La premi`ere et la deuxi`eme ´etape de DriftX visent `a mod´eliser la source `a partir de divers postulats et mod`eles physiques comme la th´eorie des jets. La premi`ere ´etape repr´esente aussi la p´en´etration des jets dans la v´eg´etation au cours d’une application assist´ee par air.
Pour valider cette approche, les quantit´es globales de pesticide ´emises au-dessus de la parcelle ont ´et´e calcul´ees et compar´ees avec les donn´ees exp´erimentales pr´esent´ees dans les chapitres 3 et 4.
Le mod`ele ne prenant pas en compte les conditions m´et´eorologiques, les r´esultats des simulations ont ´et´e compar´es aux pertes mesur´ees lorsque les variables ext´erieures sont peu influentes.
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Dans ce chapitre, on cherche `a valider les r´esultats obtenus avec la premi`ere partie du mod`ele. Dans l’article fourni, les principes du mod`ele sont d’abord d´ecrits, y compris le fond th´eorique. Ensuite, l’approche exp´erimentale est pr´esent´ee et en conclusion, les r´esultats exp´erimentaux et simul´es sont compar´es.
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Coup l ingexper imenta land mode l l ing approachestoquant ify a irbornepo l lut ion
sourcedur ingvinespraying
Jean-MarcBrun
c,a,YvanGi l
a,b,CaroleSinf ort
a,∗ Bi jan Mohammadi
caUMRITAP,CemagrefBP5095,34033 MontpellierCedex1,France
bUCV,FacultyofAgronomy,Aptdo.Postal4579 Maracay2101,Venezuela
cUniversityof MontpellierII,Departmentof Mathematics,CC51,34095 MontpellierCedex5,France.
Abstract
Thispaperpresentsacoupledapproachofexperimentalandnumericalmethods toexaminespraylossestotheairduringvinespraying.Theaimistodeterminethe quantityleavingthecanopylayer,whichisliablefortransportoverlargedistances.
ThemodelusedisamoduleofDRIFTX,alow complexitysimulationplatform for driftestimation,developedattheCemagref.ThismoduleisthepartofDRIFTX dedicatedtoevaluatethesource.Upwardspraylossassessment,during astan-dard air-assisted application,wascarriedoutusingafluorescenttracerdyeand PVClinecollectors.Twotestserieswereperformedwithtwodifferentdropletsize distributions(’veryfine’and’fine’spray,accordingtoBCPC classification).With stableatmosphericconditions,lowwindspeedandnoneevaporativeconditions,the amountofsprayedliquidcollectedat2.5m abovegroundwas10.95% ofthetotal doseappliedforveryfinespray,and6.14% forfinespray.Inthesimulationtest, theproportionofdepositscapturedbythevinecanopyisoftheorderof30% while thatlosttowardstheatmosphereisaround12% ofthetotalamountsprayed.In spiteofmodellingassumptions,bothapproachesseem tobeinagreement.Theef -fectsofthemaincharacteristicsofthesprayer(likeforwardspeed,airandnozzle outletorientations)andofthecanopy(geometryanddensity)canbesimulatedto estimatethesprayingperformancerelativelytoairpollution.
Keywords:Airpollution,EnvironmentalLowDimensionalSimulation,Jet theory,Pesticide,Similitudesolutions,Spraydrift
∗Correspondingauthor.
E mailaddress:sinfort@ensam.inra.fr(CaroleSinfort).
84
PreprintsubmittedtoComput.Electron.Agric. 12January2007
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Nomenclature
ALAD CanopyLeafAreaDensity [dimensionless] c pesticideconcentrationintheair [kg.m−3] c0 initialconcentrationontheaxisnozzle [kg.m−3] ccenterline concentrationdistribution
alongtheaxisnozzle [kg.m−3] ccanopy centerlineconcentrationdistribution, [kg.m−3] insidethecanopy [kg.m−3] cfree centerlineconcentrationinfreeair [kg.m−3] cjet 3Dconcentrationscalarfield [kg.m−3] crow concentrationontheaxisnozzle
atthecanopyentrance [kg.m−3] CD dragcoefficientofthecrop [dimensionless] d(x) penetrationdistanceinsidethevegetation,
alongthejetaxis [m]
dc collectordiameter [m]
f shapefunction [dimensionless]
h anemometerhigh [m]
Kcjet centerlineconcentrationdecaycoefficient [dimensionless]
LM Monin-Obukhovlength [m]
M globalamount/quantity/masssprayed [kg]
Q airbornesprayquantity [ml]
r radialdistancetothenozzleaxis [m]
Rejet InitialReynodsnumberofthejet [dimensionless]
Si specificflux [ml.mm−1]
U=(u,v,w) velocityvector [m.s−1] U=(u,v,w) meanvelocityvector [m.s−1] U =(u,v,w) fluctuatingvelocityvector [m.s−1] U0 initialinjectionvelocity [m.s−1]
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Us sourcedisplacementvelocity [m.s−1] Vi recoveredsprayvolumeontheline [ml]
x distancealongnozzleaxis [m] x0 virtualoriginofthejet [m]
xveg canopyentrancelocationonthenozzleaxis [m]
y distancealongtherow axis [m]
z heightabovetheground [m]
αjet spreadrateofthejet [dimensionless] θ azimuthalangleoriginatedfromthenozzleaxis [m]
1 Introduction
Turbulentdispersionofdropletsiscommonlyusedinsprayapplicationsin cropssuchasvinesororchards.Thesprayersusetheair-assistanceproduced byafan, mainlytohelpthetransportofliquidsprayedwhilehydraul icnoz-zlescreatethedrops.Airassistanceisaccompaniedbyunquestionablelosses towardsthegroundandtheatmosphere;thelossestotheaircouldbebetween 10and20% duringastandardapplication(Aubertotetal.,2006).
Driftformationduringaradialair-assistedsprayinghasbeenwellexplained byXuetal.(1998).Aflow fieldfromtheair-jetoutletandthefaninletextends beyondtheair-cropinterfaceandaffectsspraypenetrationintothecrop.Then thereisarecirculationofspraydropletsdepositedonleaves.Streamsproduced fromthesprayerandairdeflect ioncausedbycrop-screeneffectinteractgen-eratinglargeeddies.Theairflow generatesmix,entrainssprayeddropletsand thenconvectsthemoutofthetopofthecanopy.Airbornepesticidesarethen dispersedandtransportedbythewind.Thereforeitisimportanttoquantify theamountofpesticideslosttotheatmospheretopredictdown windcontam-ination,damagetocropsandlivestockrisk.
Duetothecostsoffieldtestsandtothevariabilityof microclimaticcond i-tions,modellingofcomplexvariableswhichaffectenvironmentalpollution,is asuitablealternative.Takingintoaccountthenumerousfactorsrelatedto theapplication(equipment,meteorologicalandgeographicalconditions)tools havebeendevelopedtofacilitate modellingdriftbasedonkeyparameters (Hewittetal.,2002
86
).
However, modellingandsimulationprocessesinatmosphericdispersionlead tocomplexsystems.Thiscomplexityiscausedbythesystemsize,thearising
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nonlinearities,thewiderangeofscalesinvolvedandthestochasticnatureof theprocesses.Furthermore,availabledataisoftenincompleteandwithlarge variability.Itisthereforeamainchallengetoreducethecomplexity.Thiscan bedonebyanalyticor multi-scale methods.
ComputationalFluid Dynamic(CFD)codes werefrequentlyusedtosolve theturbulentflowNavier-Stokesequations,withastandardk−εturbulence model(WeinerandParkin,1993;BrownandSidahmed,2001;Tsayetal., 2002).Studiesonpollutionsourcecouldbe madefromreducedfieldtrials todeterminetheemissionsclosetothesprayer(Crossetal.,2001), which couldbecombinedwithspraydriftmodels,todeterminethediffusionandthe transportofchemicalagents(Walklate,1992).Gaussiandispersionmodelsare lowcost modelsthatareveryusedbuttheyarenotsuitedforthenearfield (<100m)domaincalculation(Raupachetal.,2001).
Environmentalflow modellingisanarchetypal multiscaleproblem.Simu la-tionshavetosolvea multitudeofinteractingscales withanemphasison computationalaspects.Ina multi-levelapproach,asetofdifferent models, accordingtothecorrespondingscales,isdevelopedandcombinedintoanet ensemble.Toset-upthesemodels,itisnecessarytoincludeinformationabout therealprocessesondifferentscalesandtolinkthecorresponding models. Toreducethecomputationalcost,solutionspacereductionandreducedorder modellingappearasanaturalwaytoproceed.Inalow-complexityanalysis, onereplacesthecalculationoftheexactsolutionbyaproject ionoverasub-spacegenerated,forinstance,byafamilyofsolutions(’snapshots’),ofthe initialfull model.
TheseprinciplesareusedinDRIFTX,whereparticularattentionisfocused onthecomputationalaspect,inordertoobtaina manageable modelofthe entiresystem.Itallowstomodelpesticidetransportinatmosphericflowswith verylowcalculationcost making,since merelyseveralsecondsarenecessary forasimulation.
Indeed DRIFTXisbuiltwitha multi-scalestrategywithareductionind i-mensionofthesolutionspaceateachlevel.Agivenstageprovidestheinlet conditionforthelevelabove.Ateachstep,oneaimstointroduceanapriori informationinthesearchspacedefinitionforthesolutionandavoidpartial differentialequations(PDE).Thesoftincludesthreeindependentlevels.The firststepevaluatesinteractionbetweencropcanopyandairflowa longthecen-terlinesprayjet.Itallowstoidentifya meanroweffect.Thefollowingstep concernsthemodulepresentedinthisarticle,i.e.directdriftlossescalculation. Thisquantityisconsideredasthepollutionsourceforlongdistancetransport usingsimilitudeformixinglayersandplumes.Thesesolutionsarewell-known incartesian metrics(Raupachetal.,2001;Agrawaletal.,2003
87
). Oneorig i-nalcontributionofthisglobalframeworkistogeneralizesuchsolutionswitha
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non-symmetric distance to account for non uniform winds. This is the scope of the last level which concerns similitude transport solutions in a non-Euclidean metric based on travel-time (Mohammadi and Brun,2006).
For each level, model parameters identification is based on data assimilation.
The approach does not require the solution of any (PDE) and therefore is mesh free. This method permits to access the solution in one point without computing the solution over the whole domain and the inverse problem is also very low cost. This broader context, described in another paper (Moham-madi and Brun,2006), is an integrative assessment of these different models contributing to contaminant transport from the plots to the environment.
Globally, to model pesticide dispersion, the missing information is often the source itself. Studies on pollution source could be made from reduced field trials to determine the emissions close to the sprayer (Cross et al., 2001), which could be combined with spray drift models, to determine the diffusion and transport of chemical agents (Walklate, 1992). DriftX first step allows to model this source. This paper aims to validate the results obtained with this part of the model. A coupling of an experimental approach (Gil et al., 2006) with the model outputs is presented. The first part of this paper describes the principles of the model, including theoretical background. Then the experi-mental approach is presented and finally, experiexperi-mental and simulated results for the source prediction are compared.
2 Modelisation of the pesticide emission
2.1 Principle of the model
A rapid computational technique for instantaneous local spray losses calcu-lation is presented based on the jet theory. Adiabatic transport of a passive scalar is considered. Near-field solution (at the outlet of the injection device) is built in a reduced solution search space where the physical knowledge about the problem is accounted for. Wind and topography are not considered at this stage. The simulation model includes concentration distribution from the sprayer to the canopy and within the canopy.
The basic premise of this work is that two different time scales can be con-sidered, one based on the injection velocity (U0) and the other based on the velocity at which the injection source moves (Us). The injection velocity being much higher (U0 > > Us), one assumes the local concentration at the outlet of the injection device to be established instantaneously. Therefore, a steady-state behavior of the spray jet is considered. This instantaneous local flow field
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isdevotedtovanishimmediatelyandnottoaffecttheoverallatmosphericc ir-culation.Thisinjectiondistributionisonlydesignedtodeterminethepartof thepollutantleavingnear-groundareaandbeingcandidatefortransportover largedistances.Thesearestronghypothesiswhichseriouslyreducethesearch spaceforthesolution.
Usinganorderofmagnitudeanalysis,thewell-knowngoverningNavier-Stokes equationsofaviscousfluidflowcanbesimplifiedwiththeboundarylayer approximation. Notably,thecharacteristicofthe PDEbecomesparabolic, ratherthanellipticalinthefullNavier-Stokesequations.Thisgreatlysimplifies thesolutionoftheequations.
2.2 TurbulentJetsTheory
Inordertovalidatetheexperimentaltechniquedevelopedandtoprovidea benchmarkagainstwhichtocomparethecomplexflowofthesprayjetnozzle, asimple,wellinvestigatedflow mustbefirststudied. Whenafluidisissued fromacircularorifice,withsufficientlyhighReynoldsnumber,freeturbulent roundjet(alsocalled‘simplejet’)results.Thisisawell-knownaxisymmetric turbulentshearlayerflow.Thisflowstartsspreadingoutwardsbyengulfing ambientfluid,expandsconicallyintheaxialdirection,andappearstoor ig-inatefromapointsource.The momentumcontainedwithinthejetremains constantatanystreamwisecrosssection,whereasitswidthincreasesatthe costofvelocity.Jetsaregeometricallysimpleflows,amenabletoexperimental investigationandtheoreticalanalysis.Theirsymmetricalnaturehavebroad significance,forexample,toreducecomputationaltimeinnumerical mod-elling.Then,theoreticalsolutionsforthe meanflowareavailable(Agrawal etal.,2003)withcoefficientsandvalidationderivedfromexperimentalana l-ysis.GhoshandHunt(1994),intheirreview,explainedhowtheinducedair flowsinsprayjetshave manysimilaritieswiththeairflowinturbulentjets. Thecharacteristicsofsuchjetshavereceivedsignificantresearchattention bothinexperimentalandnumericalinvestigations,whicharewidelyreported intheliteratureforavarietyofflowandboundaryconditions(Stan,2000;
WebbandCastro,2006;Zastavniouk,1997;Kaijen,2004). Shinneeb(2006
89
),forexample,givesacomprehensivereviewo fthecharacter-isticsoffreeroundturbulentjetsfromthenear-exitregiontothefar-field region,inafreeenvironmentandinthepresenceofboundingsurfaces .Inpar-ticular,alotofstudiesfocusedonthesimilaritytheorythatclaimsthat,on everypositiondownstream,theflowvariablescanbedescribedbyasing lean-alyticfunction,providedthattheyarescaledproperly.Thisprovidesthebasis for modelingavarietyofpracticalandnaturalflows,includingcombustion,
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wastedisposal,coolingtowers,andcumulusclouds(Bhatand Krothapalli, 2000;Zou,2001).
Thedevelopmentofairjetsfromsprayershasbeendescribedbybothsem i-empiricalassumptionsandacompletesolutionofthefundamenta lconserva-tionlaws.Asimpleanalytical mathematical mode lisusedforitsrepresenta-tion.Intheregionoftheflowsunderconsideration,thetraditionalapproachis tofirstperformanorderofmagnitudeanalysisoftheNavier-Stokesequations. Aboundarylayerapproximationisusuallyapplied,allowingasubstantia lre-ductioninthenumberofterms.Further,byinvokingconservationo fmomen-tum,thestreamwisevariationofwidthcenterlinevelocityandconcentration canbeobtained.
Thefreeturbulentmotionofajethasanimportantpropertyincommonwith boundary-layers:the widthofthejet,b,issmallrelativetox(s lenderap-proximation),andthevelocitygradientintheradialdirectionislargerelative tothexdirection ∂v∂r>>∂u∂x .Therefore,aPrandtl’sboundarylayertypeof approximationapplies.
ApplyingtheReynoldsdecomposition,usingtheincompressibilitycondition, andneglectingthemolecularterms(viscous/molecularshearstressusuallycan beneglectedincomparisonwithturbulenteddystressesthroughouttheentire flowfield,Rejet>>1),thesimplifiedtime-averagedNavier-Stokesequations forastationaryaxisymmetricgeometryincylindricalcoordinatesbecome:
∂¯uu
∂x+1 r∂uv
∂r =−1 ρ∂p
∂x−∂uu
∂x −1 r∂ruv
∂r ,(x-moment) (1)
∂¯uv
∂x+1 r∂v¯v
∂r =−1 ρ∂p
∂r−1 r∂rvv
∂r −∂uv
∂x,(r-moment) (2)
∂u
∂x+1 r∂rv
∂r= 0,(mass/continuity) (3)
xistheaxialdistance,rtheradialoneandθindicatestheazimuthalangle. uisthe meanvelocityinthenozzleaxialdirection,x,andvisthe mean velocityintheradialdirection,r.Equation(3)describestheconservationof mass(continuity).Overbarsdenotetime-averagedquantities.Othersymbols aredefinedinthenomenclature.
FromtheNavier-Stokesequations(1),(2),(3),theboundarylayerleadstos im-plifytheequationforconservationofmomentuminthex
90
-directionbyapplying scalingandthereafterbyneglectingthetermswitharelativelysmallorderof
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magnitude: u∂u
∂x+v∂u
∂r=−1 r∂ruv
∂r (cylindricalboundary-layerequations) (4) Theconcentrationdistributioniscloselyrelatedtothevelocitydistribution.To getinsightintheturbulenttransportprocesseswithinthejet,theReyno lds-averagedtransportequationdescribingthemixingofapassivedispersedphase wasused:
∂u¯c
∂x+1 r∂rvc
∂r =∂uc
∂x−1 r∂rvc
∂r (5)
Theboundaryconditionsappliedisthattheconcentrationtendstozeroat largedistancesfromthesource.
Assaidabove,theabsenceoffixedboundariesallowsforself-similarityinfree shearflows. Hence,atsufficientdistancesfromthenozzle,theseflowshave thesamecharacteristicsandprofileshapeswhenemployingtheappropriate scaling.Dimensionalargumentstogetherwithexperimentalobservat ionssug-gestformsforthemeanflowvariables,whichareknownassimilaritysolutions (Kaijen,2004;BhatandKrothapalli,2000;Zou,2001;Walklateetal.,1996). Onelooks,inacylindricalframe(x,r,θ),forlocalinjectionsolutionsofthe form:
c(x,r,θ)
ccenterline(x,r)=f r
x (6)
wherethesearchspaceisbuiltusingtheassumptionthatfhasagivenshape. Thisdispersionmodelisbasedonstatisticaltheoreticalbasisthatmakesthem successfulin manyoutdoorapplicationsandfurnishesasimpleanalytica lso-lutionthatneeds muchlesscomputationalpowerthanCFD.Thisapproach basedontheself-similarityconceptdoesnotincludediscretizationo fthetrans-portequationbutrequiresalargenumberofsimplificationsteps.
2.3 Applicationtoavineyardspray
The methodologydescribedabovewasappliedtoderivethedirectdriftfrom thenozzleoftheairassistedsprayerusedintheexperience. Whenconsidering theinteractionbetweenturbulentaxisymetricjetsandporouswalls,veryfew informationisavailable.Thisfundamentalprobleminfluid mechanicsisstill notfullyunderstood(WebbandCastro,2006).(Walklateetal.,1996
91
)pre-senteda mathematicaldescriptionforanair-jetpenetratingauniformcrop canopy.Thisanalysisdemonstratedthatthevelocitydecayisexponentialwith respecttopenetrationdistance,anddependsontheleafareadensity(LAD) andonthedragcoefficientofthecanopy.Thisapproachisusedinsidethe canopy.
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Fig. 1. Normalized centerline concentration relatively to the distance from the noz-zle. The axis nozzle is perpendicular to the row. Comparison of profiles with (con-tinous line) and without (dashed line) the presence of vegetation canopy. Vertical straight lines indicate the location of the rows.
The concentration along the centerline axis is defined by the following contin-uous piecewise function:
ccenterline(x) =
ccanopy(x) =crowexp (−d(x)ALAD CD) , inside the canopy cf ree(x) =c0
Kcjet
x−x0 , otherwise
(7) wherex0 indicates the virtual origin of the jet,c0 the initial concentration (at the oulet nozzle), Kcjet is the centerline concentration decay coefficient, d(x) the penetration distance inside the vegetation, along the jet axis, andcrow the concentration on the nozzle axis, at the canopy entrance. Spray concentration at the canopy boundary (crow) is used to calculate spray concentration inside the canopy as a function of canopy depth and density.
It is obvious in the figure 1, that the decay rate of the mean centreline concen-tration becomes more important at downstream locations where the canopy is present.
Assuming an isotropic turbulence, the steady-state turbulent flow field and its concentration distribution are based on a similitude solution. The 3D concen-tration scalar field is then described by:
cjet(x, r, θ) =ccenterline(x) exp −αJ et
r x
2!
(8)
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whereαJ et is the spread rate of the jet. This gaussian distribution (the shape of the function f in (6)) is an approximation in a statistical sense.
One essential assumption in this model describing the spray is that, during the development of the flow in the downstream direction, the turbulence maintains its general structure, even inside the vegetation. The lateral/radial dispersion stays Gaussian inside the vegetation.
Instantaneous spray losses are computed by:
Z +∞
z0
Z +∞
−∞
Z +∞
−∞
c(x, y, z)dxdydz (9)
where z0 is the height of the canopy row.
And the conservation of mass, on the whole domain, is ensured with:
Z T
0
Z +∞ 0
Z +∞
−∞
Z −∞
−∞
c(x, y, z)dxdydzdt=M (10) where T is the total time of spraying.
2.4 Numerical Implementation
The numerical implementation is based on the best possible fit of the real experimental field geometry and sprayer characteristics, in a simple way. The code was written in FORTRAN77 and can be run on any personal computer in a real-time computation (several seconds) which permits a substantial com-putation time-saving.
In this computation, the domain is a rectangular channel of 6m (longitudi-nal) ×12m(traverse)×3m(vertical) size which encompassed the real domain field (see section 3). To represent the analytical similitude solution, the whole domain is discretized into a uniform mesh prescribed by the user. A rectan-gular pavement of size 6m×0.4m×1.mrepresents the vineyard row, supposed as a uniform medium. All these parameters are set as input variables and an automated method is employed to replicate the current characteristics of the computation domain (position, size and row characteristics) according to the parameters provided by the user.
Numerical parameters correspond to the experimental values described in sec-tion 3. In particular, the nozzle characteristics (number, locasec-tions, orienta-tions, diameters, ejection rates) are set to the experimental data and used as input parameters to compute the turbulent jet. Each nozzle produces an independent turbulent jet described by the equation (8).
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Thetestperiodissplittedintosub-intervals.Thetimestepisestimatedby dividingtherowlengthbythesprayerridevelocity,timesthetrajectoryd is-cretizationparameterdefinedbytheuser.Inthisexamplethisparameteris setto8,givingalocaltimestepofroundly1s.Thesprayerrideissimulated bythenozzle movementateachtimestep,parallelytotherow,intheyz plane(x-coordinate=0).
3 Fieldtests
3.1 Testorganisation
Theexperimentalapproachwasbasedontheuseofclassical2 mmdiameter passivecollectorsandfluorescenttracerdyetoassessnear-fieldpesticideem is-sionstotheairduringsprayingprocess(Giletal.,2006).Thespraylosseswere assessedat2.5 meterfromsoil. Anartificialvineyardwasbuiltfromshade nettingswithanapparentporosityof34%.Rowspacingandcropheightwere 2 meterseach. Theartificialplot was madeoffour8m longrowsoriented alongtheNorth-Southdirection.
Anaxialair-assistedsprayerFisherTurbo561-BerthoudLtd.-wasused.The tractorforwardspeed wassetat5.1kmh−1. Theairoutputstream was exploredwitha3Dultrasonicsensor.Its mainfeaturesareshowninFig.2. Meanairvolumetricflowwasof3.3 m3s−1andaveragedairvelocity12.8m s−1.Twosetsofnozzlesweretested,ata10baroperatingpressure: Albuz ATRwhitehollowconesandConejetgreenhollowcones.Spraycharacteristics ofthesenozzlesareshowninTable2.
Nozzle DV.10 DV.50 DV.90 Vol.>100µ m Flowrate SprayQuality Green 72 134 180 74% 1.00l min−1 Fine White 28 65 135 24% 0.38 l min−1 VeryFine
Table2
Dropletdiameter(µ m)for10%(DV.10),50%(DV.50)and90%(DV.90)ofcumulative volume,sprayvolumewithdropletdiametergreaterthan100µ m(Vol.>100µ m). SprayQualityisderivedfromtheBCPCclassificationsystem.Allinformationwas obtainedfrommanufacturersreportsandthemeasurementswereperformedwitha laserdiffractioninstrument.
Threerunswerecarriedoutforbothsetofnozzles. Microclimaticstatewas
Threerunswerecarriedoutforbothsetofnozzles. Microclimaticstatewas