Gas-Surface Interaction Models in Hypersonic Flows Aerospace Engineering

104 Pages·2016·5.31 MB·English

by  Andre C. Marta

Gas-Surface Interaction Models in Hypersonic Flows
Carlos Manuel da Cunha Teixeira
Thesis to obtain the Master of Science Degree in
Aerospace Engineering
Supervisors: Prof. Mário António Prazeres Lino da Silva
Dr. Bruno Eduardo Lopez
Examination Committee
Chairperson: Prof. Filipe Szolnoky Ramos Pinto Cunha
Supervisor: Dr. Bruno Eduardo Lopez
Member of the Committee: Prof. Vasco António Dinis Leitão Guerra
December 2015
ii
Acknowledgments
FirstlyIrecommendtothenovicetwogreatbookstoserveasfoundationstothefield. Anderson[1]has
a very good, down-to-earth pedagogical approach that stimulates the student. Vicenti and Kruger [2]
primefortheirsuccinctandyethighlydetailedexplanations.
I thank IPFN for having welcomed me in the past months and presenting me with unique and interest-
ing opportunities. I thank Prof. Ma´rio Lino for having introduced me to this fascinating field of high-
temperaturegas-dynamics, forhisenthusiasm towardsthe subjectand forhisflexibility andsupport as
supervisor. Ithankhimfurtherforthefinancialsupportprovided.
I congratulate Dr. Bruno Lopez for his elaborate work on SPARK. I acknowledge the imposing task of
beingthesoledeveloperofthecode. Ithankhimforhisdevotetutoringandinsightfulinputs.
I thank my colleagues Joa˜o Vargas, Daniel and Carolina for the enjoyable breaks from work. They
helpedmerelaxfromthestrainsofthethesisandfacemytaskswithrenewedenergy.
Lastly I thank my parents for the support in all forms on this past years, and always keeping sure I had
everythingIneeded,andmysisterforherinterestinmyachievements.
iii
iv
Resumo
Estateseconsistenaintroduc¸a˜odofeno´menodecatalicidadenoSPARK.
O SPARK e´ um co´digo de aerotermodinaˆmica que resolve numericamente as equac¸o˜es de Navier-
Stokesreactivas. Elee´ usadoparasimularoescoamentodereentradaatmosfe´ricadenavesespaciais.
OSPARKfoidesenvolvidoee´ mantidopeloIPFN.
Ate´ enta˜ooSPARKnegligenciavareacc¸o˜esheteroge´neas(reacc¸o˜esfluido/parede)atrave´sdasquais2
a´tomos,mediadospelasuperf´ıcie,recombinam,libertandoenergiaparaove´ıculo,apesardestafunc¸a˜o
estardispon´ıvelemgrandepartedeco´digossemelhantes. Acatalicidadetemumefeitonacomposic¸a˜o
qu´ımica do escoamento, e um forte impacto no fluxo de calor para a nave. Foi introduzido um modelo
de catalicidade que modela o feno´meno de forma macrosco´pica. Neste modelo a recombinac¸a˜o na
parededeespe´ciesqu´ımicasdissociadase´ caracterizadoporumu´nicoparaˆmetroquee´ constanteou
quedependentedatemperatura(daparede). Paratalfoinecessa´riomodificarasequac¸o˜esdebalanc¸o
de massa e energia na fronteira entre o escoamento e a parede. Os resultados de va´rias simulac¸o˜es
foramcomparadoscomoutrosco´digosnume´ricosedadosexperimentais.
Para ale´m disso, iniciou-se a implementac¸a˜o de um modelo mais avanc¸ado, denominado FRSC, que
permite prever feno´menos de ablac¸a˜o e piro´lise. Foi elaborada a formulac¸a˜o inicial que descreve com
grande detalhe reacc¸o˜es qu´ımicas heteroge´neas no caso de na˜o haver escoamento. Esta formulac¸a˜o
serve de base para a implementac¸a˜o final num escoamento governado pelas equac¸o˜es de Navier-
Stokesreactivas.
Palavras-chave:
TPS,catalicidade,SPARK,escoamentohiperso´nico,aerotermodinaˆmica
v
vi
Abstract
ThisthesisconsistsontheimplementationofcatalycityinSPARK.
SPARK is an aerothermodynamics code that solves the reacting Navier-Stokes equations. It is used to
simulatere-entryflowsofspacevehicles. SPARKisdevelopedandmaintainedatIPFN.
Until then SPARK neglected heterogeneous reactions (fluid/solid interaction) through which 2 atoms,
mediatedbythesurface, recombine, releasingenergyintothevehicle. However, thiscapabilityisstan-
dard in similar codes. Catalyticy has an effect on the composition of the flow and plays a pivotal role
on the heat flux into the space-ship. A model that describes catalycity macroscopically has been intro-
duced. Inthismodeltherecombinationatthewalloftwodissociatedspeciesischaracterizedbyasingle
parameterthatcanbeeitherconstantoftemperaturedependent. Thatrequiredasuitableimprovement
ofthemassandenergybalanceequationsbetweenthefluidflowandthewall. Theresultsfromvarious
simulationswerecomparedwithothernumericalcodesandexperimentaldata.
Furthermore,thefirststageoftheimplementationofamoreadvancedmodel,termedFRSC,thattakes
into account ablation and pyrolysis phenomenon has been achieved. This initial formulation describes
microscopically, and in great detail, the heterogeneous chemical reactions on the particular case of no
gas flow; and serves as the foundation for the final implementation of the FRSC on a flow governed by
thefullreactingNavier-Stokesequations.
Keywords:
TPS,catalycity,SPARK,hypersonicflow,aerothermodynamics
vii
viii
Contents
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Resumo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
ListofTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
ListofFigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
1 Introduction 1
1.1 TopicOverview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 GroundTestingandCFDModelingforre-entryproblems . . . . . . . . . . . . . . . . . . . 4
1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 ThesisOutline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 PhysicalModels 9
2.1 GoverningEquations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 ThermodynamicRelations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 TransportProperties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 NonequilibriumProcesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5 Gas-SurfaceInteractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5.1 SpeciesMassBalance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5.2 SurfaceEnergyBalance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3 NumericalMethodandImplementationAspects 23
3.1 RedesignoftheBoundaryConditionStructure . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 GhostCellConcept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 Implementationofthespeciesmassbalance . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4 Implementationofthesurfaceenergybalance . . . . . . . . . . . . . . . . . . . . . . . . . 29
4 ResultsfortheSpecifiedReactionEfficiency(SRE)model 31
4.1 SharpCones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.1.1 Semi-Angle=100,T =1200[K] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
w
ix
4.1.2 Semi-Angle=100,SEB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.3 Semi-Angle=200,SEB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.1.4 Meshconvergencestudyandcomputationalcost . . . . . . . . . . . . . . . . . . . 39
4.2 ElectreProbe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2.1 Vivianietal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2.2 Muylaertetal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2.3 Barbatoetal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2.4 Mesh,convergencestudyandcomputationalcost . . . . . . . . . . . . . . . . . . 47
4.3 TemperaturevaryingSRE,γ =γ(T) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.4 Selfassessmentoftheimplementation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5 TheFiniteRateSurfaceChemistry(FRSC)model 55
5.1 TheoreticalOverview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.2 ImplementationoftheFRSCmodelonSPARK . . . . . . . . . . . . . . . . . . . . . . . . 58
5.3 StandAloneCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.3.1 Equilibriumconstantstocomputesurfacereactionrates . . . . . . . . . . . . . . . 60
5.4 ResultsoftheStandAloneCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.4.1 FixedGasPhaseofDissociatedOxygen . . . . . . . . . . . . . . . . . . . . . . . 62
5.4.2 SilicaSublimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6 Conclusions 67
6.1 Achievements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.2 FutureWork. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Bibliography 69
A DiscretizationoftheNavier-Stokesequations 73
A.1 TransformationofVariables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
A.2 Finite-VolumeDiscretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
A.2.1 ExplicitTimeIntegration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
A.2.2 SpacialDiscretizationoftheFluxes. . . . . . . . . . . . . . . . . . . . . . . . . . . 76
B OtherComputationalResults 77
B.1 SharpCones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
B.2 ElectreProbe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
B.3 TemperaturevaryingSRE,γ =γ(T) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
B.4 FRSC-FiniteRateSurfaceChemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
x