REPORT - Investigation of GSI in PWT for Catalycity Characterization by Guerric de Crombrugghe

von Karman Institute for Fluid Dynamics Chaussee de Waterloo, 72 B - 1640 Rhode Saint Genese - Belgium

Research Master Report Investigation of Gas Surface Interactions in Plasma Wind Tunnels for Catalycity Characterization

Guerric de CROMBRUGGHE Supervisor: Pr. Olivier CHAZOT Advisor: Dr. Francesco PANERAI

June 2012

Acknowledgments The author would like to thank Pr. Olivier Chazot for all the time he spent in guidance and explanations, Pascal Collin for his support and patience during the - very long - test campaign, Dr. Francesco Panerai for his wise advices and comments on this report, Isil Sakraker 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 solar system. However, the free-stream enthalpies involved with the flow encountered are so important that flight duplication is not feasible anymore in ground testing facilities. This requires a new approach of ground testing: facilities should be used to understand and model 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: gassurface interaction (GSI). The ultimate objective is to provide a sound foundation for an accurate model of wall catalycity. To achieve that goal, two test campaigns were performed in the von Karman Institute’s main plasma wind tunnel, the Plasmatron. Information was retrieved regarding the wall catalycity and heat flux for various conditions of static pressure, free-stream specific enthalpy, wall material (test 1: minimax) and probe geometry (test 2: Damköhler probes), while keeping the wall temperature constant. Based on those experimental measurements, and with some additional numerical post-processing, the evolution the Damköhler numbers and catalycity is determined in function of the local heat transfer simulation (LHTS) parameters. The analysis is only performed for nitrogen and oxygen given that, as experimental evidences tend to show that their production is prevailing on that of other species. As a general conclusion, it was found that both gas-phase and the wall Damköhler numbers decrease for increasing outer edge enthalpy, velocity gradient, and decreasing pressure. The opposite behaviour is observed for catalycity, although for the behaviour of the later with respect to outer edge enthalpy is less obvious at low pressure. Indications are given on how to pursue those investigations towards a model of catalycity. Additional comments are made on the reference catalycity of sample testing in the Plasmatron and the correct use of chemistry models.

Contents Abstract

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Acknowledgment

List of Figures

List of Tables

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List of Symbols

1 Ground testing strategy for super-orbital re-entry 1.1 Super-orbital atmospheric re-entry . . . . . . . . . . 1.1.1 Orbital mechanics considerations . . . . . . . 1.1.2 Orders of magnitude . . . . . . . . . . . . . . 1.2 Issues for experimentation on high velocity flows . . 1.2.1 Aerothermodynamic facilities . . . . . . . . . 1.2.2 Radiative heating and ablation . . . . . . . . 1.2.3 Gas-surface interactions . . . . . . . . . . . . 1.3 New testing strategy . . . . . . . . . . . . . . . . . . 2 High temperature gas dynamics applied 2.1 Stagnation line features . . . . . . . . . 2.2 Brief overview of gas-surface interactions 2.2.1 Chemistry constants . . . . . . . 2.2.2 Diffusion coefficient . . . . . . . 2.2.3 DamkÂ¨ohler numbers . . . . . . . 2.2.4 Catalycity . . . . . . . . . . . . . 2.3 Closing remark on catalycity modelling

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atmospheric re-entry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Test campaign and results 3.1 Heat flux measurement in the Plasmatron . . . . . . 3.1.1 Heat flux and dynamic pressure measurement 3.1.2 Pre-processing numerical tools . . . . . . . . 3.2 Minimax . . . . . . . . . . . . . . . . . . . . . . . . . vii

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Table of contents . . . . . . . . .

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23 24 28 28 29 30 31 31 32

4 Gas-surface interaction analysis for catalycity modelling 4.1 Catalycity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Wall Damk¨ohler number . . . . . . . . . . . . . . . . . . . . . . 4.3 Gas-phase Damk¨ohler number . . . . . . . . . . . . . . . . . . . 4.3.1 Time-scale characteristic of the flow . . . . . . . . . . . 4.3.2 Time-scale characteristic of the homogeneous chemistry 4.3.3 Non-catalytic wall . . . . . . . . . . . . . . . . . . . . . 4.3.4 From non-catalytic to catalytic wall . . . . . . . . . . . 4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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35 35 36 37 37 38 38 40 42

3.3

3.4

3.2.1 Low pressure . . . . 3.2.2 High pressure . . . . 3.2.3 Medium pressure . . 3.2.4 Reference catalycity Damk¨ohler probes . . . . . 3.3.1 Frozen probe . . . . 3.3.2 Equilibrium probe . 3.3.3 Summary . . . . . . Uncertainty quantification .

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A Annex A

B Annex B

C Annex C

References

List of Figures 1

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

1.1

Interplanetary Hohmann transfer. . . . . . . . . . . . . . . . . . . . . . . .

1.2

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

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 function of gas temperature, according to Dunn and Kang’s chemistry model. It is represented for a mixture in thermal equilibrium at a specific enthalpy H = 36.24 M J/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 function of T and ps . Each curve is represented for a mixture in thermal equilibrium at a specific enthalpy H = 36.24 M J/kg, and for a mixture where all the species are recombined. . . . . . . . . . . . . . . . . . . . . . 15

3.1

Schematic overview of the LHTS method: the flow is duplicated in the boundary 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 outer He with γ, in logarithmic scale. Figure 2 realized for the reference probe at ps = 1, 500 P a and Qref w = 875 kW/m .

3.3

Recorded heat flux over time for the reference probe at ps = 1500 P a. . . 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 different minimax test campaigns for ps = 1, 500 P a. Each dataset consists out of two curves that are the upper and lower limits of the intervals. The ”data used” set is the one used in chapter 4. Krassilchikoff’s results are based on molybdenum rather than quartz as lower catalycist. . . . . . . . . . . . 24 ix

Table of contents 3.7

The methodology applied for figure 3.5 is not valid anymore for higher pressure: there are no common values of the outer edge enthalpy for the three probes. This figure was realized at ps = 10, 000 P a and Qref w = 861 kW/m2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.8

Figure 3.7 is here reproduced for three different chemistry models. This 2 figure was realized at ps = 10, 000 P a and Qref w = 861 kW/m . . . . . . . . 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 P a. Each dataset consists out of two curves that are the upper and lower limits of the intervals. The ”data used” set is the one used in chapter 4. Krassilchikoff’s results 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 different methodologies for ps = 5, 000 P a. Each dataset consists out of two curves that are the upper and lower limits of the intervals. Krassilchikoff’s results are based on molybdenum rather than quartz as lower catalycist, and post-processing using Dunn and Kang’s model. . . . . . . . . . . . . . . . 28 3.11 Logarithmic average of γCu as defined by the intervals obtained with the minimax methodology, in logarithmic scale, and corresponding He for different ps . The error bars represent the limits of the intervals defined by the minimax. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.12 Test campaign: Damk¨ohler probes. Picture (b) was taken after the tests, from left to right: equilibrium, reference, and frozen probes. The damage done on the equilibrium probe is clearly visible. . . . . . . . . . . . . . . . 30 ref 3.13 Qfr w with respect to Qw at ps = 1, 500 P a (a), and 10, 000 P a (b). . . . . 32 ref 3.14 Qeq w with respect to Qw at ps = 1, 500 P a. . . . . . . . . . . . . . . . . . . 32

4.1

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

4.2

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

4.3

Evolution of the inverse of the βe with respect to He at ps = 1, 500 P a (a) and ps = 10, 000 P a (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) and the frozen probe (c,d) for different He , according to the chemistry model of Dunn and Kang, at ps = 1, 500 P a. . . . . . . . . . . . . . . . . . . . . 39

4.5

Concentration of N2 (a,c) and O2 , in logarithmic scale, (b,d) at the wall and 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 equilibrium probe, at ps = 1, 500 P a (a,b) and ps = 10, 000 P a (c,d). . . . . . . . . . . 40

Table of contents 4.6

4.7 4.8

Molar concentration x of N2 (a) and O2 , in logarithmic scale, (b) within the boundary layer of the equilibrium probe for different He at ps = 1, 500 P a. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Temperature distribution within the boundary layer of the equilibrium probe for different He at ps = 1, 500 P a. . . . . . . . . . . . . . . . . . . . 41 Diffusion coefficient of atomic nitrogen (a) and oxygen (b) within the boundary layer of the equilibrium probe for different He , at ps = 1, 500 P a. 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) and the frozen probe (c,d) for different He , according to the chemistry model of Gupta, at ps = 10, 000 P a. . . . . . . . . . . . . . . . . . . . . . . . . . 53 C.2 Diffusion coefficient of atomic nitrogen N (a,c) and oxygen O (b,d) within the boundary layer of the equilibrium probe (a,b) and the frozen probe (c,d) for different He , at ps = 10, 000 P a. . . . . . . . . . . . . . . . . . . 54

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List of Tables 3.1 3.2 3.3

Values retained for γref and He versus Qref w as used for chapter 4. . . . . . 27 Geometrical characteristics of the Damk¨ohler probes. . . . . . . . . . . . . 30 Regressions tested on the data points obtained for 1, 500 P a. . . . . . . . 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 cold wall. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 backwards reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 B.1 Test conditions for the minimax campaign. . . . . . . . . . . . . . . . . . 51 B.2 Test conditions for the Damk¨ohler probes campaign. . . . . . . . . . . . . 52

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List of Symbols Acronyms ASTV CFD CERBERE ESA GSI ICP IPM LEO LHTS NDP NEBOULA PWT TPM TPS VKI

Aeroassisted Space Transfer Vehicles Computational Fluid Dynamics Catalycity and Enthalpy ReBuilding for a REference probe European Space Agency Gas-Surface Interaction Inductively Coupled Plasma Institute for Problems in Mechanics Low Earth Orbit Local Heat Transfer Simulation Non-Dimensional Parameters NonEquilibrium BOUndary LAyer Plasma Wind Tunnel Thermal Protection Material Thermal Protection System von Karman Institute for Fluid Dynamics

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List of Symbols

Roman symbols A cp Da E G H K k kB k0 L M m NA P p Q R r Re Rx T u v w˙ x

area specific heat at constant pressure Damk¨ohler number energy gravitional constant total enthalpy chemical equilibrium constant chemical rate constant Botlzmann’s constant frequency factor length number flux or third party chemical species mass Avogadro’s number power pressure heat flux gas constant radius Reynolds number molar concentration ratio temperature tangential velocity streamwise velocity mass production term chemical species molar fraction or tangential direction

Greek symbols β ∆ δ γ µ π ρ τ

energy accomodation coefficient or velocity gradient increment boundary layer thickness catalycity viscosity pi density time

− /s − mm − kg/m · s 3.14159265 kg/m3 s

m2 J/kg · K J 6.674E − 11 m3 /kg · s2 M J/kg − depends on order of reaction 1.381E − 23 m2 · kg/s2 · K − m − kg 6.022E + 23 /mol W Pa W/m2 8.315 J/mol · K m − − K m/s m/s kg/m3 · s − −

List of Symbols

Sub- and Superscripts â&#x2020;&#x2018; â&#x2020;&#x201C; a b body c dyn e eq f fr g hete homo i ref s w

backward diffusing forward diffusing activation related to the body of a probe or backwards related to the celestial body related to the corner of a probe or concentration dynamic outer edge / free-stream equilibrium related to the flow or forward frozen related to the gas phase heterogenous homogenous related to the species i reference static related to the wall

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Introduction Scope Since the very beginning of the space age, atmospheric re-entry has been considered as an 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 of robots on Mars, Venus, or even Titan. Although it remains a complicated field of engineering, all the tools needed for the design of controlled re-entry vehicles are nowadays available. One only needs to look at the recent success of Space-X to convince him-self. That private company managed to develop its own manned re-entry capsule, the Dragon, that successfully landed for the second time on the 31st of May 2012, in less than 10 years. The challenging manoeuvres for which additional tools need to be developed are uncontrolled re-entry, and super-orbital re-entry. The first one is necessary to improve the prediction of where and when space debris are going to crash on the Earth. The second one is needed for future exploration missions of the solar system, manned or robotic, and in particular for sample return missions.

Figure 1: Artistic impression of the Apollo Command Module re-entering the Earthâ&#x20AC;&#x2122;s atmosphere. Up to now, it is the fastest manned re-entry vehicle ever conceived. Credits: NASA

Introduction

Objective The present project focuses on a fluid dynamic issue associated with the second challenge. One of the main limitations of super-orbital re-entry vehicles is the poor understanding of the chemistry processes taking place in the boundary layer. This often leads to an over-estimation of the heat flux to withstand, and thereby an over-sizing of the thermal protection system (TPS), leaving only little volume and mass for the actual payload. Within that scope, the objective of this project is to investigate the driving processes of gas-surface interactions (GSI) over a cold wall, and to provide a sound foundation for an accurate model of wall catalycity. Those investigations are based on experimentations performed in the Plasmatron, a Plasma Wind Tunnel, and numerical rebuilding of the boundary layer. This report presents the steps that led to the achievement of that objective. 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 defined. 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 stagnation line of a body flying at hypersonic velocity are presented. The driving processes of 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 determination of a reference catalycity. The facility used and methodologies applied are presented. The two test campaigns are then described, and the corresponding results commented and compared to similar experiments conducted in the past. A word is also said on uncertainty quantification. In the fourth chapter, finally, the parameters described in the second chapter are qualitatively approached, and their evolution with respect to the test conditions is commented. This last chapter ends on a preliminary conclusion.

Chapter 1

Ground testing strategy for super-orbital re-entry At the root of this project is the issue of flight duplication in ground testing facilities for super-orbital re-entry probes. This first chapter exposes that problematic, so that the reader perceives how the present research is related to a wider research and exploration program. Super-orbital re-entry is first defined from an orbital mechanics point of view, with a short overview of the orders of magnitude involved. The challenges linked to high velocity flows experimentation are then explained. Finally, the new ground testing strategy for super-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 reentry, 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 the Sun. The aim of an interplanetary transfer is to leave that planet’s orbit around the Sun, 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 manoeuvres are 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 elliptic orbit tangent to both its original orbit, which is the orbit of the first planet, and its target orbit, which is the orbit of the target planet. Upon arrival at the second planet’s orbit, a second velocity increment is required to inject it on its target orbit. 3

Super-orbital re-entry

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

G · mbody rbody

(1.1)

where G is the gravitational constant, and mbody and rbody are respectively the mass and radius of the considered body. The probe’s velocity upon reaching the target planet is 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 the target planet’s centre of mass. The probe’s velocity upon reaching the target planet’s orbit is thus higher than the target planet’s escape velocity. The exact magnitude of its velocity 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 second body would require an important amount of energy, increasing considerably the overall cost of the mission. It is therefore preferred to perform the re-entry directly from the transfer orbit. The Earth’s escape velocity, for example, is 11.2 km/s. Most of the scenarios for Mars return mission foresee an arrival entry velocity ∼ 11.6 · · · 14.5 km/s, which is indeed higher than the Earth’s escape velocity. This is considerably higher than the usual re-entry velocities from elliptic orbits, e.g. 8.2 km/s for the Space Shuttle. Up to now, the Stardust probe was the fastest artificial object that entered in the Earth’s atmosphere, at a velocity of 12.8 km/s. [26]

Super-orbital re-entry

The initial specific enthalpy H, defined around the entry point (assumed to be at an altitude of ∼ 180 km), can be determined from the initial velocity v: 1 H = v2 (1.2) 2 Typical velocities for probes entering the Earth’s atmosphere from hyperbolic orbits scale from 11 to 15 km/s, which correspond to specific enthalpies between ∼ 60 and ∼ 115 M J/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 heating loads that will be encountered. The main design requirement on the TPS is to minimize its mass while ensuring the probe’s integrity, i.e. withstand the heat loads. This implies that 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 enthalpy is related to the square of the probe’s velocity (equation 1.2). Flight duplication and accurate prediction of aerothermodynamics phenomena at those enthalpies are still beyond the capabilities of the existing laboratories. The hypersonic phenomena for which an effort has to be made in ground testing facilities were classified in seven categories by Chul Park in his review of laboratory simulation of aerothermodynamics [20], from which this section is strongly inspired. Among those, two are particularly relevant for super-orbital re-entry: radiation/ablation and GSI. Although the present project focuses on GSI, both issues are quickly introduced in 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. Such facilities are divided in two categories: • Impulse facilities are only able to produce flows that last typically a fraction of a second. This is long enough to let the steady flow establish itself, but too short to study thermal effects. They are thus mainly used to investigate the aerothermodynamic effects, gas kinetic, and radiation processes. They are able to reach enthalpies up to 30 M J/kg, with an expansion tube. • Plasma wind tunnels (PWT), such as inductively coupled plasma (ICP) facilities or arc-jets, are able to operate at very high enthalpy (up to 50 M J/kg) and for longer test durations. However, they are limited in pressure (∼ 107 P a) and freestream velocity. [20] This type of facility was used for the present study, the associated methodologies are further explained in section 3.1.

Super-orbital re-entry

When studying orbital re-entry, flight duplication is possible in those facilities for a limited time (impulse facilities) or in a limited region (stagnation point in PWT). However, flight duplication is not possible anymore for super-orbital re-entry. The reason for this 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 in Earth’s atmosphere and 7 km/s in Mars’ atmosphere [20]. However, it remains smaller than 10% of the total heat flux for probes having a diameter smaller than ∼ 1 m and entry velocities smaller than 13 km/s in the Earth’s atmosphere, as it was the case for Stardust [26]. It is thus a major issue for the range of velocities corresponding to super-orbital re-entry. Two types of radiation have to be considered. For a vehicle flying only at high altitudes, such as Aeroassisted Space Transfer Vehicles (ASTV), radiative heating is dominated by chemical non-equilibrium in the shock layer. For a re-entry capsule, the peak radiative heating occurs at lower altitude, where the shock layer is expected to be in chemical equilibrium. The problem is even more complex when ablation of the heat shield occurs, which is in most cases inevitable. The product of ablation forms a gas layer that prevents the hot shock layer gas from reaching the wall and absorbs part of the shock layer radiative heat flux. An accurate estimation of the absorbed radiation is almost impossible since the thickness and thermochemical state of the ablation gas layer are difficult to predict. [20] Appropriate facilities The increasing fraction of radiative heat transfer is a problem for flight duplication in ground testing facilities. If the enthalpy is matched, a usual way of reproducing flight condition is to maintain the binary scaling parameter, which is the product of the density ρ and a typical length scale L. This approach conserves Reynolds number Re and viscous effects, binary chemical processes, and the convective heat transfer. However, the heat removed by radiation per unit of mass scales as L [18]. Rigorous flight duplication is thus not possible anymore with small-scale models. Instead of duplicating flight conditions, it is thus necessary to investigate separately the driving phenomenon and build up the corresponding models. Equilibrium radiation with ablation has to be studied in a facility able to provide high enthalpy, pressure, and a certain amount of radiative heating so as to cause ablation and spallation. Ballistic range with counterflow device can meet those requirements, providing the ambient pressure is raised to produce a radiative heat flux equal or greater than

Super-orbital re-entry

in flight. Comparison between ground testing results and flight showed that this approach gave satisfying qualitative results. The phenomenon can also be studied in PWT enhanced 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-catalytic to recombination reactions involving atomic nitrogen and oxygen considerably reduce the heat 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 own contribution. 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, among other parameters. However, accurate determination of a materialâ&#x20AC;&#x2122;s catalycity requires testing it in the same chemical, thermal, and mechanical states as in flight. It is therefore necessary to test it over long durations (in the order of minutes) at the same heat transfer rates as in flight. This can only be done in PWT. However, as already stated in section 1.2.2, it is complicated to estimate the radiative fraction of that heat flux, and requires an external radiation source. Furthermore, PWT are often unable to operate at the desired pressure ranges.

1.3

New testing strategy

Super-orbital re-entry requires thus a new approach of ground testing. Ground testing facilities should be used to investigate separately different phenomenon playing a role in the aerothermodynamic of the flow, rather than to duplicate flight as it is the case for lower 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 Computational Fluid Dynamics (CFD) codes, which would allow flight duplication on computer rather than in ground test facilities (figure 1.2). This new philosophy clearly appears in the examples cited here above, as well as in the present report.

Super-orbital re-entry

Figure 1.2: Proposed procedure for high enthalpy atmospheric entries.

Chapter 2

High temperature gas dynamics applied to atmospheric re-entry The present research being focused on GSI, and more particularly catalycity modelling, it is important for the reader to have a clear understanding of chemically reacting boundary layers. The present chapter is far from a comprehensive description of the associated theory, but it gives the necessary qualitative understanding of the phenomenon involved. The features along the stagnation line of a body flying at hypersonic velocity are first described, followed by a brief description of high temperature gas dynamics. For more 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 the beginning of the hypersonic regime. Nevertheless, the scientific community agrees on several recognizable features. One of those features is of particular interest for this study: the importance of the heat transfer at the wall. Taking a closer look at the neighbourhood of the stagnation line of a body flying in hypersonic 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 hypersonic vehicles generally have blunt nose, in order to avoid too important aerodynamic heating. • The region downstream of the shock is subsonic. A considerable part of the flow’s kinetic energy will be transformed in thermal energy across that shock. Therefore, the shock-layer temperature achieved can be incredibly high: from ∼ 8, 000 K for an orbital re-entry up to ∼ 11, 000 K for a lunar return. The flow needs a 9

High temperature gas dynamics certain time to adjust both its temperature and chemical composition to this new energetic balance. This region of adaptation is called relaxation layer. At such high temperatures, chemical effects have to be taken into account. For air at a pressure of 1 atm, vibrational excitation begins at 800 K, O2 begins to dissociate at 2, 500 K and is fully dissociated for 4, 000 K, point for which N2 begins to dissociate. At 9, 000 K, N2 is fully dissociated and ionization begins. One can easily understand that the flow downstream the shock is plasma: molecules are dissociated and atoms are partially ionized. • A transition layer may follow the relaxation region. • A chemically reacting boundary layer in which thermal and mass diffusive process take place. As it will be shown later, those three processes are complex and closely inter-connected.

It should be brought to the reader’s attention that the gas behind the shock is a chemically reacting mixture of perfect gases, and not a real gas as it often incorrectly referred to in literature. A real gas is a gas for which intermolecular forces are not negligible anymore, which implies that the molecules are closely packed together. This only applies for very large pressures (∼ 108 P a) 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 usual conductive part due to the temperature gradient. As it was demonstrated, the temperatures behind the bow shock can reach extremely high values, resulting in a very important heating. Secondly, there is a radiative part, mainly due to the shock layer but that can also be due to ablated material. As discussed in the previous chapter, this part can become a major fraction of the overall heat transfer. However, it will not be further investigated in the present study. Finally, there is a diffusive part. This is due to the diffusion of atoms throughout the boundary layer and their recombination at the wall.

High temperature gas dynamics

2.2

Brief overview of gas-surface interactions

The resolution of the laminar chemically reacting axisymmetric boundary layer equations is extremely complex, or even impossible. Indeed, in addition to the conservation of mass, momentum, and energy, one needs to take into account for the species continuity. Analytical solutions can be found at the stagnation point for limiting cases, assuming that the solutions are self-similar and applying a Mangler-Howarth transformation. 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 does not matter, and frozen1 boundary layers over walls with a finite catalycity. Although an important literature exists on the topic, it is not the goal of the present project to go into the details. The problem will be tackled by explaining the few constants and parameters used to describe the overall state of the boundary layer. The recombination of dissociated species is an exothermic reaction. It takes place either in the gas phase, in which case it is called a homogeneous reaction, or at the wall, in which case it is called an heterogeneous reaction. Typically, the recombination reactions to expect for the Earth’s atmosphere are 2 : • O + O → O2 + 500 kJ/mol • O + N → N O + 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 the reaction’s speed. For the recombination of oxygen and nitrogen in nitric oxide, for example, one can write the corresponding equilibrium equation which also takes into account the backwards reaction of decomposition: O+N ⇀ ↽ NO

(2.1)

To this particular reaction corresponds an equation describing the rate of nitrogen oxide formation: d [N O] = k · [N ]m [O]n dt

(2.2)

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

The characteristics of equilibrium and frozen boundary layers are given in section 2.2.3 In reality, the production of N O 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 aerothermal models. [19] 2

High temperature gas dynamics

The chemical rate constant, in turn, is often modelled with the two-parameter Arrhenius relation: −Ea

k = k0 · e R·T

(2.3)

where k0 is a frequency factor, Ea is the reaction’s energy of activation, R the gas constant, and T the temperature. This relation is based on the assumption that at a certain temperature, the mixture’s energy distribution follows a Boltzmann distribution, and therefore that the amount of molecules having an energy greater than Ea is proportional to the exponential term. Gas-phase reaction rate constant In reality, in the gas phase, the recombination reactions take mostly place with a third party; e.g. one molecule of dioxygen can dissociate into two atoms of oxygen only when colliding 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 following reactions, 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 the chemistry model used. In all the models used in the present study, the reaction rate coefficient is defined as: −Ea

k = C · T n · e R·T

(2.4)

This expression is obviously similar to equation 2.3, except that the frequency factor k0 has been expressed as a function of temperature. The values given to the different coefficients are summarized in table A.1 for the model of Dunn and Kang [23] that will be 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 equilibrium constant, 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 state of the mixture: if it is large, the products are favoured, and if it is small, the reactants are favoured. The reaction’s equilibrium constant Kc depends on both temperature and mixture’s composition, through the nature of the species M.

High temperature gas dynamics

However, the coefficient n remains the same for both the forward and backwards reactions of each recombination, no matter what the nature of M is. The dependency on temperature appears therefore only in the exponential terms, and indirectly through the mixture’s composition. The group Ea /R in the exponential being the same for a given recombination no matter what the nature of M is, the effect of mixture’s composition is only visible through the ratio Cf /Cb . In the model of Dunn and Kang, according to table A.1, that ratio is ≈ 5.8E − 3 for nitrogen and ≈ 8.3E − 4 for oxygen for every M . The value of Kc is thereby a strong function of temperature and a weak function of mixture’s composition, as illustrated in figure 2.2 for the recombination reaction of atomic nitrogen into dinitrogen. 8

N2 recombination reaction equilibrium coefficient (Dunn−Kang) [−]

x 10

Mixture for H = 36.24 MJ/kg Fully recombined mixture

9 8 7 6 5 4 3 2 1 0 4500

5000

5500

6000

Temperature [K]

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

Wall reaction rate constant Chemical reactions can also take place when two atoms or molecules collide with the wall rather than with another atom or molecule. It is possible to link that reaction with another reaction rate constant specific to the wall, kw , which is obviously linked with the catalycity. At the wall, for a given species i, the diffusion flux Ji is balanced by the production of consumption of species due to the catalytic surface w˙ i . Ji = w˙ i From equation 2.19, the diffusion flux can be written: ( ) Ji = mi · Mi↓ − Mi↑ = mi γi Mi↓

(2.5)

(2.6)

High temperature gas dynamics

where m is the species’ atomic mass. With equation 2.5, one can thus establish: w˙ i = mi γi Mi↓

(2.7)

Which becomes, when Mi↓ is replaced with its expression as given by kinetic theory [2]: √ 2γi kB Tw w˙ i = mi n (2.8) 2 − γi 2πmi where the kB is Boltzmann’s constant, n is the number density, and the Tw the wall’s temperature. The mass production term is also defined as: i w˙ i = kw ρw xi

(2.9)

Merging 2.8 and 2.9, one can thus finally identify an expression for the wall reaction rate constant in function of the catalycity: √ kB Tw 2γi i (2.10) kw = 2 − γi 2πmi

2.2.2

Diffusion coefficient

In the case of a multi-component mixture, the average species diffusion coefficient D is obtained from the binary diffusion coefficient D using Fick’s law: 1 − xi Di = ∑ xj

(2.11)

i̸=j Di,j

where the binary diffusion coefficient is: √ 3 2πkB T (mi + mj ) 1 Di,j = (1,1)i,j ¯ 16 mi mj nQ

(2.12)

¯ is the diffusion cross-section. The atomic mass is obtained by dividing the where Q molecular mass Mm by the Avogadro number NA . The number density is defined as n = ps / (kB T ), where ps is the static pressure. The diffusion cross-section is obtained ¯ (i,j) = Ω(i,j) · π. The collision integral, in turn, is obtained from the collision integral Q with a fitting analytical expression from [4]: Ω(i,j) =

a1 + a2 · T a3 · 10−10 a4 + a5 · T a6

(2.13)

where the factor 10−10 is necessary to convert from meters to Angstrom. The parameters for 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 depicted in figures 2.3 for atomic nitrogen and oxygen. Diffusion is promoted as temperature increases, species dissociate, and pressure decreases. It appears that oxygen diffuses slightly more efficiently than nitrogen, and is less sensitive to mixture composition.

High temperature gas dynamics

0.8

0.8 Fully recombined mixture Mixture for H = 36.24 MJ/kg

0.7 O diffusion coefficient [m2/s]

N diffusion coefficient [m2/s]

0.7 0.6 0.5

1500 Pa

0.4 0.3 5000 Pa

0.2 0.1

Fully recombined mixture Mixture for H = 36.24 MJ/kg

1500 Pa

0.6 0.5 0.4 0.3 5000 Pa 0.2 0.1

0 0

10000 Pa 1000

2000

3000 4000 Gas temperature [K]

5000

6000

(a)

7000

10000 Pa 0 0

1000

2000

3000 4000 Gas temperature [K]

5000

6000

7000

(b)

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

2.2.3

Damk¨ ohler numbers

Gas phase Damk¨ ohler number The likelihood of homogeneous reaction to happen is described with the gas phase Damk¨ohler number Dag . It is defined as the ratio between a time-scale characteristic of the flow τflow and a time-scale characteristic of the chemistry τhomo : Dag =

τflow τhomo

(2.14)

Although many definitions of τflow exist, they all aim at retrieving a qualitative sense of the time of residence of the species in the boundary layer. In the frame of the present study, 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 the tangential direction. The second time-scale, τhomo , depends on the mixture’s composition, 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 limiting cases can be defined: • For Dag → 0, the chemistry can be neglected as it is too slow or is not given the time to change the nature of the flow. This is referred to as a frozen boundary layer. • For Dag → ∞ the chemistry is so fast that equilibrium is reached instantaneously. This is referred to as an equilibrium boundary layer.

High temperature gas dynamics

Wall Damk¨ ohler number Similarly to the gas phase Damk¨ohler number describing the state of the flow within the boundary layer, the wall Damk¨ohler Daw number is used to described the state of the flow close to the body’s surface. It is defined as the ratio between a time-scale characteristic of the species diffusion in boundary layer τdiff and a time-scale characteristic of the chemistry τhete : Daw =

τdiff τhete

(2.16)

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

kw vdiff

(2.17)

vdiff =

D δ

(2.18)

with:

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 the species do no diffuse through the boundary layer. Although the over-all reaction time may be quite small, it is much larger than the diffusion time. This is referred to as a reaction-controlled surface. • For Daw → ∞, the surface is in diffusion control. Again, although the diffusion time 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 probability of dissociated species recombination at the body’s surface. Contrary to the reaction constant, it is thus not an intrinsic property of the material but also depends upon the flow conditions. For a particular species i, it is defined as the ratio between the fraction of species recombining at the surface, and the number flux of species i diffusing to the surface3 . The fraction of species recombining at the surface is the difference between the 3

More accurate definitions of the catalycity do exist. Indeed, after recombination the molecule can keep 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 is actually transferred to the wall, it is possible to defined the effective catalycity γeff = γ · β. Similarly, an apparent catalycity is defined to take into account surface roughness. For more information concerning this classification, the reader can refer to [24].

High temperature gas dynamics

number flux of species i diffusing forward Mi↓ and the number flux of species i travelling backward m↑i ,

γi =

Mi↓ − Mi↑ Mi↓

(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 the type of reactions that are taking place at the wall but also the diffusion of species through the 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 surface cause the reactant concentration to be locally depleted” then the surface characterization becomes a complicated task. Therefore, ”to the chemist interested in the interfacial reaction itself, diffusion will be seen to be a skilful falsifier and certainly an undesired intruder.” [22] However, surprisingly enough, diffusion is neglected from most of the catalycity models that are used nowadays for engineering applications. The material databases created in ground testing facilities do only take into account its variations with static pressure ps and wall temperature Tw , which are the parameters driving the recombination reaction at the wall, as if it did not depend on the test conditions. This is a conservative assumption, as it results in an over-estimation of the material’s catalycity, and therefore an over-estimation of the diffusive heat flux, and finally an over-sizing of the TPS. Space missions with stringent mass budget are therefore penalized with heavy heat shield and the payload mass is reduced.

High temperature gas dynamics

Chapter 3

Test campaign and results The conclusions of this study are based on the results obtained during wind tunnel experiments. The goal of those experiments is to perform a parametric study on processes involved in GSI. Information is retrieved regarding the wall catalycity and heat flux for various conditions of static pressure, free-stream specific enthalpy, probe geometry (DamkÂ¨ohler probes) and wall material (minimax), while keeping the wall temperature constant. The procedure to perform heat flux measurements is first detailed. The two different types of tests that were performed are then described, and the corresponding results are explained, and compared with results obtained during similar test campaigns conducted in the past. Issues concerning measurement errors and uncertainty quantification are finally commented.

3.1

Heat flux measurement in the Plasmatron

The experimental investigations were performed in the Plasmatron, the main facility for GSI research at the von Karman Institute (VKI). The Plasmatron is an ICP facility used both for research and for material response study in the frame of TPS sizing [3]. It allows reproducing the exact flight conditions in the boundary layer in the surrounding of the stagnation point, which is very likely to be the point of the vehicle submitted to the 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 on the developments of Fay and Riddell already discussed in section 2.3. Those parameters are: the outer edge (free-stream) specific enthalpy He , pressure pe and velocity gradient Î˛e (figure 3.1). This methodology has been improved at the VKI1 , and extensively 1

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

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 the boundary layer around the stagnation line (see figure 2.1) as long as He , pe and βe are reproduced. The method is divided in two parts: a measurement of heat flux and pressure, based on which the boundary layer equations are numerically solved. However, even with this approach, there is one more unknown than the number of equations. The problem is not closed. Therefore, the result is expressed as a correlation between two variables: outer edge enthalpy He , and sample catalycity γ. A high enthalpy corresponds to non-catalytic materials, and a low enthalpy to fully catalytic materials, with a monotonic transition between 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 enthalpy S-curve. To subdue this problem, the current procedure consists in performing a coldwall heat flux measurement with a reference sample of known catalycity, and thereby determine the outer edge enthalpy. The catalycity of the material to test is then the only remaining unknown. 45

Outer edge enthalpy [MJ/kg]

40 35 30 25 20 15 10 −5 10

−4

−3

−2

10 10 Catalycity (log) [−]

−1

Figure 3.2: Enthalpy S-curve, linking the outer He with γ, in logarithmic scale. Figure 2 realized for the reference probe at ps = 1, 500 P a and Qref w = 875 kW/m .

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

Test campaign and results

the VKI, the reference is often a copper sample, which catalycity is assumed to vary only with the plasma’s static pressure. In the past, it has even been considered as fully catalytic. However, it was shown that it is not the case, as some materials such as silver are more catalytic. Furthermore, cold copper would oxidize while being exposed and its catalycity would therefore decrease [19]. An approach to the exact determination of copper catalycity depending on the Plasmatron test condition is presented in section 3.2.4.

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 at the 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 corresponds to the ESA geometry for sample holders, also referred to as Euromodel. It is a cylinder 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 certain radius rc . The exact dimensions are available in table 3.3. Water is flowing through the calorimeter with a certain mass flow controlled by a calibrated rotameter. All the experiments 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 inflow and 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 exposed area. The temperatures are measured with type E thermocouples. A second mass flow is used to cool the probe’s walls that are exposed to the plasma. A proper heat flux measurement is depicted in figure 3.3. The probe is originally in stand-by position, out of the flow. The measured heat flux rises once the probe is into the plasma. The operator waits until it reaches a steady value, and then puts it back in its original stand-by position, 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 previous test campaigns were used.

3.1.2

Pre-processing numerical tools

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

Test campaign and results

1100

Heat flux [kW/m2]

900 700 500 300 100 −100 0

100

125 150 Time [s]

175

200

225

250

Figure 3.3: Recorded heat flux over time for the reference probe at ps = 1500 P a. The first one is an ICP code that allows for the reproduction of the experimental configuration. It computes the flow in the plasma torch and around the sample in the test chamber solving the time averaged magneto-hydrodynamic equation at low Mach and low magnetic Reynolds number. The output of that tool is a set of non-dimensional parameters (NDP) describing the structure of the boundary layer [16]. However, for the present study the NDP were estimated using regression laws that have been computed for 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 of two other ones: CERBERE, Catalycity and Enthalpy ReBuilding for a REference probe, and NEBOULA, NonEquilibrium BOUndary LAyer. Based on the non-dimensional parameters previously obtained and the experimental data, it solves the boundary layer equations for an axisymmetric, steady, laminar, chemically reacting gas over a catalytic surface. The chemistry model of Dunn and Kang [23] with 7 species (N2 , O2 , N , O, N O, N O+ , e− ) was used for the low pressure range, and that of Gupta [25] for the high pressure range. Although neither of them has been validated for the Plasmatron tests, Dunn and Kang’s model was considered in a previous study of Garcia as the most probable 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. At medium 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 reactions at the wall. In addition to the reference probe described in section 3.1.1, two probes with the same geometry but different types of calorimeter are used (figure 3.4). Data points are recorded for the three probes in the same plasma conditions (Qref w and ps ) and same wall temperature (cold-wall measurement). The test conditions are summarized in table B.1.

Test campaign and results

Figure 3.4: Test campaign: minimax. The minimax methodology consists in comparing a reference probe with two other probes having the same geometry, but different materials for the calorimeter: one more catalytic, and the other less. The S-curves are computed for each of the probes. Since the outer edge enthalpy is the same for all the three of them, its value can be delimited to the ones that exist for the three probes. This defines an interval of confidence for both the outer edge enthalpy, and the catalycity of the reference probe (figure 3.5). For the present research, the reference probe is a copper calorimeter γCu , the higher catalyst is made out of silver γAg and the lower one out of quartz γQuartz . More information about the minimax methodology can be found in [13] and [14].

Outer edge enthalpy [MJ/kg]

10 −5 10

Quartz calorimeter Copper calorimeter Silver calorimeter

−4

−3

−2

10 10 Catalycity (log) [−]

−1

Figure 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.

3.2.1

Low pressure

At low static pressure, 1, 500 P a, the He − γ intervals can easily be defined, as depicted in figures 3.6. The results actually obtained for this study, represented with triangles, are compared with those from previous studies. The differences with Krassilchikoff are most probably due to the different material used for the lower catalycist: molybdenum instead of quartz. What is observed, however, is that the incertitude of the outer edge enthalpy remains quite large when only the results of the present study are taken into account. During numerical rebuilding, a small change in catalycity results in an important change of

Test campaign and results

free-stream conditions due to the important gradient in the outer edge enthalpy range considered. By combining them with those from Krassilchikoff and Kadavelil, the uncertainty is considerably reduced. 50 Kadavelil (2007) Krassilchikoff (2006) Present work Data used

45 40 35 30 25 Kadavelil (2007) Krassilchikoff (2006) Present work Data used

20 15 10 400

600

800 1000 Heat flux Reference probe [kW/m2]

(a)

1200

1400

Catalycity (log) [−]

Outer edge enthalpy [MJ/kg]

−1

−2

400

600

800 1000 Heat flux Reference probe [kW/m2]

1200

1400

(b)

Figure 3.6: He (a) and γ, in logarithmic scale, (b) intervals as defined during different minimax test campaigns for ps = 1, 500 P a. Each dataset consists out of two curves that are the upper and lower limits of the intervals. The ”data used” set is the one used in chapter 4. Krassilchikoff’s results are based on molybdenum rather than quartz as lower 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 corresponding outer edge enthalpy. The reference catalycity was determined as the logarithmic average between the interval limits, using both the one defined by the present study and the one defined by Kadavelil. Those of Kadavelil were beforehand refined using the overall outer edge enthalpy limits defined by all the test campaigns combined in figure 3.6 (a). In the end, the values used are represented with diamonds in figures 3.6, and noted in table 3.1.

3.2.2

High pressure

At higher static pressure, 10, 000 P a, clean He − γ intervals such as the one depicted in figure 3.5 was only to be found for one point corresponding to low plasma power. For higher 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 they were all submitted to the same plasma conditions. This is therefore due to an error in the data acquisition or post-processing. That issue was already observed by Krassilchikoff [14]. He proposed the hypothesis made on the gas-phase chemistry model as the most likely explanation. He performed a sensitivity study using three chemistry models: Dunn and Kang, Gupta, and Park [21].

Test campaign and results

According to him, those models ”agree at low pressure, but diverge at high pressure for the low catalycities”. As we have seen in section 2.2.2, with an illustration in figure 2.3, the diffusion coefficient of both atomic nitrogen and oxygen strongly decreases as static pressure increases. At low pressure, the wall Damk¨ohler number Daw is small, and the chemistry is mainly driven by the wall. As pressure increases, Daw increases, and the gas-phase chemistry 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 explanation will be confirmed when examining the boundary layer in chapter 4.

Outer edge enthalpy [MJ/kg]

30 Quartz calorimeter Copper calorimeter Silver calorimeter

17.62 MJ/kg

16.12 MJ/kg

10 −5 10

−4

−3

−2

10 10 Catalycity (log) [−]

−1

Figure 3.7: The methodology applied for figure 3.5 is not valid anymore for higher pressure: there are no common values of the outer edge enthalpy for the three probes. 2 This figure was realized at ps = 10, 000 P a and Qref w = 861 kW/m .

Figure 3.7 is reproduced in figure 3.8, with the models of Park and Gupta in addition to the one of Dunn and Kang. As expected, the difference between models arises in the lower catalycity region, around γ = 0.01 and below. Several observations can be made on 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 lower limit of He it defines is for a fully-catalytic wall. On the contrary, the model used to post-process the quartz calorimeter should be chosen carefully. Although from the conditions of figure 3.8 the model chosen to post-process the copper calorimeter also seems irrelevant, it may be important when He is low. Indeed, the quartz calorimeter S-curve built with Park or Gupta’s model might exceed that of the copper calorimeter built with Dunn and Kang’s model in the low catalycity region. • Gupta’s model was used for all the cases, as it defines a larger interval than Park’s model and is therefore more conservative. • In the higher reference probe heat flux recorded, 1036 and 1238 kW/m2 , all the models failed to provide an interval. This could be due to the uncertainty on

Test campaign and results 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 reference probe increases, thereby also increasing the sensitivity to measurement errors. This forced 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 the low pressure analysis and for the high pressure one.

From those few points, it clearly appears that the chemistry model is a relevant parameter of the post-processing, as it results in important changes in the quantities of interest. A comprehensive sensitivity study is desirable, especially to define which chemistry model has to be used under which conditions, and why. 40 Gupta Dunn−Kang Park

Outer edge enthalpy [MJ/kg]

25 Silver calorimeter

20 Copper calorimeter

Quartz calorimeter 10 −5 10

−4

−3

−2

10 Catalycity [−]

−1

Figure 3.8: Figure 3.7 is here reproduced for three different chemistry models. This 2 figure was realized at ps = 10, 000 P a and Qref w = 861 kW/m .

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 by Krassilchikoff with Dunn and Kang’s model and a molybdenum calorimeter rather than a quartz one is also shown. The difference with the results from the present study is important, especially for the outer edge enthalpy. Reference catalycity Again, it was necessary to fix a certain reference catalycity and a corresponding outer edge enthalpy. At first, it was decided to use the logarithmic average of the limits of the catalycity interval, as for the low pressure case. The data points for which it was computed do not exactly correspond to the one measured, as it could have been interesting to retrieve information regarding catalycity for the same reference heat fluxes at different pressure levels. An interpolation on the values was therefore necessary. Since the power was monotonically increased for increasing reference heat fluxes, the He was expected to increase monotonically too. However, it was not the case (see figure 3.11). The values of γref were therefore varied gradually, always within the interval defined by the minimax, until the corresponding rebuilt He was physically consistent

Test campaign and results

−1

Krassilchikoff (2006) Dunn−Kang’s model Present work Gupta’s model Data used

Catalycity [−]

Outer edge enthalpy [MJ/kg]

Krassilchikoff (2006) Dunn−Kang’s model Present work Gupta’model Data used

−2

−3

10 350

450

550 650 750 Heat flux Reference probe [kW/m2]

850

900

350

(a)

450

550 650 750 Heat flux Reference probe [kW/m2]

850

900

(b)

Figure 3.9: He (a) and γ, in logarithmic scale, (b) intervals, in logarithmic scale, (b) as defined with different methodologies for ps = 10, 000 P a. Each dataset consists out of two curves that are the upper and lower limits of the intervals. The ”data used” set is the one used in chapter 4. Krassilchikoff’s results are based on molybdenum rather than quartz 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 the exact values are noted in table 3.1.

At this point, one could argue that the determination γref and He for the investigations conducted in chapter 4 is rather arbitrary. However, the minimax methodology is just determining an interval. From what is known, the real value of γref could be anywhere within that interval. Using an arbitrary value is thus as rigorous as using an average of the interval’s limits, as long as the corresponding He is properly rebuilt. In this case, it is even more rigorous since He rebuilt with the average of the interval’s limits was not physically consistent with the test conditions. Furthermore, the present study does not claim to provide a quantitative description of the GSI processes, but rather to investigate qualitatively their relative evolution

Qref w

ps)= 1, 500 P a kW/m2 γ (−) He 500 0.022 700 0.021 900 0.023 1, 100 0.027 (

(M J/kg) 16.22 23.74 31.18 36.45

Qref w

ps)= 10, 000 P a kW/m2 γ (−) He (M J/kg) 500 0.0025 15.95 600 0.0040 16.47 700 0.0065 17.40 800 0.0090 18.29

(

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

Test campaign and results

3.2.3

Medium pressure

Although only the two previously mentioned static pressure levels are necessary for the post-processing of the next section, one more point is investigated to have a better idea of the evolution of the reference probe’s catalycity. The choice of the chemistry model is not as straightforward as for the two other points. Therefore, both Dunn and Kang’s and Gupta’s model were used. The results are depicted in figures 3.10, where there are also compared with the results previously obtained by Krassilchikoff. The difference between both models for the present work is not apparent at low heat flux, but becomes important for higher values. In particular, Dunn and Kang’s model fails to provide an interval before Gupta’s. Krassilchikoff’s results were also obtained with the minimax methodology, but with a molybdenum calorimeter and post-processing using Dunn and Kang’s model. Present work Gupta’s model Present work Dunn−Kang’s model Krassilchikoff (2006)

Present work Gupta’s model Present work Dunn−Kang’s model Krassilchikoff (2006)

30 25

−1

Catalycity [−]

Outer edge enthalpy [MJ/kg]

−2

15 10 5

−3

200

300

400 500 600 700 Heat flux Reference probe [kW/m2]

(a)

800

900

200

300

400 500 600 700 Heat flux Reference probe [kW/m2]

800

900

(b)

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

3.2.4

Reference catalycity

The logarithmic average of the γref limits defined by the data points that were measured during the minimax test are represented in figure 3.11 as a function of the corresponding rebuilt He . The error bars drawn represent the limits of the interval defined by the minimax. These points are thus not the same as the interpolated ones used in chapter 4. Two observations can be made: • The only upper limit of the reference catalycity that can be confidently drawn, at least for the range of He considered, is that γref ≤ 0.05, regardless of the pressure level considered. However, the result obtained are compatible with that of Panerai, who defines γref = 0.1 for 1, 200 P a < ps ≤ 5, 000 P a and γref = 0.01 for 5, 000 P a < ps ≤ 10, 000 P a [19].

Test campaign and results

• The drawback of using the logarithmic mean of the limits of the interval drawn by the minimax to define γref at 10, 000 P a is clearly visible. Indeed, He slightly decreases between the first and the second data point although the plasma power was increased, which is physically impossible.

Catalycity (log) [−]

1,500 Pa 5,000 Pa 10,000 Pa −1

−2

−3

20 25 30 35 Outer edge enthalpy [MJ/kg]

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

3.3

Damk¨ ohler probes

The second test campaign’s objective is to observe the variation caused by different diffusion schemes. In addition to the reference probe described in section 3.1.1, two probes with the same calorimeter but different geometries are used (figure 3.12). Heat fluxes are recorded for the three probes in the same plasma conditions (Qwref and ps ) and same wall temperature (cold-wall measurement). Modified Newton theory shows that enlarging rb lowers the outer edge velocity gradient βe . The time-scale characteristic of the flow in equation 2.14 is often chosen as the inverse of that outer edge velocity gradient τflow = 1/βe . Therefore, enlarging the probe’s body radius should ultimately cause the Dag to increase. The larger probe is referred to as the equilibrium probe and the small one as the frozen probe. More developed numerical and experimental investigations about the Damk¨ohler probes can be found in [11]. Due an important amount of noise in the signal of the equilibrium probe, it was decided to perform the Damk¨ohler probes test campaign in two steps: first the reference probe together with the frozen one, and then the reference probe together with the equilibrium one. This way, one avoids having too many thermocouples inside the chamber that might cause interferences on each other’s signals. It was later discovered that the noise was in fact due to a defect in one of the acquisition cards. The test conditions are summarized in table B.2.

Test campaign and results

(a)

(b)

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

Name Equilibrium Reference Frozen

rb (mm) 57.5 25 15

rc (mm) 5 10 15

Table 3.2: Geometrical characteristics of the DamkÂ¨ohler probes.

3.3.1

Frozen probe

The heat fluxes measured at the frozen probe with respect to the one measured at the reference probe are depicted in figures 3.13. The data recorded during previous test campaigns 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 the one measure at the reference probe. Second, the agreement between the different test campaigns is poor at 1, 500 P a (a) but sufficiently good at 10, 000 P a (c). The source of those differences is discussed in section 3.4. As it is difficult to control the plasma power to retrieve exactly the same heat flux at the reference probe for the two series of test, it was decided to perform a regression on the data points obtained. Different regression methods were tested. Table 3.3 summarizes the results obtained for 1, 500 P a. The second order regression was abandoned as the quadratic term is negligible and it results in a more important standard deviation Ď&#x192; than the other methods. Although the linear and robust linear regressions have the lowest standard deviations, they result in a certain intercept at the origin, what is obviously not physical. Therefore, the single slope was preferred. The same analysis was performed for 10, 000 P a.

Test campaign and results Type Slope Linear Robust linear Quadratic

31 x0 − 46.20 45.80 −36.04

x1 1.69 1.65 1.65 1.90

x2 − − − −1 · 10−4

σ (%) 6.63 5.78 5.77 10.04

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

3.3.2

Equilibrium probe

Two observations can be made from the results depicted in figure 3.14. First, the heat flux 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 not with 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 P a, probably due to a pocket of air trapped in the cooling fluid. Due to time constraints, it was unfortunately not possible to wait for a new probe and record data at higher pressure. Therefore, the regression from Krassilchikoff and Panerai are used for 10, 000 P a. 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 the minimax, it appeared that regression law defined by Krassilchikoff led to a He higher than the upper limit of the interval. Panerai’s regression was therefore used as it is more consistent 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 P a ref Qeq w = 0.81 · Qw ± 32.38% (19 : 20) ref Qfr w = 1.69 · Qw ± 13.36% (19 : 20)

• At 10, 000 P a Krassilchikoff (2006): Qeq w = 0.81 · Qw ref ± 12.90% (9 : 12) Panerai (2011): Qeq w = 0.66 · Qw ref ± 12.90% (19 : 20) ref Qfr w = 1.46 · Qw ± 17.00% (19 : 20)

Test campaign and results

Heat flux Frozen probe [kW/m2]

3500 3000

Experiment Qw(frozen) = 1.6876*Qw(reference) H−W. Krass. (2006) F. Panerai (2012)

3500

Heat flux Frozen probe [kW/m2]

4000

2500 2000 1500 1000 500 0 0

500 1000 1500 Heat flux Reference probe [kW/m2]

2000

3000

F. Panerai (2012) H−W. Krass. (2006) Qw(frozen) = 1.4612*Qw(reference) Experiment

2500 2000 1500 1000 500 0 0

500

1000 1500 Heat flux Reference probe [kW/m2]

(a)

2000

(b)

ref Figure 3.13: Qfr w with respect to Qw at ps = 1, 500 P a (a), and 10, 000 P a (b).

Heat flux Equilibrium probe [kW/m2]

2000

1500

H−W. Krass. (2006) Experiment F. Panerai (2012) Qw(equilibrium) = 0.8061*Qw(reference)

1000

500

0 0

500 1000 1500 Heat flux Reference probe [kW/m2]

2000

ref Figure 3.14: Qeq w with respect to Qw at ps = 1, 500 P a.

3.4

Uncertainty quantification

For the test conducted with the Damk¨ohler probes, the quantity of interest is simply the heat flux. The overall relative uncertainty on heat flux measurement is calculated to be 10% of the recorded value, including measurement chain accuracy and uncertainty due to the fluctuation of the measurement [3]. The error bars were already depicted in figures 3.13 and 3.14. This could be part of the explanation for the difference observed between the test campaigns. However, the regression performed on those heat fluxes measurement 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 reference catalycity and outer edge enthalpy. Those values were obtained not only through heat flux measurement, but also numerical pre- and post-processing. It is therefore extremely complicated, if not impossible, to put error bars on the data points plotted in figures 3.6, 3.9 and 3.10. However, previous studies were conducted to identify which were the sensitive parameters on both the rebuilt enthalpy and the sample catalycity. Although the exact conclusion depends on the particular test conditions, the dynamic

Test campaign and results

pressure was generally identified as the most important contributor to the errors, followed by the static pressure together with the heat flux [19] [27]. Unfortunately, none of those parameters is controlled as well as it should be: pdyn is not measured but obtained from interpolated polynomial laws, ps is not recorded but only monitored by the operator 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 corresponding uncertainty quantification was performed. In the absence of that information, cross verification with other methods such as spectroscopic or heat flux measurement is desirable.

Test campaign and results

Chapter 4

Gas-surface interaction analysis for catalycity modelling The objective of this chapter is to investigate the evolution of the driving processes of GSI in function of the LHTS parameters. Those investigations are based on the results of the experiments presented in chapter 3. Although the conclusions are only qualitative, they provide the necessary sound foundation on which a quantitative model of catalycity will be developed. It was decided to focus on nitrogen and oxygen given that, as already mentioned in section 2.2, experimental evidences tend to show that their production is prevailing on that of other species [19]. The evolution of catalycity, which was directly obtained as a result from the postprocessing, is first presented. The evolution of the Damköhler numbers is then described: first the wall Damköhler number, as it is easy to estimate, and then the gas-phase Damköhler number, which requires investigations within the boundary layer. The evolution 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 experimental results of the minimax. Since this allows only defining an interval, the freestream enthalpy was arbitrarily fixed to an average value, on which a few corrections were applied to make it physically consistent. The values that were finally used are summarized in table 3.1). The free-stream condition being fixed for all the data points considered, 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 levels investigated. Several observations can be made regarding its evolution: • At low pressure, it is approximately constant for both probes, except for one point of the equilibrium probe at low He . At higher pressure, the catalycity is increasing. 35

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.

Frozen Equilibrium

−1

Catalycity (log) [−]

Frozen Equilibrium 10

−2

−3

−1

−2

−3

25 30 Outer edge enthalpy [MJ/kg]

(a)

10 15.5

16.5 17 17.5 Outer edge enthalpy [MJ/kg]

18.5

(b)

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

4.2

Wall Damk¨ ohler number

It is possible to determine Daw without need to investigate the boundary layer by directly applying equation 2.17. Indeed, assuming kw is only a function of the wall’s material and temperature, it remains the same for all the data points since they were obtained for a copper cold wall. The only variable to determine are therefore De , which is obtained with 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 pressure levels investigated. Several observations can be made regarding its evolution: • At both pressure levels, and for both nitrogen and oxygen, it is clearly increasing as He . This is mainly due to the diffusion coefficient that strongly increases with increasing temperature, as depicted in figure 2.3. This is sufficient to compensate for the decrease in boundary layer thickness, due to the increasing velocity. • It is considerably more important (∼ 5 times) for the frozen probe than for the equilibrium 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 than over the frozen one, due to its larger diameter.

GSI analysis for catalycity modelling

• It is also considerably more important (∼ 5 times) for the low pressure and for the high one. This is again due to the diffusion coefficient that drastically decreases as pressure increases. • It is slightly more important for oxygen than for nitrogen. This is once more due to the diffusion coefficient. 12

Frozen Equilibrium nitrogen oxygen

1.6 1.4 Diffusion velocity [m/s]

Diffusion velocity [m/s]

1.2 1 0.8 0.6

Frozen Equilibrium nitrogen oxygen

0.4

2 0.2 0 15

25 30 Outer edge enthalpy [MJ/kg]

0 15.5

(a)

16.5 17 17.5 Outer edge enthalpy [MJ/kg]

18.5

(b)

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

4.3

Gas-phase Damk¨ ohler 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 characteristic 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: βe · rb (4.2) ve where ve is obtained as one of the outputs of the rebuilding performed with CERBOULA. NDP2 =

Its evolution with respect to the He is depicted in figure 4.3. several observations can be made regarding its evolution: • At both pressure levels, it is clearly decreasing as He increases for the equilibrium probe. That evolution is less pronounced for the frozen probe, although a slight decay is observed. • It is considerably more important for the equilibrium probe than for the frozen one, although that difference reduces with increasing He . • It is almost one order of magnitude larger and decreases faster for the high pressure level than for the low one.

GSI analysis for catalycity modelling

−3

x 10

0.03 Inverse of outer edge velocity gradient [s]

Inverse of outer edge velocity gradient [s]

Equilibrium Frozen

3.5 3 2.5 2 1.5 1 0.5 0 15

25 30 Outer edge enthalpy [MJ/kg]

(a)

Frozen Equilibrium

0.025 0.02 0.015 0.01 0.005 0 15.5

16.5 17 17.5 Outer edge entlapy [MJ/kg]

18.5

(b)

Figure 4.3: Evolution of the inverse of the βe with respect to He at ps = 1, 500 P a (a) and ps = 10, 000 P a (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 evolution recombination equilibrium constant in the boundary layer is an indicator of its order of magnitude. It is depicted in figure 4.4 for both the equilibrium and the frozen probes, and both nitrogen and oxygen, at a pressure of ps = 1, 500 P a. It has also been plotted for a noncatalytic wall, the difference between non-catalytic and catalytic wall being investigated in section 4.3.3. The same kind of relation is obtained at ps = 10, 000 P a, depicted in figure C.1. Some observations can be made regarding its evolution: • It is several orders of magnitude larger for the chemistry of nitrogen than for the chemistry of oxygen. Indeed, it is a well-known fact that O2 dissociates at lower temperatures 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 increases exponentially and its free-stream value decrease. This is due to the higher temperature 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 some changes, 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 concentration at the wall. This was done by comparing the concentration of N2 and O2 at the wall and in the free-stream, for a catalytic wall, a non-catalytic wall, and a fully catalytic wall,

GSI analysis for catalycity modelling

x 10

10 02 recombination equilibrium constant [−] (Dunn−Kang)

N2 recombination equilibrium constant [−] (Dunn−Kang)

10 9

Catalytic wall Non−catalytic wall

8 7 6 5 4 3

He = 16.22 MJ/kg 2 1

He = 36.24 MJ/kg

0 0

0.005

0.01

0.015 0.02 0.025 Distance to wall [m]

0.03

0.035

0.04

x 10

9 Catalytic wall Non−catalytic wall

8 7 6 5 4 3 2

1 He = 36.24 MJ/kg 0 0 0.005

He = 16.22 MJ/kg 0.01

0.015 0.02 0.025 Distance to wall [m]

(a) 10 O2 recombination equilibrium constant [−] (Dunn−Kang)

N2 recombination equilibrium constant [−] (Dunn−Kang)

0.04

x 10

9 Catalytic wall Non−catalytic wall

8 7 6 5 4

He = 16.22 MJ/kg

3 2 1 0 0

0.035

(b)

0.03

He = 36.24 MJ/kg 1

3 Distance to wall [m]

(c)

6 −3

x 10

9 Catalytic wall Non−catalytic wall

8 7 6 5 4 3 2 1 0 0

He = 16.22 MJ/kg

He = 36.24 MJ/kg

3 Distance to wall [m]

6 −3

x 10

(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 frozen probe (c,d) for different He , according to the chemistry model of Dunn and Kang, at ps = 1, 500 P a. both for the frozen and the equilibrium probe, depicted in figure 4.5 for ps = 1, 500 P a. The concentrations over a non-catalytic wall and a fully catalytic wall were obtained numerically, imposing the wall catalycity and then varying the heat flux at the wall to obtain 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 than the concentration at the outer edge of the boundary layer. The only exception is oxygen at high pressure. This means that even if the wall is inactive, a small amount of recombination take place in the gas phase. In other words: Dag is small but non-zero, even though Daw is zero. • Except for oxygen at low pressure, the concentration at the wall of the non-catalytic equilibrium 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-phase recombination. The opposite is observed for oxygen.

GSI analysis for catalycity modelling

0.8

0.6 0.5 Equilibrium not catalytic Equilibrium actual Equilibrium fully catalytic Frozen not catalytic Frozen actual Frozen fully catalytic Outer edge molar fraction

0.4 0.3 0.2

Wall molar fraction of O2 (log) [−]

Wall molar fraction of N2 [−]

0.7 Equilibrium not catalytic Equilibrium actual Equilibrium fully catalytic Frozen not catalytic Frozen actual Frozen fully catalytic Outer edge molar fraction

−2

−4

−6

0.1 −8

0 15

30 35 40 Outer edge enthalpy [MJ/kg]

(a)

30 35 40 Outer edge enthalpy [MJ/kg]

(b) 0

0.75

0.7

0.6 0.55 0.5 0.45

10 Catalycity (log) [−]

Wall molar fraction of N2 [−]

−1

Equilibrium not catalytic Equilibrium actual Fully catalytic Frozen not catalytic Frozen actual Outer edge molar fraction

0.65

Equilibrium not catalytic Equilibrium actual Fully catalytic Frozen not catalytic Frozen actual Outer edge molar fraction

−2

−3

−4

10 0.4 0.35

−5

16.5

17 17.5 18 18.5 Outer edge enthalpy [MJ/kg]

19.5

(c)

16.5

17 17.5 18 18.5 Outer edge enthalpy [MJ/kg]

19.5

(d)

Figure 4.5: Concentration of N2 (a,c) and O2 , in logarithmic scale, (b,d) at the wall and 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 equilibrium probe, at ps = 1, 500 P a (a,b) and ps = 10, 000 P a (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 is preserved when passing from a non-catalytic wall to a catalytic wall. The verification is here performed for the equilibrium probe at low pressure. Nevertheless, the same holds for the frozen probe, and at high pressure. In order to convince himself, the reader can refer to the figures in appendix C.

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

GSI analysis for catalycity modelling

0.8

N2 molar concentration [−]

0.7

O2 molar concentration (log) [−]

Catalytic wall Non−catalytic wall

0.6 0.5

He = 16.22 MJ/kg

0.4 0.3 0.2

−4

He = 16.22 MJ/kg

−6

He = 36.24 MJ/kg

0.1 0 0

Catalytic wall Non−catalytic wall

−2

−8

0.005

0.01

0.015 0.02 0.025 Distance to wall [m]

0.03

0.035

0.04

0.005

0.01

0.015 0.02 0.025 Distance to wall [m]

(a)

0.03

0.035

0.04

(b)

Figure 4.6: Molar concentration x of N2 (a) and O2 , in logarithmic scale, (b) within the boundary layer of the equilibrium probe for different He at ps = 1, 500 P a. 7000 He = 36.24 MJ/kg

6000

Temperature [K]

5000

He = 16.22 MJ/kg

4000 3000 Catalytic wall Non−catalytic wall

2000 1000 0 0

0.005

0.01

0.015 0.02 0.025 Distance to wall [m]

0.03

0.035

0.04

Figure 4.7: Temperature distribution within the boundary layer of the equilibrium probe for different He at ps = 1, 500 P a. The diffusion coefficient of both nitrogen and oxygen are depicted in figure 4.8, and their recombination reaction equilibrium constant in figure 4.4. They were computed according with Dunn and Kang’s model for the chemistry, as it was already used for the numerical post-processing. Increasing γ from non-catalytic to finite catalycity: • Causes the diffusion coefficient to increase, due to the temperature rise described earlier. This, in turn, decreases τdiff . As He increases, however, the temperature rise 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 respect to the non-catalytic wall profile can even be observed in figure 4.8 (a). The effect of the mixture’s composition being close to recombined state takes over the that of 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. This causes τhomo . That effect is less visible as He increases.

GSI analysis for catalycity modelling

Globally, the effect of changing from a non-catalytic surface to a catalytic surface is to decrease Dag . That decreasing effect might could compensate the effect of decreasing Dag with increasing βe that was concluded in section 4.3.3. However, this very unlikely since the increase of τflow with increasing βe is important. 0.7

0.7 Catalytic wall Non−catalytic wall

0.6 O diffusion coefficient [m2/s]

N diffusion coefficient [m2/s]

0.6 He = 36.24 MJ/kg

0.5 0.4 0.3

He = 16.22 MJ/kg

0.2 0.1 0 0

He = 36.24 MJ/kg

Catalytic wall Non−catalytic wall

0.5 0.4 He = 16.22 MJ/kg 0.3 0.2 0.1

0.005

0.01

0.015 0.02 0.025 Distance to wall [m]

(a)

0.03

0.035

0.04

0 0

0.005

0.01

0.015 0.02 0.025 Distance to wall [m]

0.03

0.035

0.04

(b)

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

4.4

Conclusion

The overall conclusions of the present chapter are summarized in table 4.1. A few interesting points should be commented: • As mentioned in section 4.3.3, a quantitative definition of τhomo is more complex than the other time-scales. Even though a rigorous analysis of the boundary layer allowed to define it, at least qualitatively, no satisfying conclusion could be drawn for increasing βe and ps . Indeed, for βe , for example, τflow and Dag are decreasing as βe 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 oxygen as 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 it is not. However, the chemistry of nitrogen prevailing on that of oxygen, Dag is assumed to be globally increasing. • Dag is decreasing with increasing βe ; the boundary layer developing over the equilibrium and frozen probes are indeed respectively close to equilibrium and frozen state. • The observation that γ increases as He increases in only correct at high ps . At low ps , the few points computed do not allow to clearly determine a tendency.

GSI analysis for catalycity modelling

• γ tends to behave in the opposite way than Daw . Indeed, if Daw decreases for a fixed kw , it is easier for the species to diffuse through the boundary layer. Since more species diffuse to the wall, catalycity increases. This tends to prove that, at least 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 Damk¨ohler numbers evolve in the same fashion. It might therefore be desirable to consider the γ of each species separately.

τflow τhomo τdiff Dag Daw γ

He ↑ ↓ ↑ ↓ ↓ ↓ ↑

βe ↑ ↓ ? ↓ ↓ ↓ ↑

ps ↑ ↑ ? ↑ ↑ ↑ ↓

N vs. O = < > > > ?

Table 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 cold wall.

GSI analysis for catalycity modelling

Conclusion Achievements The objective of this project was to investigate the driving processes of GSI over a cold wall, to take a first step towards an accurate model for wall catalycity. That goal was achieved 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 parameters used to describe it. • Chapter 3: description of the facility used and the experimental campaign performed. Two test campaigns were performed: the minimax and the Damk¨ ohler probes. The minimax, in particular, was performed at three different pressure levels and - for the first time - post-processed using the appropriate chemistry models. • Chapter 4: investigation of the driving parameters of GSI and their evolution with respect to changes in test conditions. The conclusions of that chapter, and the methodology applied to reach it, are a sound foundation for future catalycity modelling. The driving parameters that were looked upon are the wall Damk¨ohler number Daw , the gas-phase Damk¨ohler number Dag , and the wall catalycity γ. Their respective evolution was investigated with respect to the parameters applied to duplicate the boundary layer at the stagnation point of a body flying at hypersonic velocity according to the LHTS 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, although for 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 boundary layer. Since more species diffuse to the wall, catalycity increases. Furthermore, those parameters were found to be quite different for the chemistry of nitrogen and oxygen. This tends to indicate that γ should be considered separately for nitrogen and for oxygen. However, more evidences are required to support this conclusion. 45

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-estimation of samples catalycity.

Perspectives First, the results presented in this report could be improved. Indeed, rather than using the interval limits defined with the minimax tests, in section 3.2, the maximum interval limits could be used taking into account the uncertainty on the heat flux measured and on the dynamic pressure regression. In turn, the analysis of chapter 4 could be performed for the two points at the edges of the interval rather than for one point included in that interval. Although it represents a great amount of work, it would allow drawing error bars on the figures. It is also possible to take advantage of the many experiments that were performed in the past. In addition to the S-curves obtained for the quartz, and silver probes, the one obtained for the Damk¨ohler probes and the molybdenum probe could also be superimposed on that of the reference probe, providing they were obtained for the same free-stream conditions. By doing so, the definition of the intervals could be considerably refined. This, however, should be performed carefully as it has been shown that the reproducibility of experiments in the Plasmatron is poor. Finally, the time-scale characteristic of the homogeneous chemistry could be quantified 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 parameters of GSI, it will be possible to start a quantitative model of catalycity. Catalycity modelling as such will most probably require additional experiments or numerical computation to properly understand the effect of each parameter. This can be done in two fashions; either by varying on the time-scales (τflow , τhomo , and τdiff ), or by varying on the LHTS parameters (He , βe and ps ). The most suitable option is the second one, as the LHTS parameters can be independently played with, while the time-scales are strongly correlated. Indeed, the effect of τhomo could be investigated numerically by changing the values of the chemistry constants. A variation of chemistry would inevitably cause a variation in the temperature distribution and mixture’s composition within 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 the heterogeneous chemistry, τhete , but also to have a finer definition of the relative evolution of Dag and Daw . On another topic, as mentioned in section 3.2.2, a comprehensive sensitivity study is desirable, especially to define which chemistry model has to be used under which

Conclusions

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

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

Conclusions

Appendix A

Dunn and Kang’s model numerical values Reaction

Nitrogen recombination

O, N O, O2 N N2 N, NO O O2 N2

Oxygen recombination

(Ea /R)f

(Ea /R)b

1.10E + 16 2.27E + 21 2.72E + 16 3.00E + 15 7.50E + 16 2.70E + 16 6.00E + 15

−0.5 −1.5 −0.5 −0.5 −0.5 −0.5 −0.5

0 0 0 0 0 0 0

1.900E + 17 4.085E + 22 4.700E + 17 3.600E + 18 9.000E + 19 3.240E + 19 7.200E + 18

−0.5 −1.5 −0.5 −1.0 −1.0 −1.0 −1.0

1.13E + 5 1.13E + 5 1.13E + 5 5.95E + 4 5.95E + 4 5.95E + 4 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.

Dunn and Kangâ&#x20AC;&#x2122;s model numerical values

Appendix B

Test conditions for the minimax and Damk¨ ohler probes campaigns Test (−) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

ps (P a) 1, 500 1, 500 1, 500 1, 500 1, 500 5, 000 5, 000 5, 000 5, 000 5, 000 5, 000 5, 000 10, 000 10, 000 10, 000 10, 000 10, 000

P (kW ) 72.0 92.5 115.5 135.0 145.0 59.0 71.5 81.5 107.0 124.5 122.0 134.0 87.5 87.5 95.0 119.0 124.5

( ) QCu kW/m2 w 472.86 679.98 874.72 1062.30 1241.60 281.21 471.46 647.36 849.09 1062.74 1112.69 1298.65 552.57 661.88 861.54 1036.29 1238.35

( ) QAg kW/m2 w 682.47 991.83 1315.11 1570.77 1772.41 297.42 565.65 810.45 1111.30 1440.63 1423.31 1659.93 692.96 723.60 918.45 1213.52 1507.14

( ) QQuartz kW/m2 w 236.66 443.24 594.57 622.55 746.08 177.44 342.26 375.72 420.65 505.99 493.59 490.89 481.50 443.08 525.53 538.04 670.99

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

Test conditions

Test (−) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

ps (P a) 1, 500 1, 500 1, 500 1, 500 1, 500 1, 500 1, 500 1, 500 1, 500 1, 500 10, 000 10, 000 10, 000 10, 000 10, 000 10, 000 10, 000 10, 000 10, 000 10, 000

P (kW ) 112.0 136.0 157.0 187.0 223.0 261.0 294.0 305.0 319.0 346.0 136.0 158.0 175.0 210.0 250.0 265.0 292.0 332.0 381.0 200.0

( ) Qref kW/m2 w 316.80 475.19 672.11 799.25 973.98 1257.84 1273.06 1432.91 1799.05 1967.10 408.40 572.92 805.10 982.21 1247.55 1467.21 1700.00 1889.61 2093.46 932.79

( ) 2 Qeq w kW/m 131.68 239.63 324.82 437.43 632.30 874.89 932.14 1001.54 1300.85 1321.53 / / / / / / / / / /

( ) 2 Qfr w kW/m 600.89 825.56 1016.29 1327.46 1758.10 2225.98 2329.89 2409.39 2917.54 3226.84 530.03 1030.69 1170.47 1375.49 1902.87 2220.69 2421.74 2630.01 3123.82 1346.53

Table B.2: Test conditions for the Damk¨ohler probes campaign.

Appendix C

High pressure boundary layer investigations 8

x 10

10 O2 recombination equilibrium constant [−] (Gupta)

N2 recombination equilibrium constant [−] (Gupta)

Catalytic wall Non−catalytic wall

2 He = 18.29 MJ/kg 0 0

He = 15.95 MJ/kg

0.005

0.01 0.015 Distance to wall [m]

x 10

Catalytic wall Non−catalytic wall

8 7 6 5 4 3 2 1

He = 15.95 MJ/kg

He = 18.29 MJ/kg

0 0

0.02

0.005

0.01 0.015 Distance to wall [m]

(a)

(b)

x 10

10 02 recombination equilibirum constant [−] (Gupta)

N2 recombintation equilibrium constant [−] (Gupta)

Catalytic wall Non−catalytic wall

2 He = 18.29 MJ/kg 0 0

0.02

3 Distance to wall [m]

He = 15.95 MJ/kg 4

x 10

7 6 5 4 3 2 1 0 0

6 −3

x 10

(c)

Catalytic wall Non−catalytic wall

He = 15.95 MJ/kg

He = 18.29 MJ/kg 1

3 Distance to wall [m]

6 −3

x 10

(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 frozen probe (c,d) for different He , according to the chemistry model of Gupta, at ps = 10, 000 P a.

High pressure boundary layer investigations

0.08

0.06 He = 15.95 MJ/kg

0.05 0.04 0.03

Catalytic wall Non−catalytic wall

0.02 0.01 0 0

He = 18.29 MJ/kg

0.07 He = 18.29 MJ/kg

O diffusion coefficient [−]

N diffusion coefficient [−]

0.07

He = 15.95 MJ/kg

0.06 0.05 0.04

Catalytic wall Non−catalytic wall

0.03 0.02 0.01

0.005

0.01 0.015 Distance to wall [m]

0.02

0 0

0.025

0.005

0.01 0.015 Distance to wall [m]

(a)

0.08

Catalytic wall Non−catalytic wall

0.07

He = 18.29 MJ/kg 0.06 0.05

He = 15.95 MJ/kg

0.04 0.03 0.02 0.01 0 0

0.025

(b)

O diffusion coefficient [m2/s]

N diffusion coefficient [m2/s]

0.08

0.02

He = 18.29 MJ/kg

0.07 He = 15.95 MJ/kg

0.06 0.05 0.04 0.03

Catalytic wall Non−catalytic wall

0.02 0.01

3 Distance to wall [m]

(c)

6 −3

x 10

0 0

3 Distance to wall [m]

6 −3

x 10

(d)

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

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