Simulation of the natural frequencies in a pump-turbine runner in air and water

45 Pages·2015·7.31 MB·English

by  Øyvind Moen Fjeld

Simulation of the natural frequencies in a
pump-turbine runner in air and water
Øyvind Moen Fjeld
Master of Energy and Environmental Engineering
Submission date: June 2015
Supervisor: Torbjørn Kristian Nielsen, EPT
Norwegian University of Science and Technology
Department of Energy and Process Engineering

PREFACE
ThisMasterthesiswaswrittenfortheWaterPowerLaboratory,DepartmentofEnergyandProcessEngi-
neering(EPT)atNTNUduringthespringof2015.Theproblemdescriptionwasmadeonthebasisofmy
projectthesis.Workingwithnaturalfrequenciesofstructureshasbeeninterestingandchallenging.
IwouldliketothankTorbjørnK.Nielsenforsharinghisknowledgeandexperience. ThankstoFrode
KristofferAmundsenKjøsnesforthecollaborationduringthelastmonths.AspecialthankstoEinarAgnalt
whichwasveryhelpfulsolvingproblemswiththeCADgeometry.
ØyvindMoenFjeld
Trondheim,17.06.2015
i
ABSTRACT
Structural-acousticmodelsareusedintheindustrytodeterminethenaturalfrequenciesofrunnersand
impellers in hydraulic turbomachinery under construction of the machines. The structural-acoustic
modelshavetobeabletohandlethecomplexboundaryconditionsandloadsexperienced. Thenew
trendsinwaterpowerproductionhaveledtonewoperatingregimesforseveralhydropowerplants.More
timeisspentoutsideBestEfficiencyPoint(BEP)andfrequentadjustmentofoutputiscommon.These
factorsputlargestressesonthestructure.Especiallyforhighheadturbineswhereforcesarehigh,fatigue
loadscouldcauseseriousdamageaftershorttimeofoperation. Thefatigueloadsareamplifiedifthey
getintoresonancewiththenaturalfrequencyoftherunner. Knowledgeofthenaturalfrequenciesofa
turbinearethereforeofgreatimportance.Structural-acousticmodelsoftheturbineanditssurroundings
havebecomeanimportantpartofconstructiontomaximizeefficiencyandsafety.Overthelastdecade
severalbreakdownsofnewlyinstalledturbineshaveshownthattherearechallengestoovercomeindesign,
buildingandoperationoftheseturbomachines.Inthisreport,aCADmodelofapump-turbinerunner
isusedinnumericalsimulationstoinvestigateitsstructuralbehaviorandnaturalfrequenciesinairand
submergedinwater. Thegoalistofindtheaddedmasseffectandseehowwellnumericalsimulations
matchexperimentsdoneontheexactsamepump-turbinerunnerattheWaterPowerLaboratoryatNTNU.
ANSYSMechanicalsoftwareisusedforthesimulations.Theresultsobtainedinmodalanalysisshoweda
FrequencyReductionRatio(FRR)inwaterbetween14-34%,dependingonthemodeshape.FRRinthe
harmonicresponseanalysisshowedvaluesfrom11-20%.Comparisonwiththeexperimentalinvestigation
showedlargedeviationsforallmodesexcept(2,0).
SAMMENDRAG
Structuranalysemedakustiskemodellerblirbruktiindustrienforåbestemmeegenfrekvensenetilvan-
nturbiner.Modellensomblirbruktundersimuleringenemåværekapabeltilåhåndteredekompliserte
grensebetingelseneogkreftenesomerinvolvert.Nyetrenderinnenvannkraftproduksjonharførttilnye
produksjonsmønstre.Størredelavproduksjonstidenblirtilbraktutenforpunktetforoptimalvirkningsgrad
ogstoresvingningeriproduksjonenervanlig. Dissefaktoreneførertilstorebelastningerpåturbinen.
Spesieltforhøytrykksmaskiner,derkrefteneerstore,kantrykkpulsasjonerføretilstoreskaderetterkorttid.
Trykkpulsasjoneneblirforsterkethvisdekommeriresonansmedegenfrekvensenetilturbinen.Påbak-
grunnavdetteerdetviktigåhakunnskapomegenfrekvensenetilturbinen.Strukturanalysemedakustiske
modelleravturbinenogomgivelseneharutvikletsegtilåblienstordelavproduksjonsprosessenforåøke
effektivitetenogsikkerheten.Overdesistetiåreneharfleretretthetsbruddinyliginstallerteturbinervistat
deterutfordringeråoverkommeidesignogproduksjonsprosessen.IdennerapportenblirenCADmodel
avenpumpe-turbinbruktinumeriskesimuleringerforåundersøkebevegelseneogegenfrekvensenei
luftogivann.Måleteråfinnefrekvensreduksjonenforårsaketavekstra-masseeffektenogsehvorgodt
numeriskesimuleringeretterliknereksprimenterpådensammepumpe-turbineniVannkraftlaboratoriet
vedNTNU.ANSYSMechanicalprogramvareerbruktforågjennomføresimuleringene.Resultatenefunnet
imodalanalysenviserenfrekvensreduksjonpåmellom14-34%,avhengigavmodalformen.Frekvensre-
duksjoneniharmoniskresponseanalysenerpåmellom11-20%.Sammenlikningermedeksperimentet
viserstorevariasjonerforallemoderbortsettfra(2,0).
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CONTENTS
Preface i
Abstract ii
Nomenclature vii
1 Introduction 1
1.1 Trendsinwaterpowerproduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Newoperatingregime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Newbuildingmaterialandproductionregime . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.3 Higherloads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.4 Computersimulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 NaturalFrequencyofstructures 3
2.1 Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Modeshapes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Excitationforcesonturbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.1 RunnerFrequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.2 Bladepassingfrequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.3 Guidevanefrequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 Structuralanalysis 10
3.1 FiniteElementMethod. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 FEMinANSYS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2.1 ModalAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2.2 Harmonicresponseanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4 Structuralacoustics 16
4.1 FluidSolidInteraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.2 FluidElements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5 Previousworkdoneonnumericalsimulationsofsubmergedstructures 21
6 Numericalsimulations 22
7 Resultsanddiscussion 25
7.1 Modalanalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
7.2 Harmonicresponseanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
7.3 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
8 Conclusion 31
9 Furtherwork 32
References 33
iii
LIST OF FIGURES
1 Spring-masssystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Tahomabridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4 Modeshapesofbar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
5 Modeshapesofdisk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6 Guidevanewakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
7 RSI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
8 "Seaofsprings" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
9 BasicsofFEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
10 Acousticelements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
11 Acousticelements2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
12 FSItransfermatrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
13 Tetrahedralelement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
14 Turbinewithsurroundingfluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
15 Turbineandmesh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
16 Comparisonoffrequenciesinairandinwater . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
17 FRR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
18 Comparisonofthefrequencyresponseinairandinwater . . . . . . . . . . . . . . . . . . . . . 27
19 Unidentifiedmodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
20 Frequencyplotfromtheexperimentwiththepump-turbineinair . . . . . . . . . . . . . . . . 30
iv
LIST OF TABLES
1 Materialpropertiesofthebronzepump-turbine. . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2 Meshinfo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Timeconsumptionofthesimulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4 Pump-turbinespecifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5 Resultsfromthemodalanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
6 Frequenciesofmodesfromtheharmonicresponseanalysis. . . . . . . . . . . . . . . . . . . . 28
7 Deviationsoffrequenciesbetweenmodalanalysisandharmonicresponseinwater . . . . . 28
8 Experimentalresultsofthepump-turbineinair . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
v
NOMENCLATURE
[C] Structuraldampingmatrix
[K] Structuralstiffnessmatrix
[L] Lowertriangularmatrix
[M] Structuralmassmatrix
[R] Acousticfluidboundarymatrix
[U] Uppertriangularmatrix
→−
n outwardnormalunitvectoroffluiddomain
{u¨} Nodalaccelerationvector
{u˙} Nodalvelocityvector
{F} Loadvector
{u} Nodaldisplacementvector
FS Fluid-solidboundary
k Stiffnessconstant N/m
c speedofsound m/s
Hz Hertz 1/s
p acousticpressure Pa
Q masssource m3/s
t time s
u displacment m
GreekSymbols
α massmatrixmultiplier
β stiffnessmatrixmultiplier
µ dynamicviscosity kg/ms
ω Frequency rad/s
Φ Displacementpotential
φ Displacementphaseshift rad/s
ρ meanfluiddensity kg/m3
ζ constantmodaldampingratio
Sub-andsuperscripts
F Fluid
S Solid
i counter
vi