Effect of Chemical Reaction Rates on Aero-heating Prediction in Re

172 Pages·2012·7.44 MB·English

Effect of Chemical Reaction Rates on Aero-heating
Prediction in Re-entry Flows
A thesis submitted in partial fulfillment of
the requirements for the degree of
Doctor of Philosophy
by
D. Siva Krishna Reddy
(Roll No. 06401001)
Under the guidance of
Prof. Krishnendu Sinha
and
Prof. Viren Menezes
Department of Aerospace Engineering
INDIAN INSTITUTE OF TECHNOLOGY–BOMBAY
2012
Toallthosepersonsandincidentswhoandwhichincultivatedscienticcuracity;inspiredmeto
takeupdoctorialstudiesandmotivatedmeduring thethesiswork.

c CopyrightbyD.SivaKrishnaReddy2012
(cid:13)
AllRightsReserved

Abstract
A re-entry capsule encounters a high temperature and chemically reacting flow during the re-
entry phase. Computational Fluid Dynamics is extensively used to simulate these flows, as
high enthalpy and low density associated with the flight conditions are difficult to reproduce in
wind tunnels or shock tunnels at each re-entry trajectory point. Flowfield solution and surface
predictions, such as surface heat flux and pressure, at these conditions are sensitive to chemi-
cal reaction rate constants used in the simulation. Uncertainty in the rate constants, which is
inherentintheirmeasurement,inducescorrespondingchangesinthesurfaceproperties. Under-
standingtheroleofrateconstantsontheflowsolution andtheassociatedsurfacepredictions is
important.
The present thesis investigates the effect of variation in chemical reaction rate constants
on aero-thermal predictions at flight conditions. With in this scope, numerical simulations are
performed by varying the reaction rate constants over their uncertainty range. Freestream con-
ditions at 35 km, 62 km and 70 km condition are chosen as the test cases. They represent
typical low, intermediate and high altitude flight in the earth atmosphere. These conditions are
chosensothattheeffectsoffreestreamdensityandstagnationenthalpyontheheatingratevari-
ations can be examined. The computations are performed with an in-house CFD code and the
aero-thermalpredictionsarevalidatedagainstavailableflightdata. Flowfieldsolutionsarecom-
puted by altering the reaction rates from their baseline values and they are carefully analyzed
to understand the physical effects that influence the surface heat transfer rate. A controlled
zonal analysis is performed to isolate the effects of shock-layer and boundary-layer chemistry
onheatfluxvariations. Theanalysisisperformedatdifferentpointsalongthevehicleforebody,
afterbodyandshoulder.
It is found that the dominant chemical reactions in the gas mixture; chemical state of the
gas, i.e. equilibrium, frozen and non-equilibrium; and the extent of recombination reactions
at the vehicle surface are the critical factors that influence the heat flux variations due to the
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uncertainty in the reaction rate constants. The stagnation enthalpy of the flow determines the
dominant reactions to which the surface heating rate is sensitive. On the other hand, the gas
densitydeterminesthechemicalstateofthegas,whichinturnaffectsthemagnitudeofheating
ratevariations. Ingeneralincreasingthereactionratesenhancestherecombinationreactionsin
the boundary layer that leads to higher surface heat flux. An opposite effect is observed when
the rate constants are decreased. When the gas is in chemical equilibrium state, increasing the
rateconstantsfurtherhasasmalleffectonthesurfaceheatingrate. Ontheotherhand,whenthe
gas is in non-equilibrium state, increase or decrease of rate constants can lead to large changes
in theheat fluxpredictions. Thesetrends arestudied in the threetest casesoutlined above. The
results are then extrapolated to cover the entire range of Earth-reentry trajectory points with
stagnationenthalpybetween2MJ/kgand32MJ/kg.
Keywords: Re-entryflows,Computationalfluiddynamics,Thermo-chemicalnon-equilibrium,
Chemicalreactionrateconstants.
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Contents
Abstract i
ListofTables vii
ListofFigures ix
Nomenclature xvi
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 ReviewofLiterature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 MotivationandObjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 ScopeofThesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 SimulationMethodology 11
2.1 Non-equilibrium ViscousLaminarFlows . . . . . . . . . . . . . . . . . . . . . 12
2.1.1 EquationofState . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.2 SpeciesandMixtureTransportProperties . . . . . . . . . . . . . . . . 15
2.1.3 SpeciesDiffusion Coefficients . . . . . . . . . . . . . . . . . . . . . . 16
2.1.4 ChemicalSourceTerms . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.5 Vibrational SourceTerm . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 GoverningEquationsforTurbulentFlows . . . . . . . . . . . . . . . . . . . . 20
2.2.1 FavreAveragedEquations . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.2 Spalart-Allmaras Model[34] . . . . . . . . . . . . . . . . . . . . . . . 24
2.3 FiniteVolumeMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.1 Integration oftheInviscidFluxes . . . . . . . . . . . . . . . . . . . . 27
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2.3.2 SecondOrderSpacialAccuracy . . . . . . . . . . . . . . . . . . . . . 29
2.3.3 EvaluationoftheViscousFluxes . . . . . . . . . . . . . . . . . . . . . 29
2.3.4 TimeIntegration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.5 SolutionProcedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3 Aero-heatingPredictionsatFlightCondition 33
3.1 FIREIIConfiguration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 SimulationMethodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.1 Computational Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.2 IterativeConvergence . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.1 DescriptionoftheSurfaceProperties . . . . . . . . . . . . . . . . . . 45
3.3.2 EffectofGeometricSimplifications . . . . . . . . . . . . . . . . . . . 46
3.3.3 Comparison withFlightData . . . . . . . . . . . . . . . . . . . . . . . 48
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4 HeatingRateVariationsat35kmAltitude 51
4.1 SimulationMethodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.1.1 ChemicalReactionKinetics . . . . . . . . . . . . . . . . . . . . . . . 51
4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2.1 EffectofReactionRatesVariationontheHeatingrate . . . . . . . . . 58
4.2.2 NoseStagnationPoint . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2.3 ExpansionRegion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2.4 Afterbody . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2.5 IncreasedReactivityintheEntireDomain . . . . . . . . . . . . . . . . 64
4.2.6 DecreasedReactivityintheEntireDomain . . . . . . . . . . . . . . . 69
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5 HeatingRateVariationsat70kmAltitude 73
5.1 SimulationMethodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.1.1 GridConvergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
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5.2.1 BoundaryLayerThermo-Chemistry . . . . . . . . . . . . . . . . . . . 79
5.2.2 AlteredReactivityintheBoundarylayer . . . . . . . . . . . . . . . . 83
5.2.3 EffectonSurfaceHeatFlux . . . . . . . . . . . . . . . . . . . . . . . 89
5.2.4 IncreasedReactivityintheEntireDomain . . . . . . . . . . . . . . . . 94
5.2.5 DecreasedReactivityintheEntireDomain . . . . . . . . . . . . . . . 98
5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6 HeatingRateVariationsat62kmAltitude 103
6.1 SimulationMethodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.1.1 GridConvergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.2.1 Thermo-Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.2.2 AlteredReactivityintheEntireDomain . . . . . . . . . . . . . . . . . 109
6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7 Variation withaltitude 118
7.1 ChemicalReactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.1.1 Shock-layerChemistry . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.1.2 TemperatureVariationwithAltitude . . . . . . . . . . . . . . . . . . . 119
7.1.3 Boundary-layer Chemistry . . . . . . . . . . . . . . . . . . . . . . . . 120
7.2 DegreeofNon-equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
7.2.1 ThermalNon-equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 124
7.2.2 ChemicalNon-equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 126
7.3 HeatingRateVariations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
7.3.1 CriticalFactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.3.2 HeatingRateVariationsattheNoseStagnationPoint . . . . . . . . . . 130
7.3.3 EffectofStagnationEnthalpy . . . . . . . . . . . . . . . . . . . . . . 131
7.3.4 EffectofDensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
8 ConclusionsandFutureWork 134
8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
8.2 FutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
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