CONFERENCE PAPER - Investigation of GSI and Modeling of Catalycity for TPM testing in PWT by Guerric de Crombrugghe

IAC-12-C2.8.8 INVESTIGATION OF GAS-SURFACE INTERACTIONS AND MODELLING OF THE REFERENCE CATALYCITY FOR THERMAL PROTECTION MATERIAL TESTING IN PLASMA WIND TUNNELS Guerric de Crombrugghe* von Karman Institute, Belgium, g.crombrugg@gmail.com Olivier Chazot von Karman Institute, Belgium, chazot@vki.ac.be Atmospheric re-entry is integral to further developments in space exploration, whether it concerns the safe return of astronauts or payload to Earth or the landing of robots on Mars, Venus, and even Titan. Despite the important heritage acquired since the beginning of the space age, it remains a complicated field of study, especially when it comes to super-orbital re-entry. The understanding of the chemistry processes taking place in the boundary layer is among the areas of improvement for the design of re-entry vehicles. One of the main parameters currently used for the sizing of thermal protection systems (TPS) is the catalycity of the thermal protection material (TPM), usually defined as the ratio between the number of atoms that recombine on the surface and the number of atoms that impact it. As recombination is an exothermic process, high catalycity is undesirable as it increases the heat flux that the thermal protection system has to withstand. Catalycity is experimentally determined in plasma wind tunnels, based on the comparison with a material of known catalycity. That reference is often a copper sample, assumed to be of high catalycity. However, it was demonstrated in previous studies that this assumption is not always correct, resulting in an over-estimation of TPM catalycity and over-sizing of TPS. Space missions with stringent mass budget are therefore penalized with heavier heat shield and reduced payload mass. A new model for the reference catalycity is thus necessary, especially for super-orbital entries. This paper presents a qualitative analysis of the relative influence of all the test parameters involved in experimental determination of gas-surface interactions (GSI) phenomena for wall catalysis. The analysis is based on experimental results obtained in the von Karman Instituteâ&#x20AC;&#x2122;s Plasmatron, and numerical rebuilding of the boundary layer with in-house software. It appears that the wall recombination coefficient depends on the material properties as well as the environment conditions through a diffusion-reaction process. I.

INTRODUCTION

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 and payloads to Earth or the landing of robots on Mars, Venus, and even Titan. One of the main areas of improvement for the design of reentry vehicles is the understanding of the gas-surface interactions (GSI) processes in flight conditions. Within that scope, this paper presents experimental research that was conducted on the driving processes of GSI over a cold copper wall in order to provide a foundation for an accurate model of wall catalycity. Those investigations are based on experimentations performed at the von Karman Institute (VKI) in the Plasmatron, an Inductive Coupled Plasma (ICP) wind tunnel, and numerical rebuilding of the boundary layer with in-house software. The issue of catalycity modelling and its importance in the frame of re-entry technologies is first presented together with a definition of the investigated GSI parameters. The facilities and methods for catalycity

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and heat flux measurements are then described, as well as the experimental campaigns conducted. The GSI are then analyzed in details through the qualitative evolution of GSI parameters depending on the test parameters. Finally, recommendations are given for a more developed model of catalycity. The results presented in this paper are the extension of a research project available in (de Crombrugghe 2012). II.

CATALYCITY MODELLING

High-temperature gas dynamics When a vehicle flies in hypersonic regime, a strong bow shock appears in front of its nose. Across that shock, a considerable part of the flow's kinetic energy will be transformed in thermal energy. The shock-layer temperature achieved is considerable: from 8,000 K for an orbital re-entry up to 11,000 K for a lunar return, and even higher for super-orbital re-entry. At such 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

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which N2 begins to dissociate. At 9,000 K, N2 is fully dissociated and ionization begins. (Anderson 2006) The recombination of dissociated species 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 a heterogeneous reaction. Since recombination is an exothermic reaction, it contributes for a nonnegligible part to the already important heat flux when it takes place at the wall. It is therefore important to include in the design requirements of the thermal protection system the tendency of its wall to promote recombination, referred to as catalycity. Catalycity The catalycity coefficient γ of a sample corresponds to the fraction of dissociated species that recombine at the sample’s surface. Two limiting cases can be distinguished: for γ = 0, none of the species recombine at the wall, and for γ = 1, all the species recombine at the wall. A way to quantify it is to investigate the concentration profile of a particular species i in the wall’s neighbourhood. The sample’s catalycity for that species i is then defined as the ratio between two differences: that of the species’ outer concentration and the species’ concentration at the wall, over that of the species’ outer concentration and the species’ concentration at the wall that would have been obtained for a fully catalytic sample:

γi =

X ie − X iw X ie − X iw,γ =1

[1]

where X stands for a concentration, the superscript e stands for the outer flow, and the superscript w stands for the wall. € Catalycity is therefore a balance between diffusion of dissociated species to the wall, and reaction rate at the wall. It is not an intrinsic property of the material, but also depends upon the flow conditions. State of the art The determination of catalycity requires knowledge of the flow enthalpy, which is rebuilt from measurement based on a reference catalycity. The current procedure at the VKI consists in using different values of reference catalycity depending on the static pressure interval in which the experiment is conducted. Those values were determined based on various values obtained in literature (Panerai 2012). The catalycity of the sample itself is then assumed to vary only with its temperature and the plasma’s static pressure. Recent studies, however, proved that different values of catalycity could be obtained for the same material while keeping its temperature and the plasma’s static pressure constant. This was achieved by varying

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other parameters such as the probe’s geometry and the plasma’s enthalpy (Marotta 2011). It is thus important to build a model of catalycity including all the relevant test parameters. This research focused on cold copper catalycity, a simpler case that is of prime interest for catalycity determination as it is used as reference. Damköhler numbers Two non-dimensional numbers are used to describe the relative importance of homogeneous and heterogeneous reactions. The gas phase Damköhler number Dag is a measure of the likelihood of homogeneous reaction to happen. It is defined as the ratio between a time-scale characteristic of the flow τf and a time-scale characteristic of the homogeneous (gas) chemistry τho:

Da g = τ f τ ho

[2]

Depending on the magnitude of Dag, two limiting cases are distinguished. 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. In the frame of the present study, τf is defined as the inverse of the outer edge velocity gradient βe:

1 τ f = β e = ∂u e ∂x

[3]

where ue is the tangential velocity at the outer edge of the boundary layer and x is the direction parallel to the wall. The € second time-scale, τho, depends on the mixture's composition, the temperature, and the reaction constants. Similarly to Dag describing the state of the flow within the boundary layer, the wall Damköhler number Daw is used to describe the state of the flow at the wall. It is defined as the ratio between a time-scale characteristic of the species diffusion in the boundary layer τd and a time-scale characteristic of the heterogeneous (wall) chemistry τhe:

Da w = τ d τ he

[4]

Depending on the magnitude of Daw, two limiting cases are distinguished. For Daw → 0, the overall reaction € larger than the diffusion time. The quality time is much of species diffusion is then irrelevant to the chemistry at the wall, as everything is controlled by the reaction. This is referred to as a reaction-controlled surface. For Daw → ∞, the surface is in diffusion control. Again,

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Da w = k w v D

[5]

with:

45 40 Outer edge enthalpy [MJ/kg]

although the diffusion time may be quite small, it is much larger than the reaction time. That ratio can be numerically estimated as the ratio between the wall reaction rate constant kw, which has dimensions of velocity, and the diffusion velocity vD:

35 30 25 20 15

€

v D = De δ

[6]

where De is the diffusion coefficient at the boundary layer’s edge, and δ the boundary layer’s thickness. € III.

HEAT FLUX AND CATALYCITY MEASUREMENT AT THE VKI

The VKI Plasmatron The experimental investigations were performed in the Plasmatron, the main facility for GSI research at the VKI. The Plasmatron is an ICP wind tunnel used both for research and for material response study in the frame of TPS sizing. It allows for reproduction of the exact flight conditions in the boundary layer in the neighbourhood of the stagnation point, which is very likely to be the point of the vehicle experiencing to the highest heat flux. (Bottin, et al. 1999) 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 (Fay and Riddell 1958). Those parameters are: the outer edge (freestream) specific enthalpy He, pressure pe, and velocity gradient βe. This methodology has been improved at the VKI, and extensively applied to Plasmatron testing. The method consists in measurements of heat flux and pressure, which are used for the characterization of the boundary layer, with γ as a parameter. The result is therefore expressed as a correlation between two variables: He, and γ. High enthalpy corresponds to noncatalytic materials, and 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 1), referred to as the enthalpy S-curve. To subdue this problem, first heat flux measurements are performed with a reference sample of known catalycity submitted to the same test conditions (He, pe, and βe) as the sample being characterized. Based on that measurement, He is determined. The catalycity of the material to test is then the only remaining unknown.

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10 ï5 10

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10 10 Catalycity (log) [ï]

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Fig. 1: Enthalpy S-curve, correlation between He and γ, in logarithmic scale. Figure realized for the reference probe at ps = 1,500 Pa and Qrefw = 875 kW/m2. Heat flux measurement The plasma conditions can be regulated in terms of input power, gas mass flow, and static pressure ps. In turn, the instrumentation allows for measurements of the heat flux at the wall and the dynamic pressure at the stagnation point. Different probes can be used to hold material samples. The reference probe corresponds to the ESA standard geometry for sample holders, also referred to as the 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, whose corner has been rounded with a certain radius Rc. The exact dimensions are available in table 1, with the corresponding schematic drawn on figure 4. Water is flowing through the calorimeter with a certain mass flow rate controlled by a calibrated rotameter. All the experiments described in the present project were performed for a cold wall at 350 K. The water mass ˙ is measured together with the temperature flow rate m difference between the inflow and the outflow ΔT, and Qw is thereby determined: m˙ ⋅ c p ⋅ ΔT € Qw = [7] A 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 in order to minimize signal interference with the facility’s electromagnetic noise. A second mass flow is used to cool the probe's walls that are exposed to the plasma. A typical heat flux measurement is depicted in figure 2. Dynamic pressure measurement The dynamic pressure is usually measured with a Pitot probe, also cooled down with water. For the present study, however, regressions laws from (Marotta 2011) made on the data from previous test campaigns were used.

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1100

Outer edge enthalpy [MJ/kg]

Heat flux [kW/m2]

900 700 500 300 100 ï100 0

100

125 150 Time [s]

175

200

225

250

Fig. 2: Recorded heat flux over time for the reference probe at ps = 1,500 Pa. 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 S-curve of the test. This is performed with the help of two numerical tools. 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 (Magin 2004). For the present study the NDP were obtained from a database using regression laws from (Panerai 2012) 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 (Shinn, Gnoffo and Gupta 1989) with 7 species (N2, O2, N, O, NO, NO+, e-) was used for the low pressure range, and that of Gupta (Thompson, et al. 1990) for the high pressure range. The choice of the chemical model for the different pressure was based on previous studies (Garcia 2001) (Krassilchikoff 2006) (de Crombrugghe 2012). IV. EXPERIMENTS CONDUCTED Two sets of experiments were conducted: the minimax, and the Damköhler probes.

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10 ï5 10

Quartz calorimeter Copper calorimeter Silver calorimeter

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Fig. 3: The minimax methodology: the three S-curves define an interval for He, and thereby also for the catalycity of the copper calorimeter. This figure is the complement of figure 1. Minimax The minimax methodology consists in comparing the S-curve obtained with a reference probe with two other probes having the same geometry and the same test conditions, but having calorimeters made out of different materials: one more catalytic, and the other less. The S-curves are computed for each of the probes. Since the outer edge enthalpy is unique for all 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). More information about the minimax methodology can be found in (Krassilchikoff 2006) and (Krassilchikoff, Chazot and Thomel 2007). For the present research, the reference probe is a copper calorimeter, the higher catalyst is made out of silver, and the lower one out of quartz. From the results obtained with the minimax test campaign, it was possible to determine the catalycity of the reference probe, namely the Euromodel geometry equipped with a copper calorimeter, depending on the static pressure and heat flux recorded. This has been performed for two different static pressure levels, 1,500 Pa and 10,000 Pa. The experiment and its results are fully described in (de Crombrugghe 2012). Damköhler probes Considering the testing configuration, once could observe that enlarging the probe’s body radius Rb lowers βe. Two additional probes were thus manufactured in order to observe the effect of variations of βe. Their dimensions are available in table 3, with the corresponding schematic in figure 4. According to equation 3, one can conclude that enlarging Rb 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, according to the state of the boundary layer they are likely to promote. More developed

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Name Rb (mm) Rc (mm) Equilibrium 57.5 5 Reference 25 10 Frozen 15 15 Table 1: Geometrical characteristics of the probes.

Fig. 4: Geometrical characteristics of the probes. Measurements were performed with the three probes at two different static pressure levels, 1,500 Pa and 10,000 Pa, over a certain range of plasma enthalpy He. A linear regression was done on the data points so as to obtain the relationship between the heat flux measurement at a certain probe and that measured at the reference probe Qwref. Knowing the reference probe’s catalycity from the minimax test, it is possible to infer He from Qwref. The heat flux measurement results are, for 1,500 Pa:

Qwfr = 1.69 ⋅Qwref ± 13.36% (19 : 20)

[8]

where the superscript eq stands for the equilibrium probe, and fr for the frozen probe. It immediately € appears that the relative uncertainty on the heat flux measurement of the equilibrium probe is higher than that of the frozen probe. This is due to the difficulty of measuring smaller heat fluxes. Similarly, for 10,000 Pa, where the equilibrium probe data points were taken from (Panerai 2012):

Qweq

0.66 ⋅Qwref

± 12.90% (19 : 20)

Qwfr

= 1.46 ⋅Qwref

± 17.00% (19 : 20)

€

Frozen Equilibrium ï1

ï2

ï3

25 30 Outer edge enthalpy [MJ/kg]

Fig. 5: Evolution of γ, in logarithmic scale, for the equilibrium and frozen probes with respect to He at ps= 1,500 Pa. 0

Frozen Equilibrium

[9]

GAS-SURFACE INTERACTIONS ANALYSIS

It is now possible to investigate the evolution of the non-dimensional numbers describing GSI, namely γ, Dag and Daw, with respect to the LHTS parameters, namely He, ps and βe. Indeed, the test conditions are known in terms of He and ps, and the respective magnitude of βe are known for the two probes.

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Catalycity (log) [ï]

Qweq = 0.81⋅Qwref ± 32.38% (19 : 20)

Catalycity The evolution γ with respect to He is depicted in figures 5 and 6 respectively for ps= 1,500 Pa and ps= 10,000 Pa. At low pressure, it is approximately constant for both probes, except for one point of the equilibrium probe at low He. That point, however, should be carefully considered with regards to the higher uncertainty on the corresponding heat flux measurement (equation 8). Due to the nature of the rebuilding code, and particularly due to the shape of the S-curve, those uncertainties propagate non-linearly and may result in important modifications of the final result. More precise results on these aspects will require using specific uncertainty quantification methodologies, such as Monte Carlo methods. Efforts in that direction performed on similar research are described in (Panerai 2012) and (Villedieu, et al. 2011), but were not applied to the present research. Catalycity increases at higher pressure (figure 6). It is slightly larger for the frozen probe than for the equilibrium one, except for the same point at low ps and He. Finally, it is globally smaller at high pressure than at low pressure.

Catalycity (log) [ï]

numerical and experimental investigations about the Damköhler probes can be found in (Herpin 2005).

ï1

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10 15.5

16.5 17 17.5 Outer edge enthalpy [MJ/kg]

18.5

Fig. 6: Evolution of γ, in logarithmic scale, for the equilibrium and frozen probes with respect to He at ps= 10,000 Pa.

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[10] e

where the ve is the velocity at the outer edge of the boundary layer, obtained as one of the outputs of the numerical rebuilding performed by CERBOULA. € The evolution of βe with respect to He is depicted in figures 7 and 8 respectively for ps = 1,500 Pa and ps = 10,000 Pa. At both pressure levels, βe is clearly decreasing as He increases for the equilibrium probe. That evolution is much less pronounced for the frozen probe, even if a slight decay is observed. βe 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. As previously mentioned, it is more complicated to retrieve a single number characterizing τho. It is therefore not presented in this paper, although the reader can refer to (de Crombrugghe 2012) for a more thorough analysis.

Diffusion velocity [m/s]

NDP2 = β e ⋅ Rb v

Frozen Equilibrium nitrogen oxygen

0 15

25 30 Outer edge enthalpy [MJ/kg]

Fig. 9: Evolution of vD for the equilibrium and frozen probes with respect to He at ps= 1,500 Pa. 1.6 1.4 Diffusion velocity [m/s]

Gas-phase Damköhler number The velocity gradient βe is retrieved from the second NDP, as determined from the regression analysis. It is defined as:

1.2 1 0.8 0.6

Frozen Equilibrium nitrogen oxygen

0.4 0.2 0 15.5

16.5 17 17.5 Outer edge enthalpy [MJ/kg]

18.5

Fig. 10: Evolution of vD for the equilibrium and frozen probes with respect to He at ps= 10,000 Pa.

ï3

Inverse of outer edge velocity gradient [s]

x 10

Equilibrium Frozen

3.5 3 2.5 2 1.5 1 0.5 0 15

25 30 Outer edge enthalpy [MJ/kg]

Fig. 7: Evolution of βe for the equilibrium and frozen probes with respect to He at ps= 1,500 Pa.

Inverse of outer edge velocity gradient [s]

0.03 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

Fig. 8: Evolution of βe for the equilibrium and frozen probes with respect to He at ps= 10,000 Pa.

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Wall Damköhler number Assuming that kw is a function of the wall's material and temperature only, it remains constant throughout the entire research as the experiments were performed for a copper cold wall. Therefore, vD is the only variable to vary. The diffusion coefficient De is determined using Fick’s law, for which the binary diffusion coefficients are computed according to the methodology described in (Capitelli, Gorse and Longo 2000). The boundary layer thickness δ is retrieved from the first NDP, which is defined as:

NDP1 = δ Rb

[10]

The evolution vD with respect to He is depicted in figures 9 and 10 respectively for ps= 1,500 Pa and ps= € 10,000 Pa. At both pressure levels, and for both species, vD is clearly increasing with He. This is mainly due to the diffusion coefficient that strongly increases with increasing temperature. This effect adds up to the decrease in boundary layer thickness due to the increasing outer edge velocity. Furthermore, vD is considerably more important for the frozen probe than for the equilibrium one. Indeed, although the freestream conditions are the same for both, and thereby also De, the boundary layer is thicker for the equilibrium

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probe than for the frozen one, due to its larger diameter. Similarly, vD is more important for the low pressure than for the high one. This is again due to the diffusion coefficient that drastically decreases as pressure increases. Finally, it is slightly more important for O than for N. Conclusion The overall observations of the present chapter are summarized in table 2. The variations of γ are linked to that of the parameters of Daw, as both describe the chemistry at the wall. From the present study one can only observe the variation of γ with the evolution of vD. If kw was to be varied, one would most probably conclude that γ also varies as kw; the fraction of species recombining at the wall being expected to increase if the wall’s reaction constant is more important. Therefore γ is described by a function γ = f (vD, kw). From that table, it can also be concluded that: i. Dag increases for nitrogen and decreases for oxygen as ps increases. This is consistent with the characteristic time-scales: for nitrogen, the increase of τf is sufficient to compensate that of τho, while for oxygen it is not. However, since the chemistry of nitrogen prevails on the chemistry of oxygen, Dag is assumed to be globally increasing. ii. 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. iii. The observation that γ increases as He increases is only correct at high ps. At low ps, the high uncertainty on the heat flux measured by the equilibrium probe precludes trend assessment. iv. Finally, a global γ that includes N and O chemistry is assumed in CERBOULA. However, it might therefore be desirable to consider the γ of each species separately. N vs. O He ↑ βe ↑ ps ↑ kw ? ↑ ↑ ↓ vD < ↓ ↓ ↑ Daw ? γ ↑ ↑ ↓ = Table 2: Summary of the observations made on the qualitative evolutions of the GSI variables depending on the LHTS parameters VI. CONCLUSION AND PERSPECTIVES This paper presented a qualitative analysis of the evolution of the main phenomena involved in the GSI process. The experimental and numerical methodologies applied to reach the conclusions were described, and the results were discussed.

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The investigations were performed for cold copper surface. It gives a sound base for understanding the evolution of the reference catalycity. Furthermore, the reference probe used at the VKI for heat flux measurement in the frame of sample catalycity determination is largely influenced by diffusion, at least in the range considered in the present study. Finally, the GSI parameters were found to be different for the chemistry of nitrogen and oxygen. This tends to indicate that surface catalycity should be considered separately for nitrogen and oxygen in the numerical rebuilding of the boundary layer. However, more evidence is required concerning the model used to support this conclusion. Perspectives As already mentioned in the introduction, this analysis is limited to a qualitative analysis. Although it was possible to identify which were the relevant parameters to include in a model of catalycity, the experimental data available at this point need to be consolidated. Additional experiments have to be conducted, at other static pressure levels and free-stream enthalpy. Moreover, to extend the model to flight conditions it will be necessary to perform experiments on hot walls considering typical TPS materials. Further studies will need to include an uncertainty quantification approach that could lead to more precise conclusion on the most influencing parameters. The results already obtained should allow the development of a phenomenological model for the reference catalycity dedicated to aerospace ground testing. VII. REFERENCES de Crombrugghe, Guerric. Investigations of GasSurface Interactions in Plasma Wind Tunnels for Catalycity Characterization. Research Master report 2012-01, von Karman Institute, 2012. Anderson, John. Hypersonic and High Temperature Gas Dynamics, Second Edition. AIAA, 2006. Panerai, Francesco. Aerothermochemistry Characterization of Thermal Protection System. Ph.D. thesis, Universita degli Studi di Perugia and von Karman Institute, 2012. Marotta, Marco. Investigations on the Driving Phenomena Characterizing GSI in Plasmatron Facility. Research Master report 2011-17, von Karman Institute, 2011. Bottin, Benoit, Olivier Chazot, Mario Carbonaro, Vincent Van Der Haegen, et Sébastien Paris. «The VKI Plasmatron Characteristics and Performance.» Measurement Techniques for High Enthalpy and Plasma Flows. NATO-RTO-EN 8, von Karman Institute, 1999.

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Fay, J., et F. R. Riddell. «Theory of Stagnation Point Heat Transfer in Dissociated Air.» Journal of the Aeronautical Sciences 25, n° 2 (1958): 73-85. Magin, Thierry. A Model for Inductive Plasma Wind Tunnel. Ph.D. thesis, von Karman Institute, 2004. Shinn, J., P. Gnoffo, et R. Gupta. Conservation Equations and Physical Models for Hypersonic Air Flows in Thermal and Chemical Non-Equilibrium. Technical report 2867, NASA, 1989. Thompson, R., R. Gupta, J. Yos, et K. Lee. A Review of Reaction Rates and Thermodynamics and Transport Properties for an 11-Species Air Model for Chemical and Thermal Non-Equilibrium Calculation to 30000K. Reference Publication 1232, NASA, 1990. Garcia, A.M. On Catalytic Recombination Rates in Hypersonic Stagnation Heat Transfer. Research Master report 2001-12, von Karman Institute, 2001.

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Krassilchikoff, H. Procedure for the Determination of Cold Copper Catalycity. Research Master report 2006-18, von Karman Institute, 2006. Krassilchikoff, H., O. Chazot, et J. Thomel. «Procedure for the Determination of Cold Copper Recombination Efficiency.» 2nd European Conference for Aerospace Sciences. Brussels, Belgium: von Karman Institute. 2-10-02. Herpin, Sophie. Chemical Aspects of Hypersonic Stagnation Point Heat Transfer. Research Master report 2005-10, von Karman Institute, 2005. Capitelli, M., C. Gorse, and S. Longo. “Collision Integrals of High-Temperature Air Species.” Journal of Thermophysics and Heat Transfer 14, no. 2 (2000): 259-268. Villedieu, N., F. Panerai, O. Chazot, et T. Magin. «Uncertainty Quantification for Gas-Surface Interactions in Plasmatron Facility.» 7th European Symposium on Aerothermodynamics. Brugges, 2011.

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