Dynamic modeling and compensation schemes for pressure sensitive paints in unsteady flows

124 Pages·2001·4.2 MB·English

by  Winslow, Neal Andrew

DYNAMICMODELINGANDCOMPENSATIONSCHEMES
FORPRESSURESENSITIVEPAINTSINUNSTEADYFLOWS
By
NEALANDREWWINSLOW
ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL
OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT
OFTHEREQUIREMENTSFORTHEDEGREEOF
DOCTOROFPHILOSOPHY
UNIVERSITYOFFLORIDA
2001
ACKNOWLEDGMENTS
IwouldfirstliketoacknowledgeDr.JoanneBedlek-Anslowforhertimeand
effortinapplyingthePSPsusedinmostoftheexperimentspresentedherein. Also,Dr.
PaulHubnerisowedmanythanksforthenumeroustimesheactedasasoimdingboard
formyvarioustheoriesandoff-the-wallideas. IwouldalsoliketothankTroy
Livingstonfortheuseofhisdigitalcameraandforhishelpinacquiringtheimagesofthe
experimentalapparatusshowninthisdissertation.
SpecialthanksgoDr.BruceCarroll,myadvisor,forhisextremepatience
throughoutmystudies. Furtherappreciationgoestotheothermembersofmycommittee.
Dr.KirkSchanze,Dr.AndrewKurdilaandDr.MartinMorris. Theyhaveeachhelped
meinmanyways.
Lastly,Iwishtothankmyparents. Withouttheirencouragement,love,and
supportIwouldhaveneverfinished.
TABLEOFCONTENTS
page
ACKNOWLEDGMENTS
ii
LISTOFTABLES v
LISTOFFIGURES vi
NOMENCLATURE
ix
ABSTRACT xi
CHAPTERS
1 INTRODUCTION 1
BasicPSPPhysics 1
PSPinSteadyPressureFields 5
PSPinUnsteadyPressureFields 7
TransverseJets 13
2 PSPMODELDEVELOPMENT 17
EmpiricalModels 17
DiffusionBasedModels 20
DiffusionBasedModelwithLinearCalibration 25
DiffusionBasedModelwithStem-VolmerCalibration 30
3 DYNAMICCOMPENSATION 36
ModelReferenceControl 36
ApplicationofMRCtoPSPSystem 40
MRCSimulationsandCompensationofExperimentalData 44
4 EXPERIMENTALSETUPANDPROCEDURES 52
PSPDynamicsTestCell 52
SupersonicWindTunnel 56
ImageProcessing 61
UncertaintyAnalysis 68
i
iii
5 RESULTS 81
6 CONCLUSIONSANDRECOMMENDATIONS 94
Conclusions 94
Recommendations 94
APPENDICES
A MATLABCODE:PSPMRCPARAMS 96
B SIMULINKCODE:PSPMRC 101
C PSPUNCERTAINTYANALYSIS 103
REFERENCES 106
BIOGRAPHICALSKETCH 110
iv
LISTOFTABLES
Table Page
1. SamplePSPIndicatedPressures 27
2. ComparisonofCurvefitValues 34
3. CalibrationFunctions,Constraints,andTypicalValues 66
4. Nominalvaluesand95%confidencelimitsofkeyvariables 69
V
1
LISTOFFIGURES
Figure Page
1.1 SchematicofatypicalPSPlayer 2
1.2 Transverseinjectionflowfieldschematic 14
2.1 Frequencyresponseofa16-|im-thickPSPsample 19
2.2 ComparisonofPSPdataandempiricalmodeldata 19
2.3 SimulatedPSPunitstepresponseusingdiffusion-basedmodelwithlinear
calibration.Notes:A)t*,;=1.1;B)t*,^=Xlln^;C)t*„=1.8 28
2.4 SimulatedPSPfrequencyresponseusingdiffusion-basedmodelwithalinear
calibration 28
2.5 ComparisonofPSPdataanddiffusion-basedmodeloutputwithalinear
calibration 29
2.6 Comparisonofcalibrations 3
2.7 Simulatedpositivestepinpressure(modelcomparison) 34
2.8 Simulatednegativestepinpressure(modelcomparison) 35
2.9 Positivestepinpressurefromexperimentaldata(modelcomparison) 35
3.1 StructureoftheModelReferenceControlscheme 37
3.2 StructureoftheModelReferenceControlschemeforuseasacompensatorfor
PSPdata 41
3.3 Linearcompensationsimulationofapositivestepinpressure 45
3.4 CompensationsimulationsusingnonlinearformofthePSPplant, (a)Positive
stepinpressure; (b)Negativestepinpressure 46
vi
3.5 CompensationsimulationsusingnonlinearformofthePSPplantwitha
sinusoidaldrivingpressure,(a)co*=1;(b)w*=3;(c)co*=10;(d)co*=30 47
3.6 Compensationofexperimentaldata,(a)Positivestepinpressure;(b)Sawtooth
drivingpressure 49
4.1 PSPDynamicTestCell:A)Digitalvalvetovacuum,B)Pressuretransducer,
C)Digitalvalvetohighpressure,D)Thermistor,E)WindowtoPSPsample,
F)Coolingfins 70
4.2 SchematicviewofthePSPDynamicTestingCell 71
4.3 HeatExchangerUnit:A)Inlet,B)Outlet 72
4.4 OrielQuartz-Tungsten-Halogen(QTH)Lamp 73
4.5 ISSILEDLamp 74
4.6 SchematicofthePSPDynamicTestingCellOptics 75
4.7 FisherControlValves:A)1 1/2"Valve,B)1"Valve 76
4.8 Stagnationchamberofthesupersonicteststandfacility 76
4.9 Mach1.56TestSection: A)3of8Staticpressuretaps,B)2of4Thermocouples,
C)Exteriorreferencemarker,D)Bottomedgeofcircularpluginsert 77
4.10 Detailedfrontviewofpluginsertshowingthecentraljetorificeandthe4static
pressuretaplocations 77
4.11 Detailedrearviewofpluginsert: A)2of4Pressuretaps,B)Thermocouple,
C)Digitalvalvecontrollingthejet 78
4.12 A)XenonStrobe,B)PhotometriesCCDCamera 78
4.13 ImageProcessingFlowchart 79
4.14 SamplePSPStaticCalibration 80
4.15 RelativeuncertaintyintheindicatedPSPpressure 80
5.1 Asequenceof10uncompensatedPSPimagestakenat5msintervalsduringafiill
cycleof50ms. Grayscaleissuchthatwhite=0.7atmandblack=0.latm.
Dimensionsarefrom-4.5Djto+5.5DjinXandfi-om-3.5Djto+3.5DjinY 86
5.2 Asequenceof10compensatedPSPimagestakenat5msintervalsduringafull
cycleof50ms. Grayscaleissuchthatwhite=0.7atmandblack=0.latm.
Dimensionsarefrom-4.5Djto+5.5DjinXandfi-om-3.5Djto+3.5DjinY 87
5.3 Athree-cycleloopofPSPdataalongthestreamwisecenterlinethroughthejet.
(a)Uncompensated;(b)Compensated.Grayscaleissuchthatwhite=0.7atmand
black=0.1atm. TheX-coordinateisorientedalongthehorizontaldirection
(positivetotheright)andtimeisorientedvertically(positiveup) 88
5.4 ComparisonofPSPdatatopressuretapdata, (a)Upstreamofthejet;(b)
Downstreamofthejet;(c)Spanwisefromthejet 89
5.5 Variationinthepaintthicknessnearabruptedges 90
5.6 Effectiveback-pressureratioatthejet 93
viii
NOMENCLATURE
a =pressuresensitivepaintthickness;Stem-Volmerintercept
A =amplitude
b =Stem-Volmerslope
B =biasuncertainty
c =calibrationconstants
C =feedbackgainsofmodelreferencecontroller
D =diffusivity;denominatorpolynomial;diameter
E =activationenergy
f =calibrationfunctionfrompressuretointensity
g =calibrationfiinctionfromintensitytopressure
G =transferfiinction
H =transferfiinction
I =integratedintensity
j =thecomplexnumber,V-T
J =momentumratio;intensityperunitthickness
k =rateconstant;highfrequencygaincoefficient
K =Stem-Volmerconstant;intensitydifferenceperunitthickness
mM ==oMxaycghennucmonbceernfrationdifferencerelativetosurfacecondition
n =oxygenconcentration
N =modelorder;numeratorpolynomial
P =pressure
Q =calibrationparameter
s =Laplacevariable
S =samplestandarddeviation
t =time
T =temperature;1^'ordersystemtimeconstant
u =imcertainty
U =inputtomodelreferencecontroller
VW ==vienltoecmiatly;stiantteeomfalmostdaetleorfefmeordeneclerceofnetrreonlcleerconfroller
X =distancefromsubsfrate
X =downstreamdistancefromjetcenter
Y =outputofmodelreferencecontroller;processedinverseintensity;spanwise
distancefromjetcenter
Z =intemalstateofmodelreferencecontroller
ix
a =modalstates
=electronsperbitoftheCCDA/Dprocess
Y =specificheatratio
A =relativedegreeofatransferfunctionorplant
X =eigenvalues
P =density
o =solubility
T =timeconstant
=quantumefficiency;phase
X =molefraction
=spatialeigenfiinctions
(0 -frequency
SuperscriptsandSubscripts
InT —rouneriransiormoiii
H =timederivativeofH
H =averagevalueofH
a =augmented
C =compensated
dik =darklevel
er =externalreference
ext =externalmarker
ff =flatfield
j =jet
in =input
m =model
P -plant
PSP =pressuresensitivepaint
q =quencher
nr =non-radiative
r =radiative
ref =atreferenceconditions
run =atrunconditions
out =output
model =modeloutput
* =dimensionless
00 =freestreamconditions
0 =initial
1 =final
O.xx =atxx%response(e.g.:0,
X