges, which were checked with a rectangular weir located at the outlet of the channel. The measurement of velocity fields in the jet was performed for nine runs, using a mirror inside of the flow. Velocity fields were measured using particle imagevelocimetry(PIV).ThelightsourcewasacoppergasLaser,withameanpowerof20Wandpulses at 10 kHz. The pulse power ranged from 60 to 140 kW. Generated wavelengths were 510.6 nm (green) and578.2nm(yellow). ACCDcamerawitharesolutionof1024pixels 1024pixelswasusedtorecord × the images. After capturing and storing the images in the computer, PIV software was applied to each image to obtain velocity vector fields by using auto-correlation calculations. 234 images were taken for each run. Figure 2 shows all cross sections used in the present study. Sections 1, 2 and 3 were used to obtain the approach flow information (velocity and water depth). Sections 4 through 8 were used for the concentrationmeasurements. AdditionalsectionsSIX andSX wereusedforvelocitymeasurementsinthe jetcore. Forvelocitymeasurementsinsections1and2,thelasersheetwasintroducedintheflowfromthe bottomofthechannel. Fig. 2–Measurementsectionsforthepresentstudy. Distancesareincentimeters. AnAcadBrasCienc(2010)82(2) “main” — 2010/5/3 — 18:15 — page 524 — #4 524 EUDES J. ARANTES et al. For velocity measurements in the jet core, a mirror was positioned downstream in the jet before the upper and lower white water regions came together, as shown in Figure 3, and the laser sheet was intro- ducedintotheflowfromthesideofthechannel. Detaileddescriptionsofthechuteandthemeasurement equipmentmaybefoundinCarvalho(1997)andLima(2004). Fig. 3–Experimentalarrangementforthevelocitymeasurementsinthejetcoreusingamirror. SIMULATIONMETHODS In this study, the inhomogeneous multiphase model was applied with the liquid and the gaseous phases considered. Thereisonesolutionfieldforeachseparatephase,andthefluidsinteractviainterphasetransfer terms. Forexample,thetwophasesmayhaveseparatedvelocityandtemperaturefields,buttherewillbea tendencyforthesetocometoanequilibriumthroughinterphasedragandheattransferterms(CFX2004). Thefollowingequationsforinhomogeneousmultiphaseflowwereusedtosimulatetheairandwater flows,andairuptake: ContinuityEquations: ∂ Np ρ ρ 0 ∂ ra a +∇ × ra a ∪a = SMSa + ab (1) t (cid:0) (cid:1) (cid:0) (cid:1) Xb=1 MomentumEquations: ∂ ρ ρ ∂ ra a ∪a +∇ × ra a ∪a ×∪a = t (cid:0) (cid:1) (cid:0) (cid:0) Np (cid:1)(cid:1) (2) μ T 0 0 −ra∇pa +∇ × ra a ∇ ∪a + ∇ ∪a + a+b ∪b − b+a ∪a +SMA + Ma (cid:0) (cid:0) (cid:0) (cid:1) (cid:1)(cid:1) Xb−1(cid:0) (cid:1) where: ra is the volume fraction of each phase (phases indicated by “a”, with “a” assuming values from ρ −→ 1 to Np, the total number of phases), a is the density of phase “a”, Ua is the velocity vector of phase μ 0 “a”, a is the viscosity of phase “a”, SMSa represents mass sources specified by the user; ab is the mass flow rate per unit volume from phase “b” to phase “a”. This term only occurs if interphase mass transfer takesplace; SMa representsmomentumsourcesduetoexternalbodyforces,and Ma representsinterfacial forces acting on phase “a” due to the presence of other phases. The term 0a+b−→Ub −0b+a−→Ua represents (cid:0) (cid:1) AnAcadBrasCienc(2010)82(2) “main” — 2010/5/3 — 18:15 — page 525 — #5 BED AERATION IN SMOOTH CHANNELS: EXPERIMENTS AND NUMERICAL SIMULATION 525 momentumtransferinducedbyinterphasemasstransfer. Thevolumefractionsofthephasessumtounity, thatis: Np ra = 1 (3) Xa=1 Thereare4NP +1equationstodescribethefluiddynamicsforthe5NP unknownsra,Ua||,||Va,Wa, −→ (componentsofthevelocityvectorialfield Ua),and Pa (thepressurefieldofeachphase). Theadditional NP − 1 equations needed to close the system of equations were supplied by assuming that all phases sharedthesamepressurefield, P,thatis: ,..., Pa = P forall a = 1 NP (4) φ Ascalarvariable inphase“a”hasthecorrespondingtransportequation: ∂ μ ρ φ ρ φ ρ (φ) ta φ (φ) (φ) ∂ ra a a +∇ × ra a ∪a a −∇ × ra aDa + ∇ a = Sa +Ta (5) t (cid:18) (cid:18) Scta(cid:19) (cid:19) (cid:0) (cid:1) (cid:0) (cid:0) (cid:1)(cid:1) (φ) φ (φ) (φ) where Da is the Diffusivity of a, Sa represents an external source in phase “a”, and Ta represents φ sourcesof a duetointerphasetransfers. DetailsofthemultiphasemodelmaybefoundinCFX(2004). Toinitializeasimulation,arelativelygrossmeshwasfirstusedtolocatetheair-waterinterface. Then, theregionsoftheupperandlowerfreesurfaceswererefined,allowingadetailedlocationoftheinterface for the definitive run. The final mesh of each case presented a higher concentration of cells in the upper andlowernappesofthejet,asshowninFigure4. DetailsaredescribedbyArantes(2007). TableIshows the main characteristics of the grids and the simulated fluids (air and water). The number of nodes and elementsofthegridsaremeanvaluesforallsimulatedconditions. Fig. 4–Exampleofrefinedmeshusedforthenumericalcalculations. The model allows the adjustment of constants and boundary conditions in order to calibrate the predictions with measured results. Different combinations were tested, but they in general reproduced only AnAcadBrasCienc(2010)82(2) “main” — 2010/5/3 — 18:15 — page 526 — #6 526 EUDES J. ARANTES et al. TABLEI TheDomain,FluidsandSimulationcharacteristics, initialandboundaryconditions. Domain(afteradaptation) NumberofNodes 550000 ≈ NumberofElements 2750000 ≈ Fluid: Water Temperature 25◦C DynamicViscosity 8.899*10−4kg.m−1.s−1 Density 998kg.m−3 SurfaceTensionCoef. 0.0732N.m−1 Fluid: Air Temperature 25◦C DynamicViscosity 1.831*10−5kg.m−1.s−1 Density 1.185kg.m−3 Simulation Timestep 0.1s SimulationTime 10s Processor Processor3.2GHz Characteristics (Opteron64bits) CPUProcessingtime 1*105s ≈ a portion of the observed results. The CFX standard constants and conditions, on the other hand, led to acceptablepredictionsforthewholesetofexperiments,beingthususedinthisstudy. Theconditionsintheinletwereimposedas: – Pressure: hydrostaticpressure, – Turbulenceintensity: fixedat5%ofthewatervelocity(standardforCFX), – Turbulence model: SSG Reynolds Stresses using CFX standard parameters. The model allows the simulationofnon-isotropicsituations,andtheuseofthelawofthewall. – Roughnessforthelawofthewall: 1.0mm. Thecalibrationwasprimarilybasedonthepredictionsofthejetlengths. RESULTSANDDISCUSSION Fourteenrunswereconductedinthechute. TableIIprovidestheexperimentalconditions. Thejetlength of run 2 is not available because the jet was longer than the channel. Velocity field measurements using PIVwereperformedintheninerunsindicatedby(*). Resultsofallfourteenrunswereusedtocheckthe reproducibilityofthedata,whiletheresultsoftheninerunswithvelocitydatawereusedtocomparewith CFDpredictions. AnAcadBrasCienc(2010)82(2) “main” — 2010/5/3 — 18:15 — page 527 — #7 BED AERATION IN SMOOTH CHANNELS: EXPERIMENTS AND NUMERICAL SIMULATION 527 TABLEII Experimentalconditions. Opening Depth Water Velocity Froude Jet Airflow Air Water ofthe Run atS2 flowrate atS2 Number Length rate Temp. Temp. floodgate h (cm) Qw (l/s) Vw (m/s) Fr L (m) Qair (l/s) (◦C) (◦C) H (cm) 1* 3.37 45.77 6.79 11.81 2.08 23.06 27.5 24.2 3 2* 3.51 63.93 9.11 15.52 NA 27.82 26.0 25.1 3* 5.26 47.65 4.53 6.31 1.08 12.66 24.0 22.0 4 5.50 58.85 5.35 7.28 1.38 18.37 24.7 24.0 6 5* 5.40 64.37 5.96 8.19 1.48 20.17 25.5 24.1 6* 5.85 92.05 7.87 10.39 2.28 29.49 23.0 24.1 7 6.00 44.44 3.70 4.82 0.78 9.92 29.0 28.0 8* 7.05 64.38 4.57 5.50 0.98 14.26 28.0 22.5 9 9* 8.31 98.20 5.91 6.55 1.48 22.92 21.4 21.0 10 8.54 119.86 7.02 7.67 2.08 31.69 29.0 22.0 11 6.92 46.58 3.37 4.09 0.68 11.28 23.8 21.8 12* 7.94 64.38 4.05 4.59 0.88 15.52 25.8 23.0 11 13* 9.10 94.64 5.20 5.50 1.18 20.28 25.8 22.1 14 10.16 128.76 6.34 6.35 1.58 27.45 21.4 21.0 COMPARISON OF MEASUREMENTS WITH LITERATURE Verificationofthejetlength L Jet lengths are commonly used to quantify the air uptake by the water flows. The jet lengths of Table II werecomparedwiththeoreticalpredictionsofSchwarzandNutt(1963)andTan(1984),givenrespectively byequations6and7,andplottedinFigure5. Alsoshownarethepredictionsoftheempiricalcorrelation ofKökpinarandGögüs(2002),givenbyequation8. Thetheoreticalequations6and7wereobtainedwith α norestrictionsto . Equation8wasadjustedfromexperimentaldata,beingthusrestrictedbytherangeof α tested during the experiments. A systematic underestimation of equation 8 is observed, which may be < α < . duetoextrapolationsofitslimitsofapplication. Forexample,therampslopeislimitedto0 9 45◦, α butinthisstudy 10◦. = Thegoodagreementbetweenmeasuredandliteratureresultsistakenasanindicationthattheexperi- mentaldataforjetlengthcanbeusedtocomparewithCFDsimulations. α( α θ) θ L 1+ tan 2 tr +ts cos tr +ts θ Fr 1 1 2 tan (6) h = cosθ (cid:26) +(cid:20) + h (αFr)2(cid:21)(cid:27)+ h Lh = gs2ihnθt2+ (V chosθ)t, t = g coVsθsi+nαρ1wgPh 1+tvuu1+2(tr +ts)g(cid:16)c(oVssθin+αρ)1w2gPh(cid:17) (7) (cid:16) (cid:17)     AnAcadBrasCienc(2010)82(2) “main” — 2010/5/3 — 18:15 — page 528 — #8 528 EUDES J. ARANTES et al. . . L . ( α)0.22 1.75 tr +ts 044 ( θ) Aa −0087 0 28 1 Fr 1 tan (8) = + + h (cid:18) h (cid:19) (cid:20) Aw(cid:21) α θ α Intheaboveequations, istherampslope, isthechute slope, isthetakeoffangle(whichisthe α α angle followed by the liquid when it leaves the ramp. is equal to because no inertial effects altered the observed direction of the flow after leaving the ramp), tr is the ramp height, ts is the step height (zero ρ 1 in the present experiments), t is the time, w is the water density, g is the gravity acceleration, P is the / relative pressure under the jet (taken positive), h, V, Fr and L are defined in Table I, and Aair Aw is the ratiobetweentheairsupplypipeentrancearea, Aa,andtheareaofthewaterflowbeforetheaerator, Aw. Figure 5: Predicted and measured jet lengths. Fig. 5–Predictedandmeasuredjetlengths. β / Verificationoftheairentrainmentcoefficient asafunctionof L h / / Pinto et al. (1992) proposed that the ratio between Qair and Qw||, ||Qair Qw, is proportional do L h, with a coefficient of proportionality between 0.023 and 0.033. Rutschmann and Hager (1990) found a β coefficient of proportionality of 0.030, for the maximum value of (zero relative pressure in the cavity β / / underthejump). Theauthorsshowedthatthestraightlineof vs. L h interceptedthe L h axisaround / β . ( / ) L h 5forafirstsetofdata,sothattheequation 0 030 L h 5 wasproposed. Forasecondsetof = = − β . / / data,thesimpleproportionality 0 030L hwasfollowed. Theauthorsmeasured L huptoaround45. = β / / < Chanson(1991)suggestedthat and L h followlineartrendswithlowerslopesfor L h 20andhigher / > / slopesfor L h 20. The L h valuesrangeduptoaround25. KökpinarandGögüs(2002)presentedthe empiricalcorrelation β . ( / )0.82 / ( θ 0.24 = 0 0189 L h Aa A2 1+tan (9) β β( / ) (cid:2)(cid:0) (cid:1) (cid:1)(cid:3)(θ) / / in which the coefficient of = L h depends on the channel slope and the ratio Aair Aw. L h β / ranged up to 30. Equation 9 shows a nonlinear dependence between and L h, and that the coefficient < θ < . maybelowerthan0.0189. Theequationisvalidfor0 51 3◦. β / β / Figure6shows against L h forthedataoftheseexperiments. Aconstant seemstooccurfor L h / < between10and15. However,asnomeasurementsweremadefor L h 10,thisapparentconstancymay beonlythescatterofthedata. Figure6alsoshowstheregioncontainingthelowernappedataofLow(1986) θ . andanalyzedbyChanson(1991),obtainedforachuteslope 52 33◦;andtheequationsofRutschmann = AnAcadBrasCienc(2010)82(2) “main” — 2010/5/3 — 18:15 — page 529 — #9 BED AERATION IN SMOOTH CHANNELS: EXPERIMENTS AND NUMERICAL SIMULATION 529 θ . θ . β β( / ) and Hager (1990), for 51 3◦ and 34 4◦. The dependence of the function L h on = = = geometricalcharacteristics,suchastheslopeofthespillway,isclearlyvisible. Applyingequation9forthe (θ , ) conditionsofthisstudy 14 5◦ ledtogoodpredictionsofthemeasureddata,withdeviationsoccurring = / forthelowerrangeof L h. Thesedeviationsmaybeduetotheextrapolationsoftheapplicationlimitsof α equation9orbiasinthemeasurements. Asalreadymentioned,theusedrampslope 10◦ extrapolates = < α < . ( ) . < < . the 0 9 45◦ limits. Also the experimental range of Froude numbers Fr , 4 08 Fr 15 5, . < < . extrapolatestheapplicationlimitsofequation4,givenas5 56 Fr 10 00. However,equation9shows thatthedatafollowedthegeneralexpectedbehaviorfortheappliedexperimentalconditions,indicatingthat theexperimentaldataforair/waterflowratiocanbeusedtocomparewithCFDsimulations. β / θ Fig. 6–Measured andL hvalues,togetherwithdataandcorrelationsfromotherauthors. istheangleofthespillwayineach experiment. ThepresentsetofdataapproximatestothegeneraltrendofthecorrelationofKökpinarandGögüs(2002). β Verificationoftheairentrainmentcoefficient asafunctionof Fr β Figure 7 shows the data of the present study (white circles) and those of Kökpinar and Gögüs (2002) (graycircles)againsttheFroudenumber. ThedataofKökpinarandGögüswereobtainedforflowsovera / stepheighttsof5cm, while, forthepresentdata, ts = 0. Moreover, their tr h valuesrangedfrom0.0to 0.4,whileinthepresentstudytheyrangedfrom0.4to1.2. Thedifferentexperimentalconditionsgenerated β cloudsofpointswithsimilartrends,butseparatedinthegraph vs. Fr,asshowninFigure7. β Fig. 7–Measured againsttheFroudenumber. β Toconsiderthedifferentparametersinacorrelationfor ,adimensionalanalysisleadsto β , tr , ts f Fr (10) = (cid:18) h h(cid:19) AnAcadBrasCienc(2010)82(2) “main” — 2010/5/3 — 18:15 — page 530 — #10 530 EUDES J. ARANTES et al. ( )/ The combined effect of tr and ts is represented here through the ratio tr +k ∙ts h, where k is an adjustedconstant. Amultipleregressionanalysisfurnishedtheresult . β . 1.044 tr +3ts −0460 0 0278Fr (11) = (cid:18) h (cid:19) Predicted and measured data are presented in Figure 8, showing that the present data and those from literature are complementary and form a single cloud of points. The agreement between present and literature data (Figs. 5, 6 and 8) allowed the use of the corresponding experimental results of air concen- trationprofiles,pressureprofiles,velocityprofilesandairdischargestocomparetotheCFDpredictions. β β Fig. 8–Calculated obtainedusingequation6againstmeasured . COMPARISON OF CFD PREDICTIONS WITH EXPERIMENTS Jetlength TableIIIshowssixpredictionsofthejetlength. Asmentioned,theturbulenceconditionswereadjustedin theinletofthenumericaldomain,buttheCFXstandardparametersoftheturbulencemodelfurnishedthe bestpredictionsforthesetofjetlengths. Theseconditionsweresimilarforallruns. Thesimulatedlengths wereintherangeof0.81to1.08timesthemeasuredlengthforthesixruns. Theserunswereusedtoobtain numericalairdischarges. TABLEIII Simulatedruns,showingpredictedandmeasured lengthsofthejet. Measured Predicted Lpredicted Run Length Length Lmeasured (m) (m) 3 1.08 1.17 1.08 5 1.48 1.18 0.81 8 0.98 1.02 1.04 9 1.48 1.32 0.89 12 0.88 0.88 1.00 13 1.18 1.21 1.03 AnAcadBrasCienc(2010)82(2)

Lower nappe aeration in smooth channels: experimental data and numerical simulation

Similar Lower nappe aeration in smooth channels: experimental data and numerical simulation