REPORT - Investigation of GSI in PWT for Catalycity Characterization

von Karman Institute for Fluid Dynamics

Chaussee de Waterloo, 72B - 1640 Rhode Saint Genese - Belgium

Research Master Report

Investigation of Gas Surface Interactions inPlasma Wind Tunnels for Catalycity

Characterization

Guerric de CROMBRUGGHE

Supervisor: Pr. Olivier CHAZOTAdvisor: Dr. Francesco PANERAI

June 2012

Acknowledgments

The author would like to thank Pr. Olivier Chazot for all the time he spent in guidanceand explanations, Pascal Collin for his support and patience during the - very long - testcampaign, Dr. Francesco Panerai for his wise advices and comments on this report, IsilSakraker for her help, and all the plasma team for their availability.

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Abstract

Controlled super-orbital re-entry is a key for future exploration missions of the solarsystem. However, the free-stream enthalpies involved with the flow encountered are soimportant that flight duplication is not feasible anymore in ground testing facilities. Thisrequires a new approach of ground testing: facilities should be used to understand andmodel the physics of the flow, rather than to qualify and size designs.

The present study focuses on one of the issues that are still poorly understand: gas-surface interaction (GSI). The ultimate objective is to provide a sound foundation foran accurate model of wall catalycity.

To achieve that goal, two test campaigns were performed in the von Karman Insti-tute’s main plasma wind tunnel, the Plasmatron. Information was retrieved regardingthe wall catalycity and heat flux for various conditions of static pressure, free-stream spe-cific enthalpy, wall material (test 1: minimax) and probe geometry (test 2: Damkohlerprobes), while keeping the wall temperature constant.

Based on those experimental measurements, and with some additional numericalpost-processing, the evolution the Damkohler numbers and catalycity is determined infunction of the local heat transfer simulation (LHTS) parameters. The analysis is onlyperformed for nitrogen and oxygen given that, as experimental evidences tend to showthat their production is prevailing on that of other species. As a general conclusion, itwas found that both gas-phase and the wall Damkohler numbers decrease for increasingouter edge enthalpy, velocity gradient, and decreasing pressure. The opposite behaviouris observed for catalycity, although for the behaviour of the later with respect to outeredge enthalpy is less obvious at low pressure.

Indications are given on how to pursue those investigations towards a model ofcatalycity. Additional comments are made on the reference catalycity of sample testingin the Plasmatron and the correct use of chemistry models.

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Contents

Abstract iii

Acknowledgment v

List of Figures ix

List of Tables xiii

List of Symbols xv

1 Ground testing strategy for super-orbital re-entry 3

1.1 Super-orbital atmospheric re-entry . . . . . . . . . . . . . . . . . . . . . . 3

1.1.1 Orbital mechanics considerations . . . . . . . . . . . . . . . . . . . 3

1.1.2 Orders of magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Issues for experimentation on high velocity flows . . . . . . . . . . . . . . 5

1.2.1 Aerothermodynamic facilities . . . . . . . . . . . . . . . . . . . . . 5

1.2.2 Radiative heating and ablation . . . . . . . . . . . . . . . . . . . . 6

1.2.3 Gas-surface interactions . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 New testing strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 High temperature gas dynamics applied to atmospheric re-entry 9

2.1 Stagnation line features . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Brief overview of gas-surface interactions . . . . . . . . . . . . . . . . . . . 11

2.2.1 Chemistry constants . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.2 Diffusion coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.3 Damkohler numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.4 Catalycity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3 Closing remark on catalycity modelling . . . . . . . . . . . . . . . . . . . 17

3 Test campaign and results 19

3.1 Heat flux measurement in the Plasmatron . . . . . . . . . . . . . . . . . . 19

3.1.1 Heat flux and dynamic pressure measurement . . . . . . . . . . . . 21

3.1.2 Pre-processing numerical tools . . . . . . . . . . . . . . . . . . . . 21

3.2 Minimax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

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viii Table of contents

3.2.1 Low pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2.2 High pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2.3 Medium pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.4 Reference catalycity . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3 Damkohler probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3.1 Frozen probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.3.2 Equilibrium probe . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.4 Uncertainty quantification . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4 Gas-surface interaction analysis for catalycity modelling 354.1 Catalycity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2 Wall Damkohler number . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.3 Gas-phase Damkohler number . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.3.1 Time-scale characteristic of the flow . . . . . . . . . . . . . . . . . 374.3.2 Time-scale characteristic of the homogeneous chemistry . . . . . . 384.3.3 Non-catalytic wall . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.3.4 From non-catalytic to catalytic wall . . . . . . . . . . . . . . . . . 40

4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

A Annex A 49

B Annex B 51

C Annex C 53

References 55

List of Figures

1 Artistic impression of the Apollo CommandModule re-entering the Earth’satmosphere. Up to now, it is the fastest manned re-entry vehicle ever con-ceived. Credits: NASA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Interplanetary Hohmann transfer. . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Proposed procedure for high enthalpy atmospheric entries. . . . . . . . . . 8

2.1 Flow features around the stagnation line of a hypersonic body. . . . . . . 10

2.2 Kc for the recombination of atomic nitrogen into dinitrogen as a functionof gas temperature, according to Dunn and Kang’s chemistry model. Itis represented for a mixture in thermal equilibrium at a specific enthalpyH = 36.24 MJ/kg, and for a mixture where all the species are recombined. 13

2.3 Diffusion coefficient D for atomic nitrogen (a) and oxygen (b) as a func-tion of T and ps. Each curve is represented for a mixture in thermalequilibrium at a specific enthalpy H = 36.24 MJ/kg, and for a mixturewhere all the species are recombined. . . . . . . . . . . . . . . . . . . . . . 15

3.1 Schematic overview of the LHTS method: the flow is duplicated in theboundary layer around the stagnation line (see figure 2.1) as long as He,pe and βe are reproduced. . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2 Enthalpy S-curve, linking the outerHe with γ, in logarithmic scale. Figurerealized for the reference probe at ps = 1, 500 Pa and Qref

w = 875 kW/m2. 20

3.3 Recorded heat flux over time for the reference probe at ps = 1500 Pa. . . 22

3.4 Test campaign: minimax. . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.5 The minimax methodology: the three S-curves define an interval for He,and thereby also for γCu. This figure is the complement of figure 3.2. . . . 23

3.6 He (a) and γ, in logarithmic scale, (b) intervals as defined during differentminimax test campaigns for ps = 1, 500 Pa. Each dataset consists out oftwo curves that are the upper and lower limits of the intervals. The ”dataused” set is the one used in chapter 4. Krassilchikoff’s results are basedon molybdenum rather than quartz as lower catalycist. . . . . . . . . . . . 24

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x Table of contents

3.7 The methodology applied for figure 3.5 is not valid anymore for higherpressure: there are no common values of the outer edge enthalpy for thethree probes. This figure was realized at ps = 10, 000 Pa and Qref

w = 861kW/m2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.8 Figure 3.7 is here reproduced for three different chemistry models. Thisfigure was realized at ps = 10, 000 Pa and Qref

w = 861 kW/m2. . . . . . . . 26

3.9 He (a) and γ, in logarithmic scale, (b) intervals, in logarithmic scale, (b)as defined with different methodologies for ps = 10, 000 Pa. Each datasetconsists out of two curves that are the upper and lower limits of theintervals. The ”data used” set is the one used in chapter 4. Krassilchikoff’sresults are based on molybdenum rather than quartz as lower catalycist,and post-processing using Dunn and Kang’s model. . . . . . . . . . . . . . 27

3.10 He (a) and γ, in logarithmic scale, (b) intervals as defined with differentmethodologies for ps = 5, 000 Pa. Each dataset consists out of two curvesthat are the upper and lower limits of the intervals. Krassilchikoff’s resultsare based on molybdenum rather than quartz as lower catalycist, andpost-processing using Dunn and Kang’s model. . . . . . . . . . . . . . . . 28

3.11 Logarithmic average of γCu as defined by the intervals obtained with theminimax methodology, in logarithmic scale, and corresponding He fordifferent ps. The error bars represent the limits of the intervals definedby the minimax. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.12 Test campaign: Damkohler probes. Picture (b) was taken after the tests,from left to right: equilibrium, reference, and frozen probes. The damagedone on the equilibrium probe is clearly visible. . . . . . . . . . . . . . . . 30

3.13 Qfrw with respect to Qref

w at ps = 1, 500 Pa (a), and 10, 000 Pa (b). . . . . 32

3.14 Qeqw with respect to Qref

w at ps = 1, 500 Pa. . . . . . . . . . . . . . . . . . . 32

4.1 Evolution γ, in logarithmic scale, for the equilibrium and frozen probeswith respect to He at ps = 1, 500 Pa (a) and ps = 10, 000 Pa (b). . . . . . 36

4.2 Evolution vdiff of nitrogen and oxygen for the equilibrium and the frozenprobes with respect to He at ps = 1, 500 Pa (a) and ps = 10, 000 Pa (b). . 37

4.3 Evolution of the inverse of the βe with respect to He at ps = 1, 500 Pa(a) and ps = 10, 000 Pa (b). . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.4 Reaction equilibrium constant for N and O into N2 (a,c) and O2 (b,d)respectively within the boundary layer of the equilibrium probe (a,b) andthe frozen probe (c,d) for different He, according to the chemistry modelof Dunn and Kang, at ps = 1, 500 Pa. . . . . . . . . . . . . . . . . . . . . 39

4.5 Concentration of N2 (a,c) and O2, in logarithmic scale, (b,d) at the walland in the free-stream, for a catalytic wall γ, a non-catalytic wall γ = 0,and a fully catalytic wall γ = 1, both for the frozen and the equilibriumprobe, at ps = 1, 500 Pa (a,b) and ps = 10, 000 Pa (c,d). . . . . . . . . . . 40

Table of contents xi

4.6 Molar concentration x of N2 (a) and O2, in logarithmic scale, (b) withinthe boundary layer of the equilibrium probe for different He at ps = 1, 500Pa. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.7 Temperature distribution within the boundary layer of the equilibriumprobe for different He at ps = 1, 500 Pa. . . . . . . . . . . . . . . . . . . . 41

4.8 Diffusion coefficient of atomic nitrogen (a) and oxygen (b) within theboundary layer of the equilibrium probe for different He, at ps = 1, 500 Pa. 42

C.1 Reaction equilibrium constant for N and O into N2 (a,c) and O2 (b,d)respectively within the boundary layer of the equilibrium probe (a,b) andthe frozen probe (c,d) for different He, according to the chemistry modelof Gupta, at ps = 10, 000 Pa. . . . . . . . . . . . . . . . . . . . . . . . . . 53

C.2 Diffusion coefficient of atomic nitrogen N (a,c) and oxygen O (b,d) withinthe boundary layer of the equilibrium probe (a,b) and the frozen probe(c,d) for different He, at ps = 10, 000 Pa. . . . . . . . . . . . . . . . . . . 54

List of Tables

3.1 Values retained for γref and He versus Qrefw as used for chapter 4. . . . . . 27

3.2 Geometrical characteristics of the Damkohler probes. . . . . . . . . . . . . 303.3 Regressions tested on the data points obtained for 1, 500 Pa. . . . . . . . 31

4.1 Summary of the observations made on the qualitative evolution of Dag,Daw and γ as a function of the LHTS parameters He, βe and ps on a coldwall. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

A.1 Dunn and Kang’s model for nitrogen and oxygen chemistry, based on [23].The subscript f refers to the forward reaction, and b to the backwardsreaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

B.1 Test conditions for the minimax campaign. . . . . . . . . . . . . . . . . . 51B.2 Test conditions for the Damkohler probes campaign. . . . . . . . . . . . . 52

xiii

List of Symbols

Acronyms

ASTV Aeroassisted Space Transfer VehiclesCFD Computational Fluid DynamicsCERBERE Catalycity and Enthalpy ReBuilding for a REference probeESA European Space AgencyGSI Gas-Surface InteractionICP Inductively Coupled PlasmaIPM Institute for Problems in MechanicsLEO Low Earth OrbitLHTS Local Heat Transfer SimulationNDP Non-Dimensional ParametersNEBOULA NonEquilibrium BOUndary LAyerPWT Plasma Wind TunnelTPM Thermal Protection MaterialTPS Thermal Protection SystemVKI von Karman Institute for Fluid Dynamics

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xvi List of Symbols

Roman symbols

A area m2

cp specific heat at constant pressure J/kg ·KDa Damkohler number -E energy JG gravitional constant 6.674E − 11 m3/kg · s2H total enthalpy MJ/kgK chemical equilibrium constant −k chemical rate constant depends on order of reactionkB Botlzmann’s constant 1.381E − 23 m2 · kg/s2 ·Kk0 frequency factor −L length mM number flux or third party chemical species −m mass kgNA Avogadro’s number 6.022E + 23 /molP power Wp pressure PaQ heat flux W/m2

R gas constant 8.315 J/mol ·Kr radius mRe Reynolds number −Rx molar concentration ratio −T temperature Ku tangential velocity m/sv streamwise velocity m/sw mass production term kg/m3 · sx chemical species molar fraction −

or tangential direction −

Greek symbols

β energy accomodation coefficient −or velocity gradient /s

∆ increment −δ boundary layer thickness mmγ catalycity −µ viscosity kg/m · sπ pi 3.14159265ρ density kg/m3

τ time s

List of Symbols xvii

Sub- and Superscripts

↑ backward diffusing↓ forward diffusinga activationb related to the body of a probe or backwardsbody related to the celestial bodyc related to the corner of a probe or concentrationdyn dynamice outer edge / free-streameq equilibriumf related to the flow or forwardfr frozeng related to the gas phasehete heterogenoushomo homogenousi related to the species iref references staticw related to the wall

Introduction

Scope

Since the very beginning of the space age, atmospheric re-entry has been considered asan important area of study. It is a key to further developments in space exploration,whether it concerns the safe return of astronauts or payload on Earth or the landing ofrobots on Mars, Venus, or even Titan.

Although it remains a complicated field of engineering, all the tools needed for thedesign of controlled re-entry vehicles are nowadays available. One only needs to look atthe recent success of Space-X to convince him-self. That private company managed todevelop its own manned re-entry capsule, the Dragon, that successfully landed for thesecond time on the 31st of May 2012, in less than 10 years.

The challenging manoeuvres for which additional tools need to be developed areuncontrolled re-entry, and super-orbital re-entry. The first one is necessary to improvethe prediction of where and when space debris are going to crash on the Earth. Thesecond one is needed for future exploration missions of the solar system, manned orrobotic, and in particular for sample return missions.

Figure 1: Artistic impression of the Apollo Command Module re-entering the Earth’satmosphere. Up to now, it is the fastest manned re-entry vehicle ever conceived. Credits:NASA

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2 Introduction

Objective

The present project focuses on a fluid dynamic issue associated with the second chal-lenge. One of the main limitations of super-orbital re-entry vehicles is the poor under-standing of the chemistry processes taking place in the boundary layer. This often leadsto an over-estimation of the heat flux to withstand, and thereby an over-sizing of thethermal protection system (TPS), leaving only little volume and mass for the actualpayload.

Within that scope, the objective of this project is to investigate the driving processesof gas-surface interactions (GSI) over a cold wall, and to provide a sound foundation foran accurate model of wall catalycity. Those investigations are based on experimentationsperformed in the Plasmatron, a Plasma Wind Tunnel, and numerical rebuilding of theboundary layer. This report presents the steps that led to the achievement of thatobjective.

The first chapter is devoted to the larger frame in which the project is contained:super-orbital re-entry. What is exactly meant with super-orbital re-entry is first de-fined. The challenges linked to ground testing for high velocity flows are then explained.Finally, a new ground testing strategy is briefly presented.

The second chapter is a brief overview of GSI theory. The features along the stag-nation line of a body flying at hypersonic velocity are presented. The driving processesof GSI are exposed in order to provide to the reader a base of knowledge on the topic.

The third chapter is dedicated to the practical investigation of GSI, and the de-termination of a reference catalycity. The facility used and methodologies applied arepresented. The two test campaigns are then described, and the corresponding resultscommented and compared to similar experiments conducted in the past. A word is alsosaid on uncertainty quantification.

In the fourth chapter, finally, the parameters described in the second chapter arequalitatively approached, and their evolution with respect to the test conditions is com-mented. This last chapter ends on a preliminary conclusion.

Chapter 1

Ground testing strategy forsuper-orbital re-entry

At the root of this project is the issue of flight duplication in ground testing facilities forsuper-orbital re-entry probes. This first chapter exposes that problematic, so that thereader perceives how the present research is related to a wider research and explorationprogram.

Super-orbital re-entry is first defined from an orbital mechanics point of view, with ashort overview of the orders of magnitude involved. The challenges linked to high velocityflows experimentation are then explained. Finally, the new ground testing strategy forsuper-orbital re-entry is briefly presented.

1.1 Super-orbital atmospheric re-entry

Super-orbital atmospheric re-entry, also referred to as high velocity or even hyperbolic re-entry, is encountered when a probe is travelling from one celestial body (planet, moon,asteroid, etc.) to another. It is typically the case for sample or crew return (Luna,Apollo, Genesis, Stardust, Hayabusa, etc.), or exploration missions (Viking, Pioneer,Mars Pathfinder, Mars Exploration Rovers, etc.).

1.1.1 Orbital mechanics considerations

While orbiting around a planet, a probe is also following that planet’s orbit around theSun. The aim of an interplanetary transfer is to leave that planet’s orbit around theSun, and reach the target planet’s orbit. This has to be made in the right time frame,so that the probe meets the target planet upon reaching its orbit. Different manoeuvresare possible, but the cheapest one from an energetic standpoint is the Hohmann transfer(figure 1.1). A velocity increment ∆v is first given to the probe to inject it on an ellipticorbit tangent to both its original orbit, which is the orbit of the first planet, and itstarget orbit, which is the orbit of the target planet. Upon arrival at the second planet’sorbit, a second velocity increment is required to inject it on its target orbit.

3

4 Super-orbital re-entry

The first velocity increment is obviously higher than the one needed to escape thegravitational influence of the first body and orbit around the Sun, which is called escapevelocity. The escape velocity of a certain body can be estimated based on equation 1.1.

vesc =

√2G ·mbody

rbody(1.1)

where G is the gravitational constant, and mbody and rbody are respectively the massand radius of the considered body. The probe’s velocity upon reaching the target planetis higher than that planet’s escape velocity. Therefore, with respect to the target planet- probe system, the transfer orbit is locally considered as a hyperbola, which focal is thetarget planet’s centre of mass. The probe’s velocity upon reaching the target planet’sorbit is thus higher than the target planet’s escape velocity. The exact magnitude of itsvelocity depends on the origin planet’s orbit velocity and the trajectory followed. [28]

Figure 1.1: Interplanetary Hohmann transfer.

1.1.2 Orders of magnitude

Slowing the probe down to orbital velocity so as to put in on orbit around the secondbody would require an important amount of energy, increasing considerably the overallcost of the mission. It is therefore preferred to perform the re-entry directly from thetransfer orbit.

The Earth’s escape velocity, for example, is 11.2 km/s. Most of the scenarios forMars return mission foresee an arrival entry velocity ∼ 11.6 · · · 14.5 km/s, which isindeed higher than the Earth’s escape velocity. This is considerably higher than theusual re-entry velocities from elliptic orbits, e.g. 8.2 km/s for the Space Shuttle. Upto now, the Stardust probe was the fastest artificial object that entered in the Earth’satmosphere, at a velocity of 12.8 km/s. [26]

Super-orbital re-entry 5

The initial specific enthalpy H, defined around the entry point (assumed to be at analtitude of ∼ 180 km), can be determined from the initial velocity v:

H =1

2v2 (1.2)

Typical velocities for probes entering the Earth’s atmosphere from hyperbolic orbitsscale from 11 to 15 km/s, which correspond to specific enthalpies between ∼ 60 and∼ 115 MJ/kg.

1.2 Issues for experimentation on high velocity flows

During re-entry, most of the probe’s initial enthalpy will be dissipated in the form of heat.The role of the probe’s TPS is to shield its structure and payload from the high heatingloads that will be encountered. The main design requirement on the TPS is to minimizeits mass while ensuring the probe’s integrity, i.e. withstand the heat loads. This impliesthat accurate flight duplication should be realized in ground testing facilities.

However, when it comes to super-orbital re-entry, those heat loads are even higher.Indeed, the probe’s velocity is higher for super-orbital re-entry, and the initial enthalpyis related to the square of the probe’s velocity (equation 1.2). Flight duplication and ac-curate prediction of aerothermodynamics phenomena at those enthalpies are still beyondthe capabilities of the existing laboratories.

The hypersonic phenomena for which an effort has to be made in ground testingfacilities were classified in seven categories by Chul Park in his review of laboratorysimulation of aerothermodynamics [20], from which this section is strongly inspired.Among those, two are particularly relevant for super-orbital re-entry: radiation/ablationand GSI. Although the present project focuses on GSI, both issues are quickly introducedin this section, after an overview of high enthalpy aerothermodynamic facilities.

1.2.1 Aerothermodynamic facilities

High enthalpy facilities are required in order to produce flows involving chemistry. Suchfacilities are divided in two categories:

• Impulse facilities are only able to produce flows that last typically a fraction ofa second. This is long enough to let the steady flow establish itself, but too shortto study thermal effects. They are thus mainly used to investigate the aerother-modynamic effects, gas kinetic, and radiation processes. They are able to reachenthalpies up to 30 MJ/kg, with an expansion tube.

• Plasma wind tunnels (PWT), such as inductively coupled plasma (ICP) facilitiesor arc-jets, are able to operate at very high enthalpy (up to 50 MJ/kg) and forlonger test durations. However, they are limited in pressure (∼ 107 Pa) and free-stream velocity. [20] This type of facility was used for the present study, theassociated methodologies are further explained in section 3.1.


When studying orbital re-entry, flight duplication is possible in those facilities for alimited time (impulse facilities) or in a limited region (stagnation point in PWT). How-ever, flight duplication is not possible anymore for super-orbital re-entry. The reason forthis can already be perceived from this brief overview: the need to reach high enthalpies.

1.2.2 Radiative heating and ablation

Problem statement

It is generally admitted that shock layer radiative heating appears around 9 km/s inEarth’s atmosphere and 7 km/s in Mars’ atmosphere [20]. However, it remains smallerthan 10% of the total heat flux for probes having a diameter smaller than ∼ 1 m andentry velocities smaller than 13 km/s in the Earth’s atmosphere, as it was the casefor Stardust [26]. It is thus a major issue for the range of velocities corresponding tosuper-orbital re-entry.

Two types of radiation have to be considered. For a vehicle flying only at high alti-tudes, such as Aeroassisted Space Transfer Vehicles (ASTV), radiative heating is domi-nated by chemical non-equilibrium in the shock layer. For a re-entry capsule, the peakradiative heating occurs at lower altitude, where the shock layer is expected to be inchemical equilibrium. The problem is even more complex when ablation of the heatshield occurs, which is in most cases inevitable. The product of ablation forms a gaslayer that prevents the hot shock layer gas from reaching the wall and absorbs part ofthe shock layer radiative heat flux. An accurate estimation of the absorbed radiation isalmost impossible since the thickness and thermochemical state of the ablation gas layerare difficult to predict. [20]

Appropriate facilities

The increasing fraction of radiative heat transfer is a problem for flight duplication inground testing facilities. If the enthalpy is matched, a usual way of reproducing flightcondition is to maintain the binary scaling parameter, which is the product of the densityρ and a typical length scale L. This approach conserves Reynolds number Re and viscouseffects, binary chemical processes, and the convective heat transfer. However, the heatremoved by radiation per unit of mass scales as L [18]. Rigorous flight duplication is thusnot possible anymore with small-scale models. Instead of duplicating flight conditions,it is thus necessary to investigate separately the driving phenomenon and build up thecorresponding models.

Equilibrium radiation with ablation has to be studied in a facility able to provide highenthalpy, pressure, and a certain amount of radiative heating so as to cause ablation andspallation. Ballistic range with counterflow device can meet those requirements, provid-ing the ambient pressure is raised to produce a radiative heat flux equal or greater than

Super-orbital re-entry 7

in flight. Comparison between ground testing results and flight showed that this ap-proach gave satisfying qualitative results. The phenomenon can also be studied in PWTenhanced with an external radiation source that reproduces the shock layer radiation.

1.2.3 Gas-surface interactions

Problem statement

It has been experimentally demonstrated - including in flight - that surfaces non-catalyticto recombination reactions involving atomic nitrogen and oxygen considerably reduce theheat transfer. However, rigorous characterization of the chemistry at the wall is complex.It is therefore difficult to have a correct understanding of the catalytic phenomenon.Catalycity modelling is the ultimate goal to which the present project brings its owncontribution. A more detailed presentation of GSI is done in chapter 2.

Appropriate facilities

The catalycity of a material depends on its temperature and surface morphology, amongother parameters. However, accurate determination of a material’s catalycity requirestesting it in the same chemical, thermal, and mechanical states as in flight. It is thereforenecessary to test it over long durations (in the order of minutes) at the same heat transferrates as in flight. This can only be done in PWT. However, as already stated in section1.2.2, it is complicated to estimate the radiative fraction of that heat flux, and requiresan external radiation source. Furthermore, PWT are often unable to operate at thedesired pressure ranges.

1.3 New testing strategy

Super-orbital re-entry requires thus a new approach of ground testing. Ground testingfacilities should be used to investigate separately different phenomenon playing a role inthe aerothermodynamic of the flow, rather than to duplicate flight as it is the case forlower velocity flows. Those investigations should be performed with a scientific approach,to understand and model the physics of the flow, rather than the engineering approach,to qualify and size designs. The resulting models should then be fed to ComputationalFluid Dynamics (CFD) codes, which would allow flight duplication on computer ratherthan in ground test facilities (figure 1.2). This new philosophy clearly appears in theexamples cited here above, as well as in the present report.


Figure 1.2: Proposed procedure for high enthalpy atmospheric entries.

Chapter 2

High temperature gas dynamicsapplied to atmospheric re-entry

The present research being focused on GSI, and more particularly catalycity modelling, itis important for the reader to have a clear understanding of chemically reacting boundarylayers. The present chapter is far from a comprehensive description of the associatedtheory, but it gives the necessary qualitative understanding of the phenomenon involved.

The features along the stagnation line of a body flying at hypersonic velocity arefirst described, followed by a brief description of high temperature gas dynamics. Formore details, the reader is invited to consult [1] and [7].

2.1 Stagnation line features

Unlike the transition from subsonic to supersonic, there is no clear definition for thebeginning of the hypersonic regime. Nevertheless, the scientific community agrees onseveral recognizable features. One of those features is of particular interest for thisstudy: the importance of the heat transfer at the wall.

Taking a closer look at the neighbourhood of the stagnation line of a body flying inhypersonic regime, depicted in figure 2.1, one can identify different region:

• The free-stream, upstream of the bow shock.

• A strong bow shock, detached from the body. It is detached because hypersonicvehicles generally have blunt nose, in order to avoid too important aerodynamicheating.

• The region downstream of the shock is subsonic. A considerable part of the flow’skinetic energy will be transformed in thermal energy across that shock. Therefore,the shock-layer temperature achieved can be incredibly high: from ∼ 8, 000 Kfor an orbital re-entry up to ∼ 11, 000 K for a lunar return. The flow needs a

9

10 High temperature gas dynamics

certain time to adjust both its temperature and chemical composition to this newenergetic balance. This region of adaptation is called relaxation layer.

At such high temperatures, chemical effects have to be taken into account. Forair at a pressure of 1 atm, vibrational excitation begins at 800 K, O2 begins todissociate at 2, 500K and is fully dissociated for 4, 000K, point for whichN2 beginsto dissociate. At 9, 000 K, N2 is fully dissociated and ionization begins. One caneasily understand that the flow downstream the shock is plasma: molecules aredissociated and atoms are partially ionized.

• A transition layer may follow the relaxation region.

• A chemically reacting boundary layer in which thermal and mass diffusive processtake place. As it will be shown later, those three processes are complex and closelyinter-connected.

It should be brought to the reader’s attention that the gas behind the shock is achemically reacting mixture of perfect gases, and not a real gas as it often incorrectlyreferred to in literature. A real gas is a gas for which intermolecular forces are notnegligible anymore, which implies that the molecules are closely packed together. Thisonly applies for very large pressures (∼ 108 Pa) and/or very low temperatures (∼ 30 K)that will not be encountered in the present study.

Figure 2.1: Flow features around the stagnation line of a hypersonic body.

From this overview, different heat sources can be identified. First, there is the usualconductive part due to the temperature gradient. As it was demonstrated, the tem-peratures behind the bow shock can reach extremely high values, resulting in a veryimportant heating. Secondly, there is a radiative part, mainly due to the shock layerbut that can also be due to ablated material. As discussed in the previous chapter, thispart can become a major fraction of the overall heat transfer. However, it will not befurther investigated in the present study. Finally, there is a diffusive part. This is dueto the diffusion of atoms throughout the boundary layer and their recombination at thewall.

High temperature gas dynamics 11

2.2 Brief overview of gas-surface interactions

The resolution of the laminar chemically reacting axisymmetric boundary layer equa-tions is extremely complex, or even impossible. Indeed, in addition to the conservationof mass, momentum, and energy, one needs to take into account for the species con-tinuity. Analytical solutions can be found at the stagnation point for limiting cases,assuming that the solutions are self-similar and applying a Mangler-Howarth transfor-mation. Those solutions were developed by Fay and Riddell [8], Goulard [10] and Lees[15]. They are available for equilibrium boundary layers, for which wall catalycity doesnot matter, and frozen1 boundary layers over walls with a finite catalycity. Althoughan important literature exists on the topic, it is not the goal of the present project togo into the details. The problem will be tackled by explaining the few constants andparameters used to describe the overall state of the boundary layer.

The recombination of dissociated species is an exothermic reaction. It takes placeeither in the gas phase, in which case it is called a homogeneous reaction, or at thewall, in which case it is called an heterogeneous reaction. Typically, the recombinationreactions to expect for the Earth’s atmosphere are 2:

• O +O → O2 + 500 kJ/mol

• O +N → NO + 630 kJ/mol

• N +N → N2 + 950 kJ/mol

2.2.1 Chemistry constants

Each reaction is characterized by a chemical rate constant k that will quantify thereaction’s speed. For the recombination of oxygen and nitrogen in nitric oxide, forexample, one can write the corresponding equilibrium equation which also takes intoaccount the backwards reaction of decomposition:

O +N NO (2.1)

To this particular reaction corresponds an equation describing the rate of nitrogen oxideformation:

d [NO]

dt= k · [N ]m [O]n (2.2)

where the terms between the straight brackets are for concentrations, and m and n arethe reaction orders. The reaction order depends on the reaction mechanism, and is equalto the stoichiometric balance (in this case m = n = 1) only in the case of elementaryreaction.

1The characteristics of equilibrium and frozen boundary layers are given in section 2.2.32In reality, the production of NO is poorly understood. Experimental evidences tend to show that

it is negligible compared to production of O2 and N2. It is therefore neglected in common aerothermalmodels. [19]


The chemical rate constant, in turn, is often modelled with the two-parameter Arrhe-nius relation:

k = k0 · e−EaR·T (2.3)

where k0 is a frequency factor, Ea is the reaction’s energy of activation, R the gasconstant, and T the temperature. This relation is based on the assumption that ata certain temperature, the mixture’s energy distribution follows a Boltzmann distribu-tion, and therefore that the amount of molecules having an energy greater than Ea isproportional to the exponential term.

Gas-phase reaction rate constant

In reality, in the gas phase, the recombination reactions take mostly place with a thirdparty; e.g. one molecule of dioxygen can dissociate into two atoms of oxygen only whencolliding with one other atom or molecule or with the wall. In the present research,the analysis of the gas phase boundary layer chemistry will be limited to the followingreactions, where M is the third party atom or molecule:

• Nitrogen recombination in dinitrogen: N +N +M N2 +M ;

• Oxygen recombination in dioxygen: O +O +M O2 +M .

The reaction rate constants can be implemented in various fashions, depending on thechemistry model used. In all the models used in the present study, the reaction ratecoefficient is defined as:

k = C · Tn · e−EaR·T (2.4)

This expression is obviously similar to equation 2.3, except that the frequency factork0 has been expressed as a function of temperature. The values given to the differentcoefficients are summarized in table A.1 for the model of Dunn and Kang [23] that willbe used to post-process the measurements in the low pressure range.

Reaction equilibrium constant

Each reaction is characterized by two reaction rate constants: one of the forward reaction,kf , and one for the backwards reaction, kb. Their ratio is the reaction equilibriumconstant, Kc. The subscript c indicates that it is defined in terms of concentration,rather than in terms of partial pressure. This constant gives an indication on the stateof the mixture: if it is large, the products are favoured, and if it is small, the reactantsare favoured. The reaction’s equilibrium constant Kc depends on both temperature andmixture’s composition, through the nature of the species M.


However, the coefficient n remains the same for both the forward and backwardsreactions of each recombination, no matter what the nature of M is. The dependencyon temperature appears therefore only in the exponential terms, and indirectly throughthe mixture’s composition. The group Ea/R in the exponential being the same for a givenrecombination no matter what the nature of M is, the effect of mixture’s compositionis only visible through the ratio Cf/Cb. In the model of Dunn and Kang, according totable A.1, that ratio is ≈ 5.8E − 3 for nitrogen and ≈ 8.3E − 4 for oxygen for everyM . The value of Kc is thereby a strong function of temperature and a weak functionof mixture’s composition, as illustrated in figure 2.2 for the recombination reaction ofatomic nitrogen into dinitrogen.

4500 5000 5500 60000

1

2

3

4

5

6

7

8

9

10x 10

8

Temperature [K]

N2 r

ecom

bin

ation r

eaction

equili

brium

coeffic

ient (D

unn−

Kang)

[−]

Mixture for H = 36.24 MJ/kg

Fully recombined mixture

Figure 2.2: Kc for the recombination of atomic nitrogen into dinitrogen as a functionof gas temperature, according to Dunn and Kang’s chemistry model. It is representedfor a mixture in thermal equilibrium at a specific enthalpy H = 36.24 MJ/kg, and fora mixture where all the species are recombined.

Wall reaction rate constant

Chemical reactions can also take place when two atoms or molecules collide with thewall rather than with another atom or molecule. It is possible to link that reaction withanother reaction rate constant specific to the wall, kw, which is obviously linked withthe catalycity.

At the wall, for a given species i, the diffusion flux Ji is balanced by the productionof consumption of species due to the catalytic surface wi.

Ji = wi (2.5)

From equation 2.19, the diffusion flux can be written:

Ji = mi ·(M↓

i −M↑i

)= miγiM

↓i (2.6)


where m is the species’ atomic mass. With equation 2.5, one can thus establish:

wi = miγiM↓i (2.7)

Which becomes, when M↓i is replaced with its expression as given by kinetic theory [2]:

wi =2γi

2− γimin

√kBTw

2πmi(2.8)

where the kB is Boltzmann’s constant, n is the number density, and the Tw the wall’stemperature. The mass production term is also defined as:

wi = kiwρwxi (2.9)

Merging 2.8 and 2.9, one can thus finally identify an expression for the wall reaction rateconstant in function of the catalycity:

kiw =2γi

2− γi

√kBTw

2πmi(2.10)

2.2.2 Diffusion coefficient

In the case of a multi-component mixture, the average species diffusion coefficient D isobtained from the binary diffusion coefficient D using Fick’s law:

Di =1− xi∑i =j

xj

Di,j

(2.11)

where the binary diffusion coefficient is:

Di,j =3

16

√2πkBT (mi +mj)

mimj

1

nQ(1,1)i,j(2.12)

where Q is the diffusion cross-section. The atomic mass is obtained by dividing themolecular mass Mm by the Avogadro number NA. The number density is defined asn = ps/ (kBT ), where ps is the static pressure. The diffusion cross-section is obtainedfrom the collision integral Q(i,j) = Ω(i,j) · π. The collision integral, in turn, is obtainedwith a fitting analytical expression from [4]:

Ω(i,j) =a1 + a2 · T a3

a4 + a5 · T a6· 10−10 (2.13)

where the factor 10−10 is necessary to convert from meters to Angstrom. The parametersfor i = j = 1 can be found in [4].

The diffusion coefficient is thus a function of temperature T , mixture composition,and static pressure ps. Its evolution is function of those three parameters is depictedin figures 2.3 for atomic nitrogen and oxygen. Diffusion is promoted as temperatureincreases, species dissociate, and pressure decreases. It appears that oxygen diffusesslightly more efficiently than nitrogen, and is less sensitive to mixture composition.


0 1000 2000 3000 4000 5000 6000 70000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Gas temperature [K]

N d

iffu

sio

n c

oeffic

ient [m

2/s

]


Mixture for H = 36.24 MJ/kg

1500 Pa

5000 Pa

10000 Pa

(a)

0 1000 2000 3000 4000 5000 6000 70000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Gas temperature [K]

O d

iffu

sio

n c

oeffic

ient [m

2/s

]


Mixture for H = 36.24 MJ/kg 1500 Pa

5000 Pa

10000 Pa

(b)

Figure 2.3: Diffusion coefficient D for atomic nitrogen (a) and oxygen (b) as a functionof T and ps. Each curve is represented for a mixture in thermal equilibrium at a specificenthalpy H = 36.24 MJ/kg, and for a mixture where all the species are recombined.

2.2.3 Damkohler numbers

Gas phase Damkohler number

The likelihood of homogeneous reaction to happen is described with the gas phaseDamkohler number Dag. It is defined as the ratio between a time-scale characteris-tic of the flow τflow and a time-scale characteristic of the chemistry τhomo:

Dag =τflowτhomo

(2.14)

Although many definitions of τflow exist, they all aim at retrieving a qualitative sense ofthe time of residence of the species in the boundary layer. In the frame of the presentstudy, it is defined as the inverse of the outer edge velocity gradient βe:

βe =∂ue∂x

(2.15)

where ue is the tangential velocity at the outer edge of the boundary layer and x is thetangential direction. The second time-scale, τhomo, depends on the mixture’s composi-tion, the temperature, and the reaction constants (see section 2.2.1).

A precise evaluation of Dag is complex and depends on how the time-scales are defined.It is rather used to have an idea of the overall state of the gas phase mixture. Two limitingcases can be defined:

• For Dag → 0, the chemistry can be neglected as it is too slow or is not given thetime to change the nature of the flow. This is referred to as a frozen boundarylayer.

• For Dag → ∞ the chemistry is so fast that equilibrium is reached instantaneously.This is referred to as an equilibrium boundary layer.


Wall Damkohler number

Similarly to the gas phase Damkohler number describing the state of the flow within theboundary layer, the wall Damkohler Daw number is used to described the state of the flowclose to the body’s surface. It is defined as the ratio between a time-scale characteristicof the species diffusion in boundary layer τdiff and a time-scale characteristic of thechemistry τhete:

Daw =τdiffτhete

(2.16)

That ratio can be numerically estimated as the ratio between the wall reaction rateconstant kw, which has the dimension of a velocity, and the diffusion velocity vD:

Daw =kwvdiff

(2.17)

with:

vdiff =D

δ(2.18)

where δ is the boundary layer thickness.

Again, two limiting cases can be distinguished:

• For Daw → 0, the over-all reaction rate corresponds to a situation in which thespecies do no diffuse through the boundary layer. Although the over-all reactiontime may be quite small, it is much larger than the diffusion time. This is referredto as a reaction-controlled surface.

• For Daw → ∞, the surface is in diffusion control. Again, although the diffusiontime may be quite small, it is much larger than the reaction time.

2.2.4 Catalycity

In the context of atmospheric re-entry vehicles, catalycity γ is defined as the probabilityof dissociated species recombination at the body’s surface. Contrary to the reactionconstant, it is thus not an intrinsic property of the material but also depends upon theflow conditions. For a particular species i, it is defined as the ratio between the fractionof species recombining at the surface, and the number flux of species i diffusing to thesurface3. The fraction of species recombining at the surface is the difference between the

3More accurate definitions of the catalycity do exist. Indeed, after recombination the molecule cankeep part of the released energy in the form of vibrational energy instead of transferring it to the wall.Introducing the chemical energy accommodation coefficient β, representing the amount of energy that isactually transferred to the wall, it is possible to defined the effective catalycity γeff = γ · β. Similarly, anapparent catalycity is defined to take into account surface roughness. For more information concerningthis classification, the reader can refer to [24].


number flux of species i diffusing forward M↓i and the number flux of species i travelling

backward m↑i ,

γi =M↓

i −M↑i

M↓i

(2.19)

Two limiting cases can be distinguished:

• For γ = 0, none of the species recombine at the wall.

• For γ = 1, all the species that reach the wall recombine there.

2.3 Closing remark on catalycity modelling

For the evaluation of catalycity, it is thus important to take into account not only thetype of reactions that are taking place at the wall but also the diffusion of species throughthe boundary layer. This was already known back in the sixties. Rosner, for example,points out that ”if the relative slowness of reactant transport to the catalytic surfacecause the reactant concentration to be locally depleted” then the surface characterizationbecomes a complicated task. Therefore, ”to the chemist interested in the interfacialreaction itself, diffusion will be seen to be a skilful falsifier and certainly an undesiredintruder.” [22]

However, surprisingly enough, diffusion is neglected from most of the catalycity mod-els that are used nowadays for engineering applications. The material databases createdin ground testing facilities do only take into account its variations with static pressureps and wall temperature Tw, which are the parameters driving the recombination reac-tion at the wall, as if it did not depend on the test conditions. This is a conservativeassumption, as it results in an over-estimation of the material’s catalycity, and thereforean over-estimation of the diffusive heat flux, and finally an over-sizing of the TPS. Spacemissions with stringent mass budget are therefore penalized with heavy heat shield andthe payload mass is reduced.

Chapter 3

Test campaign and results

The conclusions of this study are based on the results obtained during wind tunnelexperiments. The goal of those experiments is to perform a parametric study on processesinvolved in GSI. Information is retrieved regarding the wall catalycity and heat fluxfor various conditions of static pressure, free-stream specific enthalpy, probe geometry(Damkohler probes) and wall material (minimax), while keeping the wall temperatureconstant.

The procedure to perform heat flux measurements is first detailed. The two differenttypes of tests that were performed are then described, and the corresponding results areexplained, and compared with results obtained during similar test campaigns conductedin the past. Issues concerning measurement errors and uncertainty quantification arefinally commented.

3.1 Heat flux measurement in the Plasmatron

The experimental investigations were performed in the Plasmatron, the main facility forGSI research at the von Karman Institute (VKI). The Plasmatron is an ICP facilityused both for research and for material response study in the frame of TPS sizing [3]. Itallows reproducing the exact flight conditions in the boundary layer in the surroundingof the stagnation point, which is very likely to be the point of the vehicle submitted tothe highest heat flux.

This duplication is made possible by the Local Heat Transfer Simulation (LHTS)method. Originally developed at the Institute for Problems in Mechanics (IPM, Moscow),it defines the parameters to reproduce in order to duplicate the flight conditions, based onthe developments of Fay and Riddell already discussed in section 2.3. Those parametersare: the outer edge (free-stream) specific enthalpy He, pressure pe and velocity gradi-ent βe (figure 3.1). This methodology has been improved at the VKI1, and extensively

1The LHTS as applied at the IPM assumed a constant Prandtl number Pr and the transport coeffi-cients were evaluated with curve fittings. At the VKI, no assumption is made on Pr and the transportproperties are evaluated with the kinetic theory of gases.

19

20 Test campaign and results

applied to Plasmatron testing [5] [6] [12].

Figure 3.1: Schematic overview of the LHTS method: the flow is duplicated in theboundary layer around the stagnation line (see figure 2.1) as long as He, pe and βe arereproduced.

The method is divided in two parts: a measurement of heat flux and pressure, basedon which the boundary layer equations are numerically solved. However, even with thisapproach, there is one more unknown than the number of equations. The problem is notclosed. Therefore, the result is expressed as a correlation between two variables: outeredge enthalpyHe, and sample catalycity γ. A high enthalpy corresponds to non-catalyticmaterials, and a low enthalpy to fully catalytic materials, with a monotonic transitionbetween both. If the enthalpy is plotted as a function of the logarithm of catalycity,the corresponding curve is shaped liked an ”S” (figure 3.2), referred to as the enthalpyS-curve. To subdue this problem, the current procedure consists in performing a cold-wall heat flux measurement with a reference sample of known catalycity, and therebydetermine the outer edge enthalpy. The catalycity of the material to test is then theonly remaining unknown.

10−5

10−4

10−3

10−2

10−1

100

10

15

20

25

30

35

40

45

Catalycity (log) [−]

Oute

r edge e

nth

alp

y [M

J/k

g]

Figure 3.2: Enthalpy S-curve, linking the outer He with γ, in logarithmic scale. Figurerealized for the reference probe at ps = 1, 500 Pa and Qref

w = 875 kW/m2.

The catalycity values experimentally determined for different testing conditions inthe frame of the present project can be used to improve this procedure. Indeed, at

Test campaign and results 21

the VKI, the reference is often a copper sample, which catalycity is assumed to varyonly with the plasma’s static pressure. In the past, it has even been considered as fullycatalytic. However, it was shown that it is not the case, as some materials such as silverare more catalytic. Furthermore, cold copper would oxidize while being exposed andits catalycity would therefore decrease [19]. An approach to the exact determinationof copper catalycity depending on the Plasmatron test condition is presented in section3.2.4.

3.1.1 Heat flux and dynamic pressure measurement

The plasma conditions can be regulated in terms of input power P , gas mass flow m,and static pressure ps. In turn, the instrumentation allows to measure the heat flux atthe wall Qw and the dynamic pressure at the location of the stagnation point pdyn.

Different probes can be used to hold material samples. The reference probe corre-sponds to the ESA geometry for sample holders, also referred to as Euromodel. It is acylinder with a certain radius rb. The heat flux is measured with a copper calorimeter,placed in the middle of the front face, which corner has been rounded with a certainradius rc. The exact dimensions are available in table 3.3. Water is flowing throughthe calorimeter with a certain mass flow controlled by a calibrated rotameter. All theexperiments described in the present project were performed for a cold wall, ∼ 350 K.The mass flow is measured together with the temperature difference between the inflowand the outflow ∆T , and Qw is thereby determined:

Qw =m · cp ·∆T

A(3.1)

where cp is water’s specific heat at constant pressure and A the calorimeter’s exposedarea. The temperatures are measured with type E thermocouples. A second mass flowis used to cool the probe’s walls that are exposed to the plasma. A proper heat fluxmeasurement is depicted in figure 3.3. The probe is originally in stand-by position, out ofthe flow. The measured heat flux rises once the probe is into the plasma. The operatorwaits until it reaches a steady value, and then puts it back in its original stand-byposition, out of the flow.

The dynamic pressure is measured with a Pitot probe, also cooled down with water.For the present study, however, regressions made by Marotta [17] on the data of previoustest campaigns were used.

3.1.2 Pre-processing numerical tools

Based on measurements of the torch input power, mass flow, and dynamic pressure atthe position of the test sample, and the test sample wall heat flux, it is possible to rebuildthe sample’s catalycity. This is performed with the help of two numerical tools.


0 25 50 75 100 125 150 175 200 225 250−100

100

300

500

700

900

1100

Time [s]

Heat flux [kW

/m2]

Figure 3.3: Recorded heat flux over time for the reference probe at ps = 1500 Pa.

The first one is an ICP code that allows for the reproduction of the experimentalconfiguration. It computes the flow in the plasma torch and around the sample in thetest chamber solving the time averaged magneto-hydrodynamic equation at low Machand low magnetic Reynolds number. The output of that tool is a set of non-dimensionalparameters (NDP) describing the structure of the boundary layer [16]. However, for thepresent study the NDP were estimated using regression laws that have been computedfor a wide range of operating conditions in terms of power and static pressure.

The second tool is CERBOULA, a post-processing software based on the unification oftwo other ones: CERBERE, Catalycity and Enthalpy ReBuilding for a REference probe,and NEBOULA, NonEquilibrium BOUndary LAyer. Based on the non-dimensionalparameters previously obtained and the experimental data, it solves the boundary layerequations for an axisymmetric, steady, laminar, chemically reacting gas over a catalyticsurface. The chemistry model of Dunn and Kang [23] with 7 species (N2, O2, N , O,NO, NO+, e−) was used for the low pressure range, and that of Gupta [25] for thehigh pressure range. Although neither of them has been validated for the Plasmatrontests, Dunn and Kang’s model was considered in a previous study of Garcia as the mostprobable to give results which are not in contradiction with the experiment [9]. However,has it will be shown in section 3.2.2, it was not suitable in the high pressure range. Atmedium and low pressure, Gupta’s model was preferred.

3.2 Minimax

The aim of this first test campaign is to observe the variation caused by different reactionsat the wall. In addition to the reference probe described in section 3.1.1, two probeswith the same geometry but different types of calorimeter are used (figure 3.4). Datapoints are recorded for the three probes in the same plasma conditions (Qref

w and ps) andsame wall temperature (cold-wall measurement). The test conditions are summarized intable B.1.


Figure 3.4: Test campaign: minimax.

The minimax methodology consists in comparing a reference probe with two otherprobes having the same geometry, but different materials for the calorimeter: one morecatalytic, and the other less. The S-curves are computed for each of the probes. Sincethe outer edge enthalpy is the same for all the three of them, its value can be delimitedto the ones that exist for the three probes. This defines an interval of confidence for boththe outer edge enthalpy, and the catalycity of the reference probe (figure 3.5). For thepresent research, the reference probe is a copper calorimeter γCu, the higher catalyst ismade out of silver γAg and the lower one out of quartz γQuartz. More information aboutthe minimax methodology can be found in [13] and [14].

10−5

10−4

10−3

10−2

10−1

100

10

20

30

40

50

60


Oute

r edge e

nth

alp

y [M

J/k

g]

Quartz calorimeter

Copper calorimeter

Silver calorimeter

Figure 3.5: The minimax methodology: the three S-curves define an interval for He, andthereby also for γCu. This figure is the complement of figure 3.2.

3.2.1 Low pressure

At low static pressure, 1, 500 Pa, the He − γ intervals can easily be defined, as depictedin figures 3.6. The results actually obtained for this study, represented with triangles,are compared with those from previous studies. The differences with Krassilchikoff aremost probably due to the different material used for the lower catalycist: molybdenuminstead of quartz.

What is observed, however, is that the incertitude of the outer edge enthalpy remainsquite large when only the results of the present study are taken into account. Duringnumerical rebuilding, a small change in catalycity results in an important change of


free-stream conditions due to the important gradient in the outer edge enthalpy rangeconsidered. By combining them with those from Krassilchikoff and Kadavelil, the un-certainty is considerably reduced.

400 600 800 1000 1200 140010

15

20

25

30

35

40

45

50

Heat flux Reference probe [kW/m2]

Oute

r edge e

nth

alp

y [M

J/k

g]

Kadavelil (2007)

Krassilchikoff (2006)

Present work

Data used

(a)

400 600 800 1000 1200 1400

10−2

10−1


Cata

lycity (

log)

[−]

Kadavelil (2007)


Present work

Data used

(b)

Figure 3.6: He (a) and γ, in logarithmic scale, (b) intervals as defined during differentminimax test campaigns for ps = 1, 500 Pa. Each dataset consists out of two curvesthat are the upper and lower limits of the intervals. The ”data used” set is the one usedin chapter 4. Krassilchikoff’s results are based on molybdenum rather than quartz aslower catalycist.

Reference catalycity

In chapter 4, the evolution of the driving processes in GSI will be qualitatively described.To that end, it is necessary to fix a certain reference catalycity and a correspondingouter edge enthalpy. The reference catalycity was determined as the logarithmic averagebetween the interval limits, using both the one defined by the present study and the onedefined by Kadavelil. Those of Kadavelil were beforehand refined using the overall outeredge enthalpy limits defined by all the test campaigns combined in figure 3.6 (a). In theend, the values used are represented with diamonds in figures 3.6, and noted in table3.1.

3.2.2 High pressure

At higher static pressure, 10, 000 Pa, clean He − γ intervals such as the one depicted infigure 3.5 was only to be found for one point corresponding to low plasma power. Forhigher powers, such an interval did not exist (see for example figure 3.7). Physically,however, there must exist a common outer edge enthalpy for the three probes since theywere all submitted to the same plasma conditions. This is therefore due to an error inthe data acquisition or post-processing.

That issue was already observed by Krassilchikoff [14]. He proposed the hypothesismade on the gas-phase chemistry model as the most likely explanation. He performed asensitivity study using three chemistry models: Dunn and Kang, Gupta, and Park [21].


According to him, those models ”agree at low pressure, but diverge at high pressure forthe low catalycities”.

As we have seen in section 2.2.2, with an illustration in figure 2.3, the diffusioncoefficient of both atomic nitrogen and oxygen strongly decreases as static pressureincreases. At low pressure, the wall Damkohler number Daw is small, and the chemistryis mainly driven by the wall. As pressure increases, Daw increases, and the gas-phasechemistry becomes more important. The same applies when catalycity decreases. Thus,the choice of chemistry model does not influence the results inferred for low pressure,but it becomes relevant for high pressure and low catalycity. This intuitive explanationwill be confirmed when examining the boundary layer in chapter 4.

10−5

10−4

10−3

10−2

10−1

100

10

15

20

25

30


Oute

r edge e

nth

alp

y [M

J/k

g]

Quartz calorimeter

Copper calorimeter

Silver calorimeter

17.62 MJ/kg16.12 MJ/kg

Figure 3.7: The methodology applied for figure 3.5 is not valid anymore for higherpressure: there are no common values of the outer edge enthalpy for the three probes.This figure was realized at ps = 10, 000 Pa and Qref

w = 861 kW/m2.

Figure 3.7 is reproduced in figure 3.8, with the models of Park and Gupta in additionto the one of Dunn and Kang. As expected, the difference between models arises in thelower catalycity region, around γ = 0.01 and below. Several observations can be madeon that figure, and on the rest of the sensitivity analysis to chemistry model:

• The model used to post-process the silver calorimeter is irrelevant, since the lowerlimit of He it defines is for a fully-catalytic wall. On the contrary, the modelused to post-process the quartz calorimeter should be chosen carefully. Althoughfrom the conditions of figure 3.8 the model chosen to post-process the coppercalorimeter also seems irrelevant, it may be important when He is low. Indeed, thequartz calorimeter S-curve built with Park or Gupta’s model might exceed that ofthe copper calorimeter built with Dunn and Kang’s model in the low catalycityregion.

• Gupta’s model was used for all the cases, as it defines a larger interval than Park’smodel and is therefore more conservative.

• In the higher reference probe heat flux recorded, 1036 and 1238 kW/m2, all themodels failed to provide an interval. This could be due to the uncertainty on


heat flux measurement in the Plasmatron. Indeed, as it can be seen in figure 3.9(a), the outer edge enthalpy interval is shrinking as the heat flux at the referenceprobe increases, thereby also increasing the sensitivity to measurement errors. Thisforced to restrain the analysis to values for which the couple outer edge enthalpy -catalycity could be performed. The range of He considered is thus smaller for thelow pressure analysis and for the high pressure one.

From those few points, it clearly appears that the chemistry model is a relevant parameterof the post-processing, as it results in important changes in the quantities of interest. Acomprehensive sensitivity study is desirable, especially to define which chemistry modelhas to be used under which conditions, and why.

10−5

10−4

10−3

10−2

10−1

100

10

15

20

25

30

35

40

Catalycity [−]

Oute

r edge e

nth

alp

y [M

J/k

g]

Gupta

Dunn−Kang

Park

Quartz calorimeter

Silver calorimeter

Copper calorimeter

Figure 3.8: Figure 3.7 is here reproduced for three different chemistry models. Thisfigure was realized at ps = 10, 000 Pa and Qref

w = 861 kW/m2.

The results are depicted in figures 3.9. As this study is performed for the first time,it could not be compared with results from previous works. The only point obtained byKrassilchikoff with Dunn and Kang’s model and a molybdenum calorimeter rather thana quartz one is also shown. The difference with the results from the present study isimportant, especially for the outer edge enthalpy.

Reference catalycity

Again, it was necessary to fix a certain reference catalycity and a corresponding outeredge enthalpy. At first, it was decided to use the logarithmic average of the limitsof the catalycity interval, as for the low pressure case. The data points for which itwas computed do not exactly correspond to the one measured, as it could have beeninteresting to retrieve information regarding catalycity for the same reference heat fluxesat different pressure levels. An interpolation on the values was therefore necessary.

Since the power was monotonically increased for increasing reference heat fluxes, theHe was expected to increase monotonically too. However, it was not the case (see figure3.11). The values of γref were therefore varied gradually, always within the intervaldefined by the minimax, until the corresponding rebuilt He was physically consistent


350 450 550 650 750 850 90010

12

14

16

18

20


Oute

r edge e

nth

alp

y [M

J/k

g]

Krassilchikoff (2006)Dunn−Kang’s model

Present workGupta’model

Data used

(a)

350 450 550 650 750 850 90010

−3

10−2

10−1


Cata

lycity [−

]

Krassilchikoff (2006)Dunn−Kang’s model

Present workGupta’s model

Data used

(b)

Figure 3.9: He (a) and γ, in logarithmic scale, (b) intervals, in logarithmic scale, (b) asdefined with different methodologies for ps = 10, 000 Pa. Each dataset consists out oftwo curves that are the upper and lower limits of the intervals. The ”data used” set isthe one used in chapter 4. Krassilchikoff’s results are based on molybdenum rather thanquartz as lower catalycist, and post-processing using Dunn and Kang’s model.

with the test conditions. Both were represented with diamonds in figures 3.9, and theexact values are noted in table 3.1.

At this point, one could argue that the determination γref and He for the investigationsconducted in chapter 4 is rather arbitrary. However, the minimax methodology is justdetermining an interval. From what is known, the real value of γref could be anywherewithin that interval. Using an arbitrary value is thus as rigorous as using an average ofthe interval’s limits, as long as the corresponding He is properly rebuilt. In this case, itis even more rigorous since He rebuilt with the average of the interval’s limits was notphysically consistent with the test conditions. Furthermore, the present study does notclaim to provide a quantitative description of the GSI processes, but rather to investigatequalitatively their relative evolution

ps = 1, 500 PaQref

w

(kW/m2

)γ (−) He (MJ/kg)

500 0.022 16.22700 0.021 23.74900 0.023 31.181, 100 0.027 36.45

ps = 10, 000 PaQref

w

(kW/m2

)γ (−) He (MJ/kg)

500 0.0025 15.95600 0.0040 16.47700 0.0065 17.40800 0.0090 18.29

Table 3.1: Values retained for γref and He versus Qrefw as used for chapter 4.


3.2.3 Medium pressure

Although only the two previously mentioned static pressure levels are necessary for thepost-processing of the next section, one more point is investigated to have a better ideaof the evolution of the reference probe’s catalycity. The choice of the chemistry modelis not as straightforward as for the two other points. Therefore, both Dunn and Kang’sand Gupta’s model were used. The results are depicted in figures 3.10, where thereare also compared with the results previously obtained by Krassilchikoff. The differencebetween both models for the present work is not apparent at low heat flux, but becomesimportant for higher values. In particular, Dunn and Kang’s model fails to provide aninterval before Gupta’s. Krassilchikoff’s results were also obtained with the minimaxmethodology, but with a molybdenum calorimeter and post-processing using Dunn andKang’s model.

200 300 400 500 600 700 800 9005

10

15

20

25

30

35


Oute

r edge e

nth

alp

y [M

J/k

g]


Present workDunn−Kang’s model


(a)

200 300 400 500 600 700 800 90010

−3

10−2

10−1


Cata

lycity [−

]


Present workDunn−Kang’s model


(b)

Figure 3.10: He (a) and γ, in logarithmic scale, (b) intervals as defined with differentmethodologies for ps = 5, 000 Pa. Each dataset consists out of two curves that are theupper and lower limits of the intervals. Krassilchikoff’s results are based on molybdenumrather than quartz as lower catalycist, and post-processing using Dunn and Kang’smodel.

3.2.4 Reference catalycity

The logarithmic average of the γref limits defined by the data points that were measuredduring the minimax test are represented in figure 3.11 as a function of the correspondingrebuilt He. The error bars drawn represent the limits of the interval defined by theminimax. These points are thus not the same as the interpolated ones used in chapter4. Two observations can be made:

• The only upper limit of the reference catalycity that can be confidently drawn, atleast for the range of He considered, is that γref ≤ 0.05, regardless of the pressurelevel considered. However, the result obtained are compatible with that of Panerai,who defines γref = 0.1 for 1, 200 Pa < ps ≤ 5, 000 Pa and γref = 0.01 for 5, 000 Pa< ps ≤ 10, 000 Pa [19].


• The drawback of using the logarithmic mean of the limits of the interval drawnby the minimax to define γref at 10, 000 Pa is clearly visible. Indeed, He slightlydecreases between the first and the second data point although the plasma powerwas increased, which is physically impossible.

5 10 15 20 25 30 35 40 4510

−3

10−2

10−1

100

Outer edge enthalpy [MJ/kg]

Cata

lycity (

log)

[−]

1,500 Pa

5,000 Pa

10,000 Pa

Figure 3.11: Logarithmic average of γCu as defined by the intervals obtained with theminimax methodology, in logarithmic scale, and corresponding He for different ps. Theerror bars represent the limits of the intervals defined by the minimax.

3.3 Damkohler probes

The second test campaign’s objective is to observe the variation caused by differentdiffusion schemes. In addition to the reference probe described in section 3.1.1, twoprobes with the same calorimeter but different geometries are used (figure 3.12). Heatfluxes are recorded for the three probes in the same plasma conditions (Q ref

w and ps)and same wall temperature (cold-wall measurement).

Modified Newton theory shows that enlarging rb lowers the outer edge velocity gradientβe. The time-scale characteristic of the flow in equation 2.14 is often chosen as the inverseof that outer edge velocity gradient τflow = 1/βe. Therefore, enlarging the probe’s bodyradius should ultimately cause the Dag to increase. The larger probe is referred to asthe equilibrium probe and the small one as the frozen probe. More developed numericaland experimental investigations about the Damkohler probes can be found in [11].

Due an important amount of noise in the signal of the equilibrium probe, it was decidedto perform the Damkohler probes test campaign in two steps: first the reference probetogether with the frozen one, and then the reference probe together with the equilibriumone. This way, one avoids having too many thermocouples inside the chamber that mightcause interferences on each other’s signals. It was later discovered that the noise was infact due to a defect in one of the acquisition cards. The test conditions are summarizedin table B.2.


(a) (b)

Figure 3.12: Test campaign: Damkohler probes. Picture (b) was taken after the tests,from left to right: equilibrium, reference, and frozen probes. The damage done on theequilibrium probe is clearly visible.

Name rb (mm) rc (mm)

Equilibrium 57.5 5Reference 25 10Frozen 15 15

Table 3.2: Geometrical characteristics of the Damkohler probes.

3.3.1 Frozen probe

The heat fluxes measured at the frozen probe with respect to the one measured atthe reference probe are depicted in figures 3.13. The data recorded during previous testcampaigns are also depicted when available. Two observations can be made at first sight.First, the heat flux measured at the frozen probe is as expected more important than theone measure at the reference probe. Second, the agreement between the different testcampaigns is poor at 1, 500 Pa (a) but sufficiently good at 10, 000 Pa (c). The sourceof those differences is discussed in section 3.4.

As it is difficult to control the plasma power to retrieve exactly the same heat flux atthe reference probe for the two series of test, it was decided to perform a regression on thedata points obtained. Different regression methods were tested. Table 3.3 summarizesthe results obtained for 1, 500 Pa. The second order regression was abandoned as thequadratic term is negligible and it results in a more important standard deviation σ thanthe other methods. Although the linear and robust linear regressions have the loweststandard deviations, they result in a certain intercept at the origin, what is obviously notphysical. Therefore, the single slope was preferred. The same analysis was performedfor 10, 000 Pa.


Type x0 x1 x2 σ (%)

Slope − 1.69 − 6.63Linear 46.20 1.65 − 5.78Robust linear 45.80 1.65 − 5.77Quadratic −36.04 1.90 −1 · 10−4 10.04

Table 3.3: Regressions tested on the data points obtained for 1, 500 Pa.

3.3.2 Equilibrium probe

Two observations can be made from the results depicted in figure 3.14. First, the heatflux at the equilibrium probe is as expected smaller than the one at the reference probe.Second, the agreement with the data recorded by Krassilchikoff is rather good, but notwith the one recorded by Panerai.

At the end of that set of measurement, the equilibrium probe melted (figure 3.12 (b)).It happened around Qw = 1, 500 kW/m2 at 1, 500 Pa, probably due to a pocket of airtrapped in the cooling fluid. Due to time constraints, it was unfortunately not possibleto wait for a new probe and record data at higher pressure. Therefore, the regressionfrom Krassilchikoff and Panerai are used for 10, 000 Pa. Both indicate different values,which emphasizes on the difficulty to perform heat flux measurements in the Plasmatron.However, when rebuilding the free-stream conditions according to the γref defined by theminimax, it appeared that regression law defined by Krassilchikoff led to a He higherthan the upper limit of the interval. Panerai’s regression was therefore used as it is moreconsistent with the rest of the experimental campaign.

3.3.3 Summary

Finally, the regressions used for the rest of this report are:

• At 1, 500 Pa

Qeqw = 0.81 ·Qref

w ± 32.38% (19 : 20)

Qfrw = 1.69 ·Qref

w ± 13.36% (19 : 20)

• At 10, 000 Pa

Krassilchikoff (2006): Qeqw = 0.81 ·Qw ref ± 12.90% (9 : 12)

Panerai (2011): Qeqw = 0.66 ·Qw ref ± 12.90% (19 : 20)

Qfrw = 1.46 ·Qref

w ± 17.00% (19 : 20)


0 500 1000 1500 20000

500

1000

1500

2000

2500

3000

3500

4000


Heat flux F

rozen p

robe [kW

/m2]

Experiment

Qw(frozen) = 1.6876*Qw(reference)

H−W. Krass. (2006)

F. Panerai (2012)

(a)

0 500 1000 1500 20000

500

1000

1500

2000

2500

3000

3500


Heat flux F

rozen p

robe [kW

/m2]

F. Panerai (2012)

H−W. Krass. (2006)

Qw(frozen) = 1.4612*Qw(reference)

Experiment

(b)

Figure 3.13: Qfrw with respect to Qref

w at ps = 1, 500 Pa (a), and 10, 000 Pa (b).

0 500 1000 1500 20000

500

1000

1500

2000


Heat flux E

quili

brium

pro

be [kW

/m2]

H−W. Krass. (2006)

Experiment

F. Panerai (2012)

Qw(equilibrium) = 0.8061*Qw(reference)

Figure 3.14: Qeqw with respect to Qref

w at ps = 1, 500 Pa.

3.4 Uncertainty quantification

For the test conducted with the Damkohler probes, the quantity of interest is simplythe heat flux. The overall relative uncertainty on heat flux measurement is calculatedto be 10% of the recorded value, including measurement chain accuracy and uncertaintydue to the fluctuation of the measurement [3]. The error bars were already depicted infigures 3.13 and 3.14. This could be part of the explanation for the difference observedbetween the test campaigns. However, the regression performed on those heat fluxesmeasurement is used to further analyze the GSI processes in chapter 4. For that part,the same comments as for the minimax test apply.

For the minimax, those quantities of interest are the upper and lower limits of the ref-erence catalycity and outer edge enthalpy. Those values were obtained not only throughheat flux measurement, but also numerical pre- and post-processing. It is therefore ex-tremely complicated, if not impossible, to put error bars on the data points plotted infigures 3.6, 3.9 and 3.10. However, previous studies were conducted to identify whichwere the sensitive parameters on both the rebuilt enthalpy and the sample catalycity.Although the exact conclusion depends on the particular test conditions, the dynamic


pressure was generally identified as the most important contributor to the errors, fol-lowed by the static pressure together with the heat flux [19] [27]. Unfortunately, noneof those parameters is controlled as well as it should be: pdyn is not measured but ob-tained from interpolated polynomial laws, ps is not recorded but only monitored by theoperator of the Plasmatron, and there is a 10% relative uncertainty on the value of Qw.

The range definitions defined in section 3.2.4 would be greatly enhanced if the corre-sponding uncertainty quantification was performed. In the absence of that information,cross verification with other methods such as spectroscopic or heat flux measurement isdesirable.

Chapter 4

Gas-surface interaction analysisfor catalycity modelling

The objective of this chapter is to investigate the evolution of the driving processes ofGSI in function of the LHTS parameters. Those investigations are based on the resultsof the experiments presented in chapter 3. Although the conclusions are only qualitative,they provide the necessary sound foundation on which a quantitative model of catalycitywill be developed. It was decided to focus on nitrogen and oxygen given that, as alreadymentioned in section 2.2, experimental evidences tend to show that their production isprevailing on that of other species [19].

The evolution of catalycity, which was directly obtained as a result from the post-processing, is first presented. The evolution of the Damkohler numbers is then described:first the wall Damkohler number, as it is easy to estimate, and then the gas-phaseDamkohler number, which requires investigations within the boundary layer. The evo-lution from a non-catalytic wall to a catalytic wall is also briefly overviewed. Finally,the relative evolution of the different parameters is commented.

4.1 Catalycity

The free-stream conditions were determined based on the interval defined with the ex-perimental results of the minimax. Since this allows only defining an interval, the free-stream enthalpy was arbitrarily fixed to an average value, on which a few correctionswere applied to make it physically consistent. The values that were finally used aresummarized in table 3.1). The free-stream condition being fixed for all the data pointsconsidered, the catalycity of the frozen and the equilibrium probes can be determined.

The evolution γ with respect to He is depicted in figures for the two pressure levelsinvestigated. Several observations can be made regarding its evolution:

• At low pressure, it is approximately constant for both probes, except for one pointof the equilibrium probe at low He. At higher pressure, the catalycity is increasing.

35

36 GSI analysis for catalycity modelling

• It is slightly more important for the frozen probe than for the equilibrium one,except for that same point at low ps and He.

• It is less important for the low pressure case than for the high pressure one.

15 20 25 30 35 4010

−3

10−2

10−1

100


Cata

lycity (

log)

[−]

Frozen

Equilibrium

(a)

15.5 16 16.5 17 17.5 18 18.510

−3

10−2

10−1

100


Cata

lycity (

log)

[−]

Frozen

Equilibrium

(b)

Figure 4.1: Evolution γ, in logarithmic scale, for the equilibrium and frozen probes withrespect to He at ps = 1, 500 Pa (a) and ps = 10, 000 Pa (b).

4.2 Wall Damkohler number

It is possible to determine Daw without need to investigate the boundary layer by directlyapplying equation 2.17. Indeed, assuming kw is only a function of the wall’s materialand temperature, it remains the same for all the data points since they were obtained fora copper cold wall. The only variable to determine are therefore De, which is obtainedwith equation 2.11, and δ, that is retrieved from the first NDP, which is defined as:

NDP1 =δ

rb(4.1)

The evolution of vdiff with respect to He is depicted in figures 4.2 for the two pressurelevels investigated. Several observations can be made regarding its evolution:

• At both pressure levels, and for both nitrogen and oxygen, it is clearly increasingas He. This is mainly due to the diffusion coefficient that strongly increases withincreasing temperature, as depicted in figure 2.3. This is sufficient to compensatefor the decrease in boundary layer thickness, due to the increasing velocity.

• It is considerably more important (∼ 5 times) for the frozen probe than for theequilibrium one. Indeed, although the free-stream conditions are the same for both,and thereby also De, the boundary layer is thicker over the equilibrium probe thanover the frozen one, due to its larger diameter.

GSI analysis for catalycity modelling 37

• It is also considerably more important (∼ 5 times) for the low pressure and for thehigh one. This is again due to the diffusion coefficient that drastically decreasesas pressure increases.

• It is slightly more important for oxygen than for nitrogen. This is once more dueto the diffusion coefficient.

15 20 25 30 35 400

2

4

6

8

10

12


Diffu

sio

n v

elo

city [m

/s]

Frozen

Equilibrium

nitrogen

oxygen

(a)

15.5 16 16.5 17 17.5 18 18.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6


Diffu

sio

n v

elo

city [m

/s]

Frozen

Equilibrium

nitrogen

oxygen

(b)

Figure 4.2: Evolution vdiff of nitrogen and oxygen for the equilibrium and the frozenprobes with respect to He at ps = 1, 500 Pa (a) and ps = 10, 000 Pa (b).

4.3 Gas-phase Damkohler number

4.3.1 Time-scale characteristic of the flow

There is also one element of Dag that we can directly extract: the time-scale character-istic of the flow τflow. As mentioned in section 2.2.3, τflow is considered as equal to βe.That quantity can directly be retrieved from the second NDP, which is defined as:

NDP2 =βe · rbve

(4.2)

where ve is obtained as one of the outputs of the rebuilding performed with CERBOULA.

Its evolution with respect to the He is depicted in figure 4.3. several observations canbe made regarding its evolution:

• At both pressure levels, it is clearly decreasing as He increases for the equilibriumprobe. That evolution is less pronounced for the frozen probe, although a slightdecay is observed.

• It is considerably more important for the equilibrium probe than for the frozenone, although that difference reduces with increasing He.

• It is almost one order of magnitude larger and decreases faster for the high pressurelevel than for the low one.


15 20 25 30 35 400

0.5

1

1.5

2

2.5

3

3.5

4x 10

−3


Invers

e o

f oute

r edge v

elo

city g

radie

nt [s

]

Equilibrium

Frozen

(a)

15.5 16 16.5 17 17.5 18 18.50

0.005

0.01

0.015

0.02

0.025

0.03

Outer edge entlapy [MJ/kg]

Invers

e o

f oute

r edge v

elo

city g

radie

nt [s

]

Frozen

Equilibrium

(b)

Figure 4.3: Evolution of the inverse of the βe with respect to He at ps = 1, 500 Pa (a)and ps = 10, 000 Pa (b).

4.3.2 Time-scale characteristic of the homogeneous chemistry

The time-scale characteristic of the homogeneous chemistry is more complex to define,as it there is no simply way to quantify it in a single number. However, the evolutionrecombination equilibrium constant in the boundary layer is an indicator of its order ofmagnitude.

It is depicted in figure 4.4 for both the equilibrium and the frozen probes, and bothnitrogen and oxygen, at a pressure of ps = 1, 500 Pa. It has also been plotted for a non-catalytic wall, the difference between non-catalytic and catalytic wall being investigatedin section 4.3.3. The same kind of relation is obtained at ps = 10, 000 Pa, depicted infigure C.1. Some observations can be made regarding its evolution:

• It is several orders of magnitude larger for the chemistry of nitrogen than for thechemistry of oxygen. Indeed, it is a well-known fact that O2 dissociates at lowertemperatures than N2 (2, 500 K versus 4, 000 K under atmospheric pressure).

• It is refrained as He increases: both the thickness of the layer in which it increasesexponentially and its free-stream value decrease. This is due to the higher tem-perature within the boundary layer, the mixture’s composition having little effect(figure 2.2).

• The effect of βe and ps is more difficult to perceive. Although there are somechanges, they are not as pronounced as for He and/or combined with changes δ.

4.3.3 Non-catalytic wall

Another angle of attack to investigate the evolution of Dag is the species concentrationat the wall. This was done by comparing the concentration of N2 and O2 at the wall andin the free-stream, for a catalytic wall, a non-catalytic wall, and a fully catalytic wall,


0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040

1

2

3

4

5

6

7

8

9

10x 10

8

Distance to wall [m]

N2 r

ecom

bin

ation e

quili

brium

consta

nt [−

](D

unn−

Kang)

Catalytic wall

Non−catalytic wall

He = 16.22 MJ/kg

He = 36.24 MJ/kg

(a)

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040

1

2

3

4

5

6

7

8

9

10x 10

4


02 r

ecom

bin

ation e

quili

brium

consta

nt [−

](D

unn−

Kang)

Catalytic wall


He = 16.22 MJ/kg

He = 36.24 MJ/kg

(b)

0 1 2 3 4 5 6

x 10−3

0

1

2

3

4

5

6

7

8

9

10x 10

8


N2 r

ecom

bin

ation e

quili

brium

consta

nt [−

](D

unn−

Kang)

Catalytic wall


He = 36.24 MJ/kg

He = 16.22 MJ/kg

(c)

0 1 2 3 4 5 6

x 10−3

0

1

2

3

4

5

6

7

8

9

10x 10

4


O2 r

ecom

bin

ation e

quili

brium

consta

nt [−

](D

unn−

Kang)

Catalytic wall


He = 36.24 MJ/kg He = 16.22 MJ/kg

(d)

Figure 4.4: Reaction equilibrium constant for N and O into N2 (a,c) and O2 (b,d)respectively within the boundary layer of the equilibrium probe (a,b) and the frozenprobe (c,d) for different He, according to the chemistry model of Dunn and Kang, atps = 1, 500 Pa.

both for the frozen and the equilibrium probe, depicted in figure 4.5 for ps = 1, 500 Pa.The concentrations over a non-catalytic wall and a fully catalytic wall were obtainednumerically, imposing the wall catalycity and then varying the heat flux at the wall toobtain the same free-stream conditions as for the corresponding catalytic wall.

Several comments can be made:

• In most of the cases, the concentration at the non-catalytic wall is higher thanthe concentration at the outer edge of the boundary layer. The only exceptionis oxygen at high pressure. This means that even if the wall is inactive, a smallamount of recombination take place in the gas phase. In other words: Dag is smallbut non-zero, even though Daw is zero.

• Except for oxygen at low pressure, the concentration at the wall of the non-catalyticequilibrium probe is higher than that at the wall of the non-catalytic frozen one.This implies that Dag decreases as βe increases.

• In the case of nitrogen, it seems that increasing pressure is favouring gas-phaserecombination. The opposite is observed for oxygen.


15 20 25 30 35 40 45 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


Wa

ll m

ola

r fr

actio

n o

f N

2 [

−]

Equilibrium not catalytic

Equilibrium actual

Equilibrium fully catalytic

Frozen not catalytic

Frozen actual

Frozen fully catalytic

Outer edge molar fraction

(a)

15 20 25 30 35 40 45 5010

−8

10−6

10−4

10−2

100


Wa

ll m

ola

r fr

actio

n o

f O

2 (

log

) [−

]


Equilibrium actual

Equilibrium fully catalytic


Frozen actual

Frozen fully catalytic


(b)

16 16.5 17 17.5 18 18.5 19 19.50.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75


Wall

mola

r fr

action o

f N

2 [−

]


Equilibrium actual

Fully catalytic


Frozen actual


(c)

16 16.5 17 17.5 18 18.5 19 19.510

−5

10−4

10−3

10−2

10−1

100


Cata

lycity (

log)

[−]


Equilibrium actual

Fully catalytic


Frozen actual


(d)

Figure 4.5: Concentration of N2 (a,c) and O2, in logarithmic scale, (b,d) at the wall andin the free-stream, for a catalytic wall γ, a non-catalytic wall γ = 0, and a fully catalyticwall γ = 1, both for the frozen and the equilibrium probe, at ps = 1, 500 Pa (a,b) andps = 10, 000 Pa (c,d).

4.3.4 From non-catalytic to catalytic wall

However, the observations made in section 4.3.3 are correct only if the evolution of Dag ispreserved when passing from a non-catalytic wall to a catalytic wall. The verification ishere performed for the equilibrium probe at low pressure. Nevertheless, the same holdsfor the frozen probe, and at high pressure. In order to convince himself, the reader canrefer to the figures in appendix C.

The wall being catalycity, it will impose a species concentration gradient in the regionnear the wall, as depicted in figures 4.6 compared to a non-catalytic wall. That gradientforces dissociated species to recombine. The recombination reaction being exothermic,it heats up the gas, and the boundary layer’s temperature profile inflates, as depictedin figure 4.7. Replacing the non-catalytic wall with a catalytic wall will not only causeDaw to increase, but will also act on the value Dag.


0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


N2

mo

lar

co

nce

ntr

atio

n [

−]

Catalytic wall


He = 36.24 MJ/kg

He = 16.22 MJ/kg

(a)

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.0410

−8

10−6

10−4

10−2

100


O2

mo

lar

co

nce

ntr

atio

n (

log

) [−

]

Catalytic wall


He = 16.22 MJ/kg

He = 36.24 MJ/kg

(b)

Figure 4.6: Molar concentration x of N2 (a) and O2, in logarithmic scale, (b) within theboundary layer of the equilibrium probe for different He at ps = 1, 500 Pa.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040

1000

2000

3000

4000

5000

6000

7000


Tem

pera

ture

[K

]

Catalytic wall


He = 36.24 MJ/kg

He = 16.22 MJ/kg

Figure 4.7: Temperature distribution within the boundary layer of the equilibrium probefor different He at ps = 1, 500 Pa.

The diffusion coefficient of both nitrogen and oxygen are depicted in figure 4.8, andtheir recombination reaction equilibrium constant in figure 4.4. They were computedaccording with Dunn and Kang’s model for the chemistry, as it was already used for thenumerical post-processing. Increasing γ from non-catalytic to finite catalycity:

• Causes the diffusion coefficient to increase, due to the temperature rise describedearlier. This, in turn, decreases τdiff. As He increases, however, the temperaturerise is less important. The effect on the diffusion coefficient is therefore less visible,especially for nitrogen. A slight decrease on the catalytic wall profile with respectto the non-catalytic wall profile can even be observed in figure 4.8 (a). The effectof the mixture’s composition being close to recombined state takes over the thatof temperature increase (figure 2.3).

• Has a restraining effect on Kc; although its free-stream value remains the same,the layer in which it considerably increases is thinner for a catalytic wall. Thiscauses τhomo. That effect is less visible as He increases.


Globally, the effect of changing from a non-catalytic surface to a catalytic surface isto decrease Dag. That decreasing effect might could compensate the effect of decreasingDag with increasing βe that was concluded in section 4.3.3. However, this very unlikelysince the increase of τflow with increasing βe is important.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040

0.1

0.2

0.3

0.4

0.5

0.6

0.7


N d

iffu

sio

n c

oeffic

ient [m

2/s

]

Catalytic wall


He = 36.24 MJ/kg

He = 16.22 MJ/kg

(a)

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.040

0.1

0.2

0.3

0.4

0.5

0.6

0.7


O d

iffu

sio

n c

oeffic

ient [m

2/s

]

Catalytic wall

Non−catalytic wallHe = 36.24 MJ/kg

He = 16.22 MJ/kg

(b)

Figure 4.8: Diffusion coefficient of atomic nitrogen (a) and oxygen (b) within the bound-ary layer of the equilibrium probe for different He, at ps = 1, 500 Pa.

4.4 Conclusion

The overall conclusions of the present chapter are summarized in table 4.1. A fewinteresting points should be commented:

• As mentioned in section 4.3.3, a quantitative definition of τhomo is more complexthan the other time-scales. Even though a rigorous analysis of the boundary layerallowed to define it, at least qualitatively, no satisfying conclusion could be drawnfor increasing βe and ps. Indeed, for βe, for example, τflow and Dag are decreasing asβe increases, τhomo could be either decreasing, but slower than τflow, or increasing,thereby contributing to the action of τflow.

• As observed in section 4.3.3, Dag increases for nitrogen and decreases for oxygenas ps increases. This is consistent with the characteristic time-scales: for nitrogen,the increase of τflow is sufficient to compensate that of τhomo, while for oxygen itis not. However, the chemistry of nitrogen prevailing on that of oxygen, Dag isassumed to be globally increasing.

• Dag is decreasing with increasing βe; the boundary layer developing over the equi-librium and frozen probes are indeed respectively close to equilibrium and frozenstate.

• The observation that γ increases as He increases in only correct at high ps. At lowps, the few points computed do not allow to clearly determine a tendency.


• γ tends to behave in the opposite way than Daw. Indeed, if Daw decreases for afixed kw, it is easier for the species to diffuse through the boundary layer. Sincemore species diffuse to the wall, catalycity increases. This tends to prove that, atleast at high pressure, the chemistry at the surface is diffusion-controlled.

• A general γ that includes both the one for nitrogen and oxygen chemistry is usually.However, both Damkohler numbers evolve in the same fashion. It might thereforebe desirable to consider the γ of each species separately.

He ↑ βe ↑ ps ↑ N vs. O

τflow ↓ ↓ ↑ =τhomo ↑ ? ? <τdiff ↓ ↓ ↑ >

Dag ↓ ↓ ↑ >Daw ↓ ↓ ↑ >

γ ↑ ↑ ↓ ?

Table 4.1: Summary of the observations made on the qualitative evolution of Dag, Dawand γ as a function of the LHTS parameters He, βe and ps on a cold wall.

Conclusion

Achievements

The objective of this project was to investigate the driving processes of GSI over a coldwall, to take a first step towards an accurate model for wall catalycity. That goal wasachieved through the following steps:

• Chapter 1: definition of the problem - why is there a need for a model of catalycity?

• Chapter 2: deeper understanding of the GSI and identification of the parametersused to describe it.

• Chapter 3: description of the facility used and the experimental campaign per-formed. Two test campaigns were performed: the minimax and the Damkohlerprobes. The minimax, in particular, was performed at three different pressure levelsand - for the first time - post-processed using the appropriate chemistry models.

• Chapter 4: investigation of the driving parameters of GSI and their evolutionwith respect to changes in test conditions. The conclusions of that chapter, andthe methodology applied to reach it, are a sound foundation for future catalycitymodelling.

The driving parameters that were looked upon are the wall Damkohler number Daw,the gas-phase Damkohler number Dag, and the wall catalycity γ. Their respective evolu-tion was investigated with respect to the parameters applied to duplicate the boundarylayer at the stagnation point of a body flying at hypersonic velocity according to theLHTS methodology; the outer edge enthalpy He, velocity gradient βe, and pressure ps.

It was found that both Dag and Daw decrease for increasing He and increasing βe,while it increases for increasing ps. The opposite behaviour is observed for γ, althoughfor the behaviour of the later with respect to He is less obvious at low pressure. Indeed,if Daw decreases for a fixed kw, it is easier for the species to diffuse through the boundarylayer. Since more species diffuse to the wall, catalycity increases.

Furthermore, those parameters were found to be quite different for the chemistryof nitrogen and oxygen. This tends to indicate that γ should be considered separatelyfor nitrogen and for oxygen. However, more evidences are required to support thisconclusion.

45

46 Conclusions

Additionally to that primary goal, a limit of the reference catalycity (copper cold wall)for sample testing in the Plasmatron was fixed for the three pressure levels investigated.This allows for a less conservative approach in future tests, reducing the over-estimationof samples catalycity.

Perspectives

First, the results presented in this report could be improved. Indeed, rather than usingthe interval limits defined with the minimax tests, in section 3.2, the maximum intervallimits could be used taking into account the uncertainty on the heat flux measured andon the dynamic pressure regression. In turn, the analysis of chapter 4 could be performedfor the two points at the edges of the interval rather than for one point included in thatinterval. Although it represents a great amount of work, it would allow drawing errorbars on the figures.

It is also possible to take advantage of the many experiments that were performedin the past. In addition to the S-curves obtained for the quartz, and silver probes,the one obtained for the Damkohler probes and the molybdenum probe could also besuperimposed on that of the reference probe, providing they were obtained for the samefree-stream conditions. By doing so, the definition of the intervals could be considerablyrefined. This, however, should be performed carefully as it has been shown that thereproducibility of experiments in the Plasmatron is poor.

Finally, the time-scale characteristic of the homogeneous chemistry could be quanti-fied in a single number for each test condition, as it is the case for the other time-scales.Such an attempt was already done by Herpin [11].

Once finer intervals are defined, and the error bars determined for the driving param-eters of GSI, it will be possible to start a quantitative model of catalycity.

Catalycity modelling as such will most probably require additional experiments ornumerical computation to properly understand the effect of each parameter. This can bedone in two fashions; either by varying on the time-scales (τflow, τhomo, and τdiff), or byvarying on the LHTS parameters (He, βe and ps). The most suitable option is the secondone, as the LHTS parameters can be independently played with, while the time-scalesare strongly correlated. Indeed, the effect of τhomo could be investigated numericallyby changing the values of the chemistry constants. A variation of chemistry wouldinevitably cause a variation in the temperature distribution and mixture’s compositionwithin the boundary layer. This, in turn, would act on τdiff.

Furthermore, additional tests could be performed varying the wall’s temperature.This would not only allow to observe the evolution of the time-scale characteristic of theheterogeneous chemistry, τhete, but also to have a finer definition of the relative evolutionof Dag and Daw.

On another topic, as mentioned in section 3.2.2, a comprehensive sensitivity studyis desirable, especially to define which chemistry model has to be used under which

Conclusions 47

conditions, and why. That sensitivity could be considerably improved with actual mea-surements (e.g. spectroscopy) to assess which chemical models are the most accurateones depending on the test conditions.

Last word

The research presented in this report is thus a solid base for an improved understanding ofGSI, and the development of an accurate model for catalycity. That model is of primaryimportance for the proper design of future super-orbital re-entry vehicles. Those vehiclesare the one that will ensure the safe return of sample or crew return missions from othercelestial bodies such as asteroids, the Moon, or Mars.

48 Conclusions

Appendix A

Dunn and Kang’s modelnumerical values

Reaction M Cf nf (Ea/R)f Cb nb (Ea/R)bNitrogen O, NO, O2 1.10E + 16 −0.5 0 1.900E + 17 −0.5 1.13E + 5recombination N 2.27E + 21 −1.5 0 4.085E + 22 −1.5 1.13E + 5

N2 2.72E + 16 −0.5 0 4.700E + 17 −0.5 1.13E + 5

Oxygen N , NO 3.00E + 15 −0.5 0 3.600E + 18 −1.0 5.95E + 4recombination O 7.50E + 16 −0.5 0 9.000E + 19 −1.0 5.95E + 4

O2 2.70E + 16 −0.5 0 3.240E + 19 −1.0 5.95E + 4N2 6.00E + 15 −0.5 0 7.200E + 18 −1.0 5.95E + 4

Table A.1: Dunn and Kang’s model for nitrogen and oxygen chemistry, based on [23].The subscript f refers to the forward reaction, and b to the backwards reaction.

49

50 Dunn and Kang’s model numerical values

Appendix B

Test conditions for the minimaxand Damkohler probes campaigns

Test (−) ps (Pa) P (kW ) QCuw

(kW/m2

)QAg

w

(kW/m2

)QQuartz

w

(kW/m2

)1 1, 500 72.0 472.86 682.47 236.662 1, 500 92.5 679.98 991.83 443.243 1, 500 115.5 874.72 1315.11 594.574 1, 500 135.0 1062.30 1570.77 622.555 1, 500 145.0 1241.60 1772.41 746.08

6 5, 000 59.0 281.21 297.42 177.447 5, 000 71.5 471.46 565.65 342.268 5, 000 81.5 647.36 810.45 375.729 5, 000 107.0 849.09 1111.30 420.6510 5, 000 124.5 1062.74 1440.63 505.9911 5, 000 122.0 1112.69 1423.31 493.5912 5, 000 134.0 1298.65 1659.93 490.89

13 10, 000 87.5 552.57 692.96 481.5014 10, 000 87.5 661.88 723.60 443.0815 10, 000 95.0 861.54 918.45 525.5316 10, 000 119.0 1036.29 1213.52 538.0417 10, 000 124.5 1238.35 1507.14 670.99

Table B.1: Test conditions for the minimax campaign.

51

52 Test conditions

Test (−) ps (Pa) P (kW ) Qrefw

(kW/m2

)Qeq

w

(kW/m2

)Qfr

w

(kW/m2

)1 1, 500 112.0 316.80 131.68 600.892 1, 500 136.0 475.19 239.63 825.563 1, 500 157.0 672.11 324.82 1016.294 1, 500 187.0 799.25 437.43 1327.465 1, 500 223.0 973.98 632.30 1758.106 1, 500 261.0 1257.84 874.89 2225.987 1, 500 294.0 1273.06 932.14 2329.898 1, 500 305.0 1432.91 1001.54 2409.399 1, 500 319.0 1799.05 1300.85 2917.5410 1, 500 346.0 1967.10 1321.53 3226.84

11 10, 000 136.0 408.40 / 530.0312 10, 000 158.0 572.92 / 1030.6913 10, 000 175.0 805.10 / 1170.4714 10, 000 210.0 982.21 / 1375.4915 10, 000 250.0 1247.55 / 1902.8716 10, 000 265.0 1467.21 / 2220.6917 10, 000 292.0 1700.00 / 2421.7418 10, 000 332.0 1889.61 / 2630.0119 10, 000 381.0 2093.46 / 3123.8220 10, 000 200.0 932.79 / 1346.53

Table B.2: Test conditions for the Damkohler probes campaign.

Appendix C

High pressure boundary layerinvestigations

0 0.005 0.01 0.015 0.020

2

4

6

8

10x 10

8


N2 r

ecom

bin

ation e

quili

brium

consta

nt [−

](G

upta

)

Catalytic wall


He = 18.29 MJ/kg He = 15.95 MJ/kg

(a)

0 0.005 0.01 0.015 0.020

1

2

3

4

5

6

7

8

9

10x 10

4


O2 r

ecom

bin

ation e

quili

brium

consta

nt [−

](G

upta

)

Catalytic wall


He = 15.95 MJ/kgHe = 18.29 MJ/kg

(b)

0 1 2 3 4 5 6

x 10−3

0

2

4

6

8

10x 10

8


N2 r

ecom

bin

tation e

quili

brium

consta

nt [−

](G

upta

)

Catalytic wall


He = 15.95 MJ/kgHe = 18.29 MJ/kg

(c)

0 1 2 3 4 5 6

x 10−3

0

1

2

3

4

5

6

7

8

9

10x 10

4


02 r

ecom

bin

ation e

quili

birum

consta

nt [−

](G

upta

)

Catalytic wall


He = 18.29 MJ/kg He = 15.95 MJ/kg

(d)

Figure C.1: Reaction equilibrium constant for N and O into N2 (a,c) and O2 (b,d)respectively within the boundary layer of the equilibrium probe (a,b) and the frozenprobe (c,d) for different He, according to the chemistry model of Gupta, at ps = 10, 000Pa.

53

54 High pressure boundary layer investigations

0 0.005 0.01 0.015 0.02 0.0250

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08


N d

iffu

sio

n c

oeffic

ient [−

]

Catalytic wall


He = 15.95 MJ/kg

He = 18.29 MJ/kg

(a)

0 0.005 0.01 0.015 0.02 0.0250

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08


O d

iffu

sio

n c

oeffic

ient [−

]

Catalytic wall


He = 15.95 MJ/kg

He = 18.29 MJ/kg

(b)

0 1 2 3 4 5 6

x 10−3

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08


N d

iffu

sio

n c

oeffic

ient [m

2/s

]

Catalytic wall


He = 15.95 MJ/kg

He = 18.29 MJ/kg

(c)

0 1 2 3 4 5 6

x 10−3

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08


O d

iffu

sio

n c

oeffic

ient [m

2/s

]

Catalytic wall


He = 15.95 MJ/kg

He = 18.29 MJ/kg

(d)

Figure C.2: Diffusion coefficient of atomic nitrogen N (a,c) and oxygen O (b,d) withinthe boundary layer of the equilibrium probe (a,b) and the frozen probe (c,d) for differentHe, at ps = 10, 000 Pa.

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