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Numerical Simulation of Chemically Reactive Hypersonic Flows VonderFakulta¨tfu¨rMaschinenwesender Rheinisch-Westfa¨lischenTechnischenHochschuleAachen zurErlangungdesakademischenGradeseinesDoktors derIngenieurwissenschaftengenehmigteDissertation vorgelegtvon SanjeevKumar,M.Tech. aus Motihari,Indien Berichter: Universita¨tsprofessorDr.-Ing.H.Olivier Universita¨tsprofessorDr.-Ing.J.Ballmann Tagdermu¨ndlichenPru¨fung: 22.Dezember2005 DieseDissertationistaufdenInternetseitenderHochschulbibliothekonlineverfu¨gbar. Berichte aus der Luft- und Raumfahrttechnik Sanjeev Kumar Numerical Simulation of Chemically Reactive Hypersonic Flows D 82 (Diss. RWTH Aachen) Shaker Verlag Aachen 2006 Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the internet at http://dnb.ddb.de. Zugl.: Aachen, Techn. Hochsch., Diss., 2005 Copyright Shaker Verlag 2006 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publishers. Printed in Germany. ISBN-10: 3-8322-5065-4 ISBN-13: 978-3-8322-5065-2 ISSN 0945-2214 Shaker Verlag GmbH • P.O. BOX 101818 • D-52018 Aachen Phone: 0049/2407/9596-0 • Telefax: 0049/2407/9596-9 Internet: www.shaker.de • eMail: [email protected] Preface ThepresentthesisistheresultofmyworkasaresearchscholarattheShockWaveLaboratoryof theAachenUniversity,Germany.PartofthisworkwasfundedbytheGermanResearchFoundation (DFG)undertheGraduatestudyprogramme”Transportprocessesinhypersonicflow”. I am greatly indebted to Prof. Dr.-Ing. Herbert Olivier, the Institute director and my supervisor, forprovidingmetheexcitingopportunitytoworkonthisresearchproject,andforhiscompetent guidanceandmotivationthroughouttheproject.Hisdiverseinterestandexperienceinthefieldof hypersonicflows,playedamajorroleinthecompletionofthisresearchproject.Hehadbeenvery supportivetomethroughoutmystayattheinstitute.Ithasbeenagreatexperiencetoworkunderhis supervision. I would like to express my deep gratitude to Prof. Dr.-Ing. Josef Ballmann for providingme the opportunitytoworkwithQUADFLOW,andforhisexcellentsuggestionsinthepresentationofthe results.Heplayedamajorroleinshapingthemainpartofthisresearch.Thisworkcouldnothave beencompletedwithouthisfinancialsupport,whenitwasmostneeded. IamespeciallygratefultoPriv.-Doz.Dr.SiegfriedMu¨llerforthevaluablehelpandconsistentgui- danceonrealgasmodellingandgridadaptation.Hehasbeenverysupportiveonmanyoccasions duringthisresearch.IwouldliketoexpressmyspecialthankstoDr.-Ing.FrankD.Bramkampfor hisconsistentguidancerelatedtotheflowsolverpartofQUADFLOW,andDipl.-Math.PhilippLam- byforprovidingthegridsneededforthecomputations.Thesethreepeoplearethefounderdevelopers oftheQUADFLOWanditwasanenrichingexperiencewhileworkingwiththem. MyspecialthanksgoestomycolleagueDipl.-Phys.FlorianZus,whojoinedtheinstitute,atthelater stageofmythesis.Wehadsomuchfruitfuldiscussionsonrealgasmodelling,whichhelpedmealot ininterpretingthecomputationalresults.Iwasfortunatetohavesuchacolleague. IwishtothankDr.-Ing.BirgitU.Reinartzforherexcellentsuggestionsrelatedtoshock-shockinter- actionstopic. IwishtoexpressmythankstoallmycolleaguesoftheShockWaveLaboratory,fortheirsupport andthegreatenjoyableworkenvironmenttheycreatedintheinstitute.Ithasbeenagreatpleasureto workwithallofthem. Last,butnotleast,IwouldliketothankmywifePunamforhertrust,supportandencouragement throughoutthisresearchwork. Abstract Tostudytheatmosphericreentryphaseofaspacevehicle,itisnecessarytounderstandcorrectlythe thermochemicalnonequilibriumprocessescoupledwiththeaerodynamicphenomenaofthiscritical phase.Inatypicalhypersonicflowaboutabluntbody,thestrengthofthebowshockissuchthatthe regionbetweenthebodysurfaceandshockisthesiteofintensivethermochemicalprocesses.The differentinternalenergymodesofthemoleculesarefarfromtheirequilibriumstate.Theenergyex- changesbetweenthesedifferentmodesoccuraccordingtotheindividualrelaxationtimeassociated toeachprocesses.Detailedphysico-chemicalmodelsforairinchemicalandthermalnonequilibrium areneededforarealisticpredictionofhypersonicflowfields.Oneofthekeyissuesinthedesignof ahypersonicvehicleistheevaluationofaerodynamicheating.Especially,shock-shockinterference heatingphenomenaisanimportantandcriticalprobleminthedevelopmentofair-breathinghyperso- nicvehicles.OfspecialinterestistheEdneytypeIVinteraction,becauseitisknowntogeneratethe highestlocalloadsinpressureandheattransfer.Anumberofnumericalstudiesonshock-shockinter- ferenceproblemshavebeenconducted.Mostofthesestudies,however,assumeaperfectgasmodel. Forhigh-enthalpyhypersonicshock-shockinteractions,however,realgaseffectsbecomeimportant. Realgaseffectscanhaveanoticeableimpactonflowfeatures,suchasshockstand-offdistanceina bluntbodyflowandsurfaceheatingrates.Becauseoftheirimportance,realgaseffectshaverecently beenthefocusofseveralstudies.Animprovedunderstandingoftheinfluencesofrealgaseffectson theshockinteractionphenomenonreducesasignificantelementofriskinthedesignofhypersonic vehicles. Intheframeworkofthepresentwork,theadaptiveCFDcodeQUADFLOWhasbeenextendedfora fivecomponentsairmodel.Differentthermochemicalmodelswereimplemented.Theuncertainties associatedwiththephysico-chemicalmodellingandtheirinfluenceontheflowfieldsarediscussed with the help of computationalresults. Further, an attempt has been made to improvethe under- standingofinfluenceoftherealgaseffectsonthetypeIVshock-shockinteractionsbythepresent computationalstudy.Inthisregard,aseriesofnumericalsimulationsoftheexperimentsconductedat GALCITT5hypervelocityshocktunnelonshock-shockinteractionswerecarriedout.Thecomputed resultsarediscussedincomparisonwiththeexperimentalresultsandcomputationalresultsofDLR FLOWer-Code,whichisanon-adaptiveRANS-solver. Contents Listoffigures VII Listofsymbols XIV 1 Introduction 1 1.1 Relevantphysicsofhypersonicflows. . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Shock-shockinteraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Objectiveofthepresentwork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Physicalmodelling 5 2.1 Governingequations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Thermochemicalmodelling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.1 Thermodynamicrelations . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.1.1 Differentformsofenergy . . . . . . . . . . . . . . . . . . . . . . 10 2.2.1.2 Mixtureproperties . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.2 Chemicalkineticmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.3 Vibration-dissociationcoupling . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.3.1 Parkmodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.3.2 TreanorandMarronemodel . . . . . . . . . . . . . . . . . . . . . 20 2.2.4 Relaxationprocesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.4.1 Vibrational-translationalenergyexchange . . . . . . . . . . . . . 22 2.2.4.2 Vibrational-vibrationalenergyexchange . . . . . . . . . . . . . . 24 2.3 Transportphenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3.1 Masstransport-Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3.2 Momentumtransport-Viscosity . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3.3 Energytransport-Heatconduction . . . . . . . . . . . . . . . . . . . . . . 27 3 Numericalmethod 29 3.1 Gridgeneration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2 Adaptation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3 Finitevolumediscretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.3.1 Numericalfluxformulation. . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.3.1.1 Discretizationofinviscidfluxes . . . . . . . . . . . . . . . . . . . 32 Contents V 3.3.1.2 Extensiontohigherorderaccuracy . . . . . . . . . . . . . . . . . 34 3.3.1.3 Discretizationofdiffusivefluxes . . . . . . . . . . . . . . . . . . 35 3.4 Boundaryconditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.4.1 Supersonicinflowcondition . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.4.2 Supersonicoutflowcondition . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.4.3 Wallboundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.4.4 Planeofsymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.5 Time-integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.6 Two-dimensionalaxisymmetricEulerequations . . . . . . . . . . . . . . . . . . . . 37 3.7 One-dimensionalEulerequationsforsteadyflow . . . . . . . . . . . . . . . . . . . 38 4 Relaxationbehindnormalshocks 39 5 Computationoftwodimensionalflows 50 5.1 Inviscidnonreactiveflowoveradoubleellipse . . . . . . . . . . . . . . . . . . . . . 50 5.2 Inviscidairflowoveracircularcylinder . . . . . . . . . . . . . . . . . . . . . . . . 50 5.3 Nitrogenflowoveracircularcylinder . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.4 Inviscidairflowoverasphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 6 Shock-on-shockinteractioninhypersonicviscousflow 72 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 6.2 Shock-waveinterferencepatterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 6.2.1 TypeIIIinterferencepattern . . . . . . . . . . . . . . . . . . . . . . . . . . 74 6.2.2 TypeIVinterferencepattern . . . . . . . . . . . . . . . . . . . . . . . . . . 75 6.3 Realgaseffects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 6.4 Reviewofpreviouswork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.5 ResultsandDiscussions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 6.5.1 Flowswithoutshock-shockinteraction . . . . . . . . . . . . . . . . . . . . 81 6.6 Flowswithshockimpingement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 6.6.1 CaseA,shockangle . . . . . . . . . . . . . . . . . . . . . . . . 88 6.6.2 CaseA,shockangle . . . . . . . . . . . . . . . . . . . . . . . . 90 6.6.3 CaseB,shockangle . . . . . . . . . . . . . . . . . . . . . . . . . 95 6.6.4 CaseB,shockangle . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.6.5 CaseC,shockangle . . . . . . . . . . . . . . . . . . . . . . . . 102 6.6.6 CaseC,shockangle . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.7 Summaryoftheresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111