UNIVERSIDAD CARLOS III DE MADRID ABSOLUTE INSTABILITY IN THE NEAR FIELD OF LOW ...

126 Pages·2010·1.92 MB·English

UNIVERSIDAD CARLOS III DE MADRID
EscuelaPolitécnicaSuperior
ABSOLUTE INSTABILITY IN THE NEAR FIELD OF
LOW-DENSITY JETS
Tesis Doctoral
Autor
WilfriedCoenen
Director
AlejandroSevillaSantiago
DEPARTAMENTODEINGENIERÍATÉRMICAYDEFLUIDOS
Leganés,abril 2010

DEPARTAMENTODEINGENIERÍATÉRMICAYDEFLUIDOS
EscuelaPolitécnicaSuperior
ABSOLUTE INSTABILITY IN THE NEAR FIELD OF
LOW-DENSITY JETS
Autor
WilfriedCoenen
DirectordeTesis
AlejandroSevillaSantiago
Leganés,abril 2010

Tomyparents,mybrother,andtoAna

Tesisdoctoral
ABSOLUTEINSTABILITYINTHENEARFIELDOFLOW-DENSITYJETS
Autor:WilfriedCoenen
DirectordeTesis:AlejandroSevillaSantiago
FirmadelTribunalCalificador:
Firma
Presidente: D.NormanRiley
Vocal: D.RamónFernándezFeria
Vocal: D.JoséManuelGordilloAriasdeSaavedra
Vocal: D.CarlosMartínezBazán
Secretario: D.AntonioLuisSánchezPérez
Suplente: D.EnriqueSanmiguelRojas
Suplente: D.CarlosdelPinoPeñas
Calificación:
Leganés,5 de abril de 2010

Abstract
Variabledensityjetsareknowntosupportself-sustainedoscillationswhenthejet-to-
ambientdensityratioissufficientlysmall. Thischangeindynamicalresponsetosmall
perturbationsisassociatedwithatransitionfromconvectivetoabsoluteinstabilityof
theunderlyingunperturbedbaseflow. Thefocusofthisdissertationliesintheuseof
linear stability theory to describe the convective to absolute instability transition of
buoyancy-free low-density jets emerging from a circular injector tube at moderately
highReynoldsnumbersandlowMachnumbers. Particularinterestisgiventothein-
fluenceofthelengthoftheinjectortubeonthestabilitycharacteristicsoftheresulting
jetflow,whosebasevelocityprofileatthejetexitiscomputedintermsofthenondimen-
sionaltubelengthLt byintegratingtheboundarylayerequationsalongtheinjector.
Webeginwiththeinvestigationofinviscidaxisymmetricandhelicalmodesofin-
stabilityinaheatedjetfordifferentvaluesofthejet-to-ambientdensityratio.Forshort
tubesLt ≪ 1thebasevelocityprofileatthetubeexitisuniformexceptinathinsur-
roundingboundarylayer. Correspondingly,thestabilityanalysisreproducesprevious
resultsofuniformvelocityjets,accordingtowhichthejetbecomesabsolutelyunstable
toaxisymmetricmodesforacriticaldensityratioSc ≃ 0.66,andtohelicalmodesfor
Sc ≃ 0.35. Fortubesofincreasinglengththeanalysisrevealsthatbothmodesexhibit
absolutelyunstableregionsforallvaluesofLt andsmallenoughvaluesofthedensity
ratio. Inthecaseofthehelicalmode,wefindthatSc increasesmonotonicallywithLt,
reachingitsmaximumvalueSc ≃0.5astheexitvelocityapproachesthePoiseuillepro-
fileforLt ≫1.Concerningtheaxisymmetricmode,itsassociatedvalueofSc achieves
amaximumvalueSc ≃ 0.9forLt ≃ 0.04andthendecreasestoapproachSc ≃ 0.7for
Lt ≫1.Theabsolutegrowthratesinthislimitingcaseofnear-Poiseuillejetprofilesare
howeverextremelysmallform =0,inagreementwiththefactthataxisymmetricdis-
turbancesofajetwithparabolicprofileareneutrallystable.Asaresult,forS <0.5the
absolutegrowthrateofthehelicalmodebecomeslargerthanthatoftheaxisymmetric
modeforsufficientlylargevaluesofLt,suggestingthatthehelicalmodemayprevailin
theinstabilitydevelopmentofverylightjetsissuingfromlonginjectors.
Asecondpartofthisdissertationisdevotedtotheviscouslinearinstabilityofpar-
allelgasflowswithpiecewiseconstantbaseprofilesinthelimitoflowMachnumbers,
bothforplanarandaxisymmetricgeometriessuchasmixinglayers,jetsandwakes.Our
resultsgeneralizethoseofDrazin(J.FluidMech.vol.10,1961,p.571),bycontemplating
i
ii Abstract
thepossibilityofarbitraryjumpsindensityandtransportpropertiesbetweentwouni-
formstreamsseparatedbyavortexsheet. Theeigenfunctions,obtainedanalyticallyin
theregionsofuniformflow,arematchedthroughanappropriatesetofjumpconditions
atthediscontinuityofthebasicflow,whicharederivedbyrepeatedintegrationofthe
linearized conservation equations in their primitive variable form. The development
leadstoanalgebraicdispersionrelationthatisvalidatedthroughcomparisonswithsta-
bilitycalculationsperformedwithcontinuousprofilesandisapplied,inparticular,to
studytheeffectsofmoleculartransportonthespatiotemporalstabilityofparallelnon-
isothermalgaseousjetsandwakeswithverythinshearlayers.
Finallywegobacktothestabilityanalysisoflow-densityjetsemergingfromcircu-
larnozzlesortubes,thistimeconsideringviscousperturbationssothattheReynolds
numberentersthestabilityproblem.Weconsiderseparatelythetwoparticularcasesof
ahotgasjetdischargingintoacolderambientofthesamegas,aswellastheisothermal
dischargeofajetofgaswithmolecularweightsmallerthanthatoftheambientgas.In
bothcases,weconsiderthedetaileddownstreamevolutionofthelocalstabilityprop-
ertiesinthenearfieldofthejetwiththeaimatestablishingtheconvectiveorabsolute
natureoftheinstability.Wediscusstherelationshipofourresultswiththoseobtainedin
previousworkswithusemadeofparametricvelocityanddensityprofiles,andcompare
bothapproacheswiththeactualglobaltransitionobservedinexperimentsperformed
withhotandlightjets.