development of testing conditions for gas/surface ... · development of testing conditions for...
TRANSCRIPT
Development of Testing Conditions forGas/Surface Interaction Studies inAtmospheric Reentry Simulations
José Pedro Soares Pinto Leite
Dissertação para obtenção do Grau de Mestre emEngenharia Aeroespacial
Júri
Presidente: Fernando José Parracho Lau
Orientador: Luís Rego da Cunha de Eça
Vogal: Filipe Szolnoky Ramos Pinto Cunha
Novembro de 2012
Acknowledgments
⋆ To my parents that always supported me.
⋆ To Prof. Olivier Chazot for all the help, hints, coaching and the basic idea for this work.
⋆ To Francesco Panerai for his unmeasurable help for this work. My research without is PhD
Thesis and his expertise as background would have been much more darker. Sorry for all the
things I did in the wrong way and infinite amount of stupid questions.
⋆ To Pascal Collin, the super-technician, because He Is The Man.
⋆ To Bernd Helber for all the help and patience in the processing of the spectrometry results.
⋆ To Prof. Luis Eça for all the help and coaching before, during and after my stay in VKI.
⋆ To Prof. João Teixeira Borges, Prof. Luis Eça, Prof. Fernando Lau, Prof. Pedro Serrão,
Prof. Ferry Schrijer and Prof. Fluvio Scarano from IST and TUDelft for those great first courses
in Mechanics, Fluid Mechanics and Aerodynamics.
⋆ To all my friends and colleagues at the von Kármán Institute because the great environment
was a big help for the development of this work.
iii
iv
Abstract [English]
Since the beginning of the space exploration that the design of the thermal protection system (“heat
shield”) of a planetary reentry vehicle (a vehicle that enters the atmosphere of a planet coming from
the outer space) had been a challenge for the design engineers. Problems arise because of the lack of
a fully comprehension of the physico-chemical processes involved, specifically Aerothermodynamics
and Gas/Surface Interactions. In this thesis, the Local Heat Transfer Simulation methodology is used
to fully reproduce the aerothermochemical conditions in the nose stagnation point of a reentry vehicle
in a ICP Plasma Windtunnel, the Plasmatron, installed at the von Kármán Institute and capable of
produce high enthalpy flows.
Using the the LHTS methodology, the oxidation of Silicon Carbide based thermal protective
materials is investigated and both the passive-to-active transition and the operational limits of these
materials are accessed. The materials tested are going to be used in the IXV mission under project
by the European Space Agency.
A pioneer testing methodology was developed to be used in high enthalpy facilities in order to un-
derstand the effect of surface temperature in surface recombination coefficient (catalycity) and heat
flux from the plasma to the wall. Preliminary data was obtained and a sensitivity analysis were done
to access the reliability of the method. Plus, is proposed a method to construct an computationsly
efficient AeroThermodynamic DataBase for emissivity, catalycity and heat flux to be used in design
and CFD codes and applicable both for passive and active concepts of thermal protective systems.
Keywords: Thermal Protective Systems, Ground Testing, Gas/Surface Interactions, Aerothermo-
dynamics, Oxidation, Catalycity
Resumo [Português]
Desde o início da exploração do espaço que o design do sistema de protecção térmica (“escudo tér-
mico”) de um veículo espacial de reentrada planetária, ou seja, que entra na atmosfera de um planeta
vindo do espaço exterior, tem sido um desafio para os projectistas. Os problemas surgem por causa da
falta de uma boa compreensão dos processos físico-químicos envolvidos, especificamente fenómenos
aerotermodinâmicos e interacções gás/superfície. Nesta tese, a metodologia de Simulação Local de
v
vi Abstract/Resumo
Transmissão de Calor (LHTS) é utilizada para reproduzir totalmente as condições aerotermoquímicas
no ponto de estagnação do nariz de um veículo espacial de reentrada dentro de um túnel de plasma, o
Plasmatron, instalado no Instituto von Kármán e capaz de produzir jactos de muito elevada entalpia.
Utilizando a metodologia de LHTS, a oxidação e limites operacionais de materiais de protecção
térmica baseados em Carboneto de Silício são investigados. Estes materiais vão ser utilizados na
missão IXV, da responsabilidade da Agência Espacial Europeia.
Uma metodologia de teste foi desenvolvida para ser utilizada em instalações de entalpia elevada,
a fim de compreender o efeito da temperatura da superfície no coeficiente de recombinação (catalici-
dade) e no fluxo de calor do plasma para a parede. Dados preliminares foram obtidos e uma análise
de sensibilidade foi feita para testar a fiabilidade do método. Para além disso, é proposta uma me-
todologia para construir uma Base de Dados Aerotermodinâmica computacionalmente eficiente para
utilização em codigos de design e CFD e empregável em conceitos passivos e activos de sistemas de
protecção térmica.
Palavras-Chave: Sistemas de Protecção Térmica, Ensaios em Solo, Interacções Gás/Superfície,
Aerotermodinâmica, Oxidação, Coeficiente de Recombinação
Contents
List of Figures xi
List of Tables xv
List of Symbols xvii
1 Introduction 11.1 Hypersonic Flows and Atmospheric Reentry . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 The Hypersonic Flow Regime . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2 The Atmospheric Reentry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Families of Thermal Protection Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Aim of This Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Catalycity and Oxidation Research - A Bibliographical Review 72.1 Gas Surface Interaction and Catalycity . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Principles of Catalycity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.2 Catalycity, Heat Shield Design and Simulation . . . . . . . . . . . . . . . . . . 8
2.2 Passive-to-Active Oxidation Transition in TPM . . . . . . . . . . . . . . . . . . . . . . 9
3 Experimental Facilities and the LHTS Methodology 133.1 Plasmatron: The VKI’s ICP Windtunnel . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 The Local Heat Transfer Simulation method in VKI . . . . . . . . . . . . . . . . . . . 14
3.2.1 Experimental Methods for Reentry Simulation in Plasmatrons . . . . . . . . . 183.3 Recalling the Abacus – The Temperature Problem . . . . . . . . . . . . . . . . . . . . 193.4 Sample Holders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.5 Intrusive Measurement Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5.1 Heat Flux Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.5.2 Pitot Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.6 Optical Measurement Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.6.1 Two-Colour Pyrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
vii
viii Table of contents
3.6.2 Broadband Infrared Radiometer . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.6.3 In-Situ Emissivity Determination Method . . . . . . . . . . . . . . . . . . . . . 24
3.6.4 Optical Emission Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.7 New Techniques Developed in the Context of this Work . . . . . . . . . . . . . . . . . 25
3.7.1 Cooled Sample Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.7.2 New Correlation for Dynamic Pressure Estimation . . . . . . . . . . . . . . . . 29
3.8 Brief Note on the Computational Methods Used . . . . . . . . . . . . . . . . . . . . . 30
3.8.1 The heat1D script . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.8.2 The ICP code and NDPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.8.3 The CERBOULA code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.8.4 The Complete Experimental-Numerical Frame . . . . . . . . . . . . . . . . . . 35
4 Numerical Simulations 37
4.1 Cooled Sample Setup Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.1.1 ST Sample Holder Without Cooling . . . . . . . . . . . . . . . . . . . . . . . . 38
4.1.2 ST Sample Holder With Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.1.3 ST Sample Holder With Cooling and Insulation . . . . . . . . . . . . . . . . . 40
4.2 Calorimeter Adapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5 Oxidation Campaign 43
5.1 Testing Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.2.1 General Results (ST geometry) . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2.2 Passive-to-Active Oxidation Transition Line . . . . . . . . . . . . . . . . . . . . 48
5.2.3 Visual Inspection of the Samples . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.2.4 The Temperature Jump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.2.5 Optical Spectrometry Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.6 Frozen Geometry Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6 Temperature Campaign 57
6.1 Testing Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.2.1 Catalycity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7 Discussion of Results 67
7.1 Analysis of the Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
7.2 Analysis of the Oxidation Campaign . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.2.1 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.2.2 Flight Extrapolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Table of contents ix
7.3 Analysis of the Temperature Campaign . . . . . . . . . . . . . . . . . . . . . . . . . . . 707.3.1 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 707.3.2 Flight Extrapolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
7.4 Stagnation Point ATDB Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
8 Conclusions and Future Work 778.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 778.2 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
References 79
A Appendix A 85
B Appendix B 89
C Appendix C 93
x
List of Figures
1.1 Thermal Protection System Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Artist’s Impression of Different Vehicles During Reentry . . . . . . . . . . . . . . . . . 5
2.1 Limit Cases for Surface Catalycity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 IXV Surface Temperature and PA Transition Lines . . . . . . . . . . . . . . . . . . . . 11
3.1 Plasmatron Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 ICP Torch - VKI Minitorch Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.3 Plasmatron Operation Envelope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.4 Ground Testing in Plasmatron Facility under LHTS conditions . . . . . . . . . . . . . 17
3.5 Example of an Heat Flux Abacus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.6 Sample Holders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.7 Sample Holder - Radiative Equilibrium Setup . . . . . . . . . . . . . . . . . . . . . . . 21
3.8 Water-Cooled Copper Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.9 Heat Flux Probe with Water-Cooled Calorimeter . . . . . . . . . . . . . . . . . . . . . 23
3.10 Pitot Probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.11 Optical Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.12 High Temperature Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.13 CO2 Absorption Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.14 Sample Holder - Cooled Sample Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.15 pd Data and Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.16 Correlation Relative Error [%] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.17 Example of an output from heat1D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.18 The Complete Experimental-Numerical Frame . . . . . . . . . . . . . . . . . . . . . . . 35
4.1 Example of the Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2 HF Field - Cond. I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3 HF Field - Cond. II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.4 HF Field - Cond. I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
xi
xii Table of contents
4.5 HF Field - Cond. II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.6 Temperature Field - 5mm adapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.7 Temperature Field - 3mm adapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.1 Mass Loss Rate - HER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.2 Mass Loss Rate - MTA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.3 Evolution of γ with He . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.4 Passive-to-Active Transition - HER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.5 Passive-to-Active Transition - MTA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.6 Examples of HER samples tested with ps=5000Pa . . . . . . . . . . . . . . . . . . . . 50
5.7 Examples of MTA samples tested with ps=5000Pa . . . . . . . . . . . . . . . . . . . . 51
5.8 Temperature History During Two Different Tests - HER . . . . . . . . . . . . . . . . . 52
5.9 Temperature History During Two Different Tests - MTA . . . . . . . . . . . . . . . . . 53
5.10 Integrated Spectral Radiance and Emissivity History . . . . . . . . . . . . . . . . . . . 53
5.11 Temperature Jump - Evolution in Time . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.12 Spectra took during Test 21 (Active Oxidation) . . . . . . . . . . . . . . . . . . . . . . 55
5.13 Emission Line Si288 Intensity Evolution During a Temperature Jump . . . . . . . . . 56
6.1 Geometry tested and Simulated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.2 Steady State Temperature Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.3 Steady State Heat Flux Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.4 Heat Flux History of Test T1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.5 Abacus of test T1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.6 Abacus of test T2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.7 Abacus of test T3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.8 γ as function of the BL edge parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.9 Experimental HF as function of the BL edge parameters . . . . . . . . . . . . . . . . . 65
7.1 Abacus from Test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
7.2 Abacus from Test 28 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
7.3 Extrapolated Fight Conditions - Oxidation Campaign . . . . . . . . . . . . . . . . . . . 71
7.4 Extrapolated Velocity Gradient - Oxidation Campaign . . . . . . . . . . . . . . . . . . 72
7.5 Mass Fractions at the BL Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
7.6 Temperature Evolution Inside the Boundary Layer - Test T1 . . . . . . . . . . . . . . 73
7.7 Heat Flux to the Wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
7.8 Extrapolated Flight Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
7.9 Flowchart for ATDB Algorithms - Hot or Insulated Structure TPS . . . . . . . . . . . 76
7.10 Flowchart for ATDB and Algorithms - Generic TPS . . . . . . . . . . . . . . . . . . . 76
Table of contents xiii
A.1 Temperature Field - Section 4.1.1 - Condition I . . . . . . . . . . . . . . . . . . . . . . 85A.2 Temperature Field - Section 4.1.1 - Condition II . . . . . . . . . . . . . . . . . . . . . 86A.3 Temperature Field - Section 4.1.2 - Condition I . . . . . . . . . . . . . . . . . . . . . . 86A.4 Temperature Field - Section 4.1.2 - Condition II . . . . . . . . . . . . . . . . . . . . . 87A.5 Temperature Field - Section 4.1.3 - Condition I . . . . . . . . . . . . . . . . . . . . . . 87A.6 Temperature Field - Section 4.1.3 - Condition II . . . . . . . . . . . . . . . . . . . . . 88
B.1 Temperature vs. Time - Section 4.1.1 - Condition I . . . . . . . . . . . . . . . . . . . . 89B.2 Temperature vs. Time - Section 4.1.1 - Condition II . . . . . . . . . . . . . . . . . . . 90B.3 Temperature vs. Time - Section 4.1.2 - Condition I . . . . . . . . . . . . . . . . . . . . 90B.4 Temperature vs. Time - Section 4.1.2 - Condition II . . . . . . . . . . . . . . . . . . . 91B.5 Temperature vs. Time - Section 4.1.3 - Condition I . . . . . . . . . . . . . . . . . . . . 91B.6 Temperature vs. Time - Section 4.1.3 - Condition II . . . . . . . . . . . . . . . . . . . 92
xiv
List of Tables
3.1 Plasmatron Probes Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.2 Test Cases Used in the Design Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.3 Operational Map for the High Temperature Calorimeter . . . . . . . . . . . . . . . . . 283.4 Constants for the NDPs Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.1 Test Conditions for HER samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.2 Test Conditions for MTA samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.3 Summarized Test Results - HER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.4 Summarized Test Results - MTA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
6.1 Test Conditions for the Temperature Campaign . . . . . . . . . . . . . . . . . . . . . . 586.2 Test Results From the Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
7.1 Temperature results in the setup without insulation - ANSYS vs. heat1D . . . . . . . 687.2 Temperature results in the setup with insulation - ANSYS vs. heat1D . . . . . . . . . 687.3 Sensitivity Analysis for Test T1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 707.4 Extrapolated Flight Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
C.1 NDPs and Rebuilt Quantities - Oxidation Campaign (HER) . . . . . . . . . . . . . . . 94C.2 NDPs and Rebuilt Quantities - Oxidation Campaign (MTA) . . . . . . . . . . . . . . . 95C.3 NDPs and Rebuilt Quantities - Temperature Campaign . . . . . . . . . . . . . . . . . 95
xv
xvi
List of Symbols
Acronyms
AP Active-to-Passive
ARD Atmospheric Reentry Demonstrator
ATDB AeroThermodynamic DataBase
BL Boundary Layer
CERBERE Catalycity and Enthalpy ReBuilding for a REference probe
CERBOULA CERBERE + NEBOULA
CFD Computational Fluid Dynamics
CMC Ceramic Matrix Composite
CS Cooled Sample setup
C/SiC CMC with SiC matrix and Carbon fibre reinforcement
DAC Data Acquisition Card
ESA European Space Agency
FEA Finite Element Analysis
GSI Gas-Surface Interaction
HF Heat Flux
HFreq High Frequency
HER Herakles - A Safran Group Company (Previously SPS)
ICBM Inter-Continental Ballistic Missile
ICIASF International Congress on Instrumentation in Aerospace Simulation Facilities
ICP Inductively-Coupled Plasma
IPM-RAS Institute for Problems in Mechanics of the Russian Academy of Sciences
(in russian: ИПМех РАН - Институт проблем механики РАН )
IR Infrared
IST Instituto Superior Técnico - Faculty of UTL
IXV Intermediate eXperimental Vehicle
LHTS Local Heat Transfer Simulation
LTE Local Thermo-chemical Equilibrium
xvii
xviii List of Symbols
MESOX Moyen d’Essai et de DIagnostic en Ambiance Spatiale
MLR Mass Loss Rate
MTA MT Aerospace
NASA National Aeronautics and Space Administration
NDP Non-Dimensional Parameter
NEBOULA NonEquilibrium BOUndary LAyer
PA Passive-to-Active
PEGASE PErfect GAS Equation Solver
PLC Power Line Communication
PROMES Le Laboratoire PROcédés, Matériaux et Energie Solaire
RS Radiative equilibrium Sample setup
SEM Scanning Electron Microscopy
SPS Snecma Propulsion Solide - Previous name of HER
SSO Space Shuttle Orbiter
TPM Thermal Protection Material
TPS Thermal Protection System
TRP Technology Research Programme
UQ Uncertainty Quantification
UTL Technical University of Lisbon
VKI von Kármán Institute for Fluid Dynamics
Roman symbols
A Area m2
cp Specific Heat J kg−1 K−1
cp Frozen Specific Heat = ∑ yicp,i J kg−1 K−1
D Dissociation Energy of the Recombining Molecule J
D Diameter m
D Diffusion Coefficient -
Da Damköhler number = τfl/τch -
E Energy J
H Specific Total Enthalpy J kg−1
h Specific Enthalpy J kg−1
h Convection Coefficient W m−2 K−1
I Intensity a.u.
J Mass Flux kg m−2 s−1
k Catalytic Reaction Rate m s−1
Le Lewis Number = ρDcp/λ -
List of Symbols xix
M Mass Flux (atoms) kg m−2 s−1
m Mass or Particle Mass kg
m Mass Flow Rate kg s−1
NS Number of Species i -
Nu Nusselt Number = hD/λ -
n Number Density m−3
n Normal to the Wall (oriented: gas to wall) -
p Pressure Pa = kg m−1 s−2
Q Heat J
Q Heat Rate W = J s−1
q Heat Flux W m−2
R Radius m
Re Reynolds Number = ρV D/µ -
Sc Schmidt Number = µ/(ρD) -
T Temperature K
V Velocity m s−1
v Freestream Plasma Velocity m s−1
W Spectral Radiance W m−2 sr−1 µm−1
Wλ1→λ2 Integrated Spectral Radiance between λ1 and λ2 W m−2 sr−1
w Reaction Rate kg m−3 s−1
yi Mass Fraction -
y Atom Mass Fraction -
Greek symbols
B Energy Accommodation Coefficient -β Velocity Gradient s−1
γ Catalycity -∆ Boundary Layer Thickness mδ Uncertainty -ε Emissivity -λ Wavelength mλ Thermal Conductivity W kg−1 K−1
µ Viscosity kg m−1 s−1
ρ Density kg m−3
τ Characteristic Time s
xx List of Symbols
Subscripts
amb ambientapp apparentcond conductivecal calorimetercat due to catalycitych chemical reactioncw cold wallD dissociationd dynamicdiff diffusivee boundary layer outer edgeeff effectiveel electric - imposed on the HFreq generatorexp experimentalF formationfl flowgeo geometrici relative to specie iint intrinsicm modelpj post-jumppost after testpre before testrec recombinations staticsol solidt totalw wallwet wetted∞ freestream
List of Symbols xxi
Superscripts
0 blackbodyF relative to flightGT relative to the ground test(n) iteration n↓ impinging on the surface« transferred to the surface© leaving the surface
Constants
c Speed of Light 299792458 m s−1
e Base of the Natural Logarithm 2.718281 -h Planck’s Constant 6.6260693 × 1034 J skB Boltzmann’s constant 1.380658 × 10−23 J K−1
π Pi 3.14159265 -σ Stefan-Boltzmann constant 5.670373 × 10−8 W m−2 K−4
xxii
Chapter 1
Introduction
1.1 Hypersonic Flows and Atmospheric Reentry
With the birth of “faster than sound” aircrafts with the flight of Charles “Chuck” Yeager in October
14th, 1947, new and challenging problems arise and countless generations of scientists and engineers
had been fighting to break the frontiers of the human knowledge and provide safer, faster and cheaper
ways to travel around the world and beyond. But the “brand new world” of supersonic and specially
hypersonic flow showed that Socrates was more than right: “I know one thing, that I know nothing”.
Along the years, specially during the firsts flights of hypersonic vehicles, the X-15 flight tests [1],
scientists discovered several new phenomena that were not predicted by the theories at the time and
the same still keep happening today. But, before further development it is important to give the
description of what is hypersonic flow.
1.1.1 The Hypersonic Flow Regime
In fact, there isn’t an universally accepted concept that could tell us what is an hypersonic flow but
is usually accepted that it is a flow with a free stream Mach number grater than 5. Although, this is
not totally accepted by the scientific community as we can read in the citation presented in the next
page.
For the proposes of this work and simplicity, hypersonic flow will be considered a flow with a free
stream Mach number grater than 5 and in which the high temperature gas properties play a non
negligible roll. One of the fields were the hypersonic flow regime play an important roll is the so
called Atmospheric Reentry.
1
2 Introduction
1.1.2 The Atmospheric Reentry
The history of Atmospheric Reentry (also called Planetary Reentry) begins in the Cold War between
USA and USSR with scientists from both sides trying to understand the new phenomena arising from
the hypersonic flight conditions. These concerns have arisen from the design of new weapons, the
ICBMs and their reentry warheads, and consequently the investigations on these matters were also
propagated to the Space Race during the second half of the twentieth-century.
Nowadays reentry still represents one of the most fascinating challenges for scientific research in
the space technology context and both for atmospheric reentry and hypersonic cruise vehicles the
aerothermochemical environment is still the least known constrain for the design of such machines.
This is result of the extremely complicated coupled physical phenomena involved.
Reentry is defined as the trajectory of a celestial body (asteroid, spacecraft, etc.) between the
moment in which it first “fells” the planet atmosphere and the the moment in which it touches the
ground. These two limits are not absolutely fixed and usually vary according to the problem. For the
“upper” limit on Earth, for example, the altitude of 120km is usually accepted, despite the fact that
the official limit for space is the Kármán line at 100km altitude. The lower limit is more variable, and
can be defined as the moment in which the vehicle touches the ground, opens a parachute or changes
in flight condition “mode” (for example, for the Space Shuttle the hypersonic reenty is defined until
the moment in which a condition of Mach⩽ 2.5 is reached)[2].
During reentry, the spacecraft travels in a speed much higher than the speed of sound. Because
of it, a bow shock wave is formed in the front of the vehicle. In the nose stagnation point region, the
shock wave is almost a normal shock wave and through it the flow is decelerated to subsonic speeds
and both pressure and temperature increase by several orders of magnitude. In a reentry from earth
orbit the temperature is usually high enough to promote dissociation in the gas and for a spacecraft
returning from the moon or Mars it is usually enough to promote ionization [3].
Reentry can be divided in two groups, low-speed reentry and high-speed reentry. Low-speed
reentry corresponds to a reentry in which the initial speed is bellow the corresponding orbital speed
and a high-speed reentry to one in which the initial speed is in the order of magnitude of the escape
velocity. It can be also divided into ballistic or gliding reentry according to the lisft-over-drag ratio
of the vehicle. Examples of such vehicles are presented in figure 1.2. IXV, the base vehicle for this
work, can be classified as gliding reentry vehicle.
1.2 Families of Thermal Protection Systems
Thermal protection systems can be divided in 3 main groups: Active, Passive and Semi-Passive.
Figure 1.1 represents most of the current concepts for TPS and detailed information about each one
can be found in [1, 4, 5].
1Extracted form [3]
Introduction 3
Almost everyone has their own definition of the term hypersonic. If we wereto conduct something like a public opinion poll among those present, and askedeveryone to name a Mach number above which the flow of a gas should properly bedescribed as hypersonic there would be a majority of answers around five or six, butit would be quite possible for someone to advocate, and defend, numbers as small astree, or as high as 12.
P. L. Roe, comment made in a lecture atthe Von Kármán Institute, Belgium, January 1970 1
Figure 1.1: Thermal Protection System Concepts (extracted from [5])
It is important to notice that until now the samples tested in the VKI Plasmatron were always
tested according to the concept of Hot Structure or highly Insulated Structures because the samples
were in radiative equilibrium with the environment without allowing conductive heat loss [6, 7]. The
new method developed in this work (see section 3.7.1) allow the determination of the aerothemo-
chemical environment, surface catalycity and heat transfer for several different TPS concepts like
Convective Cooling, Heat Pipe, Heat Sink Structure and Insulated Structure (for insulation types in
which the conductive HF is not negligible).
1.3 Aim of This Project
The aim of this work is to further continue the work developed all over the years in VKI about
aerothermodynamics of reentry vehicles.
In this framework, as collaborator of Francesco Panerai, Post-Doc Fellow in VKI, I actively partic-
4 Introduction
ipate in the experimental TRP Oxidation campaign and in a substantial part of the post-processing
of the results. The results of this campaign is presented in chapter 5.
The development of a new experimental method to increase the Plasmatron operations capabili-
ties, including new methods for GSI research are presented in chapter 4 and 6 and are almost exclusive
responsibility of the author (except some already referenced acknowledgements).
Introduction 5
(a) Apollo Command Module - A Typical Ballistic Reentry Vehicle
(b) Space Shuttle Orbiter - A Typical Gliding Reentry Vehicle
Figure 1.2: Artist’s Impression of Different Vehicles During Reentry
6
Chapter 2
Catalycity and Oxidation Research -
A Bibliographical Review
2.1 Gas Surface Interaction and Catalycity
2.1.1 Principles of Catalycity
As we saw in section 1.1.2 the aerothermochemical environment around a reentry body in a low
speed reentry is dominated by phenomena such as chemical reactions in the flow and wall and heat
transfer by conduction, convection, recombination and radiation. All this mechanisms play a role in
the heat flux balance at the wall. This has important implications on the final surface temperature
and conduction heat flux into the wall which will be the main parameters that drive the selection of
the TPS for the mission. This selection is very complicated because the TPS itself will play a roll in
the final picture because of the chemical characteristics of the surface. This coupling between the
surface and the flow itself is usually called Gas/Surface Interaction or GSI. When dealing with the
effect of the surface in the flow several problems arise basically because of lack of knowledgeable in
this kind of phenomena at high temperature and low pressure, despite all the efforts conducted in
solving that problems since the 50s [1].
One of the factors that contribute more for the heat transfer to the wall is the exothermic reactions
occurring there. The reactants for this reactions are the dissociated and ionized atoms generated by
the bow shock wave in the front of the vehicle. These atoms eventually reach the surface which acts as
a catalyst and promotes the exothermic recombination reactions. This process is called heterogeneous
catalycity.
But not all the atoms that reach the wall undergo the recombination process into molecules.
The probability that this reaction occour is defined as the recombination coefficient or catalycity.
Catalicity can than be defined as the ratio between the flux of recombined atoms over the flux of
7
8 A Bibliographical Review
Figure 2.1: Limit Cases for Surface Catalycity
impinging atoms on the surface for a certain specie i.
γ =Mi,rec
M↓
i
(2.1)
In this work, only 2 recombination reactions were considered: O+OÐ→ O2 and N+NÐ→ N2 and
the same recombination coefficient is used for both. Some recent investigations [8, 9] shown that the
production of NO (N +OÐ→ NO) can be so important as the reactions above, but the mechanism
for its formation is not yet completely understood. In chapter 5 is also referred that the reaction
Si +OÐ→ SiO should also be taken into account due to its highly exothermic nature.
The 2 limit cases for catalicity are the fully-catalytic wall (γ = 1) and the non-catalytic wall (γ = 0)
that are represented in figure 2.1.
Following the same approach of Panerai [7], we can define the experimental values of γ as effective,
apparent catalycity, which relates with the true catalycity by the formula
γ = γapp,eff = B ⋅ γapp =E«
D⋅ γapp =
E«
D
SwetSgeo
γint (2.2)
in which γint is the true microscopic catalycity in a multi-temperature model (temperature of the flow
different from the temperature of the wall). For more information the reader is advised to consult
Thoemel [10], Barbante [11] and Panerai [7].
2.1.2 Catalycity, Heat Shield Design and Simulation
One of the biggest unknowns when designing a new hypersonic vehicle is the surface catalycity.
Usually designers assume a fully-catalytic wall1 because that’s the “worst case scenario” for surface
heating but experiences in very different facilities had proved that for common TPM the value can
1And sometimes even Super Catalytic Wall
Catalycity and Oxidation Research 9
be 3 orders of magnitude lower [12, 13, 7]. Classical references like Anderson [3] usually admit that,
for common reentry scenarios, the heat flux to a fully-catalytic wall is approx. twice the one to a
non-catalytic wall. This puts a lot of weight penalty in an “end of line” space application because a
reentry vehicle should always do the complete mission, from Earth to Earth (generally speaking: from
planet to planet). This “dead weight” (= “dead budget”) can be avoided with a better knowledge of
the reentry conditions in general and GSI phenomena in particular.
Catalycity is also a fundamental parameter that need to be accurately introduced in CFD codes
in order to correctly “connect” the flow to the surface. To complicate a little bit, usually catalycity
isn’t a single number but, instead, a variable dependent on surface temperature and boundary layer
edge parameters. This is referenced in several works like [7, 14, 15, 16] and again proved in this work
(see chapter 6). That’s why a correct ATDB, both in data and concept, is very important for the
design of future space missions.
2.2 Passive-to-Active Oxidation Transition in TPM
Since the first heat shields designed for reentry applications, reusability is an important concern for
the design engineers. For high speed reentry ablative heat shields are necessary so reusability is out of
question. On the other hand, for low speed reentry, specially when large gliding and skipping reentry
vehicles are used, reusability is a main concern, for economic reasons. We all remember the financial
disaster of the US Space-Shuttle Program, primary due to the expensive maintenance of the SSO
between flights.
So, it is essential for future designs to know if a certain material will be preserved or degraded
during a reentry maneuver. Used in the SSO and Buran (Буран), Silicon Carbide (SiC) composites
or coatings are one of the main material in study for future missions and many investigations about
it were already done in the past. It is known [7, 17, 18, 19, 20] that for high pressures and low
temperatures, SiC undergoes in a passive oxidation process that generates a net mass gain due to the
creation of a protective layer of Silica (SiO2) in the exposed surface of the material. The chemical
reaction occurring is
SiC(s) + 32O2(g)Ð→ SiO2(s) + CO(g) in a molecular oxygen atmosphere
or
SiC(s) + 3O(g)Ð→ SiO2(s) + CO(g) in a atomic oxygen atmosphere
For higher temperatures/lower pressures, the material go through an active oxidation process
which conducts to a net mass loss and degradation of the material. The chemical reaction is
SiC(s) +O2(g)Ð→ SiO(g) + CO(g) in a molecular oxygen atmosphere
or
10 A Bibliographical Review
SiC(s) + 2O(g)Ð→ SiO(g) + CO(g) in a atomic oxygen atmosphere
The frontier between this two regimes is called Passive-to-Active (PA) transition.
Despite the fact that it only became a primary issue with the start of the space-shuttle program,
the first studies about oxidation transition in SiC based materials date from the 50s, when Wagner
proposed a model that relates the transition with the partial pressure of oxygen in the mixture bulk
and surface temperature [21]. Later Turkdogan et al. [22] developed the “smoke theory” for the
vaporization of Si.
Later also Gulbransen and Jansson [23], Singhal [24], Hinze and Graham [25], Nickel [26], Keys
[27], Narushima et al. [28], Heuer and Lou [29] and Balat [17, 18], among others, also published
studies about this topic.
Particularly, Gulbransen and Jansson provided 3 possible thermodynamic equilibrium equations for
the transition:
SiC(s) + 2 SiO2(s)Ð→ 3 SiO(g) + CO(g)
SiC(s) + SiO2(s)Ð→ 2 SiO(g) + C(s)
2 SiC(s) + 2 SiO2(s)Ð→ 3 Si(g) + 2CO(g)
Laboratory tests indicated the third equation as the one that best fits the results.
Balat [17, 18], based on the work of Wagner [21], developed a model that predicts the transition
partial pressures of oxygen as function of the diffusion coefficients Di.
As we can see in figure 2.2, it is difficult to find results in accordance between the different research
groups. This is why research programs about this topic are still going on, like the one that supported
part of this work.
Catalycity and Oxidation Research 11
- 1 0 - 9 - 8 - 7 - 6 - 5 - 41 0 0
1 0 1
1 0 2
1 0 3
1 0 4
1 0 5
OXYG
EN PA
RTIAL
PRES
SURE
, Pa
- 1 0 4 / T E M P E R A T U R E , K - 1
I X V B a l a t , T h e o r y B a l a t , C V D C S i C s t a n d a r d a i r B a l a t , C V D C S i C e x c i t e d a i r G u l b r a n s e n H e u e r e t a l . , H e r d r i c h , a c t i v e - l i m i t H e u e r e t a l . , H e r d r i c h , p a s s i v e - l i m i t
Figure 2.2: IXV Surface Temperature and PA Transition Lines. The solid line represent theevolution in the temperature of the most heated point in the windward side of the vehicle.
12
Chapter 3
Experimental Facilities and the
LHTS Methodology
3.1 Plasmatron: The VKI’s ICP Windtunnel
The Plasmatron facility was designed in the early 90s in order to support the design process of Hermes,
a spacecraft also known at the time as the European Space-Shuttle. Although the main project got
cancelled, the Plasmatron project continued in order to reinforce the european knowledge in the the
fields of reentry aerothermodynamics and plasma physics. The facility was first ignited in July 18th,
1997 and it’s still the most powerful of its kind in the world. Figure 3.1 presents the complete facility
system.
Since then, a long list of lessons were learned by all the people that worked in this facility and the
most important was that nothing is easy in a Plasmatron experiment, mainly because of the extreme
temperatures and complexity of the facility. The facility and the experimental setups are continuously
being updated in order to increase the Plasmatron capabilities and the results’ quality.
To produce plasma, this facility uses a physical principle called inductive-coupled plasma generation
(ICP). Conceptually it consists in a quartz tube surrounded by a coil in which a gas is injected. The
coil is connected to a high power generator that provides high alternate voltage with an high frequency.
The current in the coil induces a powerful oscillatory electro-magnetic field inside the tube with the
field lines coaxial it. The residual charged particles in the gas are than accelerated because of the
magnetic field and additional Foucault currents appear.
This makes the gas to heat up because of Joule’s effect promoting an increase on the gas ionisation
degree, increasing the Foucault currents and making the flow entering into an heating “snowball” effect
that results in high temperature, highly ionized gas (plasma) that exits the torch in form of a jet (see
figure 3.1).
13
14 Experimental Facilities and the LHTS Methodology
Water tanks
Rotating vanesvacuum pumpsBy-pass valve
HP water pumps
Water pumps
Roots vacuum pump
Heat exchanger
ICP torch
Impe
danc
e m
atch
Test chamber
Test model
1.2 MW400 kHz
MOS inverter
12-pulse thyristor rectifier
1700 kVATransformer
Exhaust
Gas supply
200 V dc 11 kV
1050 kW air-water cooler
Figure 3.1: Plasmatron Facility
The high power generator is capable of providing 1.2MW at 2kV and 400kHz and it’s a solid
state MOS technology generator. The torch as 160mm of diameter and exits to a test chamber at
low pressure with 2.5m long and 1.4m diameter and the whole facility is cooled by deionized water
in a close circuit. The facility is computer controlled using a 719 I/O lines PLC and two PC’s for
monitoring the operation. The envelope of operation of the facility is presented in figure 3.3.
3.2 The Local Heat Transfer Simulation method in VKI
In order to correctly duplicate the reentry flight conditions in a ground test facility it’s mandatory
to use similitude relations. It is known that practical ground test facilities can’t totally reproduce
the freestream of flight conditions with Mach numbers higher than 8 [30]. In order to overcome this
problem, several different types of facilities were developed to address different parts of the problem.
For the Mach number simulation Blow-Down windtunnels and Shock Tubes are used. Blow-Down
windtunnels are cold gas facilities so no chemistry can be reproduced but Shock Tubes can actually
reproduce the complete aerothermodynamic environment for reentry vehicles. The problem with these
facilities is that they only allow testing for a fraction of second. This short amount of time is not
Experimental Facilities and the LHTS Methodology 15
Figure 3.2: ICP Torch - VKI Minitorch Facilitya
aThis facility was the Plasmatron pilot facility
0 2 4 6 8 1 00
2 0
4 0
6 0
8 0
1 0 0
1 2 0 0 2 8 1 8 3 2 5 0
P l a s m a t r o nE n v e l o p e
E X P E R T
E N T H A L P Y , M J / k g
ALTIT
UDE,
km
V E L O C I T Y , k m / s
A P O L L O
I X VS H U T T L E
S P A C E L I N E R
Figure 3.3: Plasmatron Operation Envelope
16 Experimental Facilities and the LHTS Methodology
enough to properly test TPM due to thermal inertia.
To solve this problem, high enthalpy facilities were developed and in the western countries and
the most used were diffusion reactors [31, 32, 17, 18] and Arc-Jet facilities [13, 33, 34, 35]. Arc-Jets
provide the correct testing setup but several problems arise from their operation like jet instability,
flow contamination and lack of an exact knowledge of the operation conditions. Meanwhile in Soviet
Union, at IPM-RAS, Kolesnikov and his colleges developed the LHTS methodology based on ICP
plasma generators. This method allows to know with accuracy the boundary layer edge conditions
and those condition can then be used to extrapolate the test to a flight condition.
The base for the LHTS method are the analytical formulas developed in the 50s by Fay & Riddell
[36] and Goulard [12]. Both based their work in the pioneer work of Lees [37].
Fay & Riddell proposed the following formula for the stagnation point heat transfer on the nose
of a hypersonic vehicle with a fully-catalytic surface.
q«w = 0.763Pr−0.6(ρeµe)
0.4(ρwµw)
0.1β0.5e (He − hw)[1 + (Leα − 1)(hD,e/He)] (3.1)
were
hD,e =NS
∑ yi,ehF,e (3.2)
and α is 0.63 for frozen boundary layer and equal to 0.52 for equilibrium boundary layer.
Goulard proposed a similar formula, more simplified and applicable only to frozen boundary layers,
but it allows to study walls with an arbitrary catalycity, using the factor φ.
q«w = 0.664Pr−23 (βeρeµe)
0.5He[1 + (Le23φ − 1)(hD,eye/He)] (3.3)
φ =1
1 +0.47Sc−2/3
√
2βeµeρeρwkw
Analysing these two formulas, Kolesnikov [38] concluded that to simulate the reentry aerother-
mochemical environment at the stagnation point only three parameters at the boundary layer edge
need to be equal to the flight condition: total enthalpy, total pressure and velocity gradient.
HFe =HGT
e pFt,e = pGTt,e βFe = βGTe (3.4)
Conceptually, these 3 parameters represent the conditions behind the bow shock wave that appears
in the front of an hypersonic vehicle (see figure 3.4).
Than, using the 3 parameters, it is possible to extrapolate the ground test to the hypersonic flight
of a vehicle with certain geometric characteristics using the Kolesnikov’s method [30, 38]. It uses the
following formulas:
Experimental Facilities and the LHTS Methodology 17
Figure 3.4: Ground Testing in Plasmatron Facility under LHTS conditions
HGTe =�
��0
hF∞+
1
2(V F
∞)
2⇔ V F
∞=√
2HGTe (3.5)
pGTe =���
0
pF∞+ ρFe ⋅ (V
F∞
)2⇔ ρFe =
pGTe2HGT
e
(3.6)
The hF∞
and pF∞
can be neglected because we are dealing only with hypersonic speeds, so (V F∞
)2>>
hF∞
and ρFe ⋅ (VF∞
)2>> pF
∞.
At this point, the density can be used to, through an atmospheric model, know all the remaining
parameters in flight like altitude, static pressure, static temperature and speed of sound and through
that also the flight Mach number. In this work the U.S. 1976 Standard Atmosphere model [39] was
used.
Then the boundary layer edge velocity gradient (βGTe ) can be determined using Π2 (NDP2, see
section 3.8.2) together with model radius and, using the thin shock layer theory [40], we can relate
it with flight conditions1:
βGTe =1
RFeff
¿ÁÁÀ8
3
pFe − pF∞
ρFe=V F∞
RFeff
¿ÁÁÀ8
3
ρF∞
ρFe(3.7)
Knowing that ρe can be considered a function of He [30] we can substitute ρFe by ρGTe , which is
a result of the enthalpy rebuilding process and the formula comes:
1An alternative to the thin shock layer theory is to use the modified Newtonian theory, in which the factor8/3 in equation 3.7 is substituted by 2 [3].
18 Experimental Facilities and the LHTS Methodology
RFeff =V F∞
βGTe
¿ÁÁÀ8
3
ρF∞
ρGTe(3.8)
To know the test parameters in the Plasmatron chamber, also the methods presented by Kolesnikov
are used in VKI but with some differences introduced in-house. The general methodology is address
next in section 3.2.1 and again in 3.8.4 and the differences between the methods used in IPM-RAS
and VKI are described in [41].
3.2.1 Experimental Methods for Reentry Simulation in Plasmatrons
To extrapolate the test of a TPM sample exposed to plasma to a flight condition a multi-step
methodology is used.
First, after the test and knowing m, ps and PWel is possible to calculate the corresponding
Non-Dimensional Parameters (NDPs, see section 3.8.2).
During the test, a calorimeter (see section 3.5.1) is injected into the jet and the heat flux and
surface temperature are recorded, being the surface catalycity estimated by the Minimax method in
a different experiment [6, 42, 43, 7].
With all these results, we can than use the the CERBOULA code (see section 3.8.3) in order to
calculate the boundary layer edge enthalpy (He) and other relevant properties in the boundary layer
and in its edge.
At this point, we can extrapolate the results to flight conditions using equations 3.5, 3.6 and 3.8.
If one is also interested in the TPM catalycity, the process can than be reversed: The boundary
layer edge parameters are now known, plus the surface temperature and heat flux (by optical methods,
see section 3.6) so the CERBOULA code can be run in order to determine the surface catalycity. Also
the famous Kolesnikov’s abacus (see section 3.3) can be calculated and used for the same propose.
An important remark should be done about the way how the transferred heat flux is calculated.
It is done by performing an energy balance at the surface of the sample:
q«w = q©w (3.9)
qcond + qdiff + qrad,in = qrad,out + qloss (3.10)
(−λ∂T
∂y)w,fl
+NS
∑hiJi ● nw + qrad,in = σεT4w + (−λ
∂T
∂y)w,sol
(3.11)
In which the term qrad,in is usually neglected based on the previous experiences and the term qloss
can be neglected [6, 7] in the experiments presented in chapter 5 but is measured by a calorimeter in
the experiments presented in chapter 6.
Experimental Facilities and the LHTS Methodology 19
The term qrad,out can be calculated using the Stephan-Boltzmann law (qrad = εσT 4w) being Tw
measured by the pyrometer and ε calculated form the comparison of the pyrometer data with the
radiometer data (see section 3.6.3).
At the wall, Ji,w ● nw = wi and the catalytic boundary condition is written as:
wi,cat =miMi,cat =miγiM↓
i (3.12)
If a Maxwellian distribution with the Chapman-Enskog perturbation term is used, the result for
the impinging flux of atoms comes:
M↓
i = ni
√kBTw2πmi
+1
2miJi,w ● nw (3.13)
Applying equation 3.13 in equation 3.12 the final expression comes [11]:
wi,cat =2γi
2 − γimini
√kBTw2πmi
(3.14)
A complete and comprehensive picture of the complete methodology is presented in section 3.8.4.
3.3 Recalling the Abacus – The Temperature Problem
The Heat Flux Abacus for catalycity determination come originally from the work of Kolesnikov [38]
and it is well known as a method for catalycity determination in Plasmatrons. A typical abacus can
be seen in figure 3.5. Nevertheless, it is usually misunderstood as a general picture for the behaviour
of catalycity as a function of temperature. In fact, people sometimes think that when the surface
temperature changes, the point of determined catalycity moves inside the graphic to another point
and that’s not true at all.
In fact, in all the experiments made so far, the temperature of the sample was only determined for
an unique condition: the radiative equilibrium case. So we can’t compare results from tests at two
different temperatures because the free-stream conditions, and so the boundary layer edge conditions,
are different and for different conditions we have different abacus! Also, heat flux can change due to
emissivity changes and/or aerothermodynamic factors like catalycity differences and all that must be
taken into account.
The main propose of this work is to determine the catalycity for two different temperatures and
for the same boundary edge conditions in order to plot, in the same abacus, two temperature points
and then extract information that will hopefully help the design and selection of different types of
TPS in the future, as explained in section 1.2. Results are presented in chapter 6.
As a final remark for this section the author would like to remember again that the abacus
never closes a loop: For a given flight condition/boundary layer edge condition, a specific abacus is
addressed and it allow us to relate three parameters: Tw, γ and q«w. Knowing two of them, we can
know a third.
20 Experimental Facilities and the LHTS Methodology
Figure 3.5: Example of an Heat Flux Abacus
Probe Name Symbol Rb, mm Rc, mm
Standard ST 25 10Equilibrium EQ 57.5 5
Frozen FR 15 15
Table 3.1: Plasmatron Probes Dimensions
3.4 Sample Holders
The sample holders are presented in figure 3.6. Three different shapes (FR, ST and EQ) are available
in VKI and their dimensions are presented in table 3.1. The difference in shape allow us to address
different velocity gradients keeping all the remaining test conditions constant. This difference in
velocity gradients is equivalent to changing the Damköhler number of the test Da = τfl/τch and
that’s why this probes are also called Damköhler probes. In figure 3.7 is possible to see the old
location of the calorimeter that read the qloss term (see section 3.2.1) in the classical setup.
Previous experiments [6] show that this quantity is negligible thanks to the thick layer of Procelit™
180 placed in the back of the sample, so the calorimeter wasn’t used in this setup for the test campaigns
presented in this work.
A new setup for the sample holder is presented in section 3.7.1.
3.5 Intrusive Measurement Techniques
3.5.1 Heat Flux Probes
Copper heat flux calorimeters have been used for years in high enthalpy facilities in order to precisely
measure the heat flux to an high catalytic surface. In fact, despite the first experiments using the
LHTS principle used the assumption of a fully catalytic surface for copper, later on it was concluded
Experimental Facilities and the LHTS Methodology 21
(a) FR Holder (b) ST Holder (c) EQ Holder
Figure 3.6: Sample Holders (Extracted from [7])
Figure 3.7: Sample Holder - Radiative Equilibrium Setup
22 Experimental Facilities and the LHTS Methodology
Figure 3.8: Cross-section of the classical water-cooled copper calorimeter for heat flux measure-ments. Dimensions in mm.
that this isn’t a corrected assumption. Several campaigns were conducted in VKI to estimate the
true copper catalycity for the different test conditions and nowadays it is possible to use catalycity
tables to correct the copper catalycity used in the enthalpy rebuilding process [6, 7, 42, 43]. Some
extensive information about this topic can be found in [7].
There are two types of calorimeters available in VKI: the water cooled calorimeter and the slug
calorimeter. The later one was used in the past as reference and validator of the water cooled one [6]
and it wasn’t used in this work. From now on, the water cooled calorimeter will be just referenced as
calorimeter. The calorimeter work with a steady-state energy balance principle:
qcw =Q
A=m ⋅ cp ⋅ (Tout − Tin)
A(3.15)
In reference [44] an abacus is provided for the mass flow rate necessary in order to avoid water
boiling. In [44] and [45] uncertainty quantifications are done for the probe and the latter one proposes
the following formula for the relative error:
δqcwqcw
=
¿ÁÁÀ
(δm
m)
2
+ (δcp
cp)
2
+ (δ(Tout − Tin)
(Tout − Tin))
2
+ (δA
A)
2
(3.16)
According to the uncertainties presented in [7], for typical values of qcw (100 ∼ 2000 kW m−2) the
error vary between 7% and 12%.
3.5.2 Pitot Probes
A Pitot probe with the same geometry of the heat flux probe is used to perform stagnation pressure
measurements. The Plasmatron chamber is equipped with an absolute pressure transducer (Member-
anovac DM 12, Leybold Vacuum, OC Oerlikon Corporation AG, Pfäffikon, Switzerland) that measures
the static pressure with ±0.7 hPa accuracy. The Pitot line is connected to a Validyne variable reluc-
tance pressure transducer (DP15, Validyne Engineering Corp., Northridge, CA, USA) and the output
is amplified and corrected by a voltage demodulator (CD-15, Validyne Engineering Corp., Northridge,
CA, USA). Validyne and amplifier are calibrated by means of a Betz water manometer, leading to an
Experimental Facilities and the LHTS Methodology 23
Figure 3.9: Heat Flux Probe with Water-Cooled Calorimeter
Figure 3.10: Pitot Probe
uncertainty of ±0.2% in the dynamic pressure (information extracted from [7]). In figure 3.10 one
can see an example of a pitot probe used in the Plasmatron.
3.6 Optical Measurement Techniques
3.6.1 Two-Colour Pyrometer
The two-colour pyrometers had proven to be one of the most reliable methods for practical radiative
temperature measurement. They measure the spectral radiance in two different, but close, wave-
lengths. Is allowed to assume that, between the two wavelengths, the body emissivity does not
change (gray body assumption). Then, the ratio between the spectral intensities allow to calculate
the temperature independently from the emissivity.
In the Plasmatron equipment, two two-color IR pyrometers (Marathon Series MR1SB and MR1SC,
Raytek Corp., Santa Cruz, CA) are available. They are selected according to the expected measured
24 Experimental Facilities and the LHTS Methodology
temperature: the MR1SB operate between 700 and 1800°C and the MR1SC operate between 1000 and
3000°C. They work around 1µm wavelength, with a view angle of ∼35° relative to the sample normal
and through a 1cm thick quartz window. The acquisition rate is 1Hz and the overall uncertainty is
estimated to be ±10K. More information about these equipments and a mathematical description of
the working principle of a two-colour pyrometer can be found in [7].
3.6.2 Broadband Infrared Radiometer
A broadband IR radiometer (KT19, HEITRONICS Infrarot Masstechnik GmbH, Wiesbaden, Germany)
is placed with a view angle of ∼47° relative to the sample normal and it’s in front of a 1.8cm thick
window made of KRS-5. This material provides a 70% transparency over the whole range of the
operating waveband (0.6-39 µm). More information about this material can be found in [7]. The
output is the integrated thermal radiation over the operational spectrum, within a temperature range
of 0 to 3000°C and an acquisition rate of 1Hz was selected.
3.6.3 In-Situ Emissivity Determination Method
The in-situ emissivity measurement method currently used in the Plasmatron was introduced by
Panerai [7, 19] inspired on the work of Balat at al. [46].
In essence, the method is very simple. The out-coming radiation from the sample is measured by
the radiometer between the wavelengths 0.6µm and 39µm.
This radiation is than divided by the integrated blackbody radiation over the same wavelength
interval (the temperature is known from the Pyrometer reading) and the result is emissivity.
ε ≡ ε(T ) ≡ ε0.6-39µm(T ) =W0.6→39µm(T )
W 00.6→39µm(T )
(3.17)
The Planck’s law, equation 3.18, gives the spectral radiance as function of temperature and
corresponding wavelength and is integrated using the method proposed by Widger and Woodall [47]
that results in equation 3.19 with W 00→λ coming in W m−2 sr−1.
W 0(λ) =
2hc2
λ5 (e(
hckBλT
)
− 1)(3.18)
W 00→λ = 2
k4BT
4
h3c2
∞
∑n=1
(ζ3
n+
3ζ2
n2+
6ζ
n3+
6
n4) e−nζ with ζ =
2πhc
λkBT(3.19)
For the numerical calculation of the series, ∞ is substituted by nmax and using the relation
nmax = min (2 + 2/ζ,512) one can guaranty, at least, a 10 digit precision in the integration.
Experimental Facilities and the LHTS Methodology 25
Figure 3.11: Optical Setup
3.6.4 Optical Emission Spectroscopy
The equipment for optical emission spectroscopy is described in [7] and following information is
adapted from there.
Optical emission spectroscopy is used to obtain qualitative information on the gas phase com-
position in front of the samples and detect the presence of relevant chemical species compared to
freestream conditions. The emitted light is collected through a variable aperture and focused by a
300 mm focal length converging lens (LA4579, Thorlabs GmbH, Munich, Germany) into the entry of
a 600 µm diameter optical fiber (Premium Fiber, Ocean Optics, Dunedin, FL). This lead to a broad
range (200-1100 nm) spectrometer (HR-4000, Ocean Optics, Dunedin, FL). An acquisition rate of
about 1 Hz provides real time acquisition spectra. In the present campaign the line of sight is main-
tained fixed in the stagnation line in 3 locations between 1mm and 9mm from the sample surface.
The calibration of the system in relative intensity is performed with a deuterium lamp in the UV range
(< 400 nm) and with a ribbon tungsten lamp in the visible (> 400 nm). The repeatability of the
measurements has been checked, ensuring the relative uncertainty on the total integrated emission
of the radiative signature to be less than 10%.
3.7 New Techniques Developed in the Context of this Work
3.7.1 Cooled Sample Setup
To achieve the objective of study the wall temperature effect on the catalycity of a TPS sample, a
new experimental setup was developed to be used in the Plasmatron. Recalling the equation 3.10
that is repeated were for commodity
qcond + qdiff + qrad,in = qrad,out + qloss
26 Experimental Facilities and the LHTS Methodology
Condition I Condition II
Material SPS C/SiC SPS C/SiCTest S5 S23(a)qcw 160 1540ε 0.72 0.79Tw 1200 2000ps 5000 3000pd 25 165qexp 85 717γ 0.00264 0.0184
Table 3.2: Test Cases Used in the Design Process (data from [7])
we can conclude that in order to change the surface temperature without changing the aerother-
mochemical environment we must change the amount of incoming radiation (3rd term in LHS) or
change the conductive loss term (2nd term in RHS).
Reducing the amount of the incoming radiation will not allow reducing the wall temperature
because the incoming radiation effects are already negligible and it’s very difficult to achieve in a
practical way (probably only with help of cryogenic cooling). Besides all that, changes in the plasma
properties could happen because, above a certain temperature, plasma can be considered a radiative
participating medium. Any of the points listed above are enough to discard the incoming radiation
option. However, to increase the wall temperature this method is applicable but a super-heated
surface doesn’t have any real interest in the current frame of research. The remaining option is
changing the qloss term.
Almost since the beginning, the idea for cooling the sample was to use a calorimeter in the back of
the sample. The calorimeter serves two proposes: First it acts as an heat sink allowing the reduction
of the sample surface temperature through thermal conduction across the sample. Second because
it allows the measurement of the amount of qloss which is necessary to rebuild the surface catalycity.
The initial target was to use the same setup to cover the complete range of temperatures from the
radiative equilibrium temperature (the highest possible) to a temperature near the cold wall calorimeter
temperature (approx. 350K). Another requirement was to do it with the technical solutions available
because of the short calendar for testing and budget limitations.
In order to simulate the envelope of operation of the calorimeter, a small 1D simulator, called
heat1D, was programmed using the MATLAB™ environment. This program basically receives as
input the geometry, the working fluid, the Nu = f(Re,Pr, geometry) correlations and the boundary
conditions used and it allows to investigate the range of temperatures experienced by the different
components of the calorimeter cooling system. More details about this program can be found in
section 3.8.1.
Two test cases were selected from the data available in [7]: one representing an high HF environ-
ment and another representing a low HF environment. Details can be found in table 3.2.
The first working fluid tested was water because it has been used for years in the calorimeters
used in VKI and so the technical readiness level of such setup is quite high. The problem faced
Experimental Facilities and the LHTS Methodology 27
Figure 3.12: High Temperature Calorimeter
was that it basically only allows a very narrow range for the wall temperature around 400K due to
the excellent properties of water as cooling fluid. This lead to the simulation of several different
alternative configuration by varying mass flow rate, inlet pipe diameter, materials and working fluids
in order to acess to different temperature levels. Also the idea of using a thin layer of high temperature
insulation in the back of the sample was introduced. This allow temperature levels that would be
impossible to achieve otherwise.
This finally conducted to a multi-mode solution that appears to be the optimal considering all
the constrains. An example of an operational map for this setup can be found in table 3.3. The final
design for the calorimeter is presented in figure 3.12.
Besides Water, also Air, Argon, Helium and Carbon Dioxide were tested as working fluids. Air
revealed to be the best in performance and technical simplicity for the situations were water is not
functional. Helium revealed to be an extremely good cooling fluid for this kind of applications but
in this particular case it is just “to good” because will conduct to results similar to water but with
technical and economical disadvantages. Carbon Dioxide as properties similar to air but it is interesting
for applications around 800K of calorimeter inner wall temperature because it has an abortion window
coincident with the radiative peak of a blackbody at the same temperature (approx. 4µm, see figure
3.13). Argon presents weak properties for this kind of application. In the end, Air and Water were
selected as working fluids.
The design of this calorimeter was quite challenging because of all constrains applied like maximum
metallurgic temperature, maximum outlet temperature and constructibility of all the components. For
future developments, the author recommends the reading the work of Zuckerman & Lior [48] because
of the very complete set of correlations available for jet impingement heat transfer.
Because of a heavy load of work in the VKI workshop, it was impossible in practical time to
prepare the new calorimeters needed for the original planed experience. The solution to overcome
this problem was to create an adapter to transfer the heat from the sample to an existent calorimeter
with the lowest temperature gradients in the sample as possible. The existent calorimeter can only
be used with water because of metallurgical constrains.
The final apparatus used in chapter 6 is presented in figure 3.14.
28 Experimental Facilities and the LHTS Methodology
Figure 3.13: CO2 Absorption Spectrum in Absorption Length Unit
Wall Temperature [K]
<400 400 600 800 900 1200 1900 2000
Condition I Water Air Air -Water + Radiative
- -Thin Insulation Equilibrium
Condition II Water Air Air Air - -Water + Radiative
Thin Insulation Equilibrium
Table 3.3: Example of an operational map for the High Temperature Calorimeter for the twotest cases from table 3.2
Figure 3.14: Sample Holder - Cooled Sample Setup
Experimental Facilities and the LHTS Methodology 29
50
100
150
200
200400
600800
10001200
14001600
1800
0
50
100
150
200
250
300
350
400
ps [hPa]q
cw [kW/m2]
p d [Pa]
Figure 3.15: pd Data and Correlation
3.7.2 New Correlation for Dynamic Pressure Estimation
Continuing the work of Marotta in VKI [15] it was noticed that the static pressure influence on dynamic
pressure was not explicit in the previous available correlations. To avoid time lost when post-processing
long lists of data with linear interpolations that can’t even guarantee a correct representation of the
static pressure effect, it was decided to crate a “single” formula of the type pd = f(qcw, ps) using
the previous database compiled by Marotta and also including some Plasmatron data that wasn’t
included in the previous work.
A non-linear least squares surface fit was done with help of a MATLAB™ script and several
different formulas were tested in order to achieve the best possible fit on the data. The data and the
fitted surface is represented in figure 3.15 and the final formula in equation 3.20. In this formula, qcwshould be introduced in kW m−2.
pd = A(1 +Bqcw)pCs +D
A = 31877.02
B = 0.004857
C = −0.935972
D = −0.832394
(3.20)
A study of the errors involved in the process was done and the conclusions are summarized in
figure 3.16. Despite some punctual measurements which have high relative deviations with respect
to the correlation (some times higher than 90%), one can see that the average relative error is
lower than 15% and the average absolute error is lower than 10 Pa. The r2 factor in this fit is
30 Experimental Facilities and the LHTS Methodology
0 50 100 150 2000
200
400
600
800
1000
1200
1400
1600
1800
2000
ps [hPa]
q cw [k
W/m
2 ]
RELATIVE ERROR [%] Average Relative Error = 14%
Average Absolute Error = 7.1 Pa
0
10
20
30
40
50
60
70
80
90
100
Figure 3.16: Correlation Relative Error [%]
> 0.998. This is considered acceptable considering the experimental problems in the acquisition of
this data and fluctuations on the jet. According to Panerai [7], the typical uncertainty for the dynamic
pressure measurement in the Plasmatron is 20%, so the average error in the correlation is inside the
experimental uncertainty.
3.8 Brief Note on the Computational Methods Used
3.8.1 The heat1D script
This program was created to simulate the temperature of the sample, calorimeter, intermediate
insulation and coolant fluid inside the calorimeter, as a first approximation to check if the idea of
cooling a sample was possible or not. With the idea of simplicity in mind, the big challenge was to
create a easy method to have, at least, approximate values for the boundary conditions at the sample.
In this case, even the most complete methods can’t be trusted because the boundary conditions at
the wall of the sample exposed to plasma are in fact the ultimate target of this experiments.
A first rough method was tried by using convection coefficients between plasma and sample but
the final solution was found by analysing the work of Panerai [7]. In the experiments conducted
there, the heat flux transferred to the wall (q«w) was determined with precision through a radiative
equilibrium method2. In this method the terms qrad,in and qloss from equation 3.10 are neglected:
the first because of the low temperature of the test chamber and the second because of the thick
Procelit™ insulation placed in the back of the sample [6]. So lets consider that at the edge of the
2In reference [7], q«w is called qw
Experimental Facilities and the LHTS Methodology 31
boundary layer the conditions (He, pe, βe i.e. the test conditions) remain constant with respect to the
radiative equilibrium test, ideally by submitting the two samples, in radiative equilibrium and cooled
configurations, to the same plasma jet and with the same probe geometry.
For this kind of testing, only the conditions at the wall and inside the boundary layer will change.
Lets then analyse the conditions one by one. At the wall, the variables playing are three: Temperature,
Catalycity and Emissivity. Temperature influence directly the conductive (qcond) and the “loss” (qloss)
terms as it can be checked in equation 3.11 and in combination with catalycity also the diffusion term
(qdiff ) through the species production rate at a catalytic wall (equation 3.14).
Temperature also influences the radiative heat flux (qrad,out) in combination with emissivity.
Emissivity is known to be a weak function of temperature [7, 49] but for this approximation it was
considered constant and equal to 0.8.
The main point of the approximation done was to consider that q«w does not change with wall
temperature. This is of course false but gives the “worst case scenario” for a first dimensioning of
the experience. What happens is that the qdiff term decreases with the reduction of wi,cat which
decreases with the reduction√Tw and γ. γ itself appears also to decreases with temperature which
was reported by different authors like Panerai [7] or Fourmond et al. [16].
Despite the fact that the decreasing of the wall temperature increases the conductive term (qcond)
it is known, specially for walls with an high catalycity, that this term is smaller compared with the
qdiff term so a global reduction of q«w is expected or at least a no increase of it.
The first step done in the program is to calculate the qloss term. That is made, using the
hypothesis explained above, simply by subtracting qrad,out = εσT 4w from q«w.
Then, using simple relations for 1D conduction and convection in the sample and in the calorimeter
(from Incropera et al. [49]) and imposing the calorimeter bulk temperature, all the temperatures can
be calculated.
To calculate the Nusselt number, three different correlations were used: The first come from an
old technical report written during the design phase of the Plasmatron equipment [44]. It was result
of numerical simulations and has the advantage that it was created directly for application at the
problem in study but it is only available for water. The other two are design correlations for confined
jets available in Li & Garimella [50], which result from experiments and are available for a wide range
of fluids. These last two correlations were preferred but the results from the first one are very similar.
The formula extracted from [44] is:
Nu = 2.047Re0.5(µwµin
)0.1
+ 5.848 (3.21)
The formulas extracted from [50] are:
32 Experimental Facilities and the LHTS Methodology
Figure 3.17: Example of an output from heat1D
Nu = 0.676Re0.555Pr0.441(l/d)−0.071
(De/d)−0.276Ar
+ 1.133Re0.637Pr0.441(De/d)
−1.062(1 −Ar) for Water
(3.22)
Nu = 1.826Re0.473Pr0.441(l/d)−0.071
(De/d)−0.312Ar
+ 0.501Re0.724Pr0.441(De/d)
−1.062(1 −Ar) for Air
(3.23)
where l is the length of the inlet pipe, d is the inner pipe diameter, De is the diameter of the area
cooled by the confined jet and Ar is the area of the jet impingement region normalized with the total
area and is calculated using Ar = (1.9d/De)2.
A typical output of the code is presented in figure 3.17.
3.8.2 The ICP code and NDPs
As explained before in section 3.2.1, after the test being complete, a lot of information is still
missing and we need a “bridge” that is provided by CFD. Knowing the operation conditions of the
Plasmatron, one can than use the VKI ICP code to know the non-dimensional parameters (NDPs)
for the corresponding test. This solver will not be discussed in detail in this work but it is important
to say that it is a viscous reactive flow solver coupled with an electro-magnetic solver. It uses a
second-order accurate pressure-stabilized discretization on a collocated mesh that simulates the ICP
Experimental Facilities and the LHTS Methodology 33
NDP C0 C1 C2 C3 C4 C5
Π1 +5.295E − 01 +2.005E − 07 −2.249E − 03 −3.637E − 08 +4.790E − 11 +9.125E − 06
Π2 +7.799E − 01 −1.724E − 05 −8.034E − 03 +9.231E − 08 +2.824E − 11 +3.521E − 05
Π3 +1.320E + 00 −3.090E − 05 −1.263E − 02 +1.824E − 07 +4.679E − 10 +5.528E − 05
Π4 +9.241E − 01 −1.815E − 05 −1.024E − 02 +6.531E − 08 +3.473E − 10 +4.486E − 05
Π5 +5.563E − 01 +2.126E − 06 −2.092E − 03 −7.657E − 09 −6.877E − 01 +8.847E − 06
Table 3.4: Constants for the NDPs Correlations
torch and part of the test chamber. For more details about this solver the reader is addressed to
specific literature [51, 52].
The solution depends on the power transmitted to the coil, static pressure, mass flow and swirl
angle (being this usually fixed). The power transmitted to the coil (also called ICP value) is related
with the power imposed on the High Frequency Generator by the generator efficiency. The generator
efficiency was estimated in the past as 50% [53] and recent sensitivity analysis shown that efficiencies
between 40% and 60% give a maximum difference in He with respect to the nominal efficiency bellow
0.6% [7].
To save CPU time and results processing time, the solutions for the ICP code are in a database.
Currently, solutions are available for mass flows of 16 g/s and 8 g/s. Only 16 g/s conditions were
used all along this work. The solutions for each NDP for all pairs (PW,ps) calculated in the past
were fit with polynomials. These correlations are valid for power values between 60 and 120 kW,
ICP value, and static pressures between 1500 Pa and 20000 Pa [7]. For all the NDPs, the regression
formula is
Πi = C0 +C1 ⋅ ps +C2 ⋅ PW +C3 ⋅ ps ⋅ PW +C4 ⋅ p2s +C5 ⋅ PW
2 (3.24)
Notice that in this formula the power should be in kW and the constants Ci are available in table
3.43.
Each NDP as a physical meaning that is explained in the following list4:
− Non-dimensional Thickness: Π1 =∆Rm
− Non-dimensional Velocity Gradient: Π2 = (dudx
)eRmv
− Non-dimensional Velocity Gradient Derivative: Π3 =ddy
(dudx
)e
R2m
v
− Non-dimensional Velocity: Π4 =Vev
− Modified Non-dimensional Velocity: Π5 =VeVe,d
3In fact, thanks to this correlations, the author never had to “lose” time running the ICP code in the clusteror studding it.
4Recently, the values used in the adimensionalization of NDPs have changed slightly so the following formulasshould be used very carefully.
34 Experimental Facilities and the LHTS Methodology
3.8.3 The CERBOULA code
The code CERBOULA is in fact a code in two distinct parts: CERBERE and NEBOULA5. The
program that is executed is CERBERE and this one iteratively calls NEBOULA. Each one of them
will be shortly described in the next sections.
NEBOULA
This code is a solver for stagnation point axisymmetric boundary layers under the assumption of
thermal equilibrium and chemical nonequilibrium. It is assumed that the flow is laminar and only
steady-state is considered.
It was developed by Barbante [11] and it uses the PEGASE library developed by Bottin [54] for
thermodynamic and transport properties. The equations are discretized by Hermitian polynomials
and thanks to that the solution is forth order accurate. No more detailing about this code will be
done in this work being the reader advised to consult specific literature [11, 7].
Nevertheless, is important to say that the primary inputs for the program are the conditions at
the BL edge (He,pe,βe,ci,e,µe,etc.) plus the conditions at the wall (Tw,γ) and the main outputs are
qcond, qloss and q«w plus the temperature and species distribution inside the boundary layer.
This program is written in C and during all this work a seven species Air mixture model (Air-7)6
was used for the flow. For the gas phase reaction constants, the Dunn & Kang chemistry model [55]
was used for all the calculations except in the sensitivity analysis in section 7.2.1.
CERBERE
This code acts essentially as a pre and post processor for NEBOULA.
The user has several options available like, for example, enthalpy rebuilding, catalycity rebuilding
or abacus plotting, among others [56].
For enthalpy rebuilding the user gives all the BL edge parameters available (NDPs, pd and ps)
plus the probe radius, wall conditions at the calorimeter and the measured heat flux (qcw). The code
will than iterate the BL edge temperature (and consequentially also He) with a Newton loop until
the numerical heat flux calculated by NEBOULA (that is executed in each iteration) matches the
experimental one.
For catalycity rebuilding, the process is similar but instead of He (that is now known), the iterated
variable is γ.
To plot the heat flux abacus, the user just need to input the BL edge conditions and the NEBOULA
will calculate, for user selected pairs (Tw,γ), the corresponding heat flux.
5Sometimes this code is referred in the literature as “VKI Boundary Layer Code”6This model include the following species: O2, N2, NO, NO+, O, N and e–
Experimental Facilities and the LHTS Methodology 35
NEBOULA
NDP1 …… NDP5
He , vs , ρe , βe , …
ps Rm pd
Operational Parameters
Geometry
Probe Measurements
Te(n+1)
Heat Flux Abacus
Sample Measurements
ICP Code
qcw(n) =qcw
(exp)
Tw
No
Yes
γ Catalycity
Flight
Conditions
ps m PWel Swirl ηgen
.
qcw
CERBERE
CERBOULA
PLA
SMA
TRO
N
Radiation
qloss
ε
qexp
CERBOULA
qexp(n) =qexp
(exp)
NEBOULA
NDPs
No γ(n+1)
Yes
CERBERE
Geometry
+
or
γref
Tcw
Figure 3.18: The Complete Experimental-Numerical Frame
3.8.4 The Complete Experimental-Numerical Frame
In figure 3.18 we try to give a complete view of how the data from the experiments is processed until
the final results are obtained, as explained in the previous sections.
36
Chapter 4
Numerical Simulations
In order to have a first feeling on the 2D effects in the cooled sample experiment a series of ther-
mal simulations were done using ANSYS™. It uses the finite element method and the element type
chosen for this work was a quadratic triangle and a serendipity quadratic quadrilateral. No further
considerations will be done about this method being the reader addressed to specialized literature
like Reddy [57]. The simulations were done in 2D axisymmetric mode and the symmetry axis is the
left vertical on the images. Because of the fallback of the original planed temperature campaign (see
section 3.7.1) also a quick simulation of the calorimeter adapter was made.
4.1 Cooled Sample Setup Simulation
As already explained in section 3.7.1, two different test cases were studied: one corresponding to low
HF and the other corresponding to high HF, respectively Condition I and Condition II. For simplicity,
the emissivity was considered always equal to 0.8 for the reasons already explained in section 3.8.1.
These two conditions were used to test three configurations of sample holders: without cooling, with
cooling and with cooling and intermediate insulation.
In figure 4.1 we can see an example of a mesh for the configuration with cooling. The meshes for
the other configurations are equivalent. The boundary conditions used were a convective surface in
the back with a bulk fluid temperature of 350K and a convection coefficient1 of 7000 W m−2 K−1, the
sample and cover being submitted to a constant HF and radiating to an enclosure at 400K. The initial
temperature was set to 300K. Details and results for the different configurations will be presented next.
Temperature fields for all the simulations are presented in Appendix A and Temperature vs. Time
graphics can be found in Appendix B and are from points along the symmetry axis.
1A value typical for the water calorimeters was used because no data is available for the cooling system of theholder itself.
37
38 Numerical Simulations
Figure 4.1: Example of the Mesh
4.1.1 ST Sample Holder Without Cooling
This configuration was tested to access the validity of the approximations made in section 3.8.1. The
cover material used was the same used in the tests, Silicon Carbide (SiC).
4.1.2 ST Sample Holder With Cooling
The main objective of these simulations was to find if the lateral heat flux to the calorimeter could
“polute” the measured heat flux across the sample. The Temperature vs. Time graphics show that
the steady state for the sample area is achieved in less than 10 s. The holder in general only achieve
steady state after 75 s. Heat Flux fields can be found in figures 4.2 and 4.3.
The geometry simulated is very rough because, at this point, the final experimental setup was not
it fully defined/known which lead to the need of an extra simulation presented in section 6.2. Also a
small insulation was planed to be placed between the sample and the cover but it does not exist in
the final setup.
The conclusions for these simulation are that the lateral heat flux only has a negligible effect on
the final measurement for the two conditions.
Numerical Simulations 39
Figure 4.2: HF Field - Cond. I
Figure 4.3: HF Field - Cond. II
40 Numerical Simulations
Figure 4.4: HF Field - Cond. I
4.1.3 ST Sample Holder With Cooling and Insulation
In the same way as the simulations in the previous section, the objective of these simulations was to
find the lateral heat flux to the calorimeter. According to the Temperature vs. Time graphics, the
steady state for the sample area is also achieved in less then 80 s. Heat flux fields are presented in
figures 4.4 and 4.5.
The conclusion for these simulation are equal to the ones in section 4.1.2.
4.2 Calorimeter Adapter
As explained in section 3.7.1 there was the need of designing a calorimeter adapter.
The simulations done were similar to the simulations in section 4.1 with the exception that only
the sample and the adapter were simulated for simplicity and lack of time for modelling. Simulations
were made first for pure copper (λ = 400 W kg−1 K−1) and then for commercial bronze (λ = 50 W
kg−1 K−1) and for thicknesses of 5 and 3 mm. The results show that with 5 mm it’s possible to obtain
a maximum surface temperature difference lower then 4K for an adapter made of commercial bronze
with 5mm thickness for condition I which is more than acceptable for the proposed experiments.
Numerical Simulations 41
Figure 4.5: HF Field - Cond. II
Figure 4.6: Temperature Field - 5mm adapter
42 Numerical Simulations
Figure 4.7: Temperature Field - 3mm adapter
Chapter 5
Oxidation Campaign
The objective of this campaign of tests was to establish the transition between Passive and Active
Oxidation in C/SiC TPM and also the identification of the operational limits of such material through
the investigation of the phenomena known as “temperature jump”.
The tests were done under the framework of the IXV project for the expansion of the ATDB
in order to help the design phase of this vehicle and were financed through an ESA’s Technology
Research Programme (TRP).
5.1 Testing Procedures
The testing procedure were similar for all the samples tested. Inside the Plasmatron test chamber
were installed a Pitot probe, an HF probe and the sample holder. Most of the tests were done using
the ST geometry for Pitot, HF probe and sample holder, but in the end of the test campaign some
were done using the FR geometry. These last tests are described in section 5.2.6.
The measurements with the intrusive probes were acquired before the sample injection into the
plasma and used to calibrate the jet. Afterwords, the optic instruments allow the measurement of the
sample temperature and emitted radiation. Besides that, also optical spectrometry data was acquired
from 3 points in or near the boundary layer region and the test was recorded with an High Definition
Camera. All the steps of the tests are listed below:
→ Chamber vacuum and pressure stabilization;
→ Plasma and data recording start-up;
→ Standard heat flux probe injection and power adjustment to the target heat flux;
→ Heat flux probe retraction and Pitot probe injection;
→ Pitot probe retraction and sample holder injection;
43
44 Oxidation Campaign
Test Sample Tw Tw,pj qcw∗ ps pd mpre Time PWel
K K kW m−2 Pa Pa g s kW
16 HER-A16 1917 - 1021 2000 154 2.028 600 26415 HER-A15 1928 - 998 2000 151 1.996 600 26817 HER-A17 1973 - 1099 2000 164 2.031 600 2864 HER-A4 2065 - 1215 2000 178 2.085 600 3211 HER-A1 2077 - 1283 2000 187 2.083 600 3237 HER-A7 2115** 2512 1304 2000 189 2.039 200 322
5 HER-A5 1942 - 1194 5000 74 2.070 600 2702 HER-A2 1960 - 1230 5000 76 2.018 600 2838 HER-A8 1997 - 1304 5000 80 1.985 600 2919 HER-A9 2030 - 1404 5000 85 1.973 600 30410 HER-A10 2090 - 1417 5000 86 2.024 600 33111 HER-A11 2157 - 1501 5000 90 2.053 200 35213 HER-A13 2180*** 2734 1587 5000 95 2.047 130 384
3 HER-A3 1965 - 1320 6000 68 2.010 600 3026 HER-A6 1967 - 1345 6000 69 2.038 600 29918 HER-A18 1998 - 1392 6000 71 2.018 600 30319 HER-A19 2063 - 1499 6000 76 1.956 600 328
* Preliminary data to be verified** Jump temperature. Before jump, steady state was achieve with Tw=2095K*** Jump temperature
Table 5.1: Test Conditions for HER samples
→ Sample exposure to plasma for 10 minutes at stationary temperature (possible earlier interrup-
tion of a test in presence of very high temperatures and/or cooling issues in the system);
→ Plasma off and chamber ventilation;
→ Stop of data recording;
→ Samples recovery after system cooling;
Two different kinds of TPM were tested. Both are CMC C/SiC manufactured by Herakles and
MT Aerospace, that will be referred from now on as HER for the material manufactured by Herakles
and MTA for the one from MT Aerospace. Both are identical materials and they consist in a Silicon
Carbide matrix reinforced with Carbon Fiber so they can be classified as CMC. MTA also owns an
extra SiC layer coating the surface, deposited by chemical vaporization methods. HER will be used
to construct the nose and windward side of IXV and MTA will be used for the construction of the
control flaps of the same vehicle.
The test conditions are presented in the tables 5.1 and 5.2.
5.2 Results
The results of this testing campaign will be presented in this section together with results from
literature for comparison.
In this section, the notation qw will be used to represent qexp (= q«w).
Oxidation Campaign 45
Test Sample Tw Tw,pj qcw∗ ps pd mpre Time PWel
K K kW m−2 Pa Pa g s kW
20 MTA-A1 1870 - 963 2000 146 3.623 600 26022 MTA-A3 1982 - 1122 2000 166 3.663 600 28321 MTA-A2 2014 - 1196 2000 176 3.711 600 30430 MTA-A11 2070** 2589 1237 2000 181 3.513 120 340
23 MTA-A4 1853 - 1210 5000 75 3.619 600 26024 MTA-A5 1956 - 1398 5000 85 3.701 600 29125 MTA-A6 2119 - 1575 5000 94 3.710 600 34831 MTA-A12 2060** 2542 1403 5000 85 3.501 120 283
26 MTA-A7 1981 - 1399 6000 71 3.645 600 32628 MTA-A9 2105 - 1497 6000 76 3.766 400 36232 MTA-A13 2130** 2593 1394 6000 71 3.701 120 320
* Preliminary data to be verified** Jump temperature
Table 5.2: Test Conditions for MTA samples
Test pO2 mpost rm/m Mass Loss Rate ε qw Te He γ OxidationPa g % mg cm−2 min−1 kW m−2 K MJ kg−1
16 452 2.0116 -0.814 0.297 0.747 571 5556 21.92 0.03081 P15 452 1.9453 -2.550 0.916 0.750 588 5534 21.50 0.03500 P17 454 1.9926 -1.900 0.695 0.735 631 5631 23.35 0.03531 P4 457 1.8430 -11.594 4.349 0.718 741 5739 25.47 0.04501 A1 459 1.8870 -9.418 3.531 0.696 735 5802 26.70 0.03972 A7 460 1.1751 -42.358 - 0.604* 760**|1364 5824 27.11 0.04217** J
5 1066 2.0644 -0.275 0.103 0.747 602 5826 22.65 0.01089 P2 1066 2.0098 -0.416 0.151 0.752 629 5857 23.20 0.01164 P8 1067 1.9639 -1.043 0.372 0.751 678 5920 24.33 0.01289 P9 1068 1.9470 -1.333 0.473 0.744 716 6004 25.87 0.01313 P/A10 1068 1.9139 -5.449 1.985 0.765 828 6011 25.99 0.01939 A11 1069 2.0197 -1.636 1.814 0.698 847 6077 27.19 0.01887 A13 1070 0.9123 -55.424 - 0.630 1996 6130 28.13 - J
6 1274 2.0287 -0.432 0.158 0.749 637 5985 24.61 0.00824 P18 1275 2.0060 -0.604 0.220 0.736 665 6024 25.31 0.00884 P19 1276 1.9016 -2.781 0.979 0.771 791 6109 26.83 0.01257 A
* During the steady state, the value is equal to 0.696** During the steady state. Calculated using Tw=2095K and ε =0.696
Table 5.3: Summarized Test Results - HER
5.2.1 General Results (ST geometry)
First, in tables 5.3 and 5.4, we present the rebuilt quantities calculated using the LHTS methodology,
more specifically using the ICP code results and running the CERBOULA code, and also some other
important quantities as, for example, mass loss rate. At the end of each table the estimated oxidation
regime is presented. The complete rebuilding results, including the NDPs used and the species
concentration at the boundary layer edge are presented in Appendix C.
To determine the oxidation regime, 3 criteria were used: visual inspection, mass loss rate (MLR)
and presence of a Silica layer detected using Scanning Electron Microscopy (SEM).
As a first approach, the visual appearance of the samples allow to roughly say if a sample went
through a passive, active regime or a temperature jump. The previous work of Panerai [7, 19] was
used as reference.
Description of the samples and images are presented in section 5.2.3. In the future, this is will
46 Oxidation Campaign
Test pO2 mpost rm/m Mass Loss Rate ε qw Te He γ OxidationPa g % mg cm−2 min−1 kW m−2 K MJ kg−1
20 451 3.6028 -0.5548 0.3617 0.900* 624 5499 20.87 0.043771 P22 455 3.6018 -1.6654 1.0977 0.728 637 5655 23.81 0.034667 A21 457 3.5471 -4.4114 2.9457 0.737 688 5722 25.14 0.037660 A30 458 2.4481 -30.3092 - 0.617 1572 5755 25.79 - J
23 1066 3.6130 -0.1686 0.1098 0.907 606 5838 22.87 0.010231 P24 1068 3.6897 -0.3053 0.2033 0.852 706 5998 25.76 0.012318 P25 1070 3.5547 -4.1911 2.7982 0.755 863 6140 28.31 0.017719 A31 1068 2.4330 -30.5016 0.627 1484 6003 25.85 - J
26 1275 3.6476 0.0713 -0.0468 0.875 763 6030 25.42 0.012558 P28 1276 3.7446 -0.5682 0.5776 0.733 817 6097 26.62 0.014016 P/A32 1275 2.6605 -28.1043 - 0.616 1579 6025 25.33 - J
* Estimated. Radiometer failure during experiment.
Table 5.4: Summarized Test Results - MTA
probably be helpful for spacecraft maintenance routine checks.
The MLR allow a more scientific approach. It is known, from previous experiments which used a
real-time weight measurement, like the work done by Jacobson & Myers [20], that the mass loss rate
varies dramatically between passive and active oxidation and that fact is used as transition criteria.
Results are presented in figures 5.1 and 5.2. The letter A mark the samples that were submitted to
active oxidation.
We can clearly see a large increase in the MLR of the samples subjected to active oxidation with
respect to the ones subjected to the passive regime. One can also see that lower static pressures are
more destructive for the samples.
The SEM was used as a verification measurement, which allowed to confirm the presence/absence
of a glassy silica layer over the exposed surface, hence, cross-checking the predicted regime by the
other methods. The SEM analysis were preformed at PROMES, France.
An uncertainty analysis was done for the MLR determination. Knowing that the MLR is given by
the formula
MLR =mpost −mpre
A ∆t(5.1)
than it can be deducted that the relative uncertainty is given by
δMLRMLR
=
¿ÁÁÀδmpost
2+ δmpre
2
(mpost +mpre)2+ (
δ∆t
∆t)
2
+ (2πδD
4D)
2
(5.2)
The uncertainty for the temperature is given by the pyrometer specifications and it is equal to ±10K.
The observation, using SEM, of samples without a SiO2 layer which didn’t went through a tem-
perature jump, together with the analysis of the results of the visual inspection and the MLR, can
be used to declare, with relative confidence, that the temperature jump can’t be used as a marker of
the transition.
An interesting result can be found plotting the surface catalycity as function of the boundary layer
edge enthalpy. It can be observed in figure 5.3 that the catalycity has a relative increase during the
Oxidation Campaign 47
1900 1950 2000 2050 2100 2150 22000
0.5
1
1.5
2
2.5
3
3.5
4
4.5
A
A
AA
A
Mass Loss Rate vs. Surface Temperature − HER
Surface Temperature [K]
Mas
s Lo
ss R
ate
[mg
cm−
2 min
−1 ]
HER, p
s=2000Pa
HER, ps=5000Pa
HER, ps=6000Pa
Figure 5.1: Mass Loss Rate - HER
1800 1850 1900 1950 2000 2050 2100 2150−0.5
0
0.5
1
1.5
2
2.5
3
3.5
A
A
A
A
Mass Loss Rate vs. Surface Temperature − MTA
Surface Temperature [K]
Mas
s Lo
ss R
ate
[mg
cm−
2 min
−1 ]
MTA, p
s=2000Pa
MTA, ps=5000Pa
MTA, ps=6000Pa
Figure 5.2: Mass Loss Rate - MTA
transition and such result goes in the same direction as the theory: active oxidation is equivalent to
a more reactive wall.
This sudden increase in γ can be used for determination of the PA transition but is not recom-
mended by the author. It implicate a very long measurement chain, subjected to several different
errors, which in the end conducts to an high uncertainty. In fact, previous UQ studies done by Vil-
ladieu et al. [58] and Panerai [7] point to uncertainties that can be bigger than the vertical range of
this graph. Plus, chemistry models involving Si in the gas phase are still missing in the code, including
the important exotermic reaction Si + OÐ→ SiO. Nevertheless, this method is valid but needs an
higher number of tests to guarantee its validity.
48 Oxidation Campaign
22 23 24 25 26 27 28 290.01
0.011
0.012
0.013
0.014
0.015
0.016
0.017
0.018
0.019
0.02γ vs. BL Edge Enthalpy
BL Edge Enthalpy [MJ/Kg]
γ
Active
Passive
HER, ps=5000Pa
MTA, ps=5000Pa
Figure 5.3: Catalycity Coefficient γ evolution through the PA transition. One should note thatγ also depends on βe that is varying for each test condition, so the dash-doted line should notbe strictly interpreted as the evolution of γ with He. For more information, the author advisethe reader to consult [14].
5.2.2 Passive-to-Active Oxidation Transition Line
In this section we present our results together with our propose for a PA oxidation transition line,
based on the same trending of the result from the experiments done at PROMES using the MESOX
set-up using CVD SiC on C/SiC composits under microwave-excited air and presented by Balat (fig.
11 in [18]).
As we can see, our results are in very good agreement with the reference. The results are presented
in figures 5.4 and 5.5 as function of the oxygen partial pressure and reciprocal wall temperature. The
differences in the results can be attributed to the uncertainties and differences in the tested samples.
5.2.3 Visual Inspection of the Samples
Despite that the samples were submitted to scanning electron microscopy (SEM), a simple visual
inspection of them can deliver interesting information. In figure 5.6 we can see pictures of samples
that undergone different oxidation regimes for the same static pressure level (in this case 5000 Pa).
For the sample that undergone passive oxidation a yellow/brown/blue appearance can be observed
and it is associated to the existence of a thin silica layer in the surface. The colours change according
to the thickness of the silica layer. After active oxidation, the surface as a shiny look and one can
notice the reduction of the coating protection that makes the carbon fibres more exposed. After a
temperature jump, the surface is completely eroded and the black appearance is due to the residuals
of the carbon combustion. Also an appreciable reduction in thickness is noticeable.
Similar conclusions can be extracted for the MTA samples, with the pictures presented in figure
5.7.
Oxidation Campaign 49
Figure 5.4: Passive-to-Active Transition - HER
Figure 5.5: Passive-to-Active Transition - MTA
50 Oxidation Campaign
(a) Virgin Sample (b) After Passive Regime - Test 5
(c) After Active Regime - Test 10 (d) After Temperature Jump - Test 13
Figure 5.6: Examples of HER samples tested with ps=5000Pa
Oxidation Campaign 51
(a) Virgin Sample (b) After Passive Regime - Test 24
(c) After Active Regime - Test 25 (d) After Temperature Jump - Test 31
Figure 5.7: Examples of MTA samples tested with ps=5000Pa
52 Oxidation Campaign
0 100 200 300 400 500 600 7001400
1600
1800
2000
2200
2400
2600
T w, K
, sec
HER 1
(a) TEST 1 - No Jump
0 40 80 120 160 200 2401400
1600
1800
2000
2200
2400
2600
T w, K
, sec
HER 7
(b) TEST 7 - Temperature Jump
Figure 5.8: Temperature History During Two Different Tests - HER
5.2.4 The Temperature Jump
The temperature jump is a phenomena observed in TPM containing SiC and submitted to extreme
reentry environments. It was first reported by Lacombe & Lacoste [59] and after by other scientists
[60, 61].
More recently, I. Sakraker et al. [62], Marshall et al. [63] and Panerai [7] found the same phe-
nomena in experiments done in the Plasmatron at VKI. In this work we are going to avoid detailed
comments or explanations on this topic being the reader advised to consult Hald [64] or Marshall et
al. [63].
In figures 5.8 and 5.9 one can observe the difference in temperature evolution between a test
without jump and one with the jump. One should also notice that after the jump the temperature
is several hundreds of Kelvin above the cases without jump. These extreme temperatures, in an
enough long reentry manoeuvre would conduct to the destruction of the TPM and consequently of
the spacecraft.
In figure 5.10 we can see the evolution of emissivity for the two jump examples presented in figures
5.8 and 5.9. One can notice that after the jump, emissivity is reduced with respect to the condition
pre-jump. This was noticed to be a common behaviour for all jump cases.
The emissivity peaks that appear in the graphics are just an artefact generated by the measurement
system. The pyrometer is measuring the temperature in a circle with a diameter of ∼ 3mm concentric
with the sample. On the order hand, the radiometer is measuring the radiation from almost all the
sample. This correspond to an advance/delay in the two measurements due to the slow propagation
of the “jump front” across the sample.
In figure 5.11 one can see the visual recording of the “jump front” and the corresponding temper-
ature evolution.
Only when the surface is completely immersed into the jump state, the emissivity measurement
is reliable again. In conclusion, the emissivity data recorded during the jump should be ignored.
Oxidation Campaign 53
0 100 200 300 400 5001400
1600
1800
2000
2200
2400
2600
2800T w
, K
MTA 28
(a) TEST 28 - No Jump
0 25 50 75 100 1251400
1600
1800
2000
2200
2400
2600
2800
T w, K
MTA 32
(b) TEST 32 - Temperature Jump
Figure 5.9: Temperature History During Two Different Tests - MTA
0250500750
1000
0 25 50 75 100 125 150 175 200 2250.50
0.75
1.00
W0.
6>39
m, k
W m
-2 s
r-1
Sample Blackbody
, sec
(a) TEST 7 - HER
0250500750
1000
0 25 50 75 100 1250.50
0.75
1.00
W0.
6>39
m, k
W m
-2 s
r-1
Sample Blackbody
, sec
(b) TEST 32 - MTA
Figure 5.10: Integrated Spectral Radiance and Emissivity History
Figure 5.11: Temperature Jump - Evolution in Time
54 Oxidation Campaign
5.2.5 Optical Spectrometry Results
As referred before, optical spectrometry data was took during the tests. The spectrometers were
aligned in order to record the emission from 3 points in the boundary layer, at 2mm, 5.5mm and
9mm from the sample along the stagnation point axis. In figure 5.12 one can see the spectra recorded
with the flow already calibrated for the desired conditions with and without the sample in place. The
data was obtained with the same spectrometer, pointed 1.5mm away from the sample.
5.2.6 Frozen Geometry Tests
This tests, presented in figure 5.13, show the evolution of one Si emission line (with λ=288nm)
during a temperature jump. One can observe that the increase in emission starts before the measured
temperature jump because of the diffusion of Si in the boundary layer during the jump evolution and
the fact that the spectrometer doesn’t measure the emission in a single point but instead in a line
in front of the sample. In the last image we can see that in the last 20 sec. a jump started but the
jump front didn’t reach the centre of the sample before the end of the test.
Oxidation Campaign 55
250 300 350 400 450 500 550 600 650 7000
1
2
3
4
5
6
7
8
9
10Spectra from Test 21, lower wavelengths
Wavelenghth [nm]
Inte
nsity
[a.u
.]
Si 251
Si 288
Si 391
Na 589FreestreamWith Sample, 1.5 mm
700 720 740 760 780 800 820 840 860 880 9000
10
20
30
40
50
60
Spectra from Test 21, higher wavelengths
Wavelenghth [nm]
Inte
nsity
[a.u
.]
O 777
N 742,744,746
N 818,821,824 O 844
N 868
←
←
→
← ←
←
FreestreamWith Sample, 1.5 mm
Figure 5.12: Spectra took during Test 21 (Active Oxidation). One should also notice the Sipeaks that appear in the presence of the sample. The arrows in the bottom figure indicate thereduction in intensity due to the recombination of the species in the BL and/or temperaturereduction.
56 Oxidation Campaign
0 20 40 60 80 100 120 1401250
1500
1750
2000
2250
2500
T w [K
]
Temperature
0 20 40 60 80 100 120 1400
50
100
150
200
250
300 1.5 mm 5.5 mm 9.0 mm
I, a.
u.
Time
(a) Test M2 – ps = 2000 Pa, qcw = 1.1 MW m−2
0 20 40 60 80 100 120 140 160 1801250
1500
1750
2000
2250
2500
Temperature
0 20 40 60 80 100 120 140 160 1800
50
100
150
200
250 1.5 mm 5.5 mm 9.0 mm
Time
(b) Test M3 – ps = 2000 Pa, qcw = 1.0 MW m−2
0 20 40 60 80 100 120 140 160 180 2001250
1500
1750
2000
2250
2500
T w [K
]
Temperature
0 20 40 60 80 100 120 140 160 180 2000
15
30
45
60
75 1.5 mm 5.5 mm 9.0 mm
I, a.
u.
Time
(c) Test M4 – ps = 2000 Pa, qcw = 0.9 MW m−2
Figure 5.13: Emission Line Si288 Intensity Evolution During a Temperature Jump
Chapter 6
Temperature Campaign
This campaign had the objective of investigate the effect of temperature in surface catalycity and heat
transfer on C/SiC TPM. The experience consist in fixing all the parameters in the BL edge (He, pe, βe)
and change only the surface temperature. This allow us to “isolate” the surface temperature effects.
On the original test campaign was programmed to investigate several temperature levels but in
consequence of issues in the manufacturing of the lab equipment1, only 2 temperature levels were
investigated as explained in section 6.1. The samples tested were manufactured by Snecma Propulsion
Solide.
6.1 Testing Procedures
Three tests were done in this experiment and all followed the same testing sequence which is described
below. In each test two samples were tested: one with the cooled setup, already described in
section 3.7.1 and one with the conventional insulated setup (see section 3.4). From now on the
sample installed in the cooled setup will be referred as cooled sample (CS) and the other as radiative
equilibrium sample (RS). In all the tests the geometries of the sample holder and the heat flux probe
were the ST one. Each test correspond to a different pair of (pe, βe) because we tried to keep He
constant and equal to 10MJ/kg.
→ Chamber vacuum and pressure stabilization;
→ Plasma generator and data recording start-up;
→ Heat flux probe injection and power adjustment to the target heat flux;
→ Heat flux probe retraction and cooled sample injection;
→ Cooled sample exposure to plasma for approx. 8 minutes;1One of the drawbacks of doing an experimental simulation is that it doesn’t depend only of our will
57
58 Temperature Campaign
Test Sample qcw ps pd PWelkW m−2 Pa Pa kW
T1-CS S4 343 1440 93 138T1-RS S1 343 1440 93 138S6 [7] - 360 1300 83 99
T2-CS S5 381 5000 31 149T2-RS S2 381 5000 31 149S10 [7] - 390 5000 27 130
T3-CS S6 303 10000 13 142T3-RS S3 303 10000 13 142C2a [7] - 315 10000 11.8 137
Table 6.1: Test Conditions for the Temperature Campaign and Reference [7]
→ Cooled sample retraction and radiative equilibrium sample injection;
→ Radiative equilibrium sample exposure to plasma for approx. 8 minutes;
→ Plasma off and chamber ventilation;
→ Stop of data recording;
→ Samples recovery after system cooling;
In table 6.1 the test conditions are presented as well as some reference results extracted from [7].
The target HF was calculated before the tests using the NEBOULA code in order to match a BL
edge enthalpy of 10MJ/kg. Unfortunately, it is always impossible to match exactly the the desired
condition as consequence of uncertainties in the HF measurement, because the power is “tuned” in
real time but the real average value of HF is only acquired in post-processing and also because in
the preparation only an approximate value for the power was used. Nevertheless, the difference with
respect to the target He obtained in tests T1 and T2 was 6% and in test T3 was 13%. The error in T3
is higher because of lack of accurate power estimations during the preparation of the test campaign,
which was caused by a “last-moment” change in the test condition related with Plasmatron operation
constrains.
6.2 Results
The results of the campaign are summarized in table 6.2. As for the oxidation campaign, the complete
rebuilding results are presented in Appendix C and some considerations on the degree of dissociation
of the flow and on the temperature profile across the BL are presented on section 7.3.
During the experiments was noted that the HF measurement of qloss recorded by the DAC was
much higher than expected. It was found that there was two reasons for that. First there was a
question of concept in the the HF determination: the calorimeter probe doesn’t measure directly the
HF, it measures the heat rate, this value is then divided by the area of the calorimeter and the result
is the output value of the DAC. But, in fact, the area of the sample is higher than the area of the
Temperature Campaign 59
Test βe Tw ε qrad qloss qexp Te pe He ρe γref γ
s−1 K kW m−2 kW m−2 kW m−2 K Pa MJ kg−1 kg m−3
T1-CS 6925.0 1375 0.82 167 43.7 210 4223 1440 9.3777 0.0009677418 0.10 0.026205T1-RS 6925.0 1513 0.86 257 0.0 257 4223 1440 9.3777 0.0009677418 0.10 0.079643S6 [7] 7277.0 1400 0.79 172 0.0 172 4440 1300 10.2487 0.0008190640 0.10 0.007280
T2-CS 2168.5 1374 0.78 157 52.8 210 4354 5000 9.4236 0.0032728925 0.10 0.005751T2-RS 2168.5 1528 0.82 254 0.0 254 4354 5000 9.4236 0.0032728925 0.10 0.018183S10 [7] 2097.8 1400 0.86 187 0.0 187 4485 5000 9.8197 0.0031588285 0.10 0.002204
T3-CS 935.2 1367 0.79 157 40.2 197 4085 10000 8.6575 0.0070697653 0.01 0.004082T3-RS 935.2 1449 0.94 235 0.0 235 4085 10000 8.6575 0.0070698046 0.01 0.011544C2a [7] 916.7 1515 0.90 269 0.0 269 4306 10000 9.1462 0.0066631346 0.01 0.023190
Table 6.2: Test Results From the Experiments and Reference [7]
calorimeter but the heat rate that crosses the surface of the sample is the same that crosses the
surface of the calorimeter (conservation of energy principle), than the heat rate should be divided
by the sample area, because that is the input for the 1D catalycity rebuilding process used in the
CERBOULA code (see section 3.8.3).
Second, it was found that the SiC sample holder was exchanging a huge amount of heat with the
sample (Qlat), i.e., the insulation created by the surface contact was to low to properly insulate the
sample, as it was expected prior to the experiment. In order to overcome this issue, a new numerical
simulation of the experiment was done, this time using the exact geometry tested2. A sketch of the
simulated geometry is presented in figure 6.1.
The calculation of the heat rates was done performing the heat flux integration over the area using
the HF results from the FEA considering cylindrical coordinates. The imposed heat flux in the wall
was the value obtained by measuring the radiative equilibrium sample. The final formula to correct
the measured heat flux at the calorimeter surface3 was again based on the conservation of energy
principle and it is
Qloss = Qcal − Qlat⇔
⇔Qloss = Qcal (1 −Qlat
Qcal)⇔
⇔qloss = qcalAcal
Asample(1 − F )
(6.1)
in which F is equal to 0.6894 and the numerical simulations shown that this value is a weak function
of the imposed heat flux for the ranges of this experiment. Using this method it is possible to obtain
a corrected value for the qloss term.
In figure 6.4 one can see the heat flux history graphic of test T1. The graphs for the other
experiments are similar.
2During the design phase simulations, presented in chapter 4, there were several unknowns like the exactsamples to be tested and the exact way the sample and the calorimeter would be installed.
3Output of the DAC.
60 Temperature Campaign
Figure 6.1: Geometry tested and Simulated
Figure 6.2: Steady State Temperature Simulation
Temperature Campaign 61
Figure 6.3: Steady State Heat Flux Simulation
600 800 1000 1200 1400 1600 18000
50
100
150
200
250
300Measured Heat Fluxes vs. Time − T1
Time [s]
Hea
t Flu
x [k
W/m
2 ]
CS RS
qexp
qrad
qloss
Figure 6.4: Heat Flux History of Test T1
62 Temperature Campaign
300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 16000
50
100
150
200
250
300
350
400HF Abacus − T1
Temperature [K]
Exp
erim
enta
l Hea
t Flu
x [k
W/m
2 ]
γ = 1
γ = 0.1
γ = 0.05
γ = 0.03
γ = 0.02
γ = 0.01
γ = 0.005
γ = 0
Reference (Copper)Cooled Sample (CS)Rad. Eq. Sample (RS)Cooled Sample (Rad. Only)Radiative HF (CS)Radiative HF (RS)
Figure 6.5: Abacus of test T1
6.2.1 Catalycity
The final output of the rebuilding process can than be obtained using the CERBOULA code and/or
the HF Abacus. The graphics are presented in figures 6.5, 6.6 and 6.7 and in the abacus of T2 (figure
6.6) one can observe some important HF quantities. These quantities are also presented in section
7.3.
We can also plot the result in a 3D graphic including all the boundary condition variables (except
enthalpy that is considered constant) and the result is presented in figure 6.8 together with the results
from [7]. A 2D version of the graph can be also plotted to increase the readability but one should
remember that pe and βe are independent parameters [14] and in order create the plot the βe values
were approximated (the approximation error is around 10%).
Appears that the slope of γ vs. Tw in a log scale doesn’t evolve with (pe,βe), which means that
γ is more sensible to Tw for (low pe, high βe) values. On the other hand, the slope of HF vs. Twseams to be independent of (pe,βe).
Temperature Campaign 63
300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 17000
50
100
150
200
250
300
350
400HF Abacus − T2
Temperature [K]
Exp
erim
enta
l Hea
t Flu
x [k
W/m
2 ]
← q
loss →←
(a) →
γ = 1
γ = 0.1
γ = 0.05
γ = 0.03
γ = 0.02
γ = 0.01
γ = 0.005
γ = 0
Reference (Copper)Cooled Sample (CS)Rad. Eq. Sample (RS)Cooled Sample (Rad. Only)Radiative HF (CS)Radiative HF (RS)
Figure 6.6: Abacus of test T2 - (a): Reduction on the experimental heat flux due to the reductionon the surface temperature
300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 16000
50
100
150
200
250
300
350HF Abacus − T3
Temperature [K]
Exp
erim
enta
l Hea
t Flu
x [k
W/m
2 ]
γ = 1γ = 0.08
γ = 0.03γ = 0.02
γ = 0.01
γ = 0.005
γ = 0
Reference (Copper)Cooled Sample (CS)Rad. Eq. Sample (RS)Cooled Sample (Rad. Only)Radiative HF (CS)Radiative HF (RS)
Figure 6.7: Abacus of test T3
64 Temperature Campaign
13601380
14001420
14401460
14801500
15201540
01000
20003000
40005000
60007000
800010
−3
10−2
10−1
Tw
[K]
γ vs. BL edge Parameters − He ≈ 10MJ/kg
βe [s−1]
γ
pe = 1300 Pa
pe = 1440 Pa
pe = 5000 Pa
pe = 10000 Pa
(a) Complete Plot
1360 1380 1400 1420 1440 1460 1480 1500 1520 154010
−3
10−2
10−1
γ vs. BL edge Parameters − He ≈ 10MJ/kg
Tw
[K]
γ
p
e = 1300 Pa, β
e = 7277 s−1
pe = 1440 Pa, β
e = 6925 s−1
pe = 5000 Pa, β
e ≈ 2100 s−1
pe = 10000 Pa, β
e ≈ 920 s−1
(b) Approximate Plot
Figure 6.8: γ as function of the BL edge parameters
Temperature Campaign 65
13601380
14001420
14401460
14801500
15201540
01000
20003000
40005000
60007000
8000150
200
250
300
Tw
[K]
HF vs. BL edge Parameters − He ≈ 10MJ/kg
βe [s−1]
q exp [k
W m
−2 ]
pe = 1300 Pa
pe = 1440 Pa
pe = 5000 Pa
pe = 10000 Pa
1360 1380 1400 1420 1440 1460 1480 1500 1520 1540170
180
190
200
210
220
230
240
250
260
270
HF vs. BL edge Parameters − He ≈ 10MJ/kg
Tw
[K]
q exp [k
W m
−2 ]
p
e = 1300 Pa, β
e = 7277 s−1
pe = 1440 Pa, β
e = 6925 s−1
pe = 5000 Pa, β
e ≈ 2100 s−1
pe = 10000 Pa, β
e ≈ 920 s−1
Figure 6.9: Experimental HF as function of the BL edge parameters
66
Chapter 7
Discussion of Results
7.1 Analysis of the Numerical Simulations
Taking into account the assumptions and approximations done for the boundary conditions and
material properties, it is clear that very good results in terms of temperature values can be obtained
using a finite element analysis specially for steady state.
Looking to the results of the simulation of the holder without cooling for condition I we can
observe that the holder reaches steady state after approx. 150s and the maximum temperature is
about 1070K. Considering that the time for steady state observed in the experiment was around 1min
and the temperature recorded was 1200K we can see that the numerical results are not in perfect
agreement with the experiment. Anyway, for steady state, the temperature relative error is 11%,
which is acceptable for this preliminary analysis.
The same doesn’t happen for condition II were the values are much more close to the experimental
values: time for steady state around 50s and temperature with a relative error of 0.7%. Specially for
steady state conditions, the approximation seems to give better results for higher heat flux.
For the simulation with cooling a comparison was done between the steady state results from
ANSYS™ and the results from heat1D. The values taken from the 2D simulation are from the sym-
metry axis. The results can be found in tables 7.1 and 7.2 and one can conclude that there is a good
agreement between the two methods, despite the fact that in the ANSYS™ simulations the materials
are non linear and, surfaces exchange heat through radiation with an enclosure at 400K instead of
deep space (0K) in heat1D and the convection coefficient is fixed.
67
68 Results Discussion
Condition I Condition II
Outer wall Inner wall Outer wall Inner wall
ANSYS™ 363.8 363.4 464 460.2heat1D 367.9 362.2 501.6 454.1
Rel. Error [%] 1.13 0.32 8.11 1.33
a Values adimensionalized by the result of ANSYS
Table 7.1: Temperature results in the setup without insulation - ANSYS vs. heat1D
Condition I Condition II
Outer wall Interface Inner wall Outer wall Interface Inner wall
ANSYS™ 913.3 912.5 356.8 1832.2 1818.6 378.6heat1D 906 902.3 358 1880 1870 372
Rel. Error [%] 0.8 1.12 0.33 2.61 2.82 1.75
a Values adimensionalized by the result of ANSYS
Table 7.2: Temperature results in the setup with insulation - ANSYS vs. heat1D
7.2 Analysis of the Oxidation Campaign
7.2.1 Sensitivity Analysis
To access the reliability of the method, a sensitivity analysis was done in the catalycity determination
process. That was done by calculating the HF Abacus using three different sources for the gas reaction
constants: Dunn & Kang [55], Gupta et al. [65] and Park [66]1.
Two tests were selected (Test 1 and Test 28) and the results are presented in figures 7.1 and
7.2. One can notice that, for the temperatures and HF, the differences in the catalycity results are
negligible.
7.2.2 Flight Extrapolation
Using the LHTS methodology (see section 3.2), it is possible to extrapolate the tests done in the
Plasmatron to actual flight conditions. In figure 7.3 one can see the trajectory of the IXV vehicle and
the reconstructed tests. The IXV trajectory was obtained from [7, 67]. It appears that the vehicle
starts in an active oxidation region and than evolves to an passive region but that’s only an illusion.
In fact, in the experiments we simulate a steady-state condition, what would be equivalent to a
cruise condition at the same speed and altitude. A reentry manoeuvre is typically a transient condition
and as we can see in figure 2.2 the temperature in the surface starts by being relatively low due to the
fact that the spacecraft comes from the “outer space”. Afterwords, during the surface warming up, the
pressure is also increasing keeping the vehicle in a passive oxidation regime. After critical conditions
being achieve, it goes into an active oxidation region and finally, with the increasing pressure, back
to passive again.
1The BL edge condition were rebuilt using always the Dunn & Kang reaction constants.
Results Discussion 69
300 550 800 1050 1300 1550 1800 2050 2300 2550 28000
125
250
375
500
625
750
875
1000
1125
1250
1375
1500
Temperature [K]
Wal
l Hea
t Flu
x [k
W m
−2 ]
γ = 1
γ = 0.1
γ = 0.05
γ = 0.03
γ = 0.02
γ = 0.01
γ = 0.005
γ = 0
Dunn & KangGupta et al.ParkReference (Cu)Experiment
Figure 7.1: Abacus from Test 1
300 550 800 1050 1300 1550 1800 2050 2300 2550 28000
125
250
375
500
625
750
875
1000
1125
1250
1375
1500
Temperature [K]
Wal
l Hea
t Flu
x [k
W m
−2 ]
γ = 1
γ = 0.1
γ = 0.05
γ = 0.03
γ = 0.02
γ = 0.01
γ = 0.005
γ = 0
Dunn & KangGupta et al.ParkReference (Cu)Experiment
Figure 7.2: Abacus from Test 28
70 Results Discussion
Variation in qloss qloss [kW m−2] γ γ Rel. Error [%]
-50% 21.9 0.01562 40.40% 43.7 0.02621 -
+10% 48.1 0.02877 9.8+50% 65.6 0.04109 56.8+100% 87.4 0.06349 142.3
Table 7.3: Sensitivity Analysis for Test T1
Besides, one should take into attention that the BL edge velocity gradient is not the same that in
the IXV flight condition as it can be seen in figure 7.4, so some of the tests correspond to a vehicle
with a different effective nose radius. The effective nose radius can be calculated using equation 3.8.
One should also note that the tests simulate better the IXV case for the higher pressures. In [7],
Panerai showed that the EQ geometry is better for IXV simulations at low pressure.
Future work should be directed into the development of “transient flight extrapolation” capabilities
for the Plasmatron.
7.3 Analysis of the Temperature Campaign
In this section, some considerations on the boundary layer of the samples tested in this campaign will
be made.
First, lets look into the species present at the BL edge (figure 7.5). One can observe that almost
all the O2 is dissociated and also that small quantities of atomic N appear, specially for low pressures.
Looking now to the differences between the temperature profiles in the BL (figure 7.6), one can
notice that the difference in the shape of the curves is small near the wall, despite the difference in
the wall temperature. This only results in a tiny increase in the qcond term (figure 7.7).
In figure 7.7, one can also see that the behaviour predicted in section 3.8.1 was correct: Cooling
the sample (reducing Tw) conducts to an increase in the qcond term but also to a major decrease in
the qdiff term, due to catalycity decrease, which results in a global reduction of q«w.
7.3.1 Sensitivity Analysis
A sensitivity analysis on the catalycity rebuilding process was done considering that errors on qlossmeasurement and correction can occur. Experiment T1 was selected for the sensitivity study and the
results are presented in table 7.3. One should note that even if the qloss term had been underestimated
by half of its value, the value of γ would still be lower than the value measured in the RS.
A complete UQ of the experiments was impossible in practical time because of the complexity
of the software DAKOTA+CERBOULA [7] together with the need of modifications to accommodate
the latest version of the CERBOULA code developed in the context of this work. Nevertheless the
author consider that it is a mandatory step in future work.
Results Discussion 71
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
30
40
50
60
70
80
90
100
110
120
Flight Velocity [m/s]
Alti
tude
[km
]
IXV trajectoryTests − Passive Ox.Tests − Active Ox.Tests − Temp. JumpMach = 15Mach = 20Mach = 25
5500 6000 6500 7000 7500 800065
66
67
68
69
70
71
72
73
74
75
76
Flight Velocity [m/s]
Alti
tude
[km
]
IXV trajectoryTests − Passive Ox.Tests − Active Ox.Tests − Temp. Jump
Figure 7.3: Extrapolated Fight Conditions - Oxidation Campaign
72 Results Discussion
0 5 10 15 20 25 300
2000
4000
6000
8000
10000
12000
BL Edge Enthalpy [kJ/kg]
BL
Edg
e V
eloc
ity G
radi
ent [
s−1 ]
IXVTests − p
s = 2000
Tests − ps = 5000
Tests − ps = 6000
Figure 7.4: Extrapolated Velocity Gradient - Oxidation Campaign
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
T1
T2
T3
Mass Fractions at the BL Edge
O
2
N2
NO
NO+
ON
e−
Figure 7.5: Mass Fractions at the BL Edge
Results Discussion 73
y-coordinate [m]
Tem
pera
ture
[K]
0 0.002 0.004 0.006 0.008 0.010
500
1000
1500
2000
2500
3000
3500
4000
4500
Temp. - CSTemp. - RS
Figure 7.6: Temperature Evolution Inside the Boundary Layer - Test T1
T1cs T1rs T2cs T2rs T3cs T3rs0
50
100
150
200
250
300
Wal
l Hea
t Flu
x [k
W m
−2 ]
q
cond
qdiff
Figure 7.7: Heat Flux to the Wall
74 Results Discussion
Velocity [m/s] Mach Altitude [km] Static Pressure [Pa] Static Temperature [K] Effective Nose Radius [m]
4331 14.6 69.8 4.8 218 0.294341 13.9 60.6 18.6 244 0.934161 12.8 54.4 43.3 261 2.08
Table 7.4: Extrapolated Flight Conditions
0 1000 2000 3000 4000 5000 6000 7000 8000
30
40
50
60
70
80
90
100
110
120
Flight Velocity [m/s]
Alti
tude
[km
]
IXV trajectoryT1T2T3Mach = 13Mach = 14Mach = 15
Figure 7.8: Extrapolated Flight Conditions
7.3.2 Flight Extrapolation
In figure 7.8 and table 7.4 one can see the reconstructed flight conditions and the values of the
effective nose radius of an hypothetical cruise vehicle which nose stagnation point would be subjected
to the same aerothermodynamic environment as the tested samples.
7.4 Stagnation Point ATDB Algorithm
The ultimate target of TPS testing is to help the decision process and dimensioning of the TPS to
be installed in future space missions.
Nowadays, very old and conservative formulas to estimate the heat transfer to the wall are still in
use (see section 2.1.2). This happens because design engineers like to have very simple formulas in
order to introduce them in the fast optimization loops used during the preliminary-design phase of a
project. The objective is always to know the heat flux from the plasma to the wall and it’s known
that it depends on 4 parameters: He,pe,βe,Tw besides surface material and gas mixture. In fact, for
a given material and gas mixture the HF dependencies can be summarized in the following formulas.
Results Discussion 75
q«w = q©w (7.1)
q«w = f(He, pe, βe, Tw) (7.2)
q©w = f (Tw,(−λ∂T
∂y)w,sol
, ε(Tw)) (7.3)
In equation 7.2 we can also include the term γ = f(Tw, ...) but it is a characteristic of the material
Using the current setup in the Plasmatron, it is possible to make complete reconstruction of
stagnation point boundary layer of a body immersed in an hypersonic flow. Then, knowing the
conditions in the boundary layer edge, it is possible to obtain all the other relevant properties.
One should remember that the cooled setup allows to define the surface temperature and also that
catalycity depends on wall temperature.
With all this in mind, the correct way to construct a steady-state ATDB seems to be the one
presented in the figures 7.9 and 7.10. For each flight condition, should be done a set of tests to access
different velocity gradients (it varies with nose radius and flight conditions). For radiative equilibrium
TPS types this is enough and the wall temperature is also a result but for active-passive or active
TPS types (see section 1.2), additional tests for several wall temperatures must be conducted.
All the information can then be stored in tables and allow a fast and easy method to know heat
flux or catalycity to be implemented in future design or CFD codes.
In the figures, the thick boxes represent the inputs for the ATDB and the thick dashed boxes the
results from the ATDB.
76 Results Discussion
Figure 7.9: Flowchart for ATDB Algorithms - Hot or Insulated Structure TPS
Figure 7.10: Flowchart for ATDB and Algorithms - Generic TPS
Chapter 8
Conclusions and Future Work
8.1 Conclusions
In this work, the Passive-to-Active oxidation transition of C/SiC TPM in Earth’s reentry aerothermo-
chemical environment was determined by experimental methods and the results are in good agreement
with the data available in literature. Also it was proved that the temperature jump phenomena can’t
be considered a indicator of the PA transition.
Also the method used to estimate the heat flux to cooled walls presented in section 3.8.1 and
its applicability to 2D thermal simulations, without direct fluid simulation, proved to be a valuable
method for quick estimation of heat transfer rates for Plasmatron equipment or even for reentry
spacecraft design whenever data for the TPM in radiative equilibrium conditions is available.
A new method for TPS testing was developed, allowing now the tests of Convective Cooling,
Heat Pipe and Heat Sink Structure TPS in the VKI’s Plasmatron. This new method also allows
the correctly study of the wall temperature effect on catalycity for fixed flight conditions. With this
method it was discovered that both catalicity and heat flux to the wall decrease by decreasing the
surface temperature. It was also discovered that γ is more sensible to variations in Tw for (low pe,
high βe) values and that the sensitivity of the heat flux to variations on Tw seems to independent of
(pe,βe).
Efficient computational methods for construction and use of stagnation point aerothermodynamic
databases are also presented.
8.2 Recommendations for Future Work
Further theoretical investigations must be done to understand better the temperature jump phenom-
ena and it’s causes. Introduction of more chemical reactions and models is also important, specially
in the boundary layer code (NEBOULA).
77
78 Conclusions
A redesign of the sample holders is mandatory to decrease the errors associated with the lateral
heat flux in the cooled sample configuration. Expanding the Temperature Campaign to different
velocity gradients by using the frozen and equilibrium holders in a cooled sample configuration could
be also an important improvement.
Also, further improvements are necessary to correctly simulate reentry conditions in terms of
velocity gradient and transient effects. New probes are necessary to achieve a time continuous
complete simulation of TPS in the Plasmatron.
Careful radiation analysis are also important for future work. Inside the test chamber the sample
faces the torch gas which irradiates large amounts of energy because of it’s high temperature. This
doesn’t happen in flight so must be taken into account during the calculation of the experimental
heat flux. Maps for the incoming radiation could maybe be constructed using the radiation transport
capabilities of the ICP code.
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Appendix A
Figure A.1: Temperature Field - Section 4.1.1 - Condition I
85
86 Temperature Fields
Figure A.2: Temperature Field - Section 4.1.1 - Condition II
Figure A.3: Temperature Field - Section 4.1.2 - Condition I
Numerical Simulations 87
Figure A.4: Temperature Field - Section 4.1.2 - Condition II
Figure A.5: Temperature Field - Section 4.1.3 - Condition I
88 Temperature Fields
Figure A.6: Temperature Field - Section 4.1.3 - Condition II
Appendix B
Figure B.1: Temperature vs. Time - Section 4.1.1 - Condition I
89
Figure B.2: Temperature vs. Time - Section 4.1.1 - Condition II
Figure B.3: Temperature vs. Time - Section 4.1.2 - Condition I
90
Figure B.4: Temperature vs. Time - Section 4.1.2 - Condition II
Figure B.5: Temperature vs. Time - Section 4.1.3 - Condition I
91
Figure B.6: Temperature vs. Time - Section 4.1.3 - Condition II
92
App
endi
xC
93
Test
NDP1
NDP2
NDP3
NDP4
NDP5
Te
pe
µe
[O2]
[N2]
[NO]
[NO+]
[O]
[N]
[e–]
hw
Vs
γref
KPa
kgs−
1m−1
×1010
Jkg−1
ms−
1
16
0.3826
0.3229
0.6043
0.3364
0.4363
5556
2000
0.000173
1.34E-05
4.46E-01
1.48E-03
3.69E-04
2.32E-01
3.20E-01
67
4.37E+06
587
0.1
15
0.3828
0.3259
0.6091
0.3400
0.4368
5534
2000
0.000173
1.41E-05
4.57E-01
1.53E-03
3.57E-04
2.32E-01
3.09E-01
65
3.88E+06
578
0.1
17
0.3847
0.3431
0.6366
0.3609
0.4398
5631
2000
0.000175
1.12E-05
4.09E-01
1.33E-03
4.09E-04
2.32E-01
3.58E-01
75
4.35E+06
618
0.1
40.3925
0.3927
0.7155
0.4222
0.4500
5739
2000
0.000177
8.77E-06
3.54E-01
1.14E-03
4.71E-04
2.32E-01
4.13E-01
86
4.12E+06
661
0.1
10.3931
0.3962
0.7211
0.4266
0.4507
5802
2000
0.000178
7.64E-06
3.21E-01
1.03E-03
5.09E-04
2.32E-01
4.45E-01
93
4.86E+06
689
0.1
70.3928
0.3945
0.7183
0.4244
0.4503
5824
2000
0.000178
7.29E-06
3.11E-01
9.97E-04
5.22E-04
2.32E-01
4.56E-01
95
3.89E+06
696
0.1
50.3698
0.3138
0.6027
0.3213
0.4389
5826
5000
0.000180
1.96E-05
4.37E-01
1.94E-03
4.44E-04
2.32E-01
3.29E-01
81
4.67E+06
264
0.1
20.3704
0.3279
0.6259
0.3375
0.4409
5857
5000
0.000180
1.83E-05
4.22E-01
1.86E-03
4.62E-04
2.32E-01
3.44E-01
84
4.63E+06
270
0.1
80.3712
0.3380
0.6425
0.3493
0.4425
5920
5000
0.000182
1.61E-05
3.93E-01
1.71E-03
4.99E-04
2.32E-01
3.73E-01
91
4.63E+06
281
0.1
90.3730
0.3569
0.6733
0.3716
0.4458
6004
5000
0.000183
1.35E-05
3.53E-01
1.53E-03
5.52E-04
2.32E-01
4.13E-01
101
5.03E+06
296
0.1
10
0.3793
0.4056
0.7520
0.4301
0.4550
6011
5000
0.000183
1.33E-05
3.50E-01
1.51E-03
5.56E-04
2.32E-01
4.16E-01
102
3.76E+06
298
0.1
11
0.3865
0.4523
0.8272
0.4868
0.4643
6077
5000
0.000184
1.17E-05
3.20E-01
1.38E-03
5.99E-04
2.32E-01
4.47E-01
110
4.12E+06
309
0.1
13
0.4014
0.5385
0.9652
0.5924
0.4823
6130
5000
0.000185
1.05E-05
2.95E-01
1.28E-03
6.33E-04
2.32E-01
4.71E-01
116
4.34E+06
322
0.1
30.3679
0.3508
0.6700
0.3635
0.4455
5963
6000
0.000183
1.79E-05
3.98E-01
1.84E-03
5.09E-04
2.32E-01
3.68E-01
93
3.72E+06
237
0.1
60.3675
0.3461
0.6624
0.3580
0.4447
5985
6000
0.000183
1.71E-05
3.88E-01
1.79E-03
5.22E-04
2.32E-01
3.78E-01
96
5.52E+06
240
0.1
18
0.3681
0.3524
0.6726
0.3653
0.4457
6024
6000
0.000184
1.58E-05
3.70E-01
1.70E-03
5.47E-04
2.32E-01
3.96E-01
100
5.51E+06
246
0.1
19
0.3732
0.3977
0.7464
0.4192
0.4539
6109
6000
0.000185
1.33E-05
3.31E-01
1.51E-03
6.01E-04
2.32E-01
4.35E-01
110
4.70E+06
259
0.1
Tab
leC.1:NDPsan
dRebuiltQua
ntities-Oxida
tion
Cam
paign(H
ER)
94
Test
NDP1
NDP2
NDP3
NDP4
NDP5
Te
pe
µe
[O2]
[N2]
[NO]
[NO+]
[O]
[N]
[e–]
hw
Vs
γref
KPa
kgs−
1m−1
×1010
Jkg−1
ms−
1
20
0.3825
0.3202
0.5998
0.3331
0.4358
5499
2000
0.000172
1.53E-05
4.74E-01
1.60E-03
3.40E-04
2.32E-01
2.93E-01
62
3.17E+06
564
0.1
22
0.3843
0.3398
0.6314
0.3569
0.4392
5655
2000
0.000175
1.06E-05
3.97E-01
1.29E-03
4.23E-04
2.32E-01
3.69E-01
77
4.53E+06
625
0.1
21
0.3880
0.3659
0.6730
0.3890
0.4444
5722
2000
0.000177
9.11E-06
3.62E-01
1.16E-03
4.61E-04
2.32E-01
4.04E-01
84
4.62E+06
655
0.1
30
0.3991
0.4287
0.7726
0.4670
0.4577
5755
2000
0.000177
8.46E-06
3.45E-01
1.11E-03
4.81E-04
2.32E-01
4.21E-01
88
4.23E+06
670
0.1
23
0.3699
0.3050
0.5881
0.3114
0.4378
5838
5000
0.000180
1.91E-05
4.31E-01
1.91E-03
4.51E-04
2.32E-01
3.35E-01
83
4.96E+06
267
0.1
24
0.3712
0.3380
0.6425
0.3493
0.4425
5998
5000
0.000183
1.37E-05
3.56E-01
1.54E-03
5.48E-04
2.32E-01
4.10E-01
100
5.25E+06
295
0.1
25
0.3850
0.4428
0.8119
0.4753
0.4624
6140
5000
0.000185
1.03E-05
2.91E-01
1.26E-03
6.40E-04
2.32E-01
4.75E-01
117
4.60E+06
321
0.1
31
0.3704
0.3279
0.6259
0.3375
0.4409
6003
5000
0.000183
1.35E-05
3.54E-01
1.53E-03
5.51E-04
2.32E-01
4.12E-01
101
4.29E+06
296
0.1
26
0.3727
0.3937
0.7399
0.4143
0.4532
6030
6000
0.000184
1.56E-05
3.67E-01
1.69E-03
5.50E-04
2.32E-01
3.99E-01
101
4.32E+06
246
0.1
28
0.3848
0.4771
0.8745
0.5148
0.4694
6097
6000
0.000185
1.37E-05
3.36E-01
1.54E-03
5.94E-04
2.32E-01
4.30E-01
109
4.30E+06
259
0.1
32
0.3713
0.3820
0.7209
0.4004
0.4510
6025
6000
0.000184
1.58E-05
3.69E-01
1.70E-03
5.48E-04
2.32E-01
3.97E-01
100
3.20E+06
246
0.1
Tab
leC.2:NDPsan
dRebuiltQua
ntities-Oxida
tion
Cam
paign(M
TA)
Test
NDP1
NDP2
NDP3
NDP4
NDP5
Te
pe
µe
[O2]
[N2]
[NO]
[NO+]
[O]
[N]
[e–]
hw
Vs
γref
KPa
kgs−
1m−1
×1010
Jkg−1
ms−
1
T1-C
S0.4177
0.3930
0.7115
0.4309
0.4541
4223
1440
0.000139
4.12E-04
7.49E-01
5.83E-03
2.60E-05
2.29E-01
1.54E-02
52.08E+06
418
0.10
T1-R
S0.4177
0.3930
0.7115
0.4309
0.4541
4223
1440
0.000139
4.12E-04
7.49E-01
5.83E-03
2.60E-05
2.29E-01
1.54E-02
51.17E+06
418
0.10
S6[7]
0.4385
0.4521
0.8026
0.5083
0.4766
4440
1300
0.000145
1.80E-04
7.33E-01
4.32E-03
4.68E-05
2.30E-01
3.18E-02
93.59E+06
429
0.10
T2-C
S0.4125
0.3763
0.6850
0.4095
0.4496
4354
5000
0.000142
9.04E-04
7.50E-01
9.33E-03
2.67E-05
2.27E-01
1.25E-02
52.32E+06
131
0.10
T2-R
S0.4125
0.3763
0.6850
0.4095
0.4496
4354
5000
0.000142
9.04E-04
7.50E-01
9.33E-03
2.67E-05
2.27E-01
1.25E-02
51.34E+06
131
0.10
S10[7]
0.4123
0.3510
0.6491
0.3872
0.4641
4485
5000
0.000146
5.96E-04
7.45E-01
8.11E-03
3.72E-05
2.28E-01
1.85E-02
73.15E+06
125
0.10
T3-C
S0.3968
0.2829
0.5692
0.3228
0.4613
4085
10000
0.000135
4.37E-03
7.55E-01
1.75E-02
1.06E-05
2.19E-01
3.65E-03
21.76E+06
58
0.01
T3-R
S0.3968
0.2829
0.5692
0.3228
0.4613
4085
10000
0.000135
4.37E-03
7.55E-01
1.75E-02
1.06E-05
2.19E-01
3.64E-03
21.10E+06
58
0.01
C2a[7]
0.4001
0.2884
0.5770
0.3311
0.4636
4306
10000
0.000141
2.07E-03
7.53E-01
1.37E-02
1.97E-05
2.24E-01
7.61E-03
48.18E+05
57
0.01
Tab
leC.3:NDPsan
dRebuiltQua
ntities-Tem
perature
Cam
paign
95