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Experimental and numerical investigations of axisymmetric turbulence [Elektronische Ressource] / vorgelegt von Özgür Ertunç

257 pages
ExperimentalandNumericalInvestigationsofAxisymmetricTurbulenceDerTechnischenFakultat¨ derUniversitat¨ Erlangen N urnber¨ gzurErlangungdesGradesDOKTOR INGENIEURvorgelegtvon¨Ozgur¨ Ertunc¸Erlangen,2007AlsDissertationgenehmigtvonderTechnischenFakultat¨ derUniversitat¨ Erlangen N urnber¨ gTagderEinreichtung: 10.07.2006TagderPromotion: 08.11.2006Dekan: Prof. Dr. Ing. AlfredLeipertzBerichterstatter: Prof. Dr. Dr. h.c. Franz. DurstProf. Dr. Ing. Dr. Ing. habil. C.TropeaAcknowledgmentsDuring the Summer Academy 1997, I met with Prof. Dr. Dr. h.c. Franz Durst for thefirsttime. Atthattime,wehadanicetalkontheimpactoffluidmechanicsonourdailylifeandtheresearchactivitiesatLSTM Erlangen,whichfindusuallydirectapplicationin important aspects of our society, such as industry, environment and science. Atthat time, his approach to fluid mechanics encouraged me to pursue my PhD workat LSTM Erlangen. However, this occasion would never be possible when Prof. Dr.Gurb¨ uz¨ Atagund¨ uz¨ encouragedmetojointheSummerAcademy.I have many reasons to be grateful to Prof. Dr. Dr. h.c. Franz Durst: most impor-tantlyforthefreeresearchenvironmentthatheandhisco workersgeneratedatLSTM Erlangeninwhichonecanlearntomakescientificresearch,todevelopideas,torealizethese ideas and to take responsibility.
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ExperimentalandNumerical
Investigationsof
AxisymmetricTurbulence
DerTechnischenFakultat¨ der
Universitat¨ Erlangen N urnber¨ g
zurErlangungdesGrades
DOKTOR INGENIEUR
vorgelegtvon
¨Ozgur¨ Ertunc¸
Erlangen,2007AlsDissertationgenehmigtvon
derTechnischenFakultat¨ der
Universitat¨ Erlangen N urnber¨ g
TagderEinreichtung: 10.07.2006
TagderPromotion: 08.11.2006
Dekan: Prof. Dr. Ing. AlfredLeipertz
Berichterstatter: Prof. Dr. Dr. h.c. Franz. Durst
Prof. Dr. Ing. Dr. Ing. habil. C.TropeaAcknowledgments
During the Summer Academy 1997, I met with Prof. Dr. Dr. h.c. Franz Durst for the
firsttime. Atthattime,wehadanicetalkontheimpactoffluidmechanicsonourdaily
lifeandtheresearchactivitiesatLSTM Erlangen,whichfindusuallydirectapplication
in important aspects of our society, such as industry, environment and science. At
that time, his approach to fluid mechanics encouraged me to pursue my PhD work
at LSTM Erlangen. However, this occasion would never be possible when Prof. Dr.
Gurb¨ uz¨ Atagund¨ uz¨ encouragedmetojointheSummerAcademy.
I have many reasons to be grateful to Prof. Dr. Dr. h.c. Franz Durst: most impor-
tantlyforthefreeresearchenvironmentthatheandhisco workersgeneratedatLSTM
Erlangeninwhichonecanlearntomakescientificresearch,todevelopideas,torealize
these ideas and to take responsibility. In addition to these, I would like to express my
deepandsinceregratitudetohimformakingmyresearchpossibleathisinstitute,for
supervisingme,providingresourcesandsubjects,andofferingdirectionandpenetrat
ing criticism. His critiques eventually enabled me to grasp the rich complexity of the
investigatedmatterandforcedmetobemoresoundinmyinvestigations. Hisunlim
ited passion to learn, to invent, to do research and equally unlimited energy to work
andtomakehisideasrealinspiredmeallthetime.
SpecialthanksareduetoHermannLienhartforhisinvaluablesuggestionsduringthe
construction of the experimental facility, for the time he devoted for very useful dis
cussions on my results, for proofreading and finally for making the painful transla
tion. Our discussions, which were enriched by his unconventional thinking and his
approachtoproblems,wereofessencetotheprogressofthiswork. Mostimportantly,
IamveryhappythatIgainedsuchafriendwhoencouragedmeinmystudiesandlet
mesharehiswisdom.
I give my respects to my co supervisor PD Dr. Jovan Jovanovi c,´ who helped me to
getthescholarshipfromBavarianResearchFoundationandsuggestedmetostudyax
isymmetric turbulence. I appreciated a lot his written works on turbulence in which
onecanseethechallengethathemettoestablishanewapproachonmod
eling. HisstudiesformedthebasisofmyPhDwork.
I would like to thank the rest of my thesis committee: Prof. Dr. Ing. Dr. Ing. habil.
C. Tropea, PD Dr. Ing. Andreas Otto and Prof. Dr. Peter Otto Brunn for their kind
iiiiv Acknowledgments
acceptancetoexaminemyPhDwork.
WithouttheveryfruitfuldiscussionswithMr. C¸agatayKoksoy¨ ,Dr. SubhasisRay,Prof.
Dr. MohamedGad ElHak,Prof. Dr. HassanNagib,Prof. PeterBradshaw,somepartof
thethesiscouldnotbethatgood. Altoughwecouldnotworktogetherforalongtime,
IamverygratefulthatDr. Ing. ThoralfSchenk,Dr. Ing. MartinFischerandMr. Horst
Weber could spare their valuable time and energy to teach me hot wire anemometry
and laser Doppler anemometry. I should note that I profited a lot from the thesis of
Dr. Ing. Thoralf Schenk in the experimental part of my investigations. Moreover, I
would like to thank to Bastian Haubner and Babu Gorle Suresh for their patience to
have a supervisor like me, when they performed experimental investigations which
werepartiallyusedinthepresentthesis.
The adaptation to a foreign country became possible and very exciting with good
friends. In this respect, I benefited spiritually a lot from the our friendship with Dr.
Ivan Otic¸, my German teacher Gdrun Brug and Murat Avas. I have shared many un
forgettable hard, good and funny times with my friends Dr. Ing. Alejandro Peugnet,
Ferhat S¸engul,¨ Dr. Ing. Mira Pashtrapanska and Dr. Ing Jo ao˜ Pedro Pegoˆ who have
accompaniedmesincethesedays.
I always received very friendly support from our administrative staff Ina Paulus, Jo
hanna Grasser, Iris Knopf, Ilse Grim, and Margot Hill. Without their help the life
at LSTM Erlangen would be considerably harder. I have to express my gratitude to
Ina for sacrificing her nights for translating some part of my thesis. I always worked
closelytoourtechnicalstaffandappreciatedverymuchthevalueoftheirprecisework
andtheiractiveroleinthedevelopment. Hence,Iamverypleasedtoacknowledgethe
efforts of Claus Bakeberg, Werner Sipl, Robert Pavlik, Stefan Knopf, Heinz Hedwik,
Josef Svejda, Herbert Kaiser, Franz Kaschak, Max Brandt, Rolf Zech and Horst Weber.
I am indebted very much to Rolf Zech whose wisdom and humor enabled him to for-
give me for my fatal failure. I felt always better when I see Mr. Pavlik and experience
hisstillinghumanity.
My special appreciation goes to my mother in law and families of the sisters of my
wife for their thrust in me and for their help during the preparation of the wonderful
party,wemadeafterexaminationatLSTM Erlangen.
I am forever thankful to my parents Perihan and S¸evket who brought me up in an
environment in which I learned critical and creative thinking. I felt always their un
conditional support at each turn of the road. I am intimately indebted to my mother
for her silent bearing my absence from home. I always felt the warm prayers of my
grandparents,BekirandCemileUludag,˘ myaunts,NerimanandNermin.
Finally,IgratefullyacknowledgethescholarshipsprovidedtomebytheScientificand
Technological Research Council of Turkey and the Bavarian Research Foundation for
my Ph.D. studies at FAU LSTM Erlangen. Without the financial support of LSTM
Erlangen and theVolkswagen Foundation for theconstruction of the experimental fa
cilitiesthisstudywouldnothavebeenpossible.ToNevin,mybelovedandcompanion,
whoenduredthemosthardestpartofthiseffort,
toleratedtheobsessionandthelatenights
thatseemednecessarytobringittocompletion.
ToherIowemorethanIcantell.Abstract
Axisymmetricturbulentflowswereexperimentallyandnumericallyinvestigated. Dif
ferent aspects of axisymmetric turbulent flows related to anisotropy invariant model
´of turbulence (AI model), which was constructed at LSTM Erlangen by Jovanovi c,
Otic´ & Bradshaw (2003), are highlighted. For this purpose, decay of nearly isotropic
grid generatedturbulence,decayofanisotropicaxisymmetricturbulence,axisymmet
ric contraction, axisymmetric expansion and successive axisymmetric strain were in
vestigated for the turbulence Reynolds number range 15 < Re < 60. Measurementsλ
of velocity fluctuations were performed with hot wire anemometry in two different
flow facilities at LSTM Erlangen: the closed loop wind tunnel and the axisymmetric
straintunnel,whichwasdesignedandconstructedinordertoinvestigateaxisymmet
ricstrainedgrid generatedturbulence.
ItwasfoundthattheincreaseinlongitudinalReynoldsstressalongaxisymmetriccon
tractions having high contraction ratios, which were reported in the literature, cannot
be predicted with the rapid distortion theory and direct numerical simulations. This
anomalous trend of measured longitudinal Reynolds stresses is referred to as the high
contraction ratio anomaly in the present work. Experimental evidence is provided that
theanomalyisduetoinaccuraciesinthemeasurements. Theimperfectspatialresolu
tion of X wire probes, the mass flow rate fluctuations in the flow facility and the elec
tronic noise of measurement instrumentation contaminate measurements of velocity
fluctuationsandbecomesignificantdownstreaminthecontractions,especiallyinthose
havinghighcontractionratios. Ameasurementmethodemployingtwo pointcorrela
tionmeasurementswasdevelopedtoseparatetheturbulentvelocityfluctuationsfrom
non turbulentmassflowratefluctuationsandelectronicnoise. Theimperfectwireres
olution effect on the measurements was removed by a second measurement method,
which was developed by adopting the correction methods proposed for isotropic tur-
bulence,whichareavailableintheliterature,totheinvestigatedanisotropicturbulent
flows. After the application of the proposed methods for correcting measurements,
notonlywasacontinuousdecreaseinlongitudinalReynoldsstressobserved,butalso
an increase in transverse Reynolds stress was captured. These measurement methods
weresubsequentlyemployedtoalltheselectedaxisymmetricturbulentflowcases.
As turbulence was generated with grids in the present study and homogeneity is a
basicpropertyofaxisymmetricturbulence,thespatialinhomogeneityofturbulenceat
thewakeofthegridwasinvestigated. Itisshownthattheinhomogeneous
viiviii Abstract
fieldgeneratedinthevicinityofthegridisconservedatlongdistancesawayfromthe
grid,evenforgridshavinglowsolidity. Theinhomogeneitylevelwasfoundtobe±5%
inReynoldsstressesand±20%intheanisotropyofReynoldsstressesatlocationsmore
than40meshawayfromthegrid. Similarhomogeneitymeasurementswereperformed
inaxisymmetriccontractionandexpansions. Itisshownthattheinhomogeneityofthe
grid generatedturbulencedisappearsafterbecomingisotropicinacontraction.
After resolving the aforementioned experimental ambiguities,measurements of Reyn
olds stresses, length scales, velocity correlation functions and velocity spectra were
performedforunstrainedandstrainedaxisymmetricturbulentflowcases. Itisshown
that grid generated turbulence is nearly isotropic in terms of the Reynolds stresses;
however,asitdecays,ithasnotendencytoreachalong lastingisotropicstate. Similar
observations were made for grid generated turbulence whose anisotropy is reduced
after contracting it slightly. As regards the inhomogeneity of grid generated turbu
lence, the constants of the power law decay of grid generated turbulence are shown
to be dependent on the location of the measurements axis relative to the grid. One
modeled term in the dissipation equation of the AI model was checked against the
measured unstrained turbulent flows in the present study and those in the literature,
and also another model reported in the literature. No agreement could be detected
amongthem.
All the measured turbulent flow cases were analyzed in terms of various statistical
quantities. Special emphasis is given to the development of the Reynolds stress ani
sotropy as the flow is strained in the streamwise direction. Owing to the corrections
applied in the measurements, the rapid distortion theory was experimentally vali
dated, for the first time, for axisymmetric contractions with high contraction ratios. It
is shown that rapid distortion theory predicts the anisotropy along rapid contractions
verywellandalongmoderatelyrapidcontractionsrelativelywell.
Reynolds stress predictions for the measured turbulent flow cases were performed
with the AI model, the rapid distortion theory and the k− model. The AI model
yields good predictions for unstrained and slowly strained cases, but fails consider-
ably for rapid axisymmetric strain. It is shown that the rapid pressure strain term in
theAI modelcanbeimprovedbycalibratingitagainsttherapiddistortiontheory.Contents
Acknowledgments iii
Abstract vii
Contents xiii
Nomenclature xv
1 Introduction 1
1.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 BackgroundonNumericalSimulations . . . . . . . . . . . . . . . . . . . 5
1.3 BackgroundonAxisymmetricTurbulence . . . . . . . . . . . . . . . . . . 6
1.4 MotivationoftheWorkandStructureofThesis . . . . . . . . . . . . . . . 13
2 TheoreticalBackground 17
2.1 GoverningTransportEquations . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 HomogeneousTurbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.1 TransportEquationsforHomogeneousTurbulence . . . . . . . . 20
2.2.2 ClassificationofHomogeneousTurbulence . . . . . . . . . . . . . 22
2.3 AxisymmetricTurbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.1 FormsofCorrelationTensors . . . . . . . . . . . . . . . . . . . . . 23
ixx Contents
2.3.2 Anisotropy invariantMapandLimitingStatesofTurbulence . . 24
2.3.3 Two pointCorrelationFunctionsandLengthScales . . . . . . . . 27
2.4 TheVortexStretchingand
theRapidDistortionTheory . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.5 TheEddyViscosityConceptandthek−Model . . . . . . . . . . . . . . 34
2.6 Anisotropy invariantModelingof
AxisymmetricTurbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.6.1 RelationsBetweenUnclosedCorrelations . . . . . . . . . . . . . . 38
2.6.2 Scalar invariantFunctions . . . . . . . . . . . . . . . . . . . . . . . 40
2.6.3 OverviewoftheModeledSystemofEquations . . . . . . . . . . . 42
2.6.4 ExpandedFormsofModeledEquations . . . . . . . . . . . . . . 43
3 ExperimentalFacilitiesand
OverviewofExperimentalInvestigations 47
3.1 FlowFacilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.1.1 AxisymmetricStrainTunnel(AST) . . . . . . . . . . . . . . . . . . 47
3.1.2 StrainingDucts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.1.3 WindTunnelofLSTM Erlangen . . . . . . . . . . . . . . . . . . . 50
3.2 InstrumentationforTurbulenceMeasurements . . . . . . . . . . . . . . . 50
3.2.1 CalibrationoftheHot wireProbes . . . . . . . . . . . . . . . . . . 53
3.3 FlowQualityoftheFlowFacilities . . . . . . . . . . . . . . . . . . . . . . 56
3.3.1 TheAST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.3.2 TheWindTunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.4 DescriptionoftheTestCases . . . . . . . . . . . . . . . . . . . . . . . . . 61
4 InhomogeneityofGrid generatedTurbulenceUnderZeroStrain
andFiniteStrain 65

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